Upcoming Events (Archive)
Many events are currently organized online. Information on how to access these events can be found by clicking “more” below the respective entry.
- Friday, 26.05.2023, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr. Timo Streckenbach, WIAS:
AI-based programming
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Host
WIAS Berlin
- Thursday, 25.05.2023, 16:00 (FUB-025 026)
- Oberseminar Nonlinear Dynamics
Dr. Isabelle Schneider:
From Pythagoras to differential equations: Uncovering the mysteries of musical sound
more ... Location
Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Erdgeschoss, Raum: 025/026
Abstract
For over two millennia, the relationship between the frequency of a vibrating string monochord. Many renowned scientists and mathematicians, including Mersenne, Bernoulli, Euler, Lagrange, d' Alembert, and Helmholtz, have conducted their own investigations on this subject. Despite the fact that the linear wave equation is frequently employed to model the sound spectrum of musical instruments, it does not truly reproduce the entire sound spectrum. In this talk, we will embark on a search for the flageolet harmonics and compare our mathematical findings to what we hear during live musical experiments. We will investigate recent models for string and woodwind instruments that rely on partial and delay differential equations, and we will uncover intriguing phenomena such as stiff damping and hysteresis.
Host
Freie Universität Berlin
WIAS Berlin
- Thursday, 25.05.2023, 14:00 (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Brendan Keith, Brown University, USA:
The entropic finite element method
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
One of the longest-standing challenges in finite element analysis is to develop a stable, high-order Galerkin method that strictly enforces pointwise bound constraints. The entropic finite element method (EFEM) is a nonlinear, structure-preserving method with these properties. This talk will introduce EFEM and describe its capability for treating free-boundary problems, enforcing discrete maximum principles, and designing scalable, mesh-independent algorithms for inverse design problems. The overall methodology combines ideas from nonlinear programming, functional analysis, and differential geometry and can potentially lead to new synergies among these areas.
Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Host
WIAS Berlin
- Wednesday, 24.05.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pavel Krejči, Czech Technical University in Prague, Tschechische Republik:
Degenerate hysteresis in partially saturated porous media (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We propose a model for fluid diffusion in partially saturated porous media taking into account hysteresis effects in the pressure-saturation relation. The resulting mathematical problem leads to a diffusion equation with Robin boundary condition for the pressure in an N-dimensional domain with a Preisach hysteresis operator under the time derivative. The problem is doubly degenerate in the sense that the saturation range is bounded, and no a priori control of the time derivative of the pressure is available. A bootstrapping argument based on particular geometric properties of the hysteresis operator makes it possible to prove the existence and uniqueness of a strong solution to the problem for arbitrarily large data. This is a joint work with Chiara Gavioli from TU Wien.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 24.05.2023, 14:00 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Abramo Agosti, Università Pavia, Italy:
A Cahn--Hilliard phase field model coupled to viscoelasticity at large strains (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk I will present a new Cahn--Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. The free energy density of the system is given as the sum of a Cahn--Hilliard term and an elastic term, with a coupling between the phase field variable and the elastic deformation gradient in the elastic contribution. I will introduce different kinds of diffusive regularizations of the transport equation for the deformation gradient, and I will discuss the proof of the global existence of weak solutions in three space dimensions for the regularized system with generic nonlinear elastic energy densities with polynomial growth, comprising the relevant cases of polyconvex Mooney--Rivlin and Ogden elastic energies. I will also propose two kinds of well posed and unconditionally energy stable finite element approximations of the model, based on convex splitting ideas and on the use of a scalar auxiliary variable. Finally, I will show numerical results for different test cases with shape memory alloy type free energy, and I will discuss some possible applications and future developments of the model in the field of biomathematical modeling for computational medicine.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 24.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Renato Soares dos Santos, Universidade Federal de Minas Gerais (UFMG), Brasilien:
Ballistic random walk on the zero-range process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We consider a random walk on a dynamic random environment given by a zero-range process started from equilibrium. Assuming that the random walk is ballistic with a large enough speed, we obtain a law of large numbers for the position of the random walk. The proof is based on renormalization arguments and decoupling inequalities without appealing to renewal schemes. Joint work with Weberson Arcanjo, Rangel Baldasso and Marcelo Hilário.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 24.05.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr Jonathan Niles-Weed, New York University, USA:
Optimal transport map estimation in general function spaces (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Optimal transport map estimation in general function spaces (online talk) We consider the problem of estimating the optimal transport map between a (fixed) source distribution P and an unknown target distribution Q, based on samples from Q. The estimation of such optimal transport maps has become increasingly relevant in modern statistical applications, such as generative modeling. At present, estimation rates are only known in a few settings (e.g. when P and Q have densities bounded above and below and when the transport map lies in a Hölder class), which are often not reflected in practice. We present a unified methodology for obtaining rates of estimation of optimal transport maps in general function spaces. Our assumptions are significantly weaker than those appearing in the literature: we require only that the source measure P satisfies a Poincaré inequality and that the optimal map be the gradient of a smooth convex function that lies in a space whose metric entropy can be controlled. As a special case, we recover known estimation rates for bounded densities and Hölder transport maps, but also obtain nearly sharp results in many settings not covered by prior work. For example, we provide the first statistical rates of estimation when P is the normal distribution and the transport map is given by an infinite-width shallow neural network. Joint work with Divol and Pooladian.
Further Informations
Der Vortrag findet via Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 23.05.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Daniel Walter, Humboldt Universität zu Berlin:
Nonsmooth minimization in infinite dimensional spaces meets sparse dictionary learning (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We propose a novel method for problems involving nonsmooth but convex regularization terms over infinite dimensional function spaces . It resembles a dictionary learning algorithm which switches between the update of a dictionary $mathcalA_k$ of extremal points of the unit ball of the regularizer and of a sparse represenation of the iterate $u_k$ in its conic hull by solving a finite dimensional $ell_1$-regularized problem. Imposing additional assumptions on the involved dual variables , its asymptotic linear convergence is shown. The theoretical results are accompanied by numerical experiments involving challenging regularizers such as the Benamou-Brenier energy as well as the BV-seminorm, highlighting both, the sharpeness of our results as well as the practical applicability of the method.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 17.05.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Willem van Oosterhout, WIAS Berlin:
Analysis of poro-visco-elastic solids at finite strains (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Poro-visco-elastic solids are materials in which a species diffuses and contributes to their deformation. Taking the Biot model as starting point, we discuss the modelling of (large) deformations and diffusion processes in a physically consistent way, and show that under certain assumptions weak solutions exist. To model poro-visco-elastic materials, a free energy functional and dissipation potential are introduced. This energy functional has contributions both from the deformation gradient, i.e., an elastic contribution, and from a mixing term, which couples the deformation gradient and the concentration of the species. The dissipation potential features contributions for the viscous evolution and the diffusion process. In particular, since the focus is on finite-strain elasticity, the diffusion equation has to be pulled back to the reference configuration. As the pulledback mobility tensor depends nonlinearly on the deformation gradient, and the viscous stresses are frame-indifferent, it is analytically necessary to include the hyperstress as a higher-order regularization, which makes this a second order non-simple material. Another important property of the investigated model is that it allows for degenerate mobilities, which are more physically relevant; however, this greatly complicates the analysis, and requires an additional regularization step. This is in contrast to prior work, where only nondegenerate mobilities were considered. Still, under certain assumptions on the constitutive laws and the data, the existence of weak solutions to the coupled system is shown using variational methods. This is joint work with Matthias Liero.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 17.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Clément Erignoux, INRIA Lille, Frankreich:
Symmetric and asymmetric hydrodynamics for the facilitated exclusion process via mapping
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The facilitated exclusion process is a degenerate kinetically constrained lattice gas, in which particles can hop to an empty neighboring site provided that another neighboring site is also occupied. Because of the kinetic constraint, the system in dimension 1 exhibits two phases, a frozen phase at density less than 1/2, and a diffusive phase at density larger than 1/2. For this reason, standard entropic tools cannot be used to straightforwardly derive its macroscopic behavior, in particular its hydrodynamic limit. To workaround this issue, we exploit a classical mapping between exclusion and zero-range processes, and deduce from the hydrodynamic limit of the zero-range process that of the exclusion process. Despite the lack of smoothness of the various macroscopic limits, thanks to the attractiveness of the zero-range process, this allows to derive the hydrodynamic limits in both the symmetric and asymmetric case. Based on JW With O. Blondel, M. Sasada, M. Simon and L. Zhao
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 17.05.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Enno Mammen, Universität Heidelberg:
Random planted forest: A directly interpretable tree ensemble (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We introduce a novel interpretable, tree based algorithm for prediction in a regression setting in which each tree in a classical random forest is replaced by a family of planted trees that grow simultaneously. The motivation for our algorithm is to estimate the unknown regression function from a functional ANOVA decomposition perspective, where each tree corresponds to a function within that decomposition. Therefore, planted trees are limited in the number of interaction terms. The maximal order of approximation in the ANOVA decomposition can be specified or left unlimited. If a first order approximation is chosen, the result is an additive model. In the other extreme case, if the order of approximation is not limited, the resulting model places no restrictions on the form of the regression function. The talk reports on joint work with Munir Hiabu and Joseph T. Meyer.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 16.05.2023, 15:15 (WIAS-ESH)
- Seminar Materialmodellierung
Prof. Dr. Amit Acharya, Carnegie Mellon University, USA:
Slow time-scale behavior of fast microscopic dynamics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This talk aims to understand and exploit the slow time-scale behavior of rapidly evolving microscopic dynamics posed in terms of systems of nonlinear ordinary differential equations, not necessarily containing an a priori split into fast and slow variables. Such a question arises naturally and ubiquitously in efforts to understand macroscopic dynamics, on engineering time-scales, of well-accepted models of microscopic dynamics that, however, are not amenable to practical computing over the much, much larger macroscopic time-scales of interest. This is because there is a vast separation of time scales involved between the dynamics of the macroscopic variables of interest and the microscopic dynamics, and evolving the microscopic dynamics directly fails to address the question of the macroscopic dynamics. The methodology employed involves a computational scheme based on fundamental mathematical theory that a) defines appropriate `coarse' variables corresponding to the microscopic dynamics that evolve in a stable manner on the coarse time scale; b) determines the equation of evolution for such variables; and c) defines a practically useful strategy for accurately initializing short bursts of microscopic runs for the evolution of the slow variables, without special requirements on the nature of the microscopic dynamics. We will illustrate the theory with examples that violate ergodicity and include both conservative and dissipative behavior. A first step towards coarse graining of discrete dislocation dynamics to a pde-based plasticity model without relying on constitutive assumptions will also be demonstrated. This is joint work with Sabyasachi Chatterjee, Zvi Artstein, Giacomo Po, Xiaohan Zhang, and Nasr Ghoniem.
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Tuesday, 16.05.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Christian Bayer, WIAS Berlin:
An introduction to Hawkes processes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Hawkes processes are a prototypical example of self-exciting point processes. They are one of the most useful processes in science, engineering, and finance. Introduced as a model for time and magnitude of earthquakes, they have also been used as models for epidemics, crimes, traffic accidents, and so on. In finance, they are often used as models for order flow, for instance in order to solve the optimal execution problem, or to analyse market activity. We give a short introduction into Hawkes processes, including motivation, definitions and basic properties, and simulation.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 16.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Christian Hirsch, Aarhus University, Dänemark:
On the topology of higher-order age-dependent random connection models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
On the topology of higher-order age-dependent random connection models Abstract: Preferential attachment is a popular mechanism for generating scale-free networks. While it offers a compelling narrative, the underlying reinforced processes make it difficult to rigorously establish subtle properties. Recently, age-dependent random connection models were proposed as an alternative that is capable of generating similar networks with a mechanism that is amenable to a more refined analysis. In this talk, we analyze the asymptotic behavior of higher-order topological characteristics such as higher-order degree distributions and Betti numbers in large domains. This talk is based on joint work with Péter Juhász.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Monday, 15.05.2023, 10:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
Mini Course: A unified approach to non-gradient systems (part 3)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Recently, Makiko Sasada has published a trilogy of papers analyzing proofs for hydrodynamic limits in the context of non-gradient systems. The breakthrough lies in a conceptual change, realizing that it is useful to study the geometric properties of a system independently of the stochastic data. So far, all proofs relied on the specific structure of the underlying model. Using methods from cohomology of groups, Sasada is able to provide a unified approach to a large class of models. The aim of this Mini Course is to provide an introduction to her ideas as well as a basis for further discussion. Background: Some algebra; it might be useful to attend the presentation on May 9 as the mini course concentrates exclusively on the difficult part of the non-gradient method. Literature: "Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms", Ä Decomposition Theorem of Varadhan Type for Closed Co-Local Forms", "Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice".
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Friday, 12.05.2023, 10:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
Mini Course: A unified approach to non-gradient systems (part 2)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Recently, Makiko Sasada has published a trilogy of papers analyzing proofs for hydrodynamic limits in the context of non-gradient systems. The breakthrough lies in a conceptual change, realizing that it is useful to study the geometric properties of a system independently of the stochastic data. So far, all proofs relied on the specific structure of the underlying model. Using methods from cohomology of groups, Sasada is able to provide a unified approach to a large class of models. The aim of this Mini Course is to provide an introduction to her ideas as well as a basis for further discussion. Background: Some algebra; it might be useful to attend the presentation on May 9 as the mini course concentrates exclusively on the difficult part of the non-gradient method. Literature: "Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms", Ä Decomposition Theorem of Varadhan Type for Closed Co-Local Forms", "Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice".
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Thursday, 11.05.2023, 10:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
Mini Course: A unified approach to non-gradient systems (part 1)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Recently, Makiko Sasada has published a trilogy of papers analyzing proofs for hydrodynamic limits in the context of non-gradient systems. The breakthrough lies in a conceptual change, realizing that it is useful to study the geometric properties of a system independently of the stochastic data. So far, all proofs relied on the specific structure of the underlying model. Using methods from cohomology of groups, Sasada is able to provide a unified approach to a large class of models. The aim of this Mini Course is to provide an introduction to her ideas as well as a basis for further discussion. Background: Some algebra; it might be useful to attend the presentation on May 9 as the mini course concentrates exclusively on the difficult part of the non-gradient method. Literature: "Topological Structures of Large Scale Interacting Systems via Uniform Functions and Forms", Ä Decomposition Theorem of Varadhan Type for Closed Co-Local Forms", "Varadhan's Decomposition of Shift-Invariant Closed L2-forms for Large Scale Interacting Systems on the Euclidean Lattice".
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- May 10 – 12, 2023 (WIAS-ESH)
- Workshop/Konferenz: Frontiers of Stochastic Optimization and its Applications in Industry
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Tuesday, 09.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
The crux of the non-gradient method
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Most particle systems that have been studied so far have a so-called gradient property. However, the gradient property seems to be very special and only few systems exhibit it. Unfortunately, non-gradient systems prove to be much harder to analyze. The aim of this talk is to introduce the ideas for proving a hydrodynamic limit (= law of large numbers) for a non-gradient system. Focus is on the structure of the proof. In particular, we will identify which part of the proof becomes much more difficult without the gradient property.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Thursday, 04.05.2023, 14:00 (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Prof. Dr. Eskil Hansen, Lund University, Sweden:
Convergence analysis of the nonoverlapping Robin-Robin method for nonlinear elliptic equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The nonoverlapping Robin-Robin method is commonly encountered when discretizing elliptic equations, as it enables the usage of parallel and distributed hardware. Convergence has been derived in various linear contexts, but little has been proven for nonlinear equations. In this talk we present a convergence analysis for the Robin-Robin method applied to nonlinear elliptic equations with a p-structure, including degenerate diffusion equations governed by the p-Laplacian. The analysis relies on a new theory for nonlinear Steklov-Poincare operators based on the p-structure and the Lp-generalization of the Lions-Magenes spaces. This framework allows the reformulation of the Robin-Robin method into a Peaceman-Rachford splitting on the interfaces of the subdomains, and the convergence analysis then follows by employing elements of the abstract theory for monotone operators. This is joint work with Emil Engström (Lund University)
Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Host
WIAS Berlin
- Wednesday, 03.05.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Matthias Liero, WIAS Berlin:
Geodesic convexity in the Hellinger-Kantorovich space (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 03.05.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Luisa Andreis, Politecnico di Milano, Italien:
Rare events for sparse random graphs and some new large deviation result
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Rare events for dense random graphs are well described using the theory of large deviations and graphons. When graphs are sparse the picture is less clear, objects that describe globally the graphs and their limits, as graphons do for dense graphs, have not been defined yet. Nevertheless we do have information on how these graphs look like when explored locally from a vertex and this, under some assumptions, gives also information on global properties. In this talk I will give an overview on what is known for rare events in this regime, and I will present some recent new results, in particular on uniform graphs with a given degree. This talk is partially based on ongoing joint work with B. Chin, M. Dickson, S. Donderwinkel, R. van der Hofstad and N. Malhotra.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 03.05.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Gilles Blanchard, Université Paris Saclay, Frankreich:
Stein effect for estimating many vector means: A "blessing of dimensionality" phenomenon (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Consider the problem of joint estimation of the means for a large number of distributions in R^d using separate, independent data sets from each of them, sometimes also called "multi-task averaging" problem. We propose an improved estimator (compared to the naive empirical means of each data set) to exploit possible similarities between means, without any related information being known in advance. The idea is to shrink each mean towards a convex combination of its neighbors (determined by testing). We prove that this approach provides an improvement in mean squared error that can be quite significant when the (effective) dimensionality of the data is large, and when the unknown means exhibit structure such as clustering or concentration on a low-dimensional set (but which is totally unknown in advance). This is directly linked to the fact that the separation distance for testing is smaller than the estimation error in high dimension and generalizes the well-known James-Stein phenomenon. An application of this approach is the estimation of multiple kernel mean embeddings, which plays an important role in many modern applications. (This is based on joined work with Hannah Marienwald and Jean-Baptiste Fermanian)
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Friday, 28.04.2023, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr. Jürgen Fuhrmann, WIAS:
Some cool and (more or less) new tools for Unix and others: pandoc, rg, fzf, gitui
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstract
Where is my file ? How do I convert my markdown text to LaTeX ? What was the name of the file where I wrote that phrase ? How can I keep track of my git repository ? Stay up-to-date with tools written in Haskell, Rust an Go which complement the classical UNIX command line canon.
Further Informations
Hybrid event
Host
WIAS Berlin
- April 27 – 29, 2023 (WIAS-ESH)
- Workshop/Konferenz: 17th Annual Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Technische Universität Berlin
University of Oxford
WIAS Berlin
- Wednesday, 26.04.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Pierluigi Colli, Università di Pavia, Italien:
The Cahn--Hilliard--Oono system with control in the mass term (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The problem of optimal control for the Cahn--Hilliard--Oono system is addressed, where the control u is located in the mass term. First, well-posedness of the problem and the dependence of the phase variable on the control u are considered, all this by admitting general potentials that include both the case of regular potentials and the case of some singular potential. Next, the so-called separation property is discussed: it holds for everywhere defined regular potentials in 2D and 3D and for the logarithmic potential in 2D. Finally, in this framework, for the control problem it is shown that an optimal control exists; the control-to-state map is Frechet differentiable; a proper variational inequality involving the solution of an adjoint system is a necessary condition for optimality. The results reported in this talk have been obtained in a collaboration with G. Gilardi, E. Rocca and J. Sprekels.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 26.04.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Heide Langhammer, WIAS Berlin:
LDP for the particle statistics in a spatial coagulation process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We introduce an interacting particle system for spatial coagulation. The process that we consider starts with N particles that each have a location in a compact space and a mass that is initially equal to one. In a coagulation event two particles with positions x and x' and masses m and m' merge and form a new particle that has mass m+m' and a new location. Exponential clocks determine the next coagulation event. They run independently for each pair of particles with a rate K(x,m,x', m') depending on the properties of the particle pair. We derive a formula for the distribution of the particle configuration after a fixed time T>0 and use it as a starting point to derive a large deviations principle. The formula is obtained by identifying each particle present at time T with a binary tree that encodes the coagulation history of the particle. Indeed, we can think of the system of particles as the outcome of a Poisson point process that randomly generates trees and whose distribution is transformed by an exponential density that contains the cost of keeping each pair of trees separated up to time T. The talk is based on joint work with Luisa Andreis, Wolfgang König and Robert Patterson.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 26.04.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Estimation and inference for Error-on-Operator models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Many statistical models can be considered as particular cases of the Error-in-Operator (EiO) model. The list includes high dimensional random design regression, instrumental variables and error-in-variables regression, stochastic diffusion and interacting particle systems models among many others. The talk focuses on theoretical guarantees for the EiO model for finite samples using general theory of semiparametric estimation combined with the recent progress for stochastically linear models.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 25.04.2023, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Sven Wang, Massachusetts Institute of Technology:
On polynomial-time mixing of MCMC for high-dimensional posterior distributions (online talk)
more ... Location
Online Event
Abstract
We consider the problem of generating random samples from high-dimensional posterior distributions. We will discuss both (i) conditions under which diffusion-based MCMC algorithms mix in polynomial-time (based on https://arxiv.org/pdf/2009.05298.pdf) as well as (ii) situations in which MCMC suffers from an exponentially long mixing time (based on https://arxiv.org/pdf/2209.02001.pdf). We will focus on the setting of non-linear inverse regression models. Our positive results on polynomial-time mixing are derived under local `gradient stability' assumptions on the forward map, which can be verified for a range of well-known non-linear inverse problems involving elliptic PDE, as well as under the assumption that a good initializer is available. Our negative results on exponentially long mixing times hold for `cold-start' MCMC. We show that there exist non-linear regression models in which the posterior distribution is unimodal, but there exists a so-called `free entropy barrier', which local Markov chains take an exponentially long time to traverse.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 19.04.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Leon Schütz, WIAS Berlin:
An existence theory for solitary waves on a ferrofluid jet (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 19.04.2023, 14:00 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Daniel Hauer, The University of Sidney, Australien:
The fundamental gap conjecture (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 19.04.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Properties of recursive trees with independent fitnesses
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We study a general model of recursive trees, where nodes are equipped with random weights, arrive one at a time, and connect to existing nodes with probability proportional to a general function of their degree and their weight. We study the limiting infinite tree associated with this model, and show that, under a certain 'explosive' regime, the limiting tree has only a single node of infinite degree, or a single infinite path. We provide sufficient criteria to determine which occurs. Based, in part, on joint work with Bas Lodewijks.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 19.04.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Chen Huang, Aarhus University, Dänemark:
Arellano-Bond LASSO estimator for long panel dynamic linear models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 18.04.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Wilfried Kenmoe Nzali, WIAS Berlin:
Optimal control problem in energy finance (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- April 17 – 19, 2023 (ATB Potsdam)
- Workshop/Konferenz: Leibniz MMS Days 2023
more ... Location
Leibniz Institute for Agricultural Engineering and Bioeconomy Potsdam (ATB)
Host
Leibniz Institute for Agricultural Engineering and Bioeconomy
WIAS Berlin
- Tuesday, 11.04.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Data ordering in general metric spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Thursday, 06.04.2023, 11:00 (WIAS-ESH)
- Seminar Materialmodellierung
Dr. Markus Mittnenzweig, Weizmann Institute of Science, Israel:
From an egg to an embryo - Inferring the temporal dynamics of cells during embryonic development (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Novel single-genomics technologies allow probing biological tissues and entire embryos at unprecedented molecular resolution. In the context of developmental biology, these technologies allow measuring in a very quantitative way the emergence of spatial and molecular complexity that characterizes early embryonic development. Mouse embryonic development is a canonical model for studying mammalian cell fate acquisition. Recently, we introduced a temporal flow model for early mouse development, consisting of data from 153 individually sampled embryos spanning 36 hours of molecular diversification. Using a convex optimization framework and precise timing of embryos we infer the differentiation dynamics of individual cells along the continuum of embryonic cellular states. In the second part, I will show how to use this time-resolved model to assess the function of epigenetic regulators and intercellular signals involved in early embryonic development.
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Tuesday, 04.04.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Robert A. Vandermeulen, TU Berlin:
Beating the nonparametric curse of dimensionality using multi-view density estimators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The curse of dimensionality is a famous statistical phenomenon that is perhaps nowhere better exemplified than in the task of nonparametric density estimation. Here the curse of dimensionality is not only evident in practical applications, but there is a very robust corpus of theoretical work that demonstrate the curse of dimensionality. This talk will cover recent work on nonparametric density estimation that utilizes multi-view models, which are a type of low-rank model, to obviate the curse of dimensionality and give dimension-independent rates of convergence.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 28.03.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Luca Pelizzari, WIAS Berlin:
Primal-dual optimal stopping with signatures (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 24.03.2023, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Heike Sill, WIAS:
Kosten-Leistungs-Rechnung (KLR) am WIAS
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Further Informations
hybrid event
Host
WIAS Berlin
- Thursday, 23.03.2023, 16:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Lutz Mertenskötter, WIAS Berlin:
Laser linewidth estimation beyond the detector noise limit - Statistical inference from delayed self-heterodyne measurements
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Forschungsseminar Mathematische Modelle der Photonik
Host
WIAS Berlin
- Thursday, 23.03.2023, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, UK:
Positivity-preserving discretisations in general meshes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The quest for physical consistency in the discretisation of PDEs started as soon as the numerical methods started being proposed. By physical consistency we mean a discretisation that by design satisfies a property also satisfied by the continuous PDE. This property might be positivity of the discrete solution, or preservation of some bounds (e.g., concentrations should belong to the interval [0, 1]), or can also be energy preservation, or exactly divergence-free velocities for incompressible fluids. Regarding positivity preservation, this topic has been around since the pioneering work by Ph. Ciarlet in the late 1960s and early 1970s. In the context of finite element methods, it was shown in those early works (and not significantly improved since), that in order for a finite element method to preserve positivity the mesh needs to satisfy certain geometrical restrictions, e.g., in two space dimensions with simplicial elements the triangulation needs to be of Delaunay type (in higher dimensions or quadrilateral meshes the restrictions are more involved). Throughout the years several conclusions have been reached in this topic, but in the context of finite element methods the discretisations tend to be of first order in space. So, many important problems still remain open. In particular, one open problem is how to build a discretisation that will lead to a positive solution regardless of the geometry of the mesh and the order of the finite element method. In this talk I will review recent results addressing the last question posed in the last paragraph. More precisely, I will present a method that enforces bound-preservation (at the degrees of freedom) of the discrete solution. The method is built by first defining an algebraic projection onto the convex closed set of finite element functions that satisfy the bounds given by the solution of the PDE. Then, this projection is hardwired into the definition of the method by writing a discrete problem posed for this projected part of the solution. Since this process is done independently of the shape of the basis functions, and no result on the resulting finite element matrix is used, then the outcome is a finite element function that satisfies the bounds at the degrees of freedom. Another important observation to make is that this approach is related to variational inequalities, and this fact will be exploited in the error analysis. The core of the talk will be devoted to explaining the main idea in the context of linear (and nonlinear) reaction-diffusion equations. Then, I will explain the main difficulties encountered when extending this method to convection-diffusion equations, and, more importantly, to a finite element method defined in polytopal meshes. The results in this talk have been carried out in collaboration with Abdolreza Amiri (Strathclyde, UK), Emmanuil Geourgoulis (Heriot-Watt, UK and Athens, Greece), Tristan Pryer (Bath, UK), and Andreas Veeser (Milan, Italy).
Further Informations
Seminar Numerische Mathematik
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 22.03.2023, 10:00 (WIAS-406)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Constantin Christof, Technische Universität München:
On the identification and optimization of nonsmooth superposition operators in semilinear elliptic PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
We study an infinite-dimensional optimization problem that aims to identify the Nemytskii operator in the nonlinear part of a prototypical semilinear elliptic partial differential equation which minimizes the distance between the PDE-solution and a given desired state. In contrast to previous works, we consider this identification problem in a low-regularity regime in which the function inducing the Nemytskii operator is a-priori only known to be an element of H1loc. This makes the studied problem class a suitable point of departure for the rigorous analysis of training problems for learning-informed PDEs in which an unknown superposition operator is approximated by means of a neural network with nonsmooth activation functions (ReLU, leaky-ReLU, etc.). We establish that, despite the low regularity of the controls, it is possible to derive a classical stationarity system for local minimizers and to solve the considered problem by means of a gradient projection method. It is also shown that the established first-order necessary optimality conditions imply that locally optimal superposition operators share various characteristic properties with commonly used activation functions: They are always sigmoidal, continuously differentiable away from the origin, and typically possess a distinct kink at zero.
Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Host
WIAS Berlin
- Wednesday, 15.03.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Christof Külske, Ruhr-Universität Bochum:
New states with non-singleton localization sets for gradient models on trees
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Abstract: We consider gradient models on regular trees. These are integer-valued spin-models, where the spins (height variables) interact via a height-shift-invariant interaction between nearest neighbors on the tree. We construct spatially homogeneous infinite-volume states, which localize on finite subsets of the local state space. This holds under suitable low-temperature assumptions. These states are new, as they are not convex combinations of the previously known homogeneous states with singleton concentration set. We also discuss related existence results for delocalized states. Joint work with: Alberto Abbondando, Florian Henning, Pietro Majer (arXiv: 2302.05398)
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Tuesday, 14.03.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Emilio Ferrucci, University of Oxford:
Branched Itô formula and Itô-Stratonovich correction (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 09.03.2023, 14:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Thomas O'Leary Roseberry, University of Texas, USA:
Enabling efficient UQ and optimization with derivative-informed neural operators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Outer-loop problems arising in scientific applications such as Bayesian uncertainty quantification, and further optimization under uncertainty, require repeated evaluation of computationally intensive numerical models for varying parameters, making their solution intractable when one is constrained to use a high-fidelity model. Neural operators offer a means of explicitly learning maps from model parameters to outputs, thus enabling efficient solution of these outer loop problems. However, an essential ingredient for the scalable solution of high-dimensional is parametric derivative information, which can have the effect of reducing the dimensionality of the problem, and improving algorithmic convergence.In this talk we will present efficient strategies for learning high-dimensional derivative information via neural operators. By exploiting compactness of high-dimensional maps, if it exists, one can both generate and learn high dimensional derivative information where the dominant computational costs can be made independent of the discretization dimensions. Numerical results demonstrate that this additional derivative information improves the accuracy of the function approximation, and additionally is necessary to produce neural operators with reliable approximations of high-dimensional parametric derivatives. Numerical examples will demonstrate how these derivative informed neural operators can be used to accelerate the solutions of stochastic optimization problems and high-dimensional inference problems.This work is a collaboration with Omar Ghattas, Dingcheng Luo, Peng Chen and Umberto Villa.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/95642353605?pwd=RXRhZWVHWjc0K0dkU3FJV0p5RGdOUT09 Meeting-ID: 956 4235 3605 Kenncode: 278202
Host
WIAS Berlin
- Wednesday, 01.03.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Partha Pratim Ghosh, TU Braunschweig:
A Last Progeny Modified Branching Random Walk
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this work, we consider a modification of the usual Branching Random Walk (BRW), where we give certain independent and identically distributed (i.i.d.) displacements to all the particles at the n-th generation, which may be different from the driving increment distribution. We call this process a last progeny modified branching random walk (LPM-BRW). Depending on the value of a parameter, θ, we classify the model in three distinct cases, namely, the boundary case, below the boundary case, and above the boundary case. Under very minimal assumptions on the underlying point process of the increments, we show that at the boundary case, when θ takes a particular value θ_0, the maximum displacement converges to a limit after only an appropriate centering, which is of the form c_1n - c_2log(n). We give an explicit formula for the constants c_1 and c_2 and show that c_1 is exactly the same, while c_2 is 1/3 of the corresponding constants of the usual BRW. We also characterize the limiting distribution. We further show that below the boundary (that is, when θ < θ_0), the logarithmic correction term is absent. For above the boundary case (that is, when θ > θ_0), we have only a partial result, which indicates a possible existence of the logarithmic correction in the centering with exactly the same constant as that of the classical BRW. For θ ≤ θ_0, we further derive Brunet- Derrida-type results of point process convergence of our LPM-BRW to a decorated Poisson point process. Similar results have been obtained also for the time inhomogeneous setting. Surprisingly, the limits in this case depend only on the increments in the initial fraction of time. Under very minimal assumptions, we also derive the large deviation principle (LDP) for the right-most position of a particle in generation n. As a byproduct, we also complete the LDP for the classical model, which complements the earlier work by Gantert and Höfelsauer. Our proofs are based on a novel method of coupling the maximum displacement with a linear statistic associated with a more well-studied process in statistics, known as the smoothing transformation.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Friday, 24.02.2023, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr. Jürgen Fuhrmann, WIAS:
The software development strategy of WIAS. We want to hear your feedback
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Host
WIAS Berlin
- Thursday, 23.02.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Élie de Panafieu, Nokia Bell Labs, Frankreich:
Active clustering of a set using pairwise comparisons
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We analyze algorithms that reconstruct a set partition using pairwise comparisons, asking an oracle whether two elements belong to the same block. The goal is to minimize the average number of queries to the oracle. This problem is reminiscent of sorting: instead of a permutation, a set partition is recovered. In the case where the set partition is drawn uniformly at random, we characterize the optimal algorithms, prove they share the same distribution on the number of queries and analyze this distribution. We also investigate a random set partition model where each element chooses its block independently following a fixed distribution. This work is motivated by the annotation of training data for supervised learning. Published at Neurips with Quentin Lutz (Nokia Bell Labs), Maya Stein (University of Chile) et Alex Scott (Oxford University).
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 22.02.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. A.F.M. ter Elst, University of Auckland, Neuseeland:
Kato's inequality and degenerate elliptic operators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We consider a second-order divergence form operator with real bounded coefficients and maximal domain in L_p(R^d). We assume that the matrix of principal coefficients is positive semi-definite. Under suitable differentiability conditions on the coefficients we show that the operator is the (minus) generator of a C_0-semigroup if p is finite, and if in addition p > 1, then the space of test-functions is a core for the maximal operator. We also discuss perturbation of the maximal operator with a positive potential and optimal results in one dimension, that is if d=1. This talk is based on joint work with Wolfgang Arendt and with Tan Do.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 21.02.2023, 13:30 (WIAS-405-406)
- Seminar Materialmodellierung
Prof. Alberto Salvadori, Università degli Studi di Brescia, Italien:
Modeling and simulations towards the design of high performance batteries
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Thursday, 16.02.2023, 14:00 (Online Event)
- Seminar Nonsmooth Variational Problems and Operator Equations
Dr. Christian Parkinson, University of Arizona, USA:
The Hamilton--Jacobi formulation of optimal path planning for autonomous vehicles (online talk)
more ... Location
Online Event
Abstract
We present a partial-differential-equation-based optimal path planning framework for simple self-driving cars. This formulation relies on optimal control theory, dynamic programming, and a Hamilton-Jacobi-Bellman equation, and thus provides an interpretable alternative to black-box machine learning algorithms. We design grid-based numerical methods used to resolve the solution to the Hamilton-Jacobi-Bellman equation and generate optimal trajectories. We then describe how efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations can be used to solve similar problems in higher dimensions and in nearly real-time. We demonstrate all of our methods with several examples.
Further Informations
Seminar Nichtglatte Variationsprobleme und Operatorgleichungen
Host
WIAS Berlin
- Wednesday, 15.02.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Claude Le Bris, École des Ponts ParisTech & INRIA, Frankreich:
Defects in homogenization theory and related computational issues (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We review a series of works that address homogenization for partial differential equations with highly oscillatory coefficients. A prototypical setting is that of periodic coefficients that are locally, or more globally perturbed. We investigate the homogenization limits obtained, first for linear elliptic equations, both in conservative and non conservative forms, and next for nonlinear equations such as Hamilton--Jacobi type equations. Some emphasis will also be placed on the consequences of the above theoretical endeavour on strategies for modeling actual materials and simulating them using multiscale approaches, such as MsFEM methods. The works presented have been completed in collaboration with a number of colleagues, in particular with Y. Achdou, X. Blanc, P. Cardaliaguet, F. Legoll, P.-L. Lions, A. Lozinski, and R. Biezemans, R. Goudey.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 15.02.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Jovanka Lili Matic, Humboldt-Universität zu Berlin:
Global sensitivity analysis in the presence of missing values (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We investigate global variable importance in the presence of missing values. We assume that missing values are present in the random input vector. In this context, we analyse the dependence structure in the input vector under three missingness mechanisms: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not a Random (MNAR) (Rubin and Mealli, 2015). In case of global independence, we define the Hoeffding-Sobol/Functional ANOVA decomposition and Sobol indices in the presence of missing values. We also show that no dependent input vector satisfies the requirements for the Stone-Hooker dependent variable ANOVA. First Order Sobol indices of observed variables provide bounds for Shapley effects in the presence of missing values. Lastly, we analyze the consequences of two common missing value management techniques: Complete-case analysis (CC) and Imputation. The study is concluded with a numerical simulation.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 14.02.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Tim Laux, Universität Bonn:
The large-data limit of the MBO scheme for data clustering (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The MBO scheme is an efficient algorithm for data clustering, the task of partitioning a given dataset into several meaningful clusters. In this talk, I will present the first rigorous analysis of this scheme in the large-data limit. The starting point for the first part of the talk is that each iteration of the MBO scheme corresponds to one step of implicit gradient descent for the thresholding energy on the similarity graph of the dataset. It is then natural to think that outcomes of the MBO scheme are (local) minimizers of this energy. We prove that the algorithm is consistent, in the sense that these (local) minimizers converge to (local) minimizers of a suitably weighted optimal partition problem. To study the dynamics of the scheme, we use the theory of viscosity solutions. The main ingredients are (i) a new abstract convergence result based on quantitative estimates for heat operators and (ii) the derivation of these estimates in the setting of random geometric graphs. To implement the scheme in practice, two important parameters are the number of eigenvalues for computing the heat operator and the step size of the scheme. Our results give a theoretical justification for the choice of these parameters in relation to sample size and interaction width. This is joint work with Jona Lelmi (U Bonn).
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Monday, 13.02.2023, 10:30 (WIAS-405-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr.-Ing. Julia Kowal, Technische Universität Berlin:
Working principle and ageing of batteries
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 08.02.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Jun. Prof. Dr. Patrick Tolksdorf, Johannes Gutenberg-Universität Mainz:
Lp-extrapolation of the generalized Stokes operator (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Please see here.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 08.02.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Dave Jacobi, TU Berlin:
Super-Brownian motion with dormancy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The majority of species exhibit a behaviour called Dormancy, in which the individuals switch into a state of low metabolic activity, that protects them from harsh environmental conditions and in this way increases their chance of survival. Therefore models from mathematical population biology have to incorporate this phenomenon. We will extend the classical Super-Brownian motion, which is a measure-valued branching Markov process, to model Dormancy and retrieve a process that we will call on/off Super-Brownian motion. This process has many interesting properties that are often closely related to classical Super-Brownian motion, but at the same time exhibit new and different behaviour. We will go on a round trip of these properties. Also, if time permits, we will look at the close relation between the total mass process of superprocesses and an excursion process, which can help us understand the genealogy of these measure-valued processes.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 08.02.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Vanessa Didelez, Universität Bremen:
Causal reasoning and causal discovery with applications in epidemiology
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Many data analyses ultimately aim at answering causal research questions: We may want to assess and quantify the potential effects of certain decisions, interventions or policies, e.g. will a sugar tax or more playgrounds reduce childhood obesity? Will participation in a special training programme for the unemployed increase the chances of finding employment? Is a national mammography screening programme actually helpful in preventing deaths from breast cancer? Such questions are about causal relations and go beyond mere prediction; indeed, methods that are optimised for prediction will often give biased results for causal targets. Especially when we use non-experimental, i.e. observational data to try and answer questions about causal relations, tailored methods relying on specific assumptions are called for. The talk will review the main concepts, fundamental assumptions and basic principles for causal learning and focus on methods of causal discovery (aka structure learning). The latter have their roots in probabilistic approaches to artificial intelligence (AI) and, together with broader methods of causal inference in general, have recently seen a great revival in AI. This increased activity might be due to the realization "that many hard open problems of machine learning and AI are intrinsically related to causality" (Schölkopf, 2019). However, applications in epidemiology still pose a number of practical challenges; these include, for instance, handling incomplete, mixed, heterogenous and temporal data. I will illustrate some of the methods, their issues and proposed solutions with the analysis of a children's cohort data.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 07.02.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
PhD Alain Rossier, University of Oxford, GB:
Asymptotic analysis of deep residual networks (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation (SDE) or neither of these. Furthermore, we are able to formally prove the linear convergence of gradient descent to a global optimum for the training of deep residual networks with constant layer width and smooth activation function. We further prove that if the trained weights, as a function of the layer index, admit a scaling limit as the depth increases, then the limit has finite 2-variation.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 01.02.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Assoc. Prof. Dr. Tamara Fastovska, Karazin Kharkiv National University, Ukraine:
Asymptotic behaviour of solutions to transmission problems for elastic beams (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, we consider transmission problems describing dynamics of elastic beams consisting of two parts with dierent elastic properties. In particular, we investigate the full von Karman model and the Bresse model for arch beams. We prove the properties su cient for existence of global attractors, namely, the gradient structure and asymptotic smoothness. For the Bresse model we also investigate limiting situations as the curvature of the beam tends to zero both for finite time intervals and in the sense of upper-simicontinuity of attractors.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 01.02.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Alice Callegaro, TU München/JGU Mainz:
Survival and complete convergence for a branching annihilating random walk
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Branching systems with competition are interacting particle systems which have gained popularity as models for the reproduction of a spatial population with limited environmental resources. We study a branching annihilating random walk (BARW) in which particles move on the lattice and evolve in discrete generations. Each particle produces a Poissonian number of offspring which independently move to a uniformly chosen site within a fixed distance from their parent's position. Whenever a site is occupied by at least two particles, all the particles at that site are annihilated. This feature means that the system is not monotone and therefore the usual comparison methods are not applicable. We show that the system survives via coupling arguments and comparison with oriented percolation, making use of carefully defined density profiles which expand in time and are reminiscent of discrete travelling wave solutions. In the second part of the talk I will explain how a refinement of this technique can be employed to show complete convergence for the BARW in certain parameter regimes. The talk in based on a joint work with Matthias Birkner (JGU Mainz), Jiří Černý (University of Basel), Nina Gantert (TU Munich) and Pascal Oswald (University of Basel/JGU Mainz).
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 01.02.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Radu Stoica, Université de Lorraine , Frankreich:
Random structures and patterns in spatio-temporal data: probabilistic modelling and statistical inference (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The useful information carried by spatio-temporal data is often outlined by geometric structures and patterns. Filaments or clusters induced by galaxy positions in our Universe are such an example. Two situations are to be considered. First, the pattern of interest is hidden in the data set, hence the pattern should be detected. Second, the structure to be studied is observed, so relevant characterization of it should be done. This talk is structured in four parts. The first part presents the construction of different marked point processes together with their properties, such that characteristics of the patterns of interested are modelled by these processes. Second, tailored to the model MCMC dynamics to simulate the previous models are presented. A discussion related to the performances of these algorithms and comparison with exact simulation methods are provided. Third, on this basis, inference procedures are derived. They include level sets estimators, global optimisation, Approximate Bayesian Computation. Finally, applications on cosmological and geological real data are shown.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 31.01.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Matthias Liero, WIAS Berlin:
On the geometry of the Hellinger-Kantorovich space (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 27.01.2023, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr Karsten Tabelow, WIAS:
On criticality: orcas, sex, and the pandemic
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Host
WIAS Berlin
- Thursday, 26.01.2023, 10:15 (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Igor Voulis, Georg-August-Universität Göttingen:
Optimality of adaptive stochastic Galerkin methods for affine-parametric elliptic PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Host
WIAS Berlin
- Wednesday, 25.01.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Alexander Drewitz, Universität zu Köln:
Percolation, long-range correlations and critical exponents on transient graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Percolation models have been playing a fundamental role in statistical physics for several decades by now. They had initially been investigated in the gelation of polymers during the 1940s by chemistry Nobel laureate Flory and Stockmayer. From a mathematical point of view, the birth of percolation theory was the introduction of Bernoulli percolation by Broadbent and Hammersley in 1957, motivated by research on gas masks for coal miners. One of the key features of this model is the inherent stochastic independence which simplifies its investigation, and which has led to deep mathematical results. During recent years, the investigation of the more realistic and at the same time more complex situation of percolation models with long-range correlations has attracted significant attention. We will exhibit some recent progress for the Gaussian free field with a particular focus on the understanding of the critical parameters in the associated percolation models. What is more, we also survey recent progress in the understanding of the model at criticality via its critical exponents as well as the universality in the local geometry of the underlying graph. This talk is based on joint works with A. Prévost (U Geneva) and P.-F. Rodriguez (Imperial College).
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 25.01.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Maria Grith, Erasmus University Rotterdam, Niederlande:
The block-autoregressive model in non-standard bases (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We propose a new modeling approach for univariate time series with component dynamics that correspond to different aggregation schemes. The model is called the block-autoregressive (BAR) model, as it is based on the application of a vector autoregressive model to univariate data that is partitioned into 'blocks' of observations. These blocks of observations are transformed into linear combinations by an orthonormal basis change, which can unveil linear dynamics that can otherwise be obfuscated in the time-space. Model selection and estimation are intertwined and involve a sequential regression and testing procedure. We assess the goodness of fit of the estimated model with a parametric bootstrap and asymptotic chi-squared test. We rely upon a relationship between the covariance of the innovations in the time and transformed space, to identify and estimate the latent orthonormal basis of a process. We discuss several simulated and empirical examples which demonstrate both the flexibility and the explanatory potential of the BAR model.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 24.01.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Stochastic equations with singular drift driven by fractional Brownian motion (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 19.01.2023, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Michele Pütz, Brandenburgische Technische Universität:
Quadrature-based moment methods for the solution of population balance equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Particulate systems of many kinds are mathematically described by a multivariate number density function (NDF) whose evolution is governed by a so-called population balance equation (PBE). Typically, such equations are characterized by a high dimensionality and, accordingly, high computational costs for the numerical solution. Quadrature-based moment methods (QBMMs) aim to efficiently approximate solutions to PBEs by solving only for a set of moments instead of the NDF and closing the PBE using Gaussian quadrature rules. The upcoming presentation will give an introduction to QBMMs, elaborate on limitations and challenges associated with non-smooth terms in the moment equations using physical examples and provide some results related to the performance and accuracy of QBMMs. The talk will be conducted hybrid. Zoom coordinates are sent around in time.
Further Informations
Seminar Numerische Mathematik
Host
WIAS Berlin
- Wednesday, 18.01.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Florian Oschmann, Czech Academy of Sciences, Tschechische Republik:
Stratified fluids: On pancakes and non-local temperatures (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We investigate the rigorous derivation of two models for incompressible fluid flow: a) Majda's “stack of pancakes” model, governing essentially two-dimensional flow with momentum coupling in the vertical variable; b) the Oberbeck--Boussinesq approximation, governing the motion of a heat conducting fluid heated from below and cooled from above. Their derivation from the full compressible Navier--Stokes--Fourier system has been done for a) the inviscid (Euler) case where no coupling occurs, and b) the case of Neumann BC for the temperature. We will investigate the rigorous justification of both models for the case of viscous fluids with temperature Dirichlet BC, and show that a) indeed there is vertical coupling, and b) an unexpected temperature term arises. This is joint work with Peter Bella (TU Dortmund) and Eduard Feireisl (CAS).
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 18.01.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Tim Jahn, Universität Bonn:
Discretisation-adaptive regularisation of statistical inverse problems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We consider linear inverse problems under white (non-Gaussian) noise. We introduce a discretisation scheme to apply the discrepancy principle and the heuristic discrepancy principle, which require bounded data norm. Choosing the discretisation dimension in an adaptive fashion yields convergence, without further restrictions for the operator, the distribution of the white noise or the unknown ground solution. We discuss connections to Lepski's method and apply the technique to ill-posed integral equations with noisy point evaluations. We show that here discretisation-adaptive regularisation can be used in order to reduce the numerical complexity.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Monday, 16.01.2023, 14:00 (WIAS-406)
- Seminar Numerische Mathematik
Dr. Michael F. Herbst, RWTH Aachen:
Black-box algorithms and robust error control for density-functional theory
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Today's ubiquitous data-driven workflows allow scientists to expand the limits of length and time scales in materials simulations. In this setting questions related to the robustness and accuracy of simulation protocols as well as the reproducibility of obtained simulation data are more pressing then ever. Due to the complexity of underlying physical models (non-linear PDEs, multi-linear algebra) tackling these issues is inherently an interdisciplinary endeavour. However, close collaboration of application scientists with researchers from mathematics or computer science requires software, which can support research thrusts all the way from model problems to full-scale applications. With the aim to overcome this obstacle we started the density-functional toolkit (DFTK, https://dftk.org) about four years ago. DFTK is a Julia package for Kohn-Sham density-functional theory (DFT), which is highly accessible (only 7000 of code). Based on Julia's composable software ecosystem it integrates with standard HPC libraries (MPI, CUDA) and supports algorithmic differentiation. This has already enabled cross-disciplinary advances on error estimation or the developments of more robust algorithms. Of those I will highlight two recent efforts. Firstly our work on the DFT ground state problem involving better preconditioners for the underlying fixed-point equations and secondly the development of more efficient algorithms for response calculations. The latter are the key equations for computing many relevant materials properties and represent a central building block in our efforts to make DFTK fully algorithmically differentiable. In the final part of my talk I will sketch the current state of our work along this direction and present some application examples.
Host
WIAS Berlin
Humboldt-Universität zu Berlin
- Wednesday, 11.01.2023, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Dr. Oliver Tse, Eindhoven University of Technology, Niederlande:
Scharfetter--Gummel for aggregation-diffusion equations: Gradient structures and their limits (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, I will present some new insights into the variational structure of the Scharfetter--Gummel scheme for aggregation-diffusion equations. In particular, we propose a gradient structure that allows one to prove asymptotic limits in two regimes - the continuum limit and the zero-diffusion limit. This is a work in progress with Anastasiia Hraivoronska and André Schlichting.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 11.01.2023, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Chiranjib Mukherjee, WWU Münster:
Homogenization of Hamilton--Jacobi--Bellman equations on continuum percolation clusters
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We prove homogenization of Hamilton-Jacobi-Bellman (HJB) equations on continuum percolation clusters, almost surely w.r.t. the law of the environment when the origin belongs to the unbounded component in the continuum. Here, the viscosity term carries a degenerate matrix, the Hamiltonian is convex and coercive w.r.t. the degenerate matrix and the underlying environment is non-elliptic and its law is non-stationary w.r.t. the translation group. We do not assume uniform ellipticity inside the percolation cluster, nor any finite-range dependence (i.i.d.) on the environment. In this setup, we develop an approach based on the coercivity property of the Hamiltonian as well as a relative entropy structure (both being intrinsic properties of HJB) and make use of the random geometry of continuum percolation. Joint work with Rodrigo Bazaes (Münster) and Alexander Mielke (Berlin).
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Tuesday, 10.01.2023, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Robert Gruhlke, WIAS Berlin:
Wasserstein polynomial chaos and Langevin dynamics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
An unsupervised learning approach for the computation of an explicit functional representation of a random vector is presented, which only relies on a finite set of samples from an unknown distribution. Motivated by recent advances with computational optimal transport for estimating Wasserstein distances, we develop a generative model denoted as Wasserstein multi-element polynomial chaos expansion (WPCE). It relies on the minimization of a regularized empirical Wasserstein metric known as debiased Sinkhorn divergence. Since the used PCE grows exponentially in the number of underlying input random coordinates, we introduce an appropriate low-rank format given as stacks of tensor trains. This alleviates the curse of dimensionality, leading to only linear dependence on the input dimension. Ensemble methods nowadays are ubiquitous for the solution of Bayesian inference problems. We discuss recent advances based on state-of-the-art samplers such as Affine Invariant Langevin Dynamics (ALDI) that allow for increased convergence speed and in turn reduce the required number of forward calls encoded in the drift term of the underlying stochastic differential equation. This improvement is realised through possible adaptive ensemble enrichment and an adapted Langevin dynamics based on a homotopy formalism. Optionally, the history of particles obtained within the solution process of the Langevin dynamics then can be used to numerically construct a push forward map in terms of WPCE. Once computed, this provides functional access to the posterior without the need of further forward model evaluations.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 04.01.2023, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Franz Besold, Humboldt Universität zu Berlin:
Adaptive weights community detection (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Due to the technological progress of the last decades, Community Detection has become a major topic in machine learning. However, there is still a huge gap between practical and theoretical results, as theoretically optimal procedures often lack a feasible implementation and vice versa. This paper aims to close this gap and presents a novel algorithm that is both numerically and statistically efficient. Our procedure uses a test of homogeneity to compute adaptive weights describing local communities. The approach was inspired by the Adaptive Weights Community Detection (AWCD) algorithm by Adamyan et al. (2019). This algorithm delivered some promising results on artificial and real-life data, but our theoretical analysis reveals its performance to be suboptimal on a stochastic block model. In particular, the involved estimators are biased and the procedure does not work for sparse graphs. We propose significant modifications, addressing both shortcomings and achieving a nearly optimal rate of strong consistency on the stochastic block model. Our theoretical results are illustrated and validated by numerical experiments.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Friday, 16.12.2022, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr. Eleanor Eife-Horn, WIAS:
Introduction to the MyProTime absence management system and updates on the federal travel expenses act
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Further Informations
Online (hybrid) event
Host
WIAS Berlin
- Wednesday, 14.12.2022, 10:30 (WIAS-Library)
- Seminar in Machine Learning and Data-Driven Optimization
Heiner Kremer/Yassine Nammour, Max Planck Institute for Intelligent Systems:
Distributionally robust machine learning via conditional moment restrictions (hybrid talk)
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Further Informations
The talk is also given via Zoom: https://us02web.zoom.us/j/8994552597
Host
WIAS Berlin
- Tuesday, 13.12.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Amal Alphonse, WIAS Berlin:
Risk-averse optimal control of random elliptic variational inequalities (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this talk, I will discuss a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. I will derive two forms of first-order stationarity conditions for the problem by passing to the limit in a penalised and smoothed approximating control problem. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to delicate analytical challenges seemingly unique to the stochastic setting. To finish, I will briefly discuss a path-following stochastic approximation algorithm and demonstrate it on an example.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 13.12.2022, 13:30 (WIAS-ESH)
- Seminar Numerische Mathematik
Xu Li, Shandong University, China, Volksrepublik:
Inf-sup stabilized Scott--Vogelius elements for incompressible flows
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This talk is concerned about the finite element methods for incompressible flows such as Stokes problem and Navier-Stokes problem. When designing the schemes for incompressible flows, one should consider the continuity requirement, inf-sup stability and divergence constraint simultaneously, which is a challenging problem. Traditionally, most of the finite element methods do not satisfy the divergence constraint exactly. One exception is the Scott--Vogelius elements, i.e., P_k-P_k-1 pairs, which are stable on some special meshes such as barycentric refined meshes. Here we introduce a new class of finite elements which stabilizes the Scott--Vogelius elements by enriching the velocity space with some Raviart--Thomas functions on general mesh, while maintaining the divergence-free property. Starting with the Stokes equations, we show the inf-sup stability, the convergence analysis and the pressure-robustness property of the newly proposed element. Also a reduced version of the method, an equivalent P_k-P_0 discretization, is discussed. Finally we extend this element to the Navierß-Stokes problem, where the convection-robustness property and the discretization of the nonlinear term is also of interest and importance.
Host
WIAS Berlin
- Wednesday, 07.12.2022, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Daniel Heydecker, MPI Leipzig:
From LDPs of the Kac Process to the H-Theorem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
It is well-recognised that the large deviations of particle systems are connected to the appearance of a gradient flow formulation through a reformulation of the dynamical large deviations cost. In this talk, I will discuss a simple proof of Boltzmann's H-Theorem in the spatially homogeneous Boltzmann equation, which yields the equality between entropy and integrated entropy dissipation under quite general conditions. Time allowing, I will also discuss recent work applying the same principles to the porous medium equation.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Tuesday, 06.12.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Anomaly detection in biometric authentication (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this work we suggest a novel framework to detect user behaviour anomalies based on transfer learning approach combined with optimal transport techniques.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Monday, 05.12.2022, 10:30 (WIAS-406)
- Seminar in Machine Learning and Data-Driven Optimization
Yucen Luo, Max Planck Institute for Intelligent Systems:
Spectral representation learning for conditional moment models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Many problems in causal inference and economics can be formulated in the framework of conditional moment models, which characterize the target function through a collection of conditional moment restrictions. For nonparametric conditional moment models, efficient estimation has always relied on preimposed conditions on various measures of ill-posedness of the hypothesis space, which are hard to validate when flexible models are used. In this work, we address this issue by proposing a procedure that automatically learns representations with controlled measures of ill-posedness. Our method approximates a linear representation defined by the spectral decomposition of a conditional expectation operator, which can be used for kernelized estimators and is known to facilitate minimax optimal estimation in certain settings. We show this representation can be efficiently estimated from data, and establish $L_2$ consistency for the resulting estimator. We evaluate the proposed method on proximal causal inference tasks, exhibiting promising performance on high-dimensional, semi-synthetic data.
Further Informations
The talk is also given via Zoom: https://us02web.zoom.us/j/8994552597
Host
WIAS Berlin
- Wednesday, 30.11.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Czech Academy of Sciences, Tschechische Republik:
Magnetism in the planet Earth and its mathematical modelling (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Two main mechanisms by which the planetary magnetism is manifested, i.e. magnetodynamo and paleomagnetism, will be presented, together with their mathematical models based on continuum thermomechanics at large deformations. The latter mechanism (paleomagnetism) will be restricted on thermoremanent magnetization where the antiferro-to-ferri-magnetic (or parra-to-ferro-magnetic) transition combined with solidification-melting are interesting phenomenona to be modelled.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 30.11.2022, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Julian Kern, WIAS Berlin:
A Fleming-Viot model with varying population size
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
One drawback of the popular Fleming--Viot model in population genetics is the assumed constant population size (in time and space). We consider a variant of this model that includes variations in the size of the total population intrinsically via heavy-tailed offspring distributions and compare it to the classical model. In particular, we obtain an analogous to the Wright--Fisher diffusion in the setting of large offsprings and discuss in what way it may be viewed as an extension of it.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 30.11.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
PhD Mikołaj Kasprzak, University of Luxembourg:
How good is your Laplace approximation? Finite-sample error bounds for a variety of useful divergences (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The Laplace approximation is a popular method of approximating an intractable Bayesian posterior by a suitably chosen Gaussian distribution. But can we trust this approximation for practical use? Its theoretical justification comes from the celebrated Bernstein-von Mises theorem (also known as the Bayesian CLT or BCLT). However, an obstacle to its wider use is the lack of widely applicable post-hoc checks on its quality. Our work provides closed-form, finite-sample quality bounds for the Laplace approximation that simultaneously(1) do not require knowing the true parameter, (2) control posterior means and variances, and (3) apply generally to models that satisfy the conditions of the asymptotic BCLT. In fact, our bounds work even in the presence of misspecification. We compute exact constants in our bounds for a variety of standard models, including logistic regression, and numerically demonstrate their utility. And we provide a framework for analysis of more complex models. This is joint work with Ryan Giordano (MIT) and Tamara Broderick (MIT). A preliminary version of the work is available here: https://arxiv.org/abs/2209.14992.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 29.11.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Thomas Wagenhofer, Technische Universität Berlin:
Reconstructing volatility: Pricing of index options under rough volatility (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In [ABOBF02, ABOBF03] Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all components of the index. We here present an extension applicable to non-Markovian dynamics and in particular the case of rough volatility dynamics.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 25.11.2022, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr. Renita Danabalan, WIAS:
From Interviewee to Interviewer: Perspectives of both sides
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Host
WIAS Berlin
- Wednesday, 23.11.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Richard Schubert, Universität Bonn:
A variational approach to data-driven problems in fluid mechanics (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, we discuss a data-driven approach to viscous fluid mechanics. Typically, in order to describe the behaviour of fluids, two different kinds of modelling assumptions are used. On the one hand, there are first principles like the balance of forces or the incompressibility condition. On the other hand there are material specific constitutive laws that describe the relation between the strain and the viscous stress of the fluid. Combining both, one obtains the partial differential equations of fluid mechanics like the Stokes or Navier--Stokes equations. The constitutive laws are obtained by fitting a law from a certain class (for example linear, power law, etc.) to experimental data. This leads to modelling errors. Instead of using a constitutive relation, we introduce a data-driven formulation that has previously been examined in the context of solid mechanics and directly draws on material data. This leads to a variational solution concept, that incorporates differential constraints coming from first principles and produces fields that are optimal in terms of closeness to the data. In order to derive this formulation we recast the differential constraints of fluid mechanics in the language of constant-rank differential operators. We will see that the data-driven solutions are consistent with PDE solutions if the data are given by a constitutive law. Furthermore we show a Gamma-convergence result for the functionals arising in the data-driven fluid mechanical problem which implies that the method is well-adapted to the convergence of experimental data through increasing experimental accuracy. This is based on joint work with Christina Lienstromberg (Stuttgart) and Stefan Schiffer (Leipzig).
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 23.11.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Alexei Kroshnin, WIAS Berlin:
Robust k-means clustering in Hilbert and metric spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, we consider the robust algorithms for the k-means clustering (quantization) problem where a quantizer is constructed based on N independent observations. While the well-known asymptotic result by Pollard shows that the existence of two moments is sufficient for strong consistency of an empirically optimal quantizer in Rd, non-asymptotic bounds are usually obtained under the assumption of bounded support. We discuss a robust k-means in Hilbert and metric spaces based on trimming, and prove non-asymptotic bounds on the excess distortion, which depend on the probability mass of the lightest cluster and the second moment of the distribution.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 22.11.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Generalized self-concordant analysis of Frank-Wolfe algorithms (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We propose several variants of the Frank-Wolfe method for minimizing generalized self-concordant (GSC) functions over compact sets. Such problems are ill-conditioned and are motivated by machine learning applications such as inverse covariance estimation or distance-weighted discrimination problems in support vector machines. We obtain O(1/k) convergence rate guarantees in the general situation and linear convergence under strong convexity and additional assumptions.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 17.11.2022, 09:30 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Tim Böhnlein, Technische Universität Darmstadt:
On necessary and sucient conditions for Gaussian estimates of elliptic operators subject to mixed boundary conditions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Given an open subset in the Euclidean space, we consider divergence form operators with bounded, measurable and complex coefficients subject to mixed boundary conditions. We find equivalent conditions under which the kernel of the semigroup generated by the divergence form operator is Höolder continuous and satisfies pointwise Gaussian upper bounds. The geometric assumptions reach far beyond the Lipschitz class and we do not impose any condition on the interface between Dirichlet and Neumann part.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 16.11.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Moritz Egert, Technische Universität Darmstadt:
Four critical numbers for elliptic systems with block structure (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 16.11.2022, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Jonas Köppl, WIAS Berlin:
Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification, we prove that the relative entropy is non-increasing as a function of time and that a vanishing relative entropy loss for a translation-invariant measure implies that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure w.r.t. the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 16.11.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Aila Särkkä, Chalmers University of Technology and University of Gothenburg , Schweden:
Anisotropy analysis and modelling of spatial point patterns (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In the early spatial point process literature, observed point patterns were typically small and no repetitions were available. It was natural to assume that the patterns were realizations of stationary and isotropic point processes. Nowadays, large data sets with repetitions have become more and more common and it is important to think about the validity of these assumptions. Non-stationarity has received quite a lot of attention during the recent years and it is straightforward to include it in many point process models. Isotropy, on the other hand, is often still assumed without further checking, and even though there are several tools suggested to detect isotropy and test for it, they have not been so widely used. This talk will give an overview of nonparametric methods for anisotropy analysis of (stationary) point processes ([3], [4], [5]). Methods based on nearest neighbour and second order summary statistics as well as on spectral and wavelet analysis will be discussed. The techniques will be illustrated on both a clustered and a regular example. In the second part of the talk, one of the methods will be used to estimate the deformation history in polar ice using the measured anisotropy of air inclusions from deep ice cores [2]. In addition, an anisotropic point process model for nerve fiber data will be presented [1]. References: [1] Konstantinou K and Särkkä A (2022). Pairwise interaction Markov model for 3D epidermal nerve fiber endings. To appear in Journal of Microscopy. [2] Rajala T, Särkkä A, Redenbach C, and Sormani M (2016). Estimating geometric anisotropy in spatial point patterns. Spatial Statistics 15, 100?114. [3] Rajala T, Redenbach C, Särkkä A, and Sormani M (2018). A review on anisotropy analysis of spatial point patterns. Spatial Statistics 28, 141?168. [4] Rajala T, Redenbach C, Särkkä,A, and Sormani M (2022). Tests for isotropy in spatial point patterns. Under revision. [5] Sormani M, Redenbach C, Särkkä A and Rajala T (2020). Second order directional analysis of point processes revisited. Spatial Statistics 38, 100456.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Thursday, 10.11.2022, 11:00 (WIAS-Library)
- Seminar Nonsmooth Variational Problems and Operator Equations
Dr. Jonas Latz, Heriot-Watt University:
Analysis of stochastic gradient descent in continuous time
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Further Informations
Seminar Nichtglatte Variationsprobleme und Operatorgleichungen
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 09.11.2022, 10:00 (WIAS-HVP-3.13)
- Forschungsseminar Mathematische Statistik
Prof. Claudia Schillings, Freie Universität Berlin:
The convergence of the Laplace approximation and noise-level-robust computational methods for Bayesian inverse problems (hybrid talk)
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstract
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust w.r.t. the size of the observational noise, i.e., methods which behave well in case of concentrated posterior measures. The concentration of the posterior is a highly desirable situation in practice, since it relates to informative or large data. However, it can pose a computational challenge for numerical methods based on the prior measure. We propose to use the Laplace approximation of the posterior as the reference measure for the numerical integration and analyze the efficiency of Monte Carlo methods based on it.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- November 9 – 11, 2022 (WIAS-ESH)
- Workshop/Konferenz: MaRDI Annual Workshop 2022 (Hybrid Event)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The MaRDI annual workshop, a hybrid event, is a chance for all of us who are working in MaRDI and those who are interested in MaRDI-related topics to meet, exchange ideas and get caught up on the latest happenings within the initiative.
Host
WIAS Berlin
- Tuesday, 08.11.2022, 13:30 (WIAS-ESH)
- Seminar Materialmodellierung
Prof. Dr. Leonid Berlyand, Pennsylvania State University:
Asymptotic stability in a free boundary PDE model of active matter (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We begin with a brief overview of the rapidly developing research area of active matter (a.k.a. active materials). These materials are intrinsically out of thermal equilibrium resulting in novel physical properties whose modeling requires development of new mathematical tools. We next focus on study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two-dimensional free-boundary PDE model that generalizes a previous one-dimensional model by combining a Keller--Segel model, Hele--Shaw kinematic boundary condition, and the Young--Laplace law with a novel nonlocal regularizing term. This nonlocal term precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We found a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is the nonlinear asymptotic stability of traveling wave solutions that model observable steady cell motion. We derived and rigorously justified an explicit asymptotic formula for the stability determining eigenvalue via asymptotic expansions in a small speed of cell. This formula greatly simplifies the computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability. It also leads to interesting mathematics due to non-selfadjointness of the linearized problem which is a signature of active matter out-of-equilibrium systems. If time permits, we will discuss work in progress on fingering instability in multicellular tissue spreading. This is joint work with V. Rybalko and C. Safsten published in Transactions of AMS (to appear) and Phys. Rev.B, 2022.
Host
WIAS Berlin
- Wednesday, 02.11.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Alexander Mielke, WIAS Berlin:
On time-splitting methods for gradient flows with two dissipation mechanisms (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 02.11.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Johannes Schmidt-Hieber, University of Twente , Niederlande:
Overparametrization and the bias-variance dilemma (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
For several machine learning methods such as neural networks, good generalisation performance has been reported in the overparametrized regime. In view of the classical bias-variance trade-off, this behaviour is highly counterintuitive. The talk summarizes recent theoretical results on overparametrization and the bias-variance trade-off. This is joint work with Alexis Derumigny (Delft).
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 01.11.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Robust k-means clustering (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this work we investigate the theoretical properties of robust k-means clustering under assumption of adversarial data corruption. We provide non-asymptotic rates for excess distortion under weak model assumptions on the moments of the distribution.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 26.10.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Kerrek Stinson, Universität Bonn:
A gradient flow perspective for weak solutions of the Mullins--Sekerka flow and an application to lithium-ion batteries (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The purpose of this talk is to develop a gradient flow perspective for the Mullins--Sekerka equation, intrinsic to the evolving surface, at the level of a weak solution theory. The solution concept is motivated by the De Giorgi framework for curves of maximal slope and consideration of Gamma-convergence for gradient flows in the spirit of Sandier and Serfaty. Solutions must satisfy an optimal energy dissipation relation, where both the time derivative and metric slope are considered with respect to formal tangent spaces, arising from the mass preserving normal velocities. We prove that such solutions exist, may be recast in a PDE sense, and subsume the solution concept introduced by Le in the study of Gamma-convergence for the Cahn--Hilliard equation. As an application, we explore how a related solution concept can be used to understand the sharp interface limit of the Cahn--Hilliard reaction model for phase separation in lithium-ion batteries. Joint works with Sebastian Hensel (U. Bonn) and Tim Laux (U. Bonn).
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 25.10.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Luca Pelizzari, WIAS Berlin:
Polynomial Volterra processes and rough polynomial models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- October 24 – 26, 2022 (Novotel Berlin Mitte)
- Workshop/Konferenz: SPP 1962 Annual Meeting 2022
more ... Location
Novotel Berlin Mitte
Host
WIAS Berlin
DFG Schwerpunktprogramm 1962
- Wednesday, 19.10.2022, 14:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Nicolas Forien, Sapienza Università di Roma, Italien:
Sleepy frogs playing ping-pong on an overcrowded torus: The supercritical phase of Activated Random Walks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Consider, on each site of a graph, a certain number of frogs (or particles) which can be either active or sleeping. Each active frog performs a continuous-time random walk and falls asleep with a certain rate. Sleeping frogs stop moving, until they wake up when another frog arrives on the same site. This model on Z^d presents a phase transition: depending on the density of frogs (initially all active) and on the sleep rate, either almost surely each frog eventually falls asleep forever (fixating phase), or almost surely no frog falls asleep forever (active phase). In this talk, I will present a very recent work with Amine Asselah and Alexandre Gaudillière (arxiv.org/abs/2210.04779) about the critical density separating the two phases, showing that it is stricly below 1 for whatever value of the sleep rate. Skipping the technical details, the proof is quite geometric and intuitive, simply consisting of teams of frogs which play battles of coloured loops...
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 19.10.2022, 11:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. David Frazier, Monash University, Australien:
Guarenteed robustness via semi-modular posterior inference (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Even in relatively simple settings, model misspecification can cause Bayesian inference methods to fail spectacularly. In situations where the underlying model is built by combining different modules, an approach to guard against misspecification is to employ cutting feedback methods. These methods modify conventional Bayesian posterior inference algorithms by artificially limiting the information flows between the (potentially) misspecified and correctly specified modules. By artificially limiting the flow of information when updating our prior beliefs, we essentially "cut" the link between these modules, and ultimately produce a posterior that differs from the exact posterior. However, it is generally unknown when one should prefer this "cut posterior" over the exact posterior. Rather than choosing a single posterior on which to base our inferences, we propose a new Bayesian method that combines both posteriors in such a way that we can guard against misspecification, and decrease posterior uncertainty. We derive easily verifiable conditions under which this new posterior produces inferences that are guaranteed to be more accurate than using either posterior by itself. We demonstrate this new method in a host of applications.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Wednesday, 19.10.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Ottmar Cronie, Chalmers University of Technology & University of Gothenburg, Schweden:
Point process learning: A cross-validation-based approach to statistics for point processes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Point processes are random sets which generalise the classical notion of a random (iid) sample by allowing i) the sample size to be random and/or ii) the sample points to be dependent. Therefore, point process have become ubiquitous in the modelling of spatial and/or temporal event data, e.g. earthquakes and disease cases. Motivated by cross validation's general ability to reduce overfitting and mean square error, in this talk, we present a new cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Due to its connection to the general idea of empirical risk minimisation, it is referred to as Point Process Learning. We discuss properties of the proposed approach and its components, and we illustrate how it may be applied in different spatial statistical settings. In (at least) one of these settings, we numerically show that it outperforms the state of the art.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 18.10.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Humboldt Universität zu Berlin:
Algorithm for constrained Markov decision process with linear convergence (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy-regularized policy optimizer and Vaidya's dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 14.10.2022, 14:00 (WIAS-Library)
- E-Coffee-Lecture
Thomas Bender, WIAS:
Visual & Communication Design: Dos and Don'ts
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Host
WIAS Berlin
- Thursday, 13.10.2022, 10:15 (WIAS-HVP-3.13)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Michael Multerer, Università della Svizzera italiana, Schweiz:
Samplets: Construction and scattered data compression
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Host
WIAS Berlin
- Wednesday, 12.10.2022, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Arne Grauer, Universität zu Köln:
Short paths in scale-free geometric random graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We study the occurence of ultrasmallness in geometric random graphs defined on the points of a Poisson process in d-dimensional space, which additionally carry independent random marks. In our framework, edges are established at random using the marks of the endpoints and the distance between points in a flexible way such that a large class of graph models with scale-free degree distribution and edges spanning large distances is included. We give a sharp criteria for the absence of ultrasmallness of the graphs and in the ultrasmall regime establish a limit theorem for the chemical distance of two points. Here, the boundary of the ultrasmall regime and the limit theorem depend not only on the power-law exponent of the graphs but also on a geometric quantity, the influence of the spatial distance of two typical points on the probability of an edge connecting them. Furthermore, we study the contact process on these random graphs in the ultrasmall regime and provide exact asymptotics for the non-extinction proba- bility when the rate of infection spread is small. The talk is based on joint work with Peter Gracar and Peter Mörters.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Tuesday, 11.10.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Anja Schlömerkemper, Julius-Maximilians-Universität Würzburg:
A discussion of two models extending the Cahn--Hilliard equation to a temperature-dependent setting (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The dynamics of binary media can be modeled by the Cahn--Hilliard equation. Sometimes the phase separation depends crucially on the temperature. I will discuss two models introduced in joint work with Francesco De Anna, Chun Liu and Jan-Eric Sulzbach, arXiv:2112.14665. The models are obtained by combining ideas from non-equilibrium thermodynamics with an energetic variational approach and taking the transport property of the temperature into account. I will discuss selection criteria for these models and provide some analytical results regarding well-posedness of one of the models.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 29.09.2022, 16:00 (Online Event)
- Seminar Materialmodellierung
Prof. Dr. Robert Eisenberg, Rush University, USA:
From Maxwell to Mitochondria (online talk)
more ... Location
Online Event
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Wednesday, 28.09.2022, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Willem van Zuijlen, WIAS:
Weakly self-avoiding walk in a random potential
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We investigate a model of simple-random walk paths in a random environment that has two competing features: an attractive one towards the highest values of a random potential, and a self-repellent one in the spirit of the well-known weakly self-avoiding random walk. We tune the strength of the second effect such that they both contribute on the same scale as the time variable tends to infinity. In this talk I will discuss our results on the identification of (1) the logarithmic asymptotics of the partition function, and (2) of the path behaviour that gives the overwhelming contribution to the partition function. This is joint work with Wolfgang König, Nicolas Pétrélis and Renato Soares dos Santos.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 28.09.2022, 11:00 (Online Event)
- Seminar Weierstrass Group Data-Driven Optimization and Control
Jia Wang, Peking University, China, Volksrepublik:
Performance optimization of model predictive control algorithm and its application (online talk)
more ... Location
Online Event
Abstract
Abstract: The talk includes three main topics: (1) In order to accelerate the quadratic programming of linear MPC problem, a new iterative parameter selection method is proposed, which extends the existing proximal gradient method to high-order convergence rate. The proposed method uses the unique positive real root of a special set of higher-order polynomial equations as the iterative parameter. It can be shown that the selected polynomial order is the order of the convergence rate, so as to achieve a faster speed. (2) In order to overcome the slow convergence speed of traditional distributed MPC calculation, a novel iterative solution is proposed, which generates the next step solution according to the iterative error and error gain matrix. The iterative error is augmented to the traditional calculation process, then the new iterative formula is regarded as a nonlinear system. The convergence condition is derived by using the linear matrix inequality. Finally, the fast convergence is achieved by optimizing the error gain matrix. (3) For the economic predictive control of nonlinear systems, this study proposes an optimization method to achieve the global optimal approximation, which overcomes the deficiency that the existing MPC can only achieve local optimum. By estimating the suboptimal degree of the traditional MPC and modifying the control law according to the estimation results, the economic performance of the system is improved to approach the global optimum.
Further Informations
Seminar of Weierstrass Group DOC
Host
WIAS Berlin
- Tuesday, 27.09.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
PhD Mao Fabrice Djete, Université Paris Dauphine , Frankreich:
Non-regular McKean--Vlasov equations and calibration problem in local stochastic volatility models (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this talk, motivated by the calibration problem in local stochastic volatility models, we will investigate some McKean--Vlasov equations beyond the usual requirement of continuity of the coefficients in the measure variable for the Wasserstein topology. We will provide first an existence result for this type of McKean?Vlasov equations and explain the main idea behind the proof. In a second time, we will show an approximation by particle system for this type of equations, a result almost never rigorously proven in the literature in this context.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 27.09.2022, 15:00 (WIAS-ESH)
- Seminar Laserdynamik
Prof. Dmitry Turaev, Imperial College London, UK:
Non-ergodicity and stable coherent motions in systems of mutually repelling particles with arbitrarily high kinetic energy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Seminar Laser Dynamics
Host
WIAS Berlin
- Monday, 19.09.2022, 13:30 (Online Event)
- Seminar Materialmodellierung
Prof. Robert Jack, University of Cambridge, GB:
Examples of hydrodynamic behaviour in two-species exclusion processes (online talk)
more ... Location
Online Event
Abstract
We discuss several different results for simple exclusion processes with two species of particles. We first show numerical results where inhomogeneous states appear in two-dimensional systems where the species are driven in opposite directions, and we explain how these results can be rationalised by considering hydrodynamic PDEs for the density [1]. We then discuss how hydrodynamic equations in such models can be characterised, including a systematic analysis based on the method of matched asymptotics [2]. Finally, I will present some results [3] for large deviations in the hydrodynamic limit, associated with fluctuations of the entropy production in a simple model of active matter [4]. [1] H. Yu, K. Thijssen and R. L. Jack, arXiv:2204.08863 [2] J. Mason, R. L. Jack, and M. Bruna, arXiv:2203.01038. [3] T. Agranov, M. E. Cates and R. L. Jack, in preparation. [4] M. Kourbane-Houssene, C. Erignoux, T. Bodineau and J. Tailleur, Phys. Rev. Lett., 120, 268003 (2018).
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Tuesday, 13.09.2022, 11:30 (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Alfred Schmidt, Universität Bremen:
Multi scale models for a tool grinding process
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Host
WIAS Berlin
- Tuesday, 13.09.2022, 10:15 (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. André Massing, NTNU Trondheim, Norwegen:
CutFEM: Discretizing geometry and partial differential equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Host
WIAS Berlin
- September 12 – 14, 2022 (WIAS-ESH)
- Workshop/Konferenz: Mathematical Models for Biological Multiscale Systems (Hybrid Event)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The workshop MathBio22 - Mathematical models for biological multiscale systems discusses and identifies mathematical methods that bridge the gap in scale and complexity between microscopic descriptions of biological and biophysical systems with corresponding PDE descriptions. The focus is on the multi-scale nature innate to biological processes connecting interacting biomolecules with complex systems such as cells, tissue, and organs to elucidate macroscopic phenomena, e.g., (cross)diffusion, liquid-liquid phase separation, gelation, growth. The corresponding model hierarchies require innovative and structure-preserving numerical methods, novel simulation techniques, and new analytical tools for the resulting nonlinear PDE systems. The latter concerns in particular questions of well-posedness, long-term behavior, qualitative properties of solutions, and coupling to microscopic, stochastic, or agent-based models. Variational and energy- or entropy-based methods are of particular interest.
Host
WIAS Berlin
- Thursday, 08.09.2022, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Yiannis Hadjimichael, WIAS Berlin:
Implicit strong-stability-preserving Runge--Kutta methods with downwind-biased operators
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Strong stability preserving (SSP) time integrators have been developed to preserve certain nonlinear stability properties (e.g., positivity, monotonicity, boundedness) of the numerical solution in arbitrary norms, when coupled with suitable spatial discretizations. The existing general linear methods (including Runge-Kutta and linear multistep methods) either attain small time steps for strong stability preservation or are only first-order accurate. One way to relax the time-step restrictions is to consider time integrators that contain both upwind- and downwind-biased operators.
In this talk, we review SSP Runge-Kutta methods that use upwind- and downwind-biased discretizations in the framework of perturbations of Runge-Kutta methods. We show how downwinding improves the SSP properties of time-stepping methods and breaks some stability barriers. In particular, we focus on implicit downwind SSP Runge-Kutta methods whose SSP coefficient can vary with respect to the method's coefficients. We present a novel one-parameter family of third-order, three-stage perturbed Runge-Kutta methods, for which the CFL-like time-step restriction can be arbitrarily large. The stability of this family of methods is analyzed, and we demonstrate that such methods are accurate enough when large CFL numbers are used. Furthermore, we discuss the complexity of solving the nonlinear problem at each step and we propose a block factorization of the Jacobian that reduces the computational cost of Newton's method.
Further Informations
For zoom login details please contact Ulrich Wilbrandt ulrich.wilbrandt@wias-berlin.de
Host
WIAS Berlin
- Tuesday, 30.08.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Adéline Fermanian, Mines ParisTech, France:
Framing RNN as a kernel method: A neural ODE approach (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature set of the input sequence, known as the signature. This connection allows us to frame a RNN as a kernel method in a suitable reproducing kernel Hilbert space. As a consequence, we obtain theoretical guarantees on generalization and stability for a large class of recurrent networks. Our results are illustrated on simulated datasets.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- August 30, 2022 (WIAS-ESH)
- Workshop/Konferenz: Symposium on occasion of Uwe Bandelow's 60th anniversary
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We will organize at WIAS a Symposium on occasion of Uwe Bandelow's 60th anniversary. After the scientific program there will be also a session where you are invited to deliver personal or official greetings, share your memories, or present gifts. For guests who are unable to participate in person, the event will be available in a zoom meeting.
Host
WIAS Berlin
- August 22 – 26, 2022 (Harnack-Haus)
- Workshop/Konferenz: Stochastic & Rough Analysis
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft
Host
Freie Universität Berlin
Humboldt-Universität zu Berlin
Technische Universität Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 16.08.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Mathias Staudigl, Maastricht University, Niederlande:
Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 02.08.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr Vaios Laschos, WIAS Berlin:
Risk-sensitive partially observable Markov decision processes as fully observable multivariate utility optimization problems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 21.07.2022, 14:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Gabriel Acosta, University of Buenos Aires, Argentinien:
Nonlocal models related problems
more ... Location
Online Event
Abstract
abstract
Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de
Host
WIAS Berlin
- July 21, 2022 (Online Event)
- Workshop/Konferenz: Minisymposium for Young Researchers 2022
more ... Location
Online Event
Abstract
The "Minisymposium for Young Researchers 2022" (MSYR22) will bring together young scientists in the field of nonlinear optics and photonics. The minisymposium is related to the main workshop "Nonlinear Waves and Turbulence in Photonics" (NWTP22). The guiding idea is to provide an international platform which leads to a more comprehensive understanding of fundamental nonlinear phenomena, such as wave-turbulence, solitons, and extreme waves. The conference is fully online and available via Zoom. The link will be sent per E-Mail to the participants shortly before the conference's beginn.
Host
WIAS Berlin
- Wednesday, 20.07.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Nikita Simonov, LaMMe-Universitè d'Évry Val d'Essone, France:
Fast diffusion equations, tails and convergence rates
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Understanding the intermediate asymptotic and computing convergence rates towards equilibria are among the major problems in the study of parabolic equations. Convergence rates depend on the tail behaviour of solutions. This observation raised the following question: how can we understand the tail behaviour of solutions from the tail behaviour of the initial datum? In this talk, I will discuss the asymptotic behaviour of solutions to the fast diffusion equation. It is well known that non-negative solutions behave for large times as the Barenblatt (or fundamental) solution, which has an explicit expression. In this setting, I will introduce the Global Harnack Principle (GHP), precise global pointwise upper and lower estimates of non-negative solutions in terms of the Barenblatt profile. I will characterize the maximal (hence optimal) class of initial data such that the GHP holds by means of an integral tail condition. As a consequence, I will provide rates of convergence towards the Barenblatt profile in entropy and in stronger norms such as the uniform relative error.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 13.07.2022, 12:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Quirin Vogel, NYU Shanghai, China, Volksrepublik:
The variational principle and the Bose gas
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Variational principles often occur in large deviation theory, the most prominent example being the Varadhan lemma. Gibbs measures are often a canonical candidate for minimizers. In this talk, we will construct Gibbs measures for the interacting Bose gas and check under which circumstances they may solve certain minimization problems. This is work in progress, so a fair number of conjectures will be introduced. Joint work with Tianyi Bai, also from NYU Shanghai.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- July 13 – 15, 2022 (WIAS-ESH)
- Workshop/Konferenz: Nonlinear Waves and Turbulence in Photonics 2022
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The workshop "Nonlinear Waves and Turbulence in Photonics" (NWTP22) will bring together leading experts in the field of nonlinear optics and photonics. The workshop's guiding idea is to provide an international platform which leads to a more comprehensive understanding of fundamental nonlinear phenomena, such as wave-turbulence, solitons, and extreme waves. We expect exciting reports and fruitful discussions both on the most recent advances in the field and promising future developments.
Host
WIAS Berlin
- Tuesday, 12.07.2022, 13:30 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Zahra Lakdawala, Lahore University of Management Sciences, Pakistan:
On water wave dynamics using physics informed neural networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
A vanilla feed forward neural network consists of neurons and layers and the mapping between input and output is approximated using a non-linear function. The network is trained using data. In this work, we set up a neural network such that the spatio-temporal solution of time-dependent wave propagation models is learnt. This is done by providing the physical model, such as the 1D wave and shallow water wave equations and its associated boundary and initial conditions, as rules for learning the network. We investigate the feasibility of data-driven and model-driven network predictions against numerical solutions. We further investigate the accuracy of the trained network through different parameter configurations and look closely into the multi-objective loss function that is constructed by including the residual error of the physical equations and the associated initial and boundary conditions. We present the results of numerical solutions against solutions obtained from data and model-driven neural networks using data and physics informed rules for learning. Lastly, we construct a hybrid data and physics driven network and show that this significantly improves the accuracy of the physics-driven network.
Host
WIAS Berlin
- Tuesday, 05.07.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Alexander Marx, WIAS Berlin:
Random interactions in the mean-field Ising model (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- July 5 – 8, 2022 (WIAS-ESH)
- Workshop/Konferenz: Workshop on Numerical Methods and Analysis in CFD
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Wednesday, 29.06.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Stefanie Schindler, WIAS Berlin:
Entropy method for a coupled reaction-diffusion system on the real line (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, we investigate the long-time behavior of solutions to a nonlinear coupled reaction-diffusion system with detailed balance on the real line. By assuming that the solutions are in equilibria at infinity, we study the convergence towards a self-similar profile, which is a generalized steady-state in parabolic scaling variables. With this convergence, we answer how the solutions to the system mix the two stable asymptotic boundary values when time increases. Our strategy is to use an entropy approach with the relative Boltzmann entropy functional. This is a standard method for reaction-diffusion systems of mass-action type on bounded domains and a meaningful alternative to the linearization around an equilibrium. While this approach is well-studied on bounded domains, things become more complicated on the whole real line. This research is joint work with Alexander Mielke.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- June 29 – July 1, 2022 (Harnack-Haus)
- Workshop/Konferenz: Random Point Processes in Statistical Physics
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft
Host
WIAS Berlin
DFG Schwerpunktprogramm 2265
- Wednesday, 29.06.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Anuj Srivastava, Florida State University, USA:
Statistical shape analysis of complex natural structures (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Shape analysis of structured data is a fast-growing field with broad applications. Advances in imaging techniques have led to a rich data source for analyzing shapes across many scientific disciplines. Examples include shapes of brain structures; morphological analysis of cancer cells, leaves, or botanical trees; shapes of geographical objects; human biometrics; shapes of the human genome; and so on. Shapes are relevant even in non-imaging data contexts, e.g., the shapes of COVID rate curves or the shapes of breathing pat- terns in sleep studies. What makes shape analysis both fascinating and challenging? The main difficulty stems from the fact that shape is generally an abstract notion that is hard to quantify. Imposing statistical models and inferences on shapes seem even more daunting. I will outline developments in a particular approach called elastic shape analysis. This approach defines shape as a quantity left after the effects of so-called nuisance transformations (often translations, rotations, and parameterizations) are removed. This removal requires representations and metrics that are invariant to these transformations. Elastic Riemannian metrics provide desired invariances but can be cumberso- me in practical implementations. A family of square-root type transformations has helped simplify these computations and make this approach feasible. These geometrical tools help us compute average shapes of 3D (botanical) trees, develop a shape alphabet for representing chromosomes as letter sequences, perform principal component analysis of arterial brain networks, and model dynamics of Entamoeba Histolytica in different liquid media. Furthermore, they help us address some fundamental scientific questions: Are the shapes of mitochondria in muscle tissues affected by the lifestyle (active versus sedentary)? Can we predict the onset of cognitive disorders using subcortical structures in the human brain? How does aging affect morphologies of arterial networks in human brains? I will present some of these applications of elastic shape analysis
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
Universität Potsdam
- Tuesday, 28.06.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Karsten Tabelow, WIAS Berlin:
In-vivo tissue properties from magnetic resonance data (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 24.06.2022, 13:00 (Online Event)
- E-Coffee-Lecture
Henrik Pletat/Andrej Fink, WIAS IT Dep.:
Services of the WIAS IT-Department
more ... Location
Online Event
Host
WIAS Berlin
- Thursday, 23.06.2022, 14:00 (WIAS-ESH)
- Seminar Materialmodellierung
Dr. Giovanni Ligorio, Humboldt-Universität zu Berlin:
Neuromorphic device development: From modification of surfaces to modification of functions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The versatility offered by organic molecules and polymers holds great functional and economic potential for optoelectronic devices. The chemical modification of electrodes with organic materials is a common approach in our group for tuning the electronic landscape between interlayers in devices, thus facilitating charge carrier injection/extraction and improving device performance. A common tool to modify the electrode interfaces is to use covalently bound molecules carrying a permanent electric dipole group. Beside employing molecules with constant dipole, we also investigated the possibility to use switchable photochromic molecules which undergo structural modification when illuminated with light. This allows a dynamic and reversable control of the electronic properties. The gained control over the device performance enables additional functionalities in devices, such as neuromorphic applications. Neuromorphic engineering takes inspiration from the functionalities and structure of the brain to solve complex tasks and enable learning. Yet, hardware realization that simulates the synaptic activities realized with electrical devices is still not as advanced as the common implementation in computer software. In my talk I will present different approaches to emulate synapses and to fabricate both (i) optical and (ii) electronic synaptic devices. The first (i) were achieved by employing the above-mentioned photochromic molecules. This allowed control of the optical properties of gold films by reversibly modulating the surface plasmon resonance. The second (ii) were achieved by fabricating two-terminal devices based on mixed ionic-electronic conducting polymers that serve as active layer for ions and charge carrier conduction. The precise understanding and modeling of device functions will allow to fully exploit the potential of these synthetic synapses. For this purpose, a mathematical description of their behaviour might allow to move from single devices to networks and enable in materia computing.
Further Informations
Hybrid Event - please take into consideration that the number of on-site participants is limited to 24.
Host
WIAS Berlin
- Wednesday, 22.06.2022, 12:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Lukas Lüchtrath, Universität zu Köln:
The various phases of long-range inhomogeneous percolation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We consider a large class of inhomogeneous spatial random graphs where the vertex set is given by a Poisson process in Euclidean space and each vertex carries additionally an i.i.d. weight. Edges are drawn in such a way that short edges and edges to large-weight vertices are preferred. This allows in particular the study of models that combine long-range interactions and heavy-tailed degree distributions. The occurrence of long edges together with the hierarchy of the vertices coming from the weights typically leads to very well connected graphs. We identify a sharp phase transition where the existence of a subcritical percolation phase becomes impossible. This transition depends on both the power law of the degree distribution and on the geometric model parameter, showing the significant effect of clustering on the graph?s topology. We consider afterwards the specifics of dimension one in parameter regimes where a subcritical phase exists. Due to the geometric restrictions of the line, it is fairly hard to generate infinite clusters in this case and many established models admit no supercritical phase. We identify sharply how the combination of weights and long-range effects can lead to infinite clusters in situations where both effects alone are not strong enough for an infinite cluster to exist. Natural examples that are contained in our framework are for instance the random connection model, the Poisson Boolean model, scale-free percolation, the age-dependent random connection model and their soft versions. Joint work with Peter Gracar, Christian Mönch and Peter Mörters.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Monday, 20.06.2022, 16:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Prof. Maxim A. Olshanskii, University of Houston, USA:
Numerical analysis of surface fluids
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk we focus on numerical analysis for systems of PDEs governing the motion of material viscous surfaces, the topic motivated by continuum-based modeling of lateral organization in plasma membranes. We shall consider several systems of fluid and phase-field equations defined on evolving surfaces and discuss some recent results about well-posedness of such problems. We further introduce a computational approach and numerical analysis for the resulting systems of PDEs. The methods are combined to deliver a computationally tractable and thermodynamically consistent model describing the dynamics of a two-phase viscous layer. The talk closes with an illustration of the model capacity to predict lateral ordering in multicomponent vesicles of different lipid compositions.
Host
WIAS Berlin
- Wednesday, 15.06.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Alexandra Carpentier, Universität Potsdam:
Optimal ranking for crowd-sourcing (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 14.06.2022, 15:15 (WIAS-ESH)
- Oberseminar Nonlinear Dynamics
Dr. Babette de Wolff, Vrije Universiteit, Netherlands:
Delayed feedback stabilization & unconventional symmetries (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In 1992, the physicist Pyragas proposed a time delayed feedback scheme to stabilize periodic solutions of ordinary differential equations. The feedback scheme (now known as `Pyragas control?) has been adapted to symmetric systems whose symmetries can be described by groups. In this talk, we explore how Pyragas control can be adapted to systems with `unconventional symmetries?, i.e. symmetries that cannot be described by groups. In the first part of the talk, we review a fundamental observation that gives insight in Pyragas control without symmetry. In the second part of the talk we give an example of a system of three coupled oscillators with `unconventional symmetries?. For this example, we discuss what a Pyragas-like control scheme looks like and what the stabilization properties of this control scheme are. The first part of the talk based on joint work with Isabelle Schneider (FU Berlin/Universität Rostock); the second part of the talk is based on joint work with Bob Rink (VU Amsterdam)
Further Informations
Oberseminar Nonlinear Dynamics
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 14.06.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv. - Doz. Dr. John Schoenmakers, WIAS Berlin:
Dual randomization and empirical dual optimization for optimal stopping (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 08.06.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Robert Lasarzik, WIAS Berlin:
Energy-variational solutions and their approximation (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, energy-variational (EnVar) solutions are introduced for a large class of nonlinear evolution equations. Considering the Ericksen--Leslie equations modelling the evolution of liquid crystals, we observe that EnVar solutions emerge as the limit of a structure-preserving finite element scheme. We can show weak-strong uniqueness of the limit solution and additionally the so-called semi-flow property, which says that concatenations and restrictions of EnVar solutions are EnVar solutions again. Under certain assumptions every EnVar solution implies the existence of a measure-valued solution to the Ericksen--Leslie system. This implies that the EnVar solution concept is finer than the usual measure-valued solution concept. Finally, a time-discretization scheme is introduced via an incremental minimization, which resembles the minimizing movement scheme for gradient flows.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 08.06.2022, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
PhD Mari Myllymäki, Natural Resources Institute Finland (Luke):
Global envelopes with applications to spatial statistics and functional data analysis (online talk)
more ... Location
Online Event
Abstract
Global envelopes are nowadays quite often used in testing null models for spatial processes by means of different summary functions, because they provide a formal test and provide suggestions for alternative models through graphical interpretation of the test results. Global envelopes are however a rather general tool that can be applied in various applications. Namely, they can be employed for central regions of functional or multivariate data, for graphical Monte Carlo and permutation tests where the test statistic is multivariate or functional, and for global confidence and prediction bands. In this talk, I describe the global envelopes, illustrate the methodology on different applications including the functional general linear model and show examples of the usage of the R package GET (Myllymäki and Mrkvička, 2020) that implements global envelopes. Further, I discuss the multiple testing correction in the global envelope tests for functional test statistics, which are discretized to m highly correlated hypotheses. While the global envelopes were first developed to control the family-wise error rate, also control of false discovery rate can be introduced. Myllymäki and Mrkvička (2020). GET: Global envelopes in R. arXiv:1911.06583 [stat.ME] htt- ps://arxiv.org/abs/1911.0658
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 07.06.2022, 10:15 (WIAS-ESH)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Pedro Pérez-Aros, Universidad de O'Higgins, Chile:
Inner Moreau envelope of nonsmooth conic chance constrained optimization problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 02.06.2022, 16:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Fenja Severing, WIAS Berlin:
Instabilities in the context of the Generalized Nonlinear Schrödinger Equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Tba
Further Informations
Forschungsseminar Mathematische Modelle der Photonik
Host
WIAS Berlin
- Thursday, 02.06.2022, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Julien Moatti, Université de Lille, Frankreich:
A structure preserving hybrid finite volume scheme for semi-conductor models on general meshes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In 1996, Gajewski and Gärtner introduced a model describing semi-conductor devices in presence of an exterior magnetic field and proposed a scheme to discretise it. From a numerical point of view, the main difficulty in dealing with this model is the impact of the magnetic field over the system, which leads to anisotropic diffusion equations. In particular their scheme does not preserve the positivity of the solutions if the magnetic field is too intense.
In this talk, I will introduce a new structure preserving scheme for discretising similar systems of equations. The scheme under study is based on the Hybrid Finite Volume method, which is devised to handle anisotropic diffusion tensors alongside with very general polygonal/polyhedral meshes. It is designed to handle general statistics (including Boltzmann and Blakemore) as well as strong magnetic fields, while ensuring that the computed densities are positive.
The analysis of the scheme relies on the preservation of an entropy structure at the discrete level, which mimics the continuous behaviour of the system. I will explain how we can use this structure to show that there exist positive solutions to the scheme. As a by product, we also establish a "good discrete long-time behaviour" property: the discrete solutions converge towards a discrete thermal equilibrium as time tends to infinity.
Alongside with the theoretical results, I will present numerical results obtained with this scheme in various situations. I will especially focus on the preservation of bounds for the carrier densities and on the long-time behaviour of the solutions.
This is a joint work with Claire Chainais-Hillairet, Maxime Herda and Simon Lemaire.
Host
WIAS Berlin
- Wednesday, 01.06.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Melanie Koser, Humboldt-Universität zu Berlin:
Pattern formation in certain frustrated spin systems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 01.06.2022, 12:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Francesca Cottini, Università degli Studi di Milano-Bicocca, Italien:
Gaussian Limits for Subcritical Chaos
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this talk I will present a general and novel criterion to show the convergence towards a Gaussian limit for polynomial chaos, that is a multi-linear polynomial of independent random variables. This result is motivated by the study of 2d directed polymers in the subcritical regime and of the related 2d Stochastic Heat Equation, for which many convergence results were proved in recent years. Our criterion allows us to recover these results in a simpler way and, furthermore, to obtain novel results. I will focus on two main new Gaussian limits, for a singular product between the partition function and the disorder, and for the logarithm of the partition function, through an explicit chaos expansion. This is a joint work with Francesco Caravenna.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Tuesday, 31.05.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Laplace's approximation in high dimension, Part 2 (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 31.05.2022, 13:30 (Online Event)
- Seminar Materialmodellierung
Prof. Eric Sonnendrücker, Max-Planck-Institut für Plasmaphysik:
Geometric numerical methods for models from plasma physics (online talk)
more ... Location
Online Event
Abstract
Many kinetic and fluid plasma models, like the Vlasov--Maxwell-Landau or the Magnetohydrodynamics (MHD) models feature a Hamiltonian part that can be described by a Poisson bracket and a Hamiltonian and a dissipative part. The Hamiltonian part features in general different kinds of invariants that play a fundamental role in the evolution of the system. On the other hand the dissipative part strictly dissipates an entropy. For an accurate long time numerical simulation of these models, keeping as much as possible from the structure of the original equations is essential, which will automatically enforce the preservation of some important invariants like for example div B = 0. In this talk we will give an overview of structure preserving discretisation of such models based on Discrete Exterior Calculus. In particular we will show how a Particle In Cell discretisation of the Vlasov Equation coupled with a Finite Element Exterior Calculus discretisation for Maxwell's equations involving a discrete de Rham complex and an appropriate Finite Element approximation of each field leads to a Finite Dimensional Hamiltonian system, which then can be discretised in time with geometric integrators like Hamiltonian splitting or exact energy preserving discrete gradient methods.
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Tuesday, 31.05.2022, 13:30 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, GB:
Divergence-free finite element methods for an inviscid fluid model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk I will review some recent results on the stabilisation of linearised incompressible inviscid flows (or, with a very small viscosity).
The partial differential equation is a linearised incompressible equation similar to Euler's equation, or Oseen's equation in the vanishing viscosity limit. In the first part of the talk I will present results on the well-posedeness of the partial differential equation itself. From a numerical methods' perspective, the common point of the two parts is the aim of proving the following type of estimate:
u -
where u is the exact velocity and u_h^ is its finite element approximation. In the estimate above, the constant C is independent of the viscosity (if the problem has a viscosity), and, more importantly, independent of the pressure. This estimate mimicks what has been achieved for stabilised methods for the convection-diffusion equation in the past. Nevertheless, up to the best of our knowledge, this is the first time this type of estimate is obtained in a pressure-robust way.
I will first present results of discretisations using H(div)-conforming spaces, such as Raviart-Thomas, or Brezzi-Douglas-Marini where an estimate of the type eqrefmain-estimate is proven (besides an optimal estimate for the pressure). In the second part of the talk I will move on to H^1-conforming divergence-free elements, with the Scott-Vogelius element as the prime example. In this case, due to the H^1-conformity, extra control on the convective term needs to be added. After a (very brief) review of the idea of vorticity stabilisation, I will present very recent results on CIP stabilisation where a discussion on the type, and number, of jump terms will be presented. The method is independent of the pressure gradients, which makes it pressure-robust and leads to pressure-independent error estimates such as eqrefmain-estimate.
Finally, some numerical results will be presented and the present approach will be compared to the classical CIP method.
This work is a collaboration with E. Burman (UCL, UK), and E. Caceres and J. Guzmán (Brown, USA).
Host
WIAS Berlin - Monday, 30.05.2022, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Pier Luigi Dragotti, Imperial College London, UK:
Computational imaging and sensing: Theory and applications (online talk)
more ... Location
Online Event
Abstract
The revolution in sensing, with the emergence of many new imaging techniques, offers the possibility of gaining unprecedented access to the physical world, but this revolution can only bear fruit through the skilful interplay between the physical and computational realms. This is the domain of computational imaging which advocates that, to develop effective imaging systems, it will be necessary to go beyond the traditional decoupled imaging pipeline where device physics, image processing and the end-user application are considered separately. Instead, we need to rethink imaging as an integrated sensing and inference model. In the first part of the talk we highlight the centrality of sampling theory in computational imaging and investigate new sampling modalities which are inspired by the emergence of new sensing mechanisms. We discuss time-based sampling which is connected to event-based cameras where pixels behave like neurons and fire when an event happens. We derive sufficient conditions and propose novel algorithms for the perfect reconstruction of classes of non-bandlimited functions from time-based samples. We then develop the interplay between learning and computational imaging and present a model-based neural network for the reconstruction of video sequences from events. The architecture of the network is model-based and is designed using the unfolding technique, some element of the acquisition device are part of the network and are learned with the reconstruction algorithm. In the second part of the talk, we focus on the heritage sector which is experiencing a digital revolution driven in part by the increasing use of non-invasive, non-destructive imaging techniques. These new imaging methods provide a way to capture information about an entire painting and can give us information about features at or below the surface of the painting. We focus on Macro X-Ray Fluorescence (XRF) scanning which is a technique for the mapping of chemical elements in paintings and introduce a method that can process XRF scanning data from paintings. The results presented show the ability of our method to detect and separate weak signals related to hidden chemical elements in the paintings. We analyse the results on Leonardo's 'The Virgin of the Rocks' and show that our algorithm is able to reveal, more clearly than ever before, the hidden drawings of a previous composition that Leonardo then abandoned for the painting that we can now see. This is joint work with R. Alexandru, R. Wang, Siying Liu, J. Huang and Y.Su from Imperial College London; C. Higgitt and N. Daly from The National Gallery in London and Thierry Blu from the Chinese University of Hong Kong.
Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems
Host
WIAS Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
- Wednesday, 25.05.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
On non-autonomous and quasilinear parabolic systems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 24.05.2022, 15:15 (WIAS-ESH)
- Oberseminar Nonlinear Dynamics
Dr. Oleksandr A. Burylko, Institute of Mathematics NAS of Ukraine and Potsdam Institute for Climate Impact Research:
Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked?a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos
Further Informations
Oberseminar Nonlinear Dynamics
Host
WIAS Berlin
Freie Universität Berlin
- Friday, 20.05.2022, 13:00 (Online Event)
- E-Coffee-Lecture
Alireza Selahi Moghaddam, WIAS:
Creating nice 3d models and animations with Blender
more ... Location
Online Event
Abstract
Blender is an open source 3d modeling and animation software, which can easily compete with it's commercial counter-products. Although utilizing the full potential of such a software requires many years of learning, it is surprisingly easy to get nice results with very little effort, which can be used in scientific presentations or papers. With it's Python-interface, Blender even offers a way to fit right into the context of scientific computing.
Host
WIAS Berlin
- Friday, 20.05.2022, 13:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Prof. Andrey Shilnikov, Georgia State University, USA:
Long saga of in-depth modeling of two swim CPGs in two sea slugs (online talk)
more ... Location
Online Event
Abstract
We introduce the concepts underlying the modeling of swim CPGs of two sea slugs in control and under perturbations. The emphasis is put upon the nonlinear dynamics of both interacting cells and synapses and their synergy to produce an emergent network level bursting. We discuss some of its prominent features such feed back loops to maintain stability, including structural, as well resilience to short and long-term perturbations. Our research approaches are rooted in applied dynamical systems, parameter optimization with machine learning elements.
Further Informations
Forschungsseminar: Mathematische Modelle der Photonik
Host
WIAS Berlin
- Wednesday, 18.05.2022, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
PD Dr. Maria Neuss-Radu, Friedrich-Alexander-Universität Erlangen-Nürnberg:
Effective models for nonlinear drift-diffusion of multiple species in porous media (online talk)
more ... Location
Online Event
Abstract
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's equation for the electric potential. The diffusion terms depend nonlinearly on the concentrations. We consider non-homogeneous Neumann boundary condition for the electric potential. The aim is the rigorous derivation of an effective (homogenized) model in the limit when the scale parameter $epsilon$ tends to zero. This is based on uniform a priori estimates for the solutions of the microscopic model. The crucial result is the uniform $L^infty$-estimate for the concentration in space and time. This result exploits the fact that the system admits a nonnegative energy functional which decreases in time along the solutions of the system. By using weak and strong (two-scale) convergence properties of the microscopic solutions, effective models are derived in the limit $epsilon to 0$ for different scalings of the microscopic model. This is a joint work with Apratim Bhattacharya (Erlangen) and Markus Gahn (Heidelberg).
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 18.05.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Richard Kraaij, TU Delft:
Large deviations for weakly coupled slow-fast systems via the comparison principle of an associated Hamilton-Jacobi equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In statistical physics many interesting phenomena, e.g. behavior of systems at critical parameters or in the theory of hydrodynamic limits, arise from systems having multiple time-scales. A slow component is influenced by fast components, and as the number of interacting components tends to infinity, limiting results for the slow component are obtained in terms of 'averaged' versions of the fast components. I will consider in my talk the large deviations of coupled Markovian systems with two-time scales. The large deviations can arise from two sources: deviations of the slow process itself, or deviations of the large time averages of the fast process, effectively leading to a competition of two deviation effects. Arguing via the non-linear analogue of the "martingale problem approach" that applies for large deviations of Markov processes, we arrive at a uniqueness problem for a Hamilton-Jacobi-Bellman equation. We establish under mild conditions that this Hamilton-Jacobi-Bellman equation is well-posed, and as a consequence that we have a large deviation principle for a wide class of weakly coupled Markov processes.Based on joint work with Mikola Schlottke (Eindhoven, The Netherlands)
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin - Wednesday, 18.05.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Zdeněk Hlávka, Charles University, Tschechische Republik:
Testing dependencies in functional time series (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We discuss tests of serial independence for a sequence of functional observations and tests of independence between two (or more) time series of functional observations. The tests are based on characteristic functions which are appropriately estimated from functional observations. The limit distribution of the new test statistic is obtained under the null hypothesis, while under alternatives it is shown that the test statistics almost surely diverge as the sample size increases. In a Monte Carlo study, we investigate appropriate resampling methods and we investigate the tests? performance in finite samples. Finally, an application illustrates the use of the method with real data from financial markets, including also cumulative intraday returns of Bitcoin and Ethereum. References: Meintanis, S. G., Hušková, M., & Hlávka, Z. (2022). Fourier-type tests of mutual independence between functional time series. Journal of Multivariate Analysis, 189, 104873. Hlávka, Z., Hušková, M., & Meintanis, S. G. (2021). Testing serial independence with functional data. Test, 30(3), 603-629.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 17.05.2022, 15:15 (WIAS-ESH)
- Oberseminar Nonlinear Dynamics
Leonhard Schülen, Technische Universität Berlin:
The solitary route to chimera states
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators
Further Informations
Oberseminar Nonlinear Dynamics
Host
WIAS Berlin
Freie Universität Berlin
- May 13 – 14, 2022 (HU Berlin HVP)
- Workshop/Konferenz: 15th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, R. 0007
Host
Technische Universität Berlin
WIAS Berlin
- May 12, 2022 (TUB-MA 415)
- Workshop/Konferenz: 15th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Technische Universität, Straße des 17. Juni 136, 10623 Berlin, MA 415
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 11.05.2022, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Oğul Esen, Gebze Technical University, Türkei:
On geometry of Vlasov plasma (online talk)
more ... Location
Online Event
Abstract
This talk is about the Lie--Poisson formulation of Vlasov plasma. For the collisionless non-relativistic plasma motion, we shall introduce a system of differential equations called momentum-Vlasov equations. We shall show that this system is related to the Vlasov equation by a Poisson map. For the momentum-Vlasov equation, we shall propose a geometric pathway (involving complete lifts and vertical representatives) from the particle motion to the evolution of the field variables.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 11.05.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Vladimir Spokoiny, WIAS & HU Berlin:
Laplace approximation in high dimension with applications to statistical inference (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This note revisits the classical results on Laplace approximation in a modern non-asymptotic and dimension free form. Such an extension is motivated by the uncertainty quantification for high dimensional statistical models. The established results provide an explicit non-asymptotic bounds on the quality of a Gaussian approximation of the posterior distribution in total variation distance in terms of the so called empheffective dimension p_G defined as interplay between information contained in the data and in the prior distribution. In the contrary to prominent Bernstein-von-Mises results, the impact of the prior is not negligible and it allows to keep the effective dimension small or moderate even if the true parameter dimension is huge or infinite. We also address the important issue of using a Laplace approximation with posterior mean in place of Maximum Aposteriori Probability (MAP).
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 10.05.2022, 16:30 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Yulia Petrova, Instituto de Matemática Pura e Aplicada, Brazil:
On the impact of dissipation ratio on vanishing viscosity solutions of Riemann problems for chemical flooding models (online talk)
more ... Location
Online Event
Abstract
We are interested in solutions of the Riemann problem arising in chemical flooding models for enhanced oil recovery (EOR). To distinguish physically meaningful weak solutions we use vanishing viscosity admissibility criterion. We demonstrate that when the flow function depends non-monotonically on the chemical agent concentration (which corresponds to the surfactant flooding), non-classical undercompressive shocks appear. They correspond to the saddle-saddle connections for the traveling wave dynamical system and are sensitive to precise form of the dissipation terms. In particular we prove the monotonic dependence of the shock velocity on the ratio of dissipative coefficients. The talk is based on joint work with F. Bakharev, A. Enin and N. Rastegaev (arxiv: 2111.15001).
Further Informations
Oberseminar Nonlinear Dynamics
Host
WIAS Berlin
Freie Universität Berlin
- Tuesday, 10.05.2022, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Dr. Sergey Tikhomirov, Instituto de Matemática Pura e Aplicada, Brazil:
Mixing zone in miscible displacement: application in polymer flooding and theoretical attempts of improving (online talk)
more ... Location
Online Event
Abstract
Injection of less viscous fluid to a more viscous one generates instabilities, which are often called “viscous fingers”. In case of miscible displacement it generates a mixing zone, where both fluids are presented. This phenomenon has a negative impact on flooding using chemical slugs in oil fields. We study the mathematical model describing the behavior on the rear front of a polymer slug. It consists of conservation of mass, incompressibility condition and Darcy law. This model often is called the Peaceman model. We study the size of the mixing zone appearing on the rear end of the polymer slug, provide pessimistic estimates and its numerical validation and apply estimates to the graded viscosity banks technology (GVB or tapering) to reduce the volume of used polymer without loss of effectiveness. Further optimization is possible with more delicate estimates of the mixing zone. In current work in progress with Yu. Petrova and Ya. Efendiev we consider a simplified model replacing multidimensional space with two tubes interacting with each other. In this system we numerically observe two traveling waves with different speeds. This behavior mimics the mixing zone of the multidimensional Pieceman model. We will speak on our progress in this direction.
Further Informations
Oberseminar Nonlinear Dynamics
Host
WIAS Berlin
Freie Universität Berlin
- Tuesday, 10.05.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS & HU Berlin:
Laplace's approximation in high dimension (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 04.05.2022, 12:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Chengcheng Ling, TU Berlin:
Singular SDEs and PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Well-posed stochastic differential equations with singular coefficients, as one of the known examples among 'regularization by noise' effect, are supported from the theoretical level mainly by the well-posedness results of parabolic PDEs with singular coefficients. In this talk we will discuss both sides: well-posedness of SDEs and PDEs with singular coefficients. Two examples will be shortly introduced in the end: numerical analysis and dynamical study of SDEs, which give us the partial image on how the equations are regularized by noise.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 04.05.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Carlos Amendola, MPI Leipzig:
Likelihood geometry of correlation models (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of maximum likelihood estimation for this model and linear submodels that encode additional symmetries. We also consider the problem of minimizing two closely related functions of the covariance matrix: the Stein's loss and the symmetrized Stein's loss. Unlike the Gaussian log-likelihood, these two functions are convex and hence admit a unique positive definite optimum. This is joint work with Piotr Zwiernik (University of Toronto).
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 03.05.2022, 15:15 (WIAS-ESH)
- Oberseminar Nonlinear Dynamics
Dr. Marius Yamakou, Friedrich-Alexander-Universität Erlangen:
Transitions between weak-noise-induced resonance phenomena in a multiple timescales neural system
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We consider a stochastic slow-fast nonlinear dynamical system derived from a computational neuroscience model. Independently, we uncover the mechanisms that underlie two forms of weak-noise-induced resonance mechanisms, namely, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR) in the system. We then show that SISR and ISR are related through the relative geometric positioning (and stability) of the fixed point and the generic folded singularity of the system's critical manifold. This result could explain the experimental observation in which real biological neurons with identical physiological features and stochastic synaptic inputs sometimes encode different information.
Further Informations
Oberseminar: Nonlinear Dynamics
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 03.05.2022, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Jun.-Prof. Dr. Martin Redmann, Martin-Luther-Universität Halle-Wittenberg:
Solving high-dimensional optimal stopping problems using model order reduction (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse of dimensionality. Therefore, the objective of this presentation is to establish dimension reduction schemes for large-scale asset price models and to solve related optimal stopping problems (e.g. Bermudan option pricing) in the reduced setting, where regression is feasible. We illustrate the benefit of our approach in several numerical experiments, in which Bermudan option prices are determined.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 27.04.2022, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michael Kniely, Universität Graz, Österreich:
From energy- to electro-energy-reaction-diffusion systems (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This talk will be concerned with a thermodynamically correct formulation of reaction-diffusion systems describing the dynamics of charged species. This is achieved by employing the Onsager formalism of gradient flow systems along with Poisson's equation for the electrostatic potential. In the first part of the talk, we shall revisit some fundamental works on the thermodynamical modeling of semiconductor-type equations, while special emphasis will be placed on recent results on energy-reaction-diffusion systems. The second part will focus on electro-energy-reaction-diffusion models, in particular, the choice of appropriate entropies, the dependence of the Onsager operator on the electrostatic potential, and the existence of fundamental conservation laws. Finally, I will also comment on the expected outcome of the project concerning the well-posedness and the long-time asymptotics of our electro-energy-reaction-diffusion models. Proving the corresponding results is still work to be done and one of the goals of my two-year stay at WIAS.
Further Informations
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 27.04.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Nazgul Zakiyeva, Zuse-Institut Berlin/National University of Singapore:
Modeling and forecasting the dynamics of the natural gas transmission network in Germany with the demand and supply balance constraint (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We develop a novel large-scale Network Autoregressive model with balance Constraint (NAC) to predict hour-ahead gas flows in the gas transmission network, where the total in- and out-flows of the network are balanced over time. By integrating recent advances in optimization and statistical modeling, the NAC model can provide an accurate hour-ahead forecast of the gas flow at all of the distribution points in the network. By detecting the influential nodes of the dynamic network, taking into account that demand and supply have to be balanced, the forecast can be used to compute an optimized schdule and resource allocation. We demonstrate an application of our model in forecasting hour-ahead gas in- and out-flows at 128 nodes in the German high-pressure natural gas transmission network over a time frame of 22 months. Link to the paper: https://www.sciencedirect.com/science/article/abs/pii/S0306261920311
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 26.04.2022, 13:30 (Online Event)
- Seminar Materialmodellierung
Ass. Prof. Dr. Alessia Nota, Università degli Studi dell'Aquila, Italien:
Stationary non-equilibrium solutions for coagulation equations (online talk)
more ... Location
Online Event
Abstract
Smoluchowski's coagulation equation, an integro-differential equation of kinetic type, is a classical model for mass aggregation phenomena extensively used in the analysis of problems of polymerization, particle aggregation in aerosols, drop formation in rain and several other situations. In this talk I will present some recent results on the problem of existence or non-existence of stationary solutions to coagulation equations, for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomena. More precisely, the stationary solutions to the multi-component coagulation equation asymptotically localize into a direction determined by the source term. The localization is a universal property of these multicomponent systems. Indeed, it has been recently proved that localization phenomenon occurs with a great degree of generality also for time dependent solutions to mass conserving coagulation equations. (Joint work with M.A. Ferreira, J. Lukkarinen and J.J.L. Velázquez)
Host
WIAS Berlin
- Friday, 22.04.2022, 13:00 (Online Event)
- E-Coffee-Lecture
Dr Renita Danabalan, WIAS:
Project Management Tools: Hype or Hack
more ... Location
Online Event
Host
WIAS Berlin
- Wednesday, 20.04.2022, 12:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Martin Heida, WIAS Berlin:
Measure theoretic aspects of stochastic homogenization
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We introduce stochastic homogenization of discrete and continuous differential operators as a measure theoretic concept. We then provide several examples for application to real-world problems.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 20.04.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Wolfgang Karl Härdle, BRC Blockchain Research Center:
DAI the digital art index (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The DAI Digital Art index has been developed to reflect the increasing activities on the the Digital Art market. Based on the most liquid exchanges, NFT data and prices are collected in cooperation with artnet.com, NYC . The NFT art market has risen sharply recently and is competing with traditional arts market. The observed transactions are analysed and an index is developed on a hedonic regression framework. We present an introduction into NFTs, explain their construction and "huberize" the hedonic regression context.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 12.04.2022, 16:00 (Online Event)
- Seminar Weierstrass Group Data-Driven Optimization and Control
Adam Thorpe, University of New Mexico, USA:
Stochastic optimal control & safety via kernel embeddings: A data-driven approach
more ... Location
Online Event
Abstract
As autonomy becomes more prevalent, it is increasingly being deployed in highly uncertain environments. This motivates the need for data-driven control methods which are capable of handling complex systems, humans in the loop, poorly-structured disturbances, and also provide assurances of safety. We present a computationally efficient approach for computing stochastic policies based in the theory of kernel embeddings of distributions, a nonparametric statistical learning technique that embeds integral operators as elements in a high-dimensional function space known as a reproducing kernel Hilbert space. We demonstrate how this representation enables us to compute stochastic policies as a linear program, and enables tractability for a wide variety of systems which are resistant to traditional modeling techniques. We have implemented these techniques in a publicly-available toolbox, and apply our approach to motion planning problems and demonstrate its use for computing the safety probabilities for stochastic reachability problems.
Zoom link:
https://us02web.zoom.us/j/83039302328?pwd=S1IyTnBEZ3hDcmdNNmExallxVGp4UT09
Meeting ID: 830 3930 2328
Passcode: 596204
Host
WIAS Berlin
- April 11 – 14, 2022 (Harnack-Haus)
- Workshop/Konferenz: First Annual Conference of SPP 2265 Random Geometric Systems
more ... Location
Harnack-Haus -- Tagungsstätte der Max-Planck-Gesellschaft
Host
DFG Schwerpunktprogramm 2265
WIAS Berlin
- Wednesday, 06.04.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Simone Baldassarri, University of Florence, Italien:
Critical Droplets and sharp asymptotics for Kawasaki dynamics with strongly anisotropic interactions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk we analyze metastability and nucleation in the context of the Kawasaki dynamics for the two-dimensional Ising lattice gas at very low temperature. Particles perform simple exclusion on a finite box in the bidimensional lattice, but when they occupy neighboring sites they feel a binding energy -U_1<0 in the horizontal direction and -U_2<0 in the vertical one. We consider the parameter regime U_1>2U_2 also known as the strongly anisotropic regime. For this model the empty (respectively full) configuration is a metastable (respectively stable) configuration. We consider the asymptotic regime corresponding to finite volume in the limit as the temperature goes to zero. We investigate how the transition from empty to full takes place with particular attention to the critical configurations that asymptotically have to be crossed with probability 1. To this end, we provide a model-independent strategy to identify some unessential saddles (that are not in the union of minimal gates) for the transition from the metastable (or stable) to the stable states and we apply this method to our model. The derivation of some geometrical properties of the saddles allows us to identify the full geometry of the minimal gates and their boundaries for the nucleation in the strongly anisotropic case. We observe very different behaviors for this case with respect to the isotropic (U_1=U_2) and weakly anisotropic (U_1<2U_2) ones. Moreover, we derive sharp estimates for the asymptotic transition time for the strongly anisotropic case. This is based on a joint work with F. R. Nardi.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Thursday, 31.03.2022, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Stefano Piani, International School for advance studies, Italien:
HDG methods for the Van Roosbroeck model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In the early fifties of the twentieth century, Van Roosbroeck formulated the so-called fundamental semiconductor device equations: a system of three nonlinear coupled partial differential equations which describes potential distribution, carrier concentrations, and current flow in arbitrary semiconductor devices. In this model, charge carriers move because of two physical effects: diffusion and convection, with the latter often dominant. Performing a numerical simulation of the Van Roosbroeck equations represent a challenging problem, mainly because of their stiffness. A classical solution to this problem has been found in 1969 by Scharfetter and Gummel, who developed a nonstandard discretization method: a finite-volume scheme with a tailored numerical flux.
At the beginning of this century, instead, it has become more and more common to address convection-dominated problems using discontinuous Galerkin methods (DG methods). One of the main advantages of these methods is their ability to handle adaptive algorithms, working with meshes with hanging nodes and approximation of varying polynomial degrees. Unfortunately, when compared with the standard continuous finite elements, DG methods were often criticized for using too many globally coupled degrees of freedom.
During my talk, I will introduce a particular class of DG methods, the Hybridizable Discontinuous Galerkin Methods which exploit the classic techniques of static condensation to reduce the total number of globally coupled degrees of freedom and I will discuss the possibility of applying these methods to the Van Roosbroeck system, exploiting their similarities with the Scharfetter-Gummel scheme.
Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de.
Host
WIAS Berlin
- Tuesday, 29.03.2022, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. William Salkeld, WIAS Berlin:
Lions calculs and mean-field elementary differentials (online talk)
more ... Location
Online Event
Abstract
This talk will explore higher order Lions derivatives and provide some applications to the modelling of mean-field dynamic systems.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 25.03.2022, 13:00 (Online Event)
- E-Coffee-Lecture
Dr. Karsten Tabelow/Dr. Thomas Koprucki, WIAS:
HackMD
more ... Location
Online Event
Abstract
Collaborative online markdown editor
Host
WIAS Berlin
- Thursday, 24.03.2022, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Nicola Courtier, University of Oxford, UK:
Part I: Accurate and adaptable charge transport modelling of perovskite solar cells using IonMonger (hybrid talk)
Part II: Parameter/state estimation using the measure-moment approach to polynomial optimisation (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This talk will cover the two main foci of my work to-date on the simulation of perovskite solar cell and lithium-ion battery models. Firstly, the development of a fast and accurate finite element scheme for a one-dimensional drift-diffusion model of a perovskite solar cell. This scheme underpins the open-source Matlab code IonMonger released in 2019 [1]. The latest version simulates a 100-point impedance spectroscopy measurement in less than a minute on a desktop computer. The ability of the scheme to cope with nonlinear terms, while maintaining second-order local accuracy, enables it to be applied to a variety of similar models e.g. [2].
Secondly, we address the problem of global parameter estimation of the four parameters of a reduced-order model for the impedance spectra of a perovskite solar cell. The reduced model is derived via asymptotic analysis of the drift-diffusion model [3]. Parameter estimation is performed using a novel approach to polynomial optimisation based on advancements in the field of measure-moment theory, via the numerical solution of a sequence of semi-definite programs [4]. Though limited by the curse of dimensionality, the measure-moment approach may also be used for state estimation and optimal control of reduced-order models. We benchmark the method via application to battery models containing 2 or 4 states.
[1] N.E. Courtier, G. Richardson, and J.M. Foster. A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells. Applied Mathematical Modelling, 63, 329348 (2018)
[2] I. Korotkin, S. Sahu, S. E. J. O'Kane, G. Richardson, and J. M. Foster. DandeLiion v1: An Extremely Fast Solver for the Newman Model of Lithium-Ion Battery (Dis)charge. Journal of The Electrochemical Society, 168, 060544 (2021)
[3] L. J. Bennett, A. J. Riquelme, N. E. Courtier, J. A. Anta, and G. Richardson. A new ideality factor for perovskite solar cells and an analytical theory for their impedance spectroscopy response. arXiv:2105.11226 (2021)
[4] D. Henrion, J.-B. Lasserre, and J. Löfberg. GloptiPoly 3: moments, optimization and semidefinite programming. Optimization Methods & Software, 24:4-5, 761-779 (2009)
Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 23.03.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Florian Nie, Technische Universität Berlin:
The stochastic F-KPP Equation and on/off branching coalescing Brownian Motion
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Thursday, 10.03.2022, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Xu Li, Shandong University, China:
Two divergence-free reconstructions for Navier--Stokes simulations regarding EMA and robust estimates of kinetic energy error (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Navier--Stokes simulations with divergence-free elements have many fascinating properties such as EMA-conservation (EMA: kinetic energy, linear momentum and angular momentum), pressure-robustness and Re-semi-robustness. Due to the complexity of divergence-free elements, developing novel discretizations for the commonly used elements which possess similar properties is a very popular way in Navier-Stokes community. In this talk, we discuss two divergence-free reconstruction methods for Navier--Stokes simulations. The first method is obtained by replacing the advective velocity of the convective trilinear form with its a divergence-free approximation. The resulting method preserves kinetic energy and linear momentum under some appropriate senses. Regarding its error estimates, we prove that the Gronwall constant in the kinetic energy error bound does not depend on the inverse powers of viscosity explicitly, which is similar to the EMAC method. The second method is based on the pressure-robust reconstruction formulation in [A. Linke & C. Merdon, CMAME, 2016]. We propose a novel trilinear form which preserves (redefined) energy, momentum and angular momentum, while maintaining pressure-robustness. It can also be proven that the constants in the kinetic energy error bound do not depend on the inverse powers of viscosity explicitly, which is similar to the methods with divergence-free elements. In both methods we discuss the reconstruction operators in detail. Finally, we also show some numerical experiments with Taylor--Hood, MINI and Bernardi--Raugel elements, doing some comparisons with the EMAC method and some low order divergence-free element methods.
(This is a joint work with Hongxing Rui, Shandong University)
Further Informations
For zoom login details please contact ulrich.wilbrandt@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 09.03.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Alexander Hinsen, WIAS Berlin:
Chase-escape on a dynamic network
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We study a malware propagation model on top of a dynamic device-to-device network. Movement of devices is generated by a random waypoint model, restricted to a Poisson-Voronoi tessellation based street system. At time zero, malware infects a typical device. Infected devices infect adjacent susceptible devices. In order to detect and contain the spread, we introduce white knights: patched devices that detect infection attempts and retaliate by purging the infection and forcing an update. As white knights and susceptible devices don't interact, the countermeasure 'spreads' on the infection. We derive regimes for the survival of the malware in the presence of the white-knight counter measure and determine regimes in which the white-knights counter measure leads to a containment of the malware. This talk presents the results of a research agreement between WIAS and Orange SA.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Friday, 25.02.2022, 13:00 (Online Event)
- E-Coffee-Lecture
Dr Pierre-Étienne Meunier:
Pijul distributed version control system
more ... Location
Online Event
Host
WIAS Berlin
- Wednesday, 23.02.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Dr. Ana Djurdjevac, Zuse Institute Berlin:
Approximation of the Dean-Kawasaki equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Dean-Kawasaki equation describes the evolution of the density function of finitely many particles obeying Langevin dynamics. This equation is extremely singular (supercritical) due to its form and the low regularity of the noise. We will formulate a nonlinear SPDE approximation. First we will study the well-posedness of the approximated equation and its conservation properties. Furthermore, we will show the bound of the weak error. This is the joint work with H. Kremp and N. Perkowski.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Tuesday, 22.02.2022, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Hessian barrier algorithms for non-convex conic optimization (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 16.02.2022, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Petr Pelech, WIAS Berlin:
Penrose-Fife model with activated phase transformation - existence and effective model for slow-loading regimes (online talk)
more ... Location
Online Event
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 16.02.2022, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Céline Duval, Université de Paris:
Interacting Hawkes processes with multiplicative inhibition (online talk)
more ... Location
Online Event
Abstract
After a short introduction on Hawkes processes, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two features: inhibition, which acts as a multiplicative factor onto the intensity of the excitatory population and additive retroaction from the excitatory neurons onto the inhibitory ones. We detail the well-posedness of this interacting system as well as its dynamics in large population. The analysis of the longtime behavior of the mean-field limit process can be explicated. We illustrate numerically that inhibition and retroaction may be responsible for the emergence of limit cycles. (j.w. with E. Luçon and C. Pouzat)
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 10.02.2022, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Shulin Wohlfeil, Ferdinand-Braun-Institut:
Experimental investigations of passively modelocked ridge-waveguide and tapered lasers emitting at 830 nm (online talk)
more ... Location
Online Event
Host
WIAS Berlin
Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik
- Wednesday, 09.02.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Tobias Paul, HU Berlin:
Modelling interactions of mutation, dormancy and transfer
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Recently, a toy model for the interaction of mutation and horizontal transfer was proposed by Champagnat, Méléard and Tran (2021). We extend their model to include the effects of competition induced dormancy and recover the convergence of the logarithmic population sizes. While the result remains unchanged, the qualitative behaviour of the limiting functions may exhibit properties of the model without dormancy but also entirely new phenomena. As an example we can observe an interesting non-monotonicity in the success of the dormancy traits depending on the strength of the dormancy initiation probability. Furthermore, we will discuss possible extensions and generalizations of the model. (This is joint work with Jochen Blath and András Tóbiás, TU Berlin)
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 09.02.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Erwan Scornet, Ecole Polytechnique Paris, Frankreich:
Variable importance in random forests (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Nowadays, machine learning procedures are used in many fields with the notable exception of so-called sensitive areas (health, justice, defense, to name a few) in which the decisions to be taken are fraught with consequences. In these fields, it is necessary to obtain a precise decision but, to be effectively applied, these algorithms must provide an explanation of the mechanisms that lead to the decision and, in this sense, be interpretable. Unfortunately, the most accurate algorithms today are often the most complex. A classic technique to try to explain their predictions is to calculate indicators corresponding to the strength of the dependence between each input variable and the output to be predicted. In this talk, we will focus on variable importances designed for the original random forest algorithm: the Mean Decreased Impurity (MDI) and the Mean Decrease Accuracy (MDA). We will see how theoretical results provide guidance for their practical uses.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 02.02.2022, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Upanshu Sharma, Freie Universität Berlin:
Variational structures beyond gradient flows (online talk)
more ... Location
Online Event
Abstract
Gradient flows is an important subclass of evolution equations, whose solution dissipates an energy 'as fast as possible'. This distinguishing feature endows these equations with a natural variational structure, which has received enormous attention over the last two decades. In recent years, it has become clear that if the gradient-flow equation originates from an underlying (reversible) stochastic particle system, then often the aforementioned variational structure is an exact decomposition of the large-deviation rate functional for the particle system. However, this decomposition and the corresponding gradient-flow structure breaks down if the underlying particles have additional non-dissipative effects (for instance in the case of non-reversible independent particles), even though the large-deviation rate functional is still available. Using the guiding example of independent non-reversible Markov jump particles, in this talk, I will discuss the various features of the rate functional and how it connects to relative entropy and Fisher information. Furthermore, I will show that if the underlying particle system is augmented with fluxes, then it is possible to derive gradient-flow-type structures in the non-reversible setting.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 02.02.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Dr. Quirin Vogel, NYU Shanghai, China, Volksrepublik:
Infinite loops - The limit of the Feynman representation of the Bose gas (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Around 75 years ago, Feynman used path-integration to represent a gas of (interacting) bosons in a finite volume by an ensemble of brownian bridges, aka loops. Bosons exhibit Bose--Einstein condensation - a state of matter in which a macroscopic proportion of the particles occupy the same quantum state. It has been conjectured that the condensate is represented by “infinite” loops. We “verify” this for several cases by proving that the finite volume representation converges to the superposition of finite loops and the random interlacements. Prior knowledge of bosons/mathematical physics is not required for this talk.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 02.02.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Alessandra Menafoglio, Politecnico Milano , Italien:
Object oriented data analysis in Bayes spaces: From distributional data to the analysis of complex shapes (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In the presence of increasingly massive and heterogeneous data, the statistical modeling of distributional observations plays a key role. Choosing the 'right' embedding space for these data is of paramount importance for their statistical processing, to account for their nature and inherent constraints. The Bayes space theory is a natural embedding space for (spatial) distributional data, and was successfully applied in varied settings. In this presentation, I will discuss the state-of-the-art methods for the modelling, analysis, and prediction of distributional data, with a particular attention to cases when their spatial dependence cannot be neglected. I will embrace the viewpoint of object-oriented spatial statistics (O2S2), a system of ideas for the analysis of complex data with spatial dependence. All the theoretical developments will be illustrated through their application on real data, highlighting the intrinsic challenges of a statistical analysis which follows the Bayes spaces approach. Applications will cover a varied range of fields, from the assessment of COVID-19 on mortality data to the analysis of complex shapes produced in additive manufacturing.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 01.02.2022, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Robust k-means clustering in metric spaces (online talk)
more ... Location
Online Event
Abstract
In this work we investigate the theoretical properties of robust k-means clustering under assumption of adversarial data corruption. Namely, we provide non-asymptotic rates for excess distortion under weak model assumptions on the moments of the distribution.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 26.01.2022, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Alexander Mielke, WIAS Berlin:
On two coupled degenerate parabolic equations motivated by thermodynamics (online talk)
more ... Location
Online Event
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 26.01.2022, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Pierre Jacob, ESSEC Business School, Frankreich:
Some methods based on couplings of Markov chain Monte Carlo algorithms (online talk)
more ... Location
Online Event
Abstract
Markov chain Monte Carlo algorithms are commonly used to approximate a variety of probability distributions, such as posterior distributions arising in Bayesian analysis. I will review the idea of coupling in the context of Markov chains, and how this idea not only leads to theoretical analyses of Markov chains but also to new Monte Carlo methods. In particular, the talk will describe how coupled Markov chains can be used to obtain 1) unbiased estimators of expectations and of normalizing constants, 2) non-asymptotic convergence diagnostics for Markov chains, and 3) unbiased estimators of the asymptotic variance of MCMC ergodic averages.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Friday, 21.01.2022, 13:00 (WIAS-Library)
- E-Coffee-Lecture
Dr. Matthias Liero, WIAS:
Coffee-Lecture: Automated building and testing of software projects using the WIAS Gitlab server
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411
Abstract
This talk gives an introduction to Gitlab pipelines on the recently installed Gitlab server at WIAS. We will discuss the basic ideas and concepts and go through a simple example of setting up such a pipeline.
Further Informations
The coffee-lecture will probably take place online
Host
WIAS Berlin
- Wednesday, 19.01.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Denis Belomestny, Universität Duisburg-Essen:
Achieving optimal sample complexity in reinforcement learning via upper solutions (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 18.01.2022, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yangwen Sun, Humboldt-Universität zu Berlin:
High dimensional change-point detection: A complete graph approach (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 12.01.2022, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Ass. Prof. Dr. Sebastian Schwarzacher, Charles University Prague, Tschechische Republik:
A variational approach to fluid-structure interactions (online talk)
more ... Location
Online Event
Abstract
In this talk some recent existence results in fluid-structure interactions are discussed. It focuses on the case when visco-elastic bulk solids are interacting with fluids. One of the characteristic difficulties of the respective PDE systems is the variable-in-time fluid domain being a part of the solution. The construction of solutions is by step-wise minimization. Such a variational approximation seems to be irreplaceable for large deformation solids, since the respective state spaces are (for physical reasons) non-convex. We introduce a two time-scale approximation scheme that is capable to construct second-order in time PDEs via step-wise minimization. Further it allows to construct weak solutions describing bulk solids interacting with fluids governed by the incompressible or compressible Navier-Stokes equations. The talk is based on collaborations with Benesova, Breit and Kampschulte.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 12.01.2022, 12:30 (WIAS-ESH)
- Seminar Interacting Random Systems
Prof. Dr. Wolfgang König, WIAS Berlin:
The free energy of a box version of the interacting Bose gas Joint works with Adams and Collevecchio (2011) and with Collin and Jahnel (ongoing)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the famous Bose?Einstein condensation phase transition is sought for. We introduce a simplified version of the model in $mathbb Z^d$ instead of $mathbb R^d$ and with an organisation of the particles in deterministic boxes instead of Brownian cycles as the marks of a reference Poisson point process. We derive an explicit and interpretable variational formula in the thermodynamic limit for the canonical ensemble for any value of the particle density. In this formula, each of the microscopic particles and the macroscopic part of the configuration are seen explicitly (if they exist); the latter receives the interpretation of the condensate. The methods comprises a two step large-deviation approach for marked Poisson point processes and an explicit distinction into microscopic and macroscopic marks. We discuss the condensate phase transition in terms of existence of minimizer.
Further Informations
Seminar Interacting Random Systems (Hybrid Event)
Host
WIAS Berlin
- Wednesday, 12.01.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Martin Wahl, Humboldt-Universität zu Berlin:
Functional estimation in log-concave location-scale families (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 11.01.2022, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Feliks Nüske, Universität Paderborn:
Tensor-based methods for learning the Koopman semigroup (online talk)
more ... Location
Online Event
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Wednesday, 05.01.2022, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Alexandra Suvorikova, WIAS Berlin:
Robust k-means in metric spaces and spaces of probability measures (online talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Friday, 17.12.2021, 13:00 (Online Event)
- E-Coffee-Lecture
Dr. Silvia Polla, WIAS:
Research support services at the WIAS library
more ... Location
Online Event
Host
WIAS Berlin
- Friday, 17.12.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Prof. Dr. Daniel Ueltschi, University of Warwick, GB:
Loop models and the universal distribution of the loop lengths (online talk)
more ... Location
Online Event
Abstract
I will review several models that consist of one-dimensional loops living in three-dimensional space. These models describe bosonic systems, and classical or quantum spin systems.. Their common feature is that the joint distribution of their loop lengths has universal behaviour: It is always a Poisson-Dirichlet distribution. Most of this theory is conjectural, but it is backed by numerical studies and some partial rigorous results.
Further Informations
Seminar Interactin Random Systems (Online Event) [attention: day of week changed]
Host
WIAS Berlin
- Wednesday, 15.12.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Jun.-Prof. Lara Trussardi, Universität Konstanz:
Two structure-preserving time discretizations for gradient flow. An application to GENERIC systems (online talk)
more ... Location
Online Event
Abstract
The equality between dissipation and energy drop is a structural property of gradient-flow dynamics. The classical implicit Euler scheme fails to reproduce this equality at the discrete level. We discuss two modifications of the Euler scheme satisfying an exact energy equality at the discrete level. Eventually, we address extensions to GENERIC flows and implement the case of the damped harmonic oscillator. This is based on a series of joint works with A. Jüngel and U. Stefanelli.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 14.12.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Uli Sauerland/Dr. Anton Benz, Leibniz-Zentrum Allgemeine Sprachwissenschaft:
Numerical challenges in linguistic pragmatics (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 10.12.2021, 14:00 (Online Event)
- MATH+ Thematic Einstein Semester on “Mathematics of Imaging in Real-World Challenges”
Prof. Dr. Bernhard Schmitzer, U Göttingen; Prof. Dr. G. Steidl, TU Berlin:
https://mathplus.de/topic-development-lab/tes-winter-2021-22/#tandemtalks
Christmas talk: Santa Claus needs optimal transport
more ... Location
Online Event
Abstract
Please find below the zoom details. No registration is required.
https://tu-berlin.zoom.us/j/69089092360?pwd=aklyWDJFcmwzSkdFRGtWSkorK3pvUT09 Passcode: 797448
Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
- Wednesday, 08.12.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
Some new insights in second order divergence operators (online talk)
more ... Location
Online Event
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 08.12.2021, 12:30 (Online Event)
- Seminar Interacting Random Systems
Elena Magnanini, WIAS Berlin:
Limit theorems for the edge density in exponential random graphs (online talk)
more ... Location
Online Event
Abstract
In the present talk we focus on the derivation of some asymptotic properties for the family of exponential random graphs. This model can be seen as the generalization of the dense Erd?s-Rényi random graph and follows the statistical mechanics approach of defining a Hamiltonian to weight the probability measure on the space of graphs, assigning higher mass to graphs with ?desirable? properties. In particular our analysis will be focused on the edge-triangle model, a two-parameter family of exponential random graphs where the Hamiltonian only includes edge and triangle densities. We borrow tools from statistical mechanics together with large deviations techniques to obtain limit theorems for the edge density in the so-called replica symmetric regime, where the limiting free energy of the model is known together with a complete characterization of the phase diagram. First, we determine the asymptotic distribution of the edge density, as the graph size n tends to infinity, in the entire replica symmetric regime. In particular, we obtain a strong law of large numbers when the parameters are chosen outside the critical curve and the convergence to a mixture of Dirac measures whenever working on the critical curve. We then study the fluctuations of the edge density around its average for all parameter values outside the critical curve and off the critical point and we formulate conjectures about the behavior at criticality based on the analysis of a mean-field approximation of the model. Joint work with Alessandra Bianchi and Francesca Collet.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 08.12.2021, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Davy Paindaveine, Université Libre de Bruxelles, Belgien:
Hypothesis testing on high-dimensional spheres: The Le Cam approach (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Hypothesis testing in high dimensions has been a most active research topics in the last decade. Both theoretical and practical considerations make it natural to restrict to sign tests, that is, to tests that uses observations only through their directions from a given center. This obviously maps the original Euclidean problem to a spherical one, still in high dimensions. With this motivation in mind, we tackle two testing problems on high-dimensional spheres, both under a symmetry assumption that specifies that the distribution at hand is invariant under rotations with respect to a given axis. More precisely, we consider the problem of testing the null hypothesis of uniformity ("detecting the signal") and the problem of testing the null hypothesis that the symmetry axis coincides with a given direction ("learning the signal direction"). We solve both problems by exploiting Le Cam's asymptotic theory of statistical experiments, in a double- or triple-asymptotic framework. Interestingly, contiguity rates depend in a subtle way on how well the parameters involved are identified as well as on a possible further antipodally-symmetric nature of the distribution. In many cases, strong optimality results are obtained from local asymptotic normality. When this cannot be achieved, it is still possible to establish minimax rate optimality.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 07.12.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Inverting the Markovian projection: A reproducing kernel Hilbert space approach (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 07.12.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
André Eikmeier, Technische Universität Berlin:
Existence of weak solutions to a general multivalued differential equation (online talk)
more ... Location
Online Event
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Monday, 06.12.2021, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Dr. Juan Carlos de los Reyes, Escuela Politécnica Nacional, Ecuador:
Bilevel learning for inverse problems
more ... Location
Online Event
Abstract
In recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based on a training set is used. When confronted with inverse problems with nonsmooth regularizers or nonlinear operators, however, the bilevel optimization problem structure becomes quite involved to be analyzed, as classical nonlinear or bilevel programming results cannot be directly utilized. In this talk, I will discuss on the different challenges that these problems pose, and provide some analytical results as well as a numerical solution strategy. Access to seminar over Zoom link on page https://www.wias-berlin.de/research/rgs/fg8/Seminar_Opt_Con_Inv_Prob/index.jsp?lang=1
Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 01.12.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Lukas Wessels, Technische Universität Berlin:
Pontryagin's maximum principle for SPDEs and its relation to dynamic programming (online talk)
more ... Location
Online Event
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 01.12.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Nikita Puchkin, Higher School of Economics Moscow, Russische Föderation:
Rates of convergence for density estimation with GANs (online talk)
more ... Location
Online Event
Abstract
We undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We derive theoretical guarantees for the density estimation with GANs under a proper choice of the deep neural networks classes representing generators and discriminators. In particular, we prove that the resulting estimate converges to the true density p* in terms of Jensen-Shannon (JS) divergence at the rate (logn/n)2β/(2β+d) where n is the sample size and β determines the smoothness of p*. Moreover, we show that the obtained rate is minimax optimal (up to logarithmic factors) for the considered class of densities.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 30.11.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Long-Hao Xu, University of Manchester:
Limiting behavior of the gap between the largest two representative points of statistical distributions (online talk)
more ... Location
Online Event
Abstract
The problem of selecting a given number of representative points retaining as much information as possible arises in many situations. It can also be considered as a problem of approximating a continuous distribution by a discrete distribution. In this talk, we are interested in these points reaching the minimum value of mean squared error (we call these points MSE RPs). We illustrate the relationship between MSE RPs and doubly truncated mean residual life (DMRL) as well as mean residual life (MRL), and we discuss the limiting behavior of the gap between the largest two MSE RPs. In simulation studies, we assess the statistical performance of MSE RPs for various distributions in terms of moment estimation and resampling technique. We also discuss the relationship between the tail of the distribution and the gap of MSE RPs.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 30.11.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Paul Hagemann, Technische Universität Berlin:
Stochastic normalizing flows and inverse problems (online talk)
more ... Location
Online Event
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Wednesday, 24.11.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Czech Academy of Sciences, Tschechische Republik:
Visco-plastic elastodynamics at large deformations by Eulerian approaches (online talk)
more ... Location
Online Event
Abstract
Two models of hardening-free plasticity or creep at large deformations will be presented in an Eulerian rate formulation based on two standard concepts, Green--Naghdi additive decomposition and Kroner--Lee--Liu multiplicative decomposition of the total strain. Extensions towards poroelasticity and thermodynamics will be outlined, too.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 24.11.2021, 14:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Matthew Reimherr, Penn State University:
Pure differential privacy in functional data analysis (online talk)
more ... Location
Online Event
Abstract
We consider the problem of achieving pure differential privacy in the context of functional data analysis, or more general nonparametric statistics, where the summary of interest can naturally be viewed as an element of a function space. In this talk I will give a brief overview and motivation for differential privacy before delving into the challenges that arise in the sanitization of an infinite dimensional summary. I will present a new mechanism, called the Independent Component Laplace Process, for achieving privacy followed by several applications and examples.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 24.11.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Sanjoy Kumar Jhawar, WIAS Berlin:
Percolation in enhanced random connection models (online talk)
more ... Location
Online Event
Abstract
This work contains the study of phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a homogeneous Poisson point process P(s) with intensity parameter s, on the 2-d plane. In the homogeneous RCM, the vertices at x and y are connected with probability, which is a function of distance between the points, independent of everything else. In the inhomogeneous version of the model, points of P(s) are endowed with weights that are non-negative independent random variables W, having power law distribution. Vertices located at x, y with weights W(x), W(y) are connected with probability, that is a connection function depending on the distance between x, y and the weights attached to them, independent of all else. The edges of the graph are viewed as straight line segments starting and ending at points of P(s). The Poisson stick model consists of line segments of independent random lengths and orientation with the midpoint of each line located at a distinct point of P(s). Intersecting line segments form a path in the graph. In other words, a path in these graphs is a continuous curve that is a subset of the collection of all these line segments. A graph is said to percolate if there is an infinite connected component or path. The conditions for the existence of non-trivial phase transition has been derived. Under some additional conditions it has been shown that there is no percolation at criticality using Russo--Seymour-Welsh theory as a fundamental tool.
Host
WIAS Berlin
- Tuesday, 23.11.2021, 13:30 (Online Event)
- Seminar Materialmodellierung
Dr.-Ing. Silvia Budday, Friedrich-Alexander Universität Erlangen-Nürnberg:
Brain mechanics across scales (online talk)
more ... Location
Online Event
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- Tuesday, 23.11.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Jia-Jie Zhu, WIAS Berlin:
Numerical, statistical, and functional analysis of robust optimization-learning-control
more ... Location
Online Event
Abstract
In this talk, I will first introduce our works in establishing computational algorithms for robust learning and optimization algorithms, highlighting the use of kernel methods and optimal transport in treating the ubiquitous data distribution shift that plagues modern-day machine learning. I will do so by presenting perspectives from numerical optimization and optimal control, statistical learning theory, function spaces and approximations. In the latter half, the talk will focus on the outlook on multi-stage problems and topics beyond the classical notion of robustness, highlighting technical limitations, what we already know, and what we do not yet know.
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Thursday, 18.11.2021, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Lasse Ermoneit, WIAS Berlin:
Multi-physics device-scale modeling for solid-state spin-qubits (online talk)
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/83433220391?pwd=UzNsUktDSTR3K0tkOU1KNTRSRjFBdz09
Host
WIAS Berlin
Humboldt-Universität zu Berlin
- Thursday, 18.11.2021, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Felipe Galarce Marín, WIAS Berlin:
Physics-based assimilation of displacements data from magnetic resonance elastography (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This work addresses the state estimation problem of reconstructing 3D displacement fields from partial 2D data acquired with Magnetic Resonance Elastography (MRE). MRE is a medical imaging technique sensitive to mechanical properties of tissues. Recent studies demonstrated its potential for the non-invasive estimation of pathological interstitial pressure, e.g., in the contexts of hydrocephalus (brain). We use a variational data assimilation framework based on a background parametric PDE (poroelasticity) for the tissue dynamics and on model order reduction (POD) of the admissible solution space. Preliminary results for the reconstruction of displacement field and characterization of the pressure field are presented.
For zoom login details please contact Ulrich Wilbrandt wilbrandt@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 17.11.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. André Schlichting, Westfälische Wilhelms-Universität Münster:
Dynamic behavior of growth processes: Phase separation, self-similarity, and oscillations (online talk)
more ... Location
Online Event
Abstract
The talk reviews some growth processes describing the evolution of clusters consisting of atomic parts called monomers. The growth and shrinkage can only occur by adding and removing single monomers, specified through a rate kernel depending solely on the involved clusters' size. First, I discuss the exchange-driven growth model, obtained as the mean-field limit of stochastic particle systems (zero-range process). Under a detailed balance condition on the kernel, the model's longtime behavior can be described entirely. Here, the total mass density, determined by the initial data, acts as an order parameter in which the system shows a phase separation. Next, we consider the model for a family of product kernels, which do not satisfy a detailed balance condition. After a suitable rescaling to self-similar variables, the equation becomes a discrete Laplace with a power-law as diffusion coefficient, which in particular degenerates at the origin and grows at infinity. We will see that the solution converges to a stretched exponential self-similar profile. Lastly, we consider the now-classic Becker-Döring system to which an injection of monomers and a depletion of large clusters is added. These equations have been extensively used to model chemical-physical systems, especially bubbleator dynamics. The model approximates a transport equation with a conservation law entering the boundary condition by formal asymptotics. For the limit model, a Hopf bifurcation is shown, indicating temporal oscillations in the model. joint works with Constantin Eichenberg, Barbara Niethammer, Robert Pego, and Juan Velazquez.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 17.11.2021, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Christophe Giraud, Université Paris-Saclay, Frankreich:
A geometric approach to fair online learning (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Machine learning is ubiquitous in daily decisions and producing fair and non-discriminatory predictions is a major societal concern. Various criteria of fairness have been proposed in the literature, and we will start with a (biased!) tour on fairness concepts in machine learning. Many decision problems are of a sequential nature, and efforts are needed to better handle such settings. We consider a general setting of fair online learning with stochastic sensitive and non-sensitive contexts. We propose a unified approach for fair learning in this setting, by interpreting this problem as an approachability problem. This point of view offers a generic way to produce algorithms and theoretical results. Adapting Blackwell?s approachability theory, we exhibit a general necessary and sufficient condition for some learning objectives to be compatible with some fairness constraints, and we characterize the optimal trade-off between the two, when they are not compatible. (joint work with E. Chzhen and G. Stoltz)
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Friday, 12.11.2021, 15:00 (Online Event)
- MATH+ Thematic Einstein Semester on “Mathematics of Imaging in Real-World Challenges”
Prof. Dr. Tobias Schäffter, TU Berlin and PTB; Prof. Dr. Michael Hintermüller, WIAS and HU Berlin:
Tandem Talk: Quantitative Magnetic Resonance Imaging: Applications and Mathematics (online talks):
Tobias Schäffter (TU Berlin, PTB): Quantitative MR Imaging -- Added Value
Michael Hintermüller (WIAS, HU Berlin): Mathematics of Quantitative Imaging
https://mathplus.de/topic-development-lab/tes-winter-2021-22/#tandemtalks
more ... Location
Online Event
Abstract
Please find below the zoom details. No registration is required.
Topic: TES Tandem Talk: qMRI - Applications and Mathematics
Time: Nov 12, 2021 15:00 Amsterdam, Berlin, Rome, Stockholm, Vienna
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Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
- Thursday, 11.11.2021, 16:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Dr. Mindaugas Radziunas, WIAS Berlin:
Steady states in the Traveling Wave model of multisection edge emitting semiconductor lasers (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Diesen Vortrag können Sie auch mit Zoom verfolgen unter: https://us02web.zoom.us/j/83433220391?pwd=UzNsUktDSTR3K0tkOU1KNTRSRjFBdz09
Host
WIAS Berlin
Humboldt-Universität zu Berlin
- Wednesday, 10.11.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Petr Vágner, WIAS Berlin:
GENERIC, geometry and continuum electro-thermodynamics (online talk)
more ... Location
Online Event
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 10.11.2021, 14:00 (HU)
- Forschungsseminar Mathematische Statistik
Nikita Zhivotovsky, Google Research:
Distribution--free robust linear regression
more ... Location
Humboldt-Universität zu Berlin, Dorotheenstr. 1, 10117 Berlin, Raum 005
Abstract
We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy--tailed response variable. When learning without assumptions on the covariates, we establish boundedness of the conditional second moment of the response variable as a necessary and sufficient condition for achieving deviation-optimal excess risk bounds. First, we prove an optimal version of the classical in-expectation bound for the truncated least squares estimator due to Györfi, Kohler, Krzyzak, and Walk. However, in spite of its optimal in--expectation performance, we show that this procedure fails with constant probability for some distributions. Combining the ideas of truncated least squares, median-- of--means procedures, and aggregation theory, we construct a non--linear estimator achieving excess risk of order O(d/n) with the optimal sub-exponential tail. Joint work with Jaouad Mourtada (CREST, ENSAE) and Tomas Vaškevičius (University of Oxford)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 10.11.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Anh Duc Vu, WIAS Berlin:
Percolation theory and effective conductivity (online talk)
more ... Location
Online Event
Abstract
Percolation theory is getting more and more attention in recent years and we have already seen applications in previous IRS talks, e.g. in the modelling of device-to-device networks. The motivation for this talk lies in a different field, namely PDEs on randomly perforated domains. This field is highly driven by the analysis of composite materials. We derive a formula for the so-called "effective conductivity" of an ergodic random perforation. While there are many ways to calculate the effective conductivity in an analytic way, this formula uses percolation properties of the random perforation to derive its value. As a direct application, we show that the Boolean model of a Poisson point process has non-trivial effective conductivity.
Host
WIAS Berlin
- Wednesday, 10.11.2021, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Marc Hoffmann, Université Paris-Dauphine:
Some statistical inference results for interacting particle models in a mean-field limit (hybrid talk)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We propose a systematic--theoretical--statistical analysis for systems of interacting diffusions, possibly with common noise and/or degenerate diffusion components, in a mean-field regime. These models are more or less widely used in finance, MFG, systemic risk analysis, behaviourial sociology or ecology. We consider several inference issues such as: i) nonparametric estimation of the solution of the underlying Fokker-Planck type equation or the drift of the system ii) testing for the interaction between components iii) estimation of the interaction range between particles. This talk is based on joint results with C. Fonte, L. Della Maestra and R. Maillet.
Further Informations
Der Vortrag findet auch bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 09.11.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Simon Breneis, WIAS Berlin:
Markovian approximations of stochastic Volterra equations with the fractional kernel (online talk)
more ... Location
Online Event
Abstract
We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low Hölder-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an $N$-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in $N$. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 03.11.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Evgeny Stepanov, Russian Academy of Sciences, Russische Föderation:
The story of a fish in a turbulent ocean: How to survive and how to return home
more ... Location
Online Event
Abstract
Can a fish with limited velocity capabilities reach any point in the (possibly unbounded) ocean? In a recent paper by D. Burago, S. Ivanov and A. Novikov, “A survival guide for feeble fish", an affirmative answer has been given under the condition that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This brilliant result extends some known point-to-point global controllability theorems though being substantially non constructive. We will give a fish a different recipe of how to survive in a turbulent ocean, and show how this is related to structural stability of dynamical systems by providing a constructive way to change slightly a divergence free vector field with vanishing mean drift to produce a non dissipative dynamics. This immediately leads to closing lemmas for dynamical systems, in particular to C. Pugh's closing lemma, saying also that the fish can eventually return home. Joint work with Sergey Kryzhevich (St. Petersburg).
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 02.11.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Jaroslav Hlinka, Institute of Computer Science of the Czech Academy of Sciences:
Perturbations both trigger and delay seizures due to generic properties of slow--fast relaxation oscillators (online talk)
more ... Location
Online Event
Abstract
The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this work, we analyze white and how perturbations, exogenous or endogenous, may promote or delay seizure emergence [1], following previous observations in vivo, in vitro and in silico [2]. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.
References
[1] Alberto Pérez-Cervera, Jaroslav Hlinka. Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators. PLOS Computational Biology, 17(3): e1008521, 2021.
[2] Chang, Wei-Chih, et al. "Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations." Nature neuroscience 21.12 (2018): 1742-1752.
Host
Freie Universität Berlin
WIAS Berlin
- Wednesday, 27.10.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Matthias Liero, WIAS Berlin:
Electrothermal drift-diffusion models for organic semiconductor devices (online talk)
more ... Location
Online Event
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 27.10.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
András Tóbiás, TU Berlin:
Virus dynamics in the presence of contact-mediated host dormancy (online talk)
more ... Location
Online Event
Abstract
Abstract: We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a dormancy-based defence mechanism was described in Bautista et al (2015). We first analyse the effect of the dormancy-related model parameters on the probability of invasion of a newly arriving virus into a resident host population. It turns out that the probability of dormancy initiation upon virus contact plays a crucial role, while the lengths of the dormancy periods or the death rate during dormancy are largely irrelevant. Given successful invasion, we then show that the emergence of a persistent virus infection ('epidemic') in the host population corresponds to the existence of a coexistence equilibrium for the deterministic many-particle limit of our model. In this context, all dormancy-related parameters have a significant impact. Indeed, while related systems without recovery of infected individuals and dormancy may exhibit a Hopf bifurcation, giving rise to a variant of the 'paradox of enrichment', we provide simulations and rigorous partial results showing that the inclusion of dormancy and recovery can prevent this loss of stability. Finally, we show that the presence of contact-mediated dormancy enables the host population to maintain higher equilibrium sizes (resp. fitness values) - while still being able to avoid a persistent epidemic - than host populations without this trait, for which high fitness values would imply a high risk for the emergence of a persistent epidemic. This adds a twist to the relevance of 'reproductive trade-offs' usually associated with costly dormancy traits. The subject of this talk is joint work with Jochen Blath.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 20.10.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Willem van Oosterhout, WIAS Berlin:
Longtime dynamics of a non-autonomous Chafee--Infante equation (online talk)
more ... Location
Online Event
Abstract
In this talk, we study the longtime dynamics of a one-dimensional Chafee--Infante equation, a particular type of reaction-diffusion equation. We start by giving a thorough description of the longtime dynamics of the autonomous equation. Then, we turn to a non-autonomous version of the Chafee--Infante equation, and see which autonomous results can be generalized to the nonautonomous case. To this end, we consider, for example, the notions of a pullback attractor and non-autonomous equilibria, which can be seen as generalizations of the autonomous concepts of a global attractor and equilibrium solutions.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 19.10.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Jan Hauffen, Technische Universität Berlin:
Deep unfolding: Learned block regularization with application in photothermal superresolution (online talk)
more ... Location
Online Event
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Wednesday, 13.10.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Degrees of fixed vertices and power law degree distributions in preferential attachment trees with neighbourhood influence (online talk)
more ... Location
Online Event
Abstract
Motivated by the structure of complex networks such as the internet, we consider a growing model of preferential attachment trees with neighbourhood influence, where vertices arrive one at a time, are equipped with independent weights, and connect to existing vertices with probability proportional to their fitness function: a function of their own weight and the weights of their neighbours. In this model we prove almost sure limiting statements for the proportion of vertices with a given degree having weight belonging to a given measurable set, and the proportion of edges in the tree with endpoint belonging to a measurable set. We show that under certain conditions, the latter quantity demonstrates a condensation phenomenon, in which a positive proportion of edges in the network accumulate among those of weight that confers maximal reinforcement of fitness. Finally, we derive almost sure limiting statements for the log of the degree of a fixed vertex in this model, and prove that in this model the degree distribution behaves like a power law - a ubiquitous feature of many real-world complex networks.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 29.09.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Michiel Renger, WIAS Berlin:
Open problem: large deviations of transport maps (online talk)
more ... Location
Online Event
Abstract
Motivated by nonequilibrium thermodynamics, we are interested in large deviations for transport maps as the number of particles n goes to infinity. We first focus on the simplest setting of independent Markovian particles on a finite state space, which already poses mathematical challenges. Let n Γ _xy(s,t) be the number of particles that were at position x at time s and at position y at time t. Common large-deviation techniques for random trajectories exploit the Markov property (in one time variable). However, Γ has two time dimensions; can we reformulate Γ as a Markov process?
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 15.09.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Alexander Zass, WIAS Berlin:
Gibbs point processes on path space: existence, cluster expansion and uniqueness (online talk)
more ... Location
Online Event
Abstract
In this talk we present a class of infinite-dimensional diffusions under Gibbsian interactions, viewed in the context of marked point configurations: the starting points belong to R^d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- August 23 – 27, 2021 (Schloss Dagstuhl)
- Workshop/Konferenz: Leibniz MMS Summer School 2021 “Mathematical Methods for Machine Learning”
more ... Location
Leibniz-Zentrum für Informatik, Schloss Dagstuhl
Abstract
Fundamental and advanced aspects of ML methods are presented with the aim to enable the participants to apply such methods to their specific research problems. The topics that will be discussed include kernel methods and Gaussian processes, stochastic and robust optimization, deep Neural Networks. In addition to daily lectures, the participants will get the opportunity to become familiar with the presented methods in accompanying practical lab sessions.
Host
WIAS Berlin
- Tuesday, 17.08.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Jia-Jie Zhu, WIAS Berlin/MPI-IS Tübingen:
Kernel methods for distributionally robust optimization and machine learning (online talk)
more ... Location
Online Event
Abstract
Learning under distribution shift brings new challenges that cannot be addressed by canonical statistical learning theory. In this talk, I will present the use of reproducing kernel Hilbert spaces (RKHS) as the dual spaces for enforcing distributional robustness in stochastic optimization and machine learning. I then prove a generalized strong duality for distributionally robust optimization (DRO) using the integral probability metrics (IPM), of which the type-1 Wasserstein metric is a special instance. Our analysis highlights the roles that smooth function majorants, such as RKHS functions and Moreau envelope, play in enforcing distributional robustness in optimization. Finally, I will introduce a new class of kernel semi-infinite programs that originated from the DRO reformulation.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 10.08.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Darina Dvinskikh, WIAS Berlin:
Decentralized algorithms for Wasserstein barycenters (online talk)
more ... Location
Online Event
Abstract
We consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides in two scenarios: (i) the measures are given and we need to compute their Wasserstein barycenter, and (ii) the measures are generated from a probability distribution and we need to calculate the population barycenter of the distribution defined by the notion of Fréchet mean. The statistical focus is estimating the sample size of measures necessary to calculate an approximation for Fréchet mean (barycenter) of a probability distribution with a given precision. For empirical risk minimization approaches, the question of the regularization is also studied together with proposing a new regularization which contributes to the better complexity bounds in comparison with quadratic regularization. The computational focus is developing algorithms for calculating Wasserstein barycenters: both primal and dual algorithms which can be executed in a decentralized manner.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 15.07.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Marc-Andre Keip, Universität Stuttgart:
Multiscale analysis of instability-induced pattern transformations of composite active solids
more ... Location
Online Event
Abstract
We discuss instability phenomena of active solids with periodic microstructures. Depending on the material, instabilities can be triggered by different means. In a first part of the talk, we analyze instability-induced pattern transformations of electroactive polymer composites and magnetorheological elastomers. In a second part, we widen the view towards the transient analysis of diffusion-driven instabilities of hydrogels, where we study pattern transformations of composite hydrogel thin films at different length scales.
Acknowledgements: Elten Polukhov, Siddharth Sriram
References
[1] G. Geymonat, S. Müller and N. Triantafyllidis. Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Archive for Rational Mechanics and Analysis 122:231-290 (1993)
[2] K. Bertoldi, M. Boyce, S. Deschanel, S. Prange and T. Mullin. Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures. Journal of the Mechanics and Physics of Solids 56:2642-2668 (2008)
[3] C. Tipton, E. Han and T. Mullin. Magneto-elastic buckling of a soft cellular solid. Soft Matter 8:6880-6883 (2012)
[4] Wu, G., Xia, Y., Yang, S. Buckling, symmetry breaking, and cavitation in periodically micro-structured hydrogel membranes. Soft Matter 10:1392-1399 (2014)
[5] Polukhov, E., Vallicotti, D. and Keip, M.-A. Computational stability analysis of periodic electroactive polymer composites across scales. Computer Methods in Applied Mechanics and Engineering 337:165-197 (2018)
[6] Polukhov, E. and Keip, M.-A. Multiscale stability analysis of periodic magnetorheological elastomers. Mechanics of Materials, 159:103699 (2021)
[7] Sriram, S., Polukhov, E. and Keip, M.-A. Transient stability analysis of composite hydrogel structures based on a minimization-type variational formulation. International Journal of Solids and Structures, 111080 (2021)
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 14.07.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Xin Liu, WIAS Berlin:
Well-posedness of Hibler's dynamical sea-ice model (online talk)
more ... Location
Online Event
Abstract
We establish the local-in-time well-posedness of solutions to an approximating system constrcuted by mildly regularizing the dynamical sea ice model of W.D. Hibler in 1979, which is widely used in the prediction of evolution of Artic sea ice. Our choice of regularization has been carefully designed, prompted by physical considerations, to retain the original coupled hyperbolic-parabolic character of Hibler's model. The well-posedness theory of such a system provides a first-step groundwork in both numerical study and future analytical study. This is joint work with Marita Thomas and Edriss Titi.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 13.07.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Dr. Messoud Efendiyev, Helmholtz Zentrum München:
Mathematical modeling of biofilms and their long-time dynamics (online talk)
more ... Location
Online Event
Abstract
In this talk we deal with mathematical modelling of biofilms, that show biofilm performance is non-uniform. Moreover, our model leads to a new class of degenerate PDEs. Effect of degeneracy to large time behavior of solutions will also be considered.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSlI3TjAxV1U1S2xFQT09
Host
Freie Universität Berlin
WIAS Berlin
- July 8, 2021 (Online Event)
- Workshop/Konferenz: Minisymposium ”Perspectives of Gradient-Robustness”
more ... Location
Online Event
Host
WIAS Berlin
- Wednesday, 07.07.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Klaas Hendrik Poelstra, Technische Universität Dortmund:
Dimension reduction for elastoplastic rods and homogenization of elastoplastic lattices (online talk)
more ... Location
Online Event
Abstract
We derive effective equations for periodic lattices of linearly elastoplastic rods in the limit of both infinitesimal periodicity and infinitesimal relative width of the rods. For this derivation we use the method of evolutionary Gamma-convergence for quadratic rate-independent systems. As a first step towards that goal we derive effective equations for a single rod. After introducing appropriate scalings, the main difficulty lies in the proof of Gamma-convergence for the stored energy. For the study of periodic lattices we then introduce the notion of periodic graph frameworks, discuss infinitesimal rigidity properties of such frameworks and define a simple notion of two-scale convergence. The stored energy of a lattice of rods ist just the sum of the energies of the individual rods, coupled by boundary conditions at the nodes. For this energy we again prove Gamma-convergence. In the presence of volume loads we observe qualitatively different behaviour depending on the relative rate of convergence of the periodicity parameter and the thickness parameter.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 07.07.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Daoyi Wang, Leiden University:
The Parabolic Anderson Model on a Galton-Watson tree with unbounded degrees (online talk)
more ... Location
Online Event
Abstract
A detailed analysis was given by den Hollander, König and dos Santos (2020), of the large-time asymptotics of the total mass of the solution to the parabolic Anderson model on a supercritical Galton-Watson random tree, with an i.i.d. random potential whose marginal distribution is double-exponential. Under the assumption that the degree distribution has bounded support, two terms in the asymptotic expansion were identified under the quenched law, i.e., conditional on the realisation of the random tree and the random potential. We extend the analysis to degree distributions with unbounded support. We identify the weakest condition on the tail of the degree distribution under which the arguments can be pushed through. This is joint work with my supervisor Frank den Hollander.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 07.07.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Victor Panaretos, École Polytechnique Fédérale de Lausanne, Schweiz:
Testing for the rank of a covariance operator (online talk)
more ... Location
Online Event
Abstract
How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of con dence? This question is central to a great deal of methods for functional data, which require low-dimensional representations whether by functional PCA or other methods. The difficulty is that the determination is to be made on the basis of i.i.d. replications of the process observed discretely and with measurement error contamination. This adds a ridge to the empirical covariance, obfuscating the underlying dimension. We describe a matrix-completion inspired test statistic that circumvents this issue by measuring the best possible least square fit of the empirical covariance's off -diagonal elements, optimised over covariances of given nite rank. For a fixed grid of sufficiently large size, we determine the statistic's asymptotic null distribution as the number of replications grows. We then use it to construct a bootstrap implementation of a stepwise testing procedure controlling the family-wise error rate corresponding to the collection of hypotheses formalising the question at hand. Under minimal regularity assumptions we prove that the procedure is consistent and that its bootstrap implementation is valid. The procedure circumvents smoothing and associated smoothing parameters, is indi fferent to measurement error heteroskedasticity, and does not assume a low-noise regime. (Based on joint work with Anirvan Chakraborty.)
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 06.07.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Dr. Carsten Conradi, Hochschule für Technik und Wirtschaft Berlin:
Monomial parameterizations in the analysis of biochemical reaction networks (online talk)
more ... Location
Online Event
Abstract
The dynamics of biochemical reaction networks can be described by ODEs with polynomial right hand side. In this presentation networks are considered where the steady state variety can be parameterized by monomials. I present two applications of these monomial parameterizations in the analysis of reaction networks: (i) deciding multistationarity and (ii) establishing Hopf bifurcations. Here multistationarity refers to the existence of at least two positive solutions to the polynomial steady state equations. And if a monomial parameterization exists, then this question is equivalent to the feasibility of at least one linear inequality system (out of many). The results presented here can be used to determine parameter values where multistationarity or Hopf bifurcations occur.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSlI3TjAxV1U1S2xFQT09
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 06.07.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Luisa Plato, WIAS Berlin:
Biological pest control -- Analysis and numerics for a spatio-temporal predator-prey system
more ... Location
Online Event
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Monday, 05.07.2021, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Assoc. Prof. Patrick E. Farrell, University of Oxford, UK:
Computing disconnected bifurcation diagrams of partial differential equations
more ... Location
Online Event
Abstract
Computing the distinct solutions u of an equation f(u, lambda)=0 as a parameter lambda in IR is varied is a central task in applied mathematics and engineering. The solutions are captured in a bifurcation diagram, plotting (some functional of) u as a function of lambda. In this talk I will present a new algorithm, deflated continuation, for this task. Deflated continuation has three advantages. First, it is capable of computing disconnected bifurcation diagrams; previous algorithms only aimed to compute that part of the bifurcation diagram continuously connected to the initial data. Second, its implementation is very simple: it only requires a minor modification to an existing Newton-based solver. Third, it can scale to very large discretisations if a good preconditioner is available; no auxiliary problems must be solved. We will present applications to hyperelastic structures, liquid crystals, and Bose-Einstein condensates, among others.
Further Informations
Berlin Oberseminar: Optimization, Control and Inverse Problems
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 30.06.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Stefanie Schindler, WIAS Berlin:
Self-similar diffusive equilibration for a coupled reaction-diffusion system with mass-action kinetics (online talk)
more ... Location
Online Event
Abstract
We study a coupled system of two nonlinear reaction-diffusion equations on the unbounded domain ℝ, where we consider reaction kinetics of the reaction nX1 ⇌ mX2 according to the mass-action law. We show the global existence and uniqueness of classical solutions and prove the existence of invariant rectangles, that is, bounded regions ∑ ⊂ ℝ2 in which the solutions stay for all times, provided that the initial data lies entirely in ∑. Further, by assuming that the reaction is equilibrated and that the asymptotic boundary conditions at infinity are given by constant steady-state solutions, the diffusive mixing is studied. Here the theory of self-similar solutions in the sense of Barenblatt is applicable. Combined with the theory of monotone operators, this enables us to prove that there exists for each choice of asymptotic boundary conditions a similarity profile. This research is joint work with Alexander Mielke.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 29.06.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Sebastian Wieczorek, University College Cork:
Rate-induced tipping points (online talk)
more ... Location
Online Event
Abstract
Many systems are subject to external disturbances or changing external conditions. For a system near a stable state (an attractor) we might expect that, as external conditions change with time, the stable state will change too. In many cases the system may adapt to changing external conditions and track the moving stable state. However, tracking may not always be possible owing to nonlinearities and feedbacks in the system. So far, the focus has been on critical levels of external conditions (dangerous autonomous bifurcation points) where the stable state turns unstable or disappears, causing the system to suddenly move to a different and often undesired state. We describe this phenomenon as bifurcation-induced tipping or B-tipping. However, critical levels are not the only critical factor for tipping. Some systems can be particularly sensitive to how fast the external conditions change and have critical rates: they suddenly and unexpectedly move to a different state if the external input changes too fast. This happens even though the moving stable state never loses stability in the classical autonomous sense! We describe this phenomenon as rate-induced tipping or R-tipping. Being a genuine non-autonomous bifurcation, R-tipping is not captured by the classical bifurcation theory and requires an alternative framework. In the first part of the talk, we demonstrate R-tipping in a simple ecosystem model where environmental changes are represented by time-varying parameters. We then introduce the concept of basin instability and show how to complement the classical bifurcation diagram with information on nonautonomous R-tipping that cannot be captured by the classical bifurcation analysis. In the second part of the talk, we develop a general mathematical framework for R-tipping with decaying inputs based on the concepts of thresholds, edge states and special compactification of the nonautonomous system. This allows us to transform the R-tipping problem into a connecting heteroclinic orbit problem in the compactified system, which greatly simplifies the analysis. We explain the key concept of threshold instability and give rigorous testable criteria for R-tipping to occur in arbitrary dimension. In the third part of the talk, we discuss the so-called “compost-bomb instability", which is an example of R-tipping without an obvious threshold. We use geometric singular perturbation theory and desingularisation to reveal non-obvious R-tipping thresholds and edge states.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 29.06.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Ingo Bremer, WIAS Berlin:
Parameterbestimmung zur Anpassung des SEIR-Models an Covid-19 Zeitreihen
more ... Location
Online Event
Further Informations
You can follow this talk by zoom: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Thursday, 24.06.2021, 13:00 (Online Event)
- Seminar Numerische Mathematik
Felipe Galarce Marín, WIAS Berlin:
Inverse problems in haemodynamics. Fast estimation of blood flows on non-parametric domains from medical data
more ... Location
Online Event
Abstract
This seminar presents a work at the interface between applied mathematics and biomedical engineering. The work's main subject is the estimation of blood flows and quantities of medical interest in diagnosing certain diseases concerning the cardiovascular system. We propose a complete pipeline, providing the theoretical foundations for state estimation from medical data using reduced-order models, and addressing inter-patient variability. Extensive numerical tests are shown in realistic 3D scenarios that verify the potential impact of the work in the medical comunnity.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 23.06.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Martin Brokate, Technische Universität München:
A variational inequality for the derivative of the play operator (online talk)
more ... Location
Online Event
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 23.06.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Tejas Iyer, WIAS Berlin:
Degree and Edge Distributions in Inhomogeneous Random Recursive Trees (online talk)
more ... Location
Online Event
Abstract
We introduce general models of inhomogeneous random recursive trees, where either one or several nodes arrive at a time, and are equipped with i.i.d random weights. At each time-step, an existing vertex is chosen with probability proportional to its fitness function, and the newly arriving node(s) connect to it. This may be a function of its weight, and possibly the weights of its neighbours. We study two main quantities: the empirical measures associated with the number of vertices with a given degree and weight and the empirical measure corresponding proportion of edges in the structure with endpoint having a given weight. We show that, under certain technical conditions, the limit of both quantities exists when normalised by the size of the network, as the number of nodes tends to infinity. However, when the trees take certain forms, we show that interesting, non-trivial behaviour can emerge when these conditions fail: in particular, the trees may exhibit emphcondensation where a positive proportion of edges accumulate around vertices with weight that maximises the reinforcement of their fitness, or, more drastically, may have a emphdegenerate limiting degree distribution where the entire proportion of edges accumulate around these vertices. This non-trivial behaviour may be of interest when considering the trees as toy models for the evolution of complex networks.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 22.06.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Bhumika Thakur, Jacobs University, Bremen:
Data driven identification of nonlinear dynamics using sparse regression with applications in plasma physics
more ... Location
Online Event
Abstract
Data driven techniques are increasingly finding applications in physical sciences and plasma physics is no exception. Many plasma processes are highly complex and nonlinear and often the exact form of the equations governing their dynamics is not known. If we can construct these equations from the experimental data, then we can further our understanding of these processes and use techniques such as model reduction to isolate dominant physical mechanisms. A large number of regression techniques are available for identification of system dynamics from data, with varying degrees of generality and complexity. Sparse identification of nonlinear dynamics (SINDy) algorithm is one such technique that can be used to find parsimonious models. I will talk about this algorithm and discuss some examples where it is being applied in plasma physics with a focus on our ongoing attempt at finding the model equations for anode glow oscillations observed in a glow discharge plasma device.
Host
Freie Universität Berlin
WIAS Berlin
- Wednesday, 16.06.2021, 12:30 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Irène Gijbels, KU Leuven, Netherlands:
Extremiles and extremile regression (online talk)
more ... Location
Online Event
Abstract
Quantiles and expectiles of a distribution are found to be useful descriptors of its tail in the same way as the median and mean are related to its central behavior. In this talk we discuss an alternative class to expectiles, called extremiles. The new class is motivated via several angles, which reveals its speci c merits and strengths. Extremiles suggest better capability of tting both location and spread in data points and provide an appropriate theory that better displays the interesting features of long-tailed distributions. We brie y discuss estimation of extremiles. A large part of the talk will be on regression extremiles, which thus de ne a least squares analogue of regression quantiles.We discuss estimation of conditional extremiles, in which we rely on local linear (least squares) checkfunction minimization. An asymptotic normality result for the estimators is established. Attention also goes to extending extremile regression far into the tails of heavy-tailed distributions. For this purpose extrapolated estimators are constructed and their asymptotic theory is developed. Applications to real data illustrate how extremiles and related tools can be used in practice.)
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- June 16 – 18, 2021 (Online Event)
- Workshop/Konferenz: Nonlinear Dynamics in Semiconductor Lasers
more ... Location
Online Event
Host
WIAS Berlin
- Tuesday, 15.06.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Philipp Lorenz-Spreen, MPI for Human Development, Berlin:
Modeling radicalization dynamics and polarization in temporal networks
more ... Location
Online Event
Abstract
Echo chambers and opinion polarization have been recently quantified in several sociopolitical contexts, across different social media, raising concerns for the potential impact on the spread of misinformation and the openness of debates. Despite increasing efforts, the dynamics leading to the emergence of these phenomena remain unclear. Here, we propose a model that introduces the phenomenon of radicalization, as a reinforcing mechanism driving the evolution to extreme opinions from moderate initial conditions. Empirically inspired by the dynamics of social interaction, we consider agents characterized by heterogeneous activities and homophily. We analytically characterize the transition from a global consensus to an emerging radicalization that depends on parameters, which can be interpreted as the controversialness of a topic and the strength of social influence people exert on each other. Finally, we offer a definition of echo-chambers via our model and contrast the model's behavior against empirical data of polarized debates on Twitter, qualitatively reproducing the observed relation between users' engagement and opinions, as well as opinion segregation based on the interaction network. Our findings shed light on the dynamics that may lie at the core of the emergence of echo chambers and polarization in social media.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 15.06.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Lennard Henze, Humboldt-Universität zu Berlin:
Classification of quantum dot images using machine learning (online talk)
more ... Location
Online Event
Abstract
A possibility of classifying quantum dot images obtained out of a simulation using a machine learning algorithm and image augmentation techniques is explored. The results on the similar MNIST data set suggest that a classification using machine learning techniques is indeed possible. Furthermore, a theoretical result concerning the extrapolation properties of artificial neural networks will be presented.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 15.06.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Maximilian Reiter, TU Berlin:
Numerical approximation of the Ericksen--Leslie equations (online talk)
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Monday, 14.06.2021, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Dr. Ozan Öktem, KTH Royal Institute of Technology, Stockholm:
Data driven large-scale convex optimisation
more ... Location
Online Event
Abstract
This joint work with Jevgenjia Rudzusika (KTH), Sebastian Banert (Lund University) and Jonas Adler (DeepMind) introduces a framework for using deep-learning to accelerate optimisation solvers with convergence guarantees. The approach builds on ideas from the analysis of accelerated forward-backward schemes, like FISTA. Instead of the classical approach of proving convergence for a choice of parameters, such as a step-size, we show convergence whenever the update is chosen in a specific set. Rather than picking a point in this set through a handcrafted method, we train a deep neural network to pick the best update. The method is applicable to several smooth and non-smooth convex optimisation problems and it outperforms established accelerated solvers.
Host
WIAS Berlin
- Wednesday, 09.06.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Julian Fischer, Institute of Science and Technology Austria (IST Austria):
Uniqueness and stability properties of multiphase mean curvature flow: An approach based on the variational (gradient flow) structure of the problem (online talk)
more ... Location
Online Event
Abstract
For many evolution problems for interfaces - like for instance multiphase mean curvature flow or the Mullins--Sekerka equation - appropriate weak solutions are known to exist globally in time, but the uniqueness of such weak solutions is either unknown or even known to fail. At the same time, due to geometric singularities strong solution concepts are in general limited to local in time existence results. In the absence of a comparison principle, the relation between weak and strong solutions for interface evolution problems has remained a mostly open question. We establish a weak-strong uniqueness principle for planar multiphase mean curvature flow: We prove that for mean curvature flow of planar networks,there is only a single BV solution prior to the first topology change. Our approach relies on the variational structure of mean curvature flow, being the gradient flow of the interface energy functional. For many minimization problems for interface energy functionals, the method of calibrations has made it possible to deduce the uniqueness of minimizers. Our approach to weak-strong uniqueness for mean curvature flow relies on a novel gradient-flow analogue of this concept of calibrations, basically allowing us to show that the route of steepest descent in the energy landscape is unique and stable with respect to perturbations. In the last part of the talk, we will discuss possible future applications of our concept, including the quantitative convergence of phase-field approximations for mean curvature flow.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 09.06.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Wen Sun, TU Berlin:
Pathwise large deviation for the pure jump k-nary interacting particle systems (online talk)
more ... Location
Online Event
Abstract
A pathwise large deviation result is proved for the pure jump models of k-nary interacting particle system introduced by Kolokoltsov that generalize classical Boltzmann's collision model, Smoluchovski's coagulation model and many others. The upper bound is obtained by following the standard methods of using a process "perturbed" by a regular function. To show the lower bound, we propose a family of orthogonal martingale measures and prove a coupling for the general perturbations. The rate function is studied based on the idea of Léonard with a simplification by considering the conjugation of integral functionals on a subspace of L^infty.. General "gelling" solutions in the domain of the rate function are also discussed.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 08.06.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Chunming Zheng, MPI for Physics of Complex Systems, Dresden:
Transition to synchrony in the three-dimensional Noisy Kuramoto model
more ... Location
Online Event
Abstract
We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found, that alignment of the velocities occurs for arbitrary small attractive coupling. Adding noise to the system resolves this singular limit.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 01.06.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Georgi Medvedev, Drexel University:
Unfolding chimeras: Where Turing meets Penrose (online talk)
more ... Location
Online Event
Abstract
The coexistence of coherence and incoherence is arguably the most interesting effect in the theory of synchronization and possibly in nonlinear science in general discovered in the past two decades. Despite intense research chimera states still present many challenging questions to the nonlinear science community. There is no consensus on how to define chimera states. Further, the theory is only available for chimera states lying in the Ott--Antonsen manifold, which is an elegant but a very special case. In this work, we suggest a new way for studying chimera states based on the combination of the linear stability analysis of mixing and a beautiful method of Penrose for Vlasov equation in plasma physics. This approach yields a new qualitative description of chimera states and provides very accurate quantitative estimates. Our results are universal in the sense that the structure and bifurcations of chimera states are explained in terms of the qualitative properties of the distribution of intrinsic frequencies and network topology, and, thus, are relevant for interacting particle systems of all scales from neuronal networks, to power grids, to astrophysics. This talk is based on the joint work with Hayato Chiba (Tohoku University) and Matthew Mizuhara (The College of New Jersey).
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSlI3TjAxV1U1S2xFQT09
Host
Freie Universität Berlin
WIAS Berlin
- May 31 – June 2, 2021 (Online Event)
- Workshop/Konferenz: SPDEs and their friends
more ... Location
Online Event
Host
WIAS Berlin
Technische Universität Berlin
- Wednesday, 26.05.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Riccarda Rossi, Università degli Studi di Brescia, Italien:
Jump processes as generalized gradient systems (online talk)
more ... Location
Online Event
Abstract
The approach à la Jordan-Kinderlehrer-Otto to a vast class of evolutionary problems, interpreted as gradient flows in Wasserstein spaces, was extended by Maas and Mielke to Markov chains via the introduction of Benamou-Brenier type distances. Nonetheless, the study of the microscopic origin of jump processes by means of large deviations theory suggests that such processes possess a generalized gradient system structure based on non-homogeneous dissipation potentials that do not give rise to any metric structure. This talk revolves around the generalized gradient system structure that we have proposed for these processes in collaboration with Mark Peletier, Giuseppe Savaré and Oliver Tse. To build it, we have introduced a suitable `dynamical-variational' transport cost that induces a notion of length. Based on it, we can set forth an extended version of the Minimizing Movement scheme. We show the convergence of the discrete solutions arising from the time-incremental minimization scheme, to a curve fulfilling a suitable `non-metric' gradient flow formulation for the original jump process.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 26.05.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
András Tóbiás, TU Berlin:
Absence of percolation in graphs based on stationary point processes with degrees bounded by two (online talk)
more ... Location
Online Event
Abstract
We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for SINR graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional k-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2. The subject of this talk is joint work with B. Jahnel.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 26.05.2021, 09:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Hans-Georg Müller, University of California, Davis, USA:
Functional models for time-varying random objects (online talk)
more ... Location
Online Event
Abstract
In recent years, samples of random objects and time-varying object data such as time-varying distributions or networks that are not in a vector space have become increasingly prevalent. Such data can be viewed as elements of a general metric space that lacks local or global linear structure. Common approaches that have been used with great success for the analysis of functional data, such as functional principal component analysis, are therefore not applicable. The concept of metric covariance makes it possible to define a metric auto-covariance function for a sample of random curves that take values in a general metric space and it can be shown to be non-negative definite when the squared semi-metric of the underlying space is of negative type. Then the eigenfunctions of the linear operator with the auto-covariance function as kernel can be used as building blocks for an object functional principal component analysis, which includes real-valued Frechet scores and metric-space valued object functional principal components. Sample based estimates of these quantities are shown to be asymptotically consistent and are illustrated with various data. (Joint work with Paromita Dubey, Stanford University.)
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 20.05.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Thomas Richter, Universität Magdeburg:
Deep neural networks for accelerating fluid-dynamics simulations
more ... Location
Online Event
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 19.05.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Alexander Mielke, WIAS Berlin, Humboldt-Universität zu Berlin:
Towards a justification of GENERIC: coarse-graining of an infinite-dimensional Hamiltonian system (online talk)
more ... Location
Online Event
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 19.05.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Hannes Leeb, University of Vienna, Österreich:
A (tight) upper bound for the length of confidence intervals with conditional coverage
more ... Location
Online Event
Abstract
We show that two popular selective inference procedures, namely data carving (Fithian et al., 2017) and selection with a randomized response (Tian et al., 2018b), when combined with the polyhedral method (Lee et al., 2016), result in confidence intervals whose length is bounded. This contrasts results for confidence intervals based on the polyhedral method alone, whose expected length is typically infinite (Kivaranovic and Leeb, 2020). Moreover, we show that these two procedures always dominate corresponding sample-splitting methods in terms of interval length.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 12.05.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Thomas Eiter, WIAS Berlin:
Leray--Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation (online talk)
more ... Location
Online Event
Abstract
Subject of the talk is a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba--Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. After a discussion of the model, the existence of global-in-time weak solutions, which satisfy an energy inequality, is shown under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 12.05.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Tal Orenshtein, WIAS Berlin/TU Berlin:
Rough walks in random environment
more ... Location
Online Event
Abstract
Random walks in random environment (RWRE) have been extensively studied in the last half-century. Functional central limit theorems (FCLT) hold in some prototypical classes such the reversible and the ballistic ones. The latter are treated using rather different techniques; Kipnis-Varadhan's theory for additive functionals of Markov processes is applicable in the reversible case whereas the main feature exploited in the ballistic class is a regeneration structure. Rough path theory is a deterministic theory which extends classical notions of integration to singular integrators in a continuous manner. It typically provides a framework for pathwise solutions of ordinary and partial stochastic differential equations driven by a singular noise. In the talk we shall discuss FCLT for additive functionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels. The first one is the Brownian motion, whereas in the second we see a new feature: it is the iterated integral of the Brownian motion perturbed by a deterministic linear function called the area anomaly. The aforementioned classes of RWRE are covered as special cases. The results provide sharper information on the limiting path. In addition, the construction of new examples for SDE approximations is an immediate application. Based on collaborations (some are still in progress) with Johannes Bäumler, Noam Berger, Jean-Dominique Deuschel, Olga Lopusanschi, Nicolas Perkowski and Martin Slowik.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 11.05.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Alicia Dickenstein, U Buenos Aires:
Algebra and geometry in the study of enzymatic networks? (online talk)
more ... Location
Online Event
Abstract
I will try to show in my lecture that the question in the title has a positive answer, summarizing recent mathematical results about signaling networks in cells obtained with algebro-geometric tools.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://us02web.zoom.us/j/84203723799?pwd=bmNVcVBaazRzSll3TjAxV1U1S2xFQT09.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 11.05.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Paul Hager, Technische Universität Berlin:
Optimal stopping with signatures (online talk)
more ... Location
Online Event
Abstract
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature associated to the underlying process, and prove that maximizing over these classes of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature. By applying a deep neural network approach to approximate the non-linear signature functionals, we can efficiently solve the optimal stopping problem numerically. The only assumption on the underlying process is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion, which fail to be either semi-martingales or Markov processes, and can be used, in particular, for American-type option pricing in fractional models, e.g. on financial or electricity markets. This is a joint work with Christian Bayer, Sebastian Riedel and John Schoenmakers.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 04.05.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Maximilian Engel, FU Berlin:
Lyapunov exponents in random dynamical systems and how to find and use them
more ... Location
Online Event
Abstract
This talk aims to give an overview on various notions of Lyapunov exponents (LEs) in random dynamical systems, that is, systems whose evolution in time is governed by laws exhibiting randomness: from finite-time LEs to classical asymptotic LEs and corresponding spectra up to LEs for processes conditioned on staying in bounded domains. We demonstrate how these notions, especially of a first, dominant LE, become relevant in the context of stochastic bifurcations, in finite and infinite dimensions.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.
Host
Freie Universität Berlin
WIAS Berlin
- Monday, 03.05.2021, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Assoc. Prof. Lars Ruthotto, Emory University, USA:
A machine learning framework for mean field games and optimal control
more ... Location
Online Event
Abstract
We consider the numerical solution of mean field games and optimal control problems whose state space dimension is in the tens or hundreds. In this setting, most existing numercial solvers are affected by the curse of dimensionality (CoD). To mitigate the CoD, we present a machine learning framework that combines the approximation power of neural networks with the scalability of Lagrangian PDE solvers. Specifically, we parameterize the value function with a neural network and train its weight using the objective function with additional penalties that enforce the Hamilton Jacobi Bellman equations. A key benefit of this approach is that no training data is needed, e.g., no numerical solutions to the problem need to be computed before training. We illustrate our approach and its efficacy using numerical experiments. To show the framework's generality, we consider applications such as optimal transport, deep generative modeling, mean field games for crowd motion, and multi-agent optimal control.
Host
WIAS Berlin
- April 29, 2021 (Online Event)
- Workshop/Konferenz: FUHRI2021: Finite volUme metHods for Real-world applIcations
more ... Location
Online Event
Host
WIAS Berlin
- Wednesday, 28.04.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Katharina Hopf, WIAS Berlin:
Weak-strong uniqueness in energy-reaction-diffusion systems (online talk)
more ... Location
Online Event
Abstract
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems, which genuinely feature cross-diffusion effects. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. Weak-strong uniqueness is obtained for general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 28.04.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Alexander Hinsen, WIAS Berlin:
Percolation on a dynamical device-to-device communication system (online talk)
more ... Location
Online Event
Abstract
We model a system of moving devices on a street system with the help of a general waypoint kernel. If there is an uninterrupted communication window between devices (their space-time trajectories are close to each other) they form a connection. We study regimes for percolation and absence of percolation of the cluster of connected devices, as it can be seen as an indication for the ability of the system to transmit messages over long distances.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 27.04.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Eddie Nijholt, University of Illinois, USA:
Exotic symmetry in networks
more ... Location
Online Event
Abstract
Network dynamical systems appear all throughout science and engineering. Despite this prevalence, it remains unclear precisely how network structure impacts the dynamics. One very successful approach in answering this question is by identifying symmetry. Of course, there are many networks that do not have any form of symmetry, yet which still show remarkable dynamical behavior. Instead a wide array of other network features (such as node-dependency, synchrony spaces, and so forth) are known to impact the dynamics. We will see that most of these features can still be captured as symmetry, provided one widens the definition. That is, instead of considering classical group symmetry, one has to allow for more “exotic structures”, such as semigroups, categories and quivers. In many cases the network topology itself can even be seen as such a symmetry. An important consequence is that network structure can therefore be preserved in most reduction techniques, which in turn makes it possible to analyse bifurcations in such systems. In order to best explain these notions, l do not assume any familiarity with group symmetry -or their exotic counterparts- on the part of the audience.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 27.04.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Peter Friz, WIAS Berlin, TU Berlin:
New perspectives on rough paths, signatures and signature cumulants (online talk)
more ... Location
Online Event
Abstract
We revisit rough paths and signatures from a geometric and “smooth model" perspective. This provides a lean framework to understand and formulate key concepts of the theory, including recent insights on higher-order translation a.k.a. renormalization of rough paths. This first part is joint work with C. Bellingeri (TU Berlin), and S. Paycha (U Potsdam). In a second part, we take a semimartingale perspective and more specifically analyze the structure of expected signatures when written in exponential form. Following Bonnier-Oberhauser (2020), we call the resulting objects signature cumulants. These can be described - and recursively computed - in a way that can be seen as unification of previously unrelated pieces of mathematics, including Magnus (1954), Lyons-Ni (2015), Gatheral and coworkers (2017 onwards) and Lacoin-Rhodes-Vargas (2019). This is joint work with P. Hager and N. Tapia.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 27.04.2021, 10:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Sashikumaar Ganesan, Indian Institute of Science Bangalore; Prof. Volker John, WIAS Berlin:
Minisymposium on machine learning
more ... Location
Online Event
Further Informations
For zoom login details please contact Volker John john@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 21.04.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Nikolas Nüsken, Universität Potsdam:
The Stein geometry in machine learning: gradient flows, large deviations and convergence properties (online talk)
more ... Location
Online Event
Abstract
Sampling or approximating high-dimensional probability distributions is a key challenge in computational statistics and machine learning. This talk will present connections to gradient flow PDEs and interacting particle systems, focusing on the recently introduced Stein variational gradient descent methodology. The construction induces a novel geometrical structure on the set of probability distributions related to a positive definite kernel function.We discuss the corresponding geodesic equations as well as large deviation functionals and leverage those to shed some light on the convergence properties of the algorithm. This is joint work with A. Duncan (Imperial College London), L. Szpruch (University of Edinburgh) and M. Renger (Weierstrass Institute Berlin).
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 20.04.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Alan Rendall, Johannes Gutenberg-Universität Mainz:
Bogdanov--Takens bifurcations and the regulation of enzymatic activity by autophosphorylation
more ... Location
Online Event
Abstract
An important mechanism of information storage in molecular biology is the binding of phosphate groups to proteins. In this talk we consider the case of autophosphorylation, where the protein is an enzyme and the substrate to which it catalyses the binding of a phosphate group is that enzyme itself. It turns out that this often leads to more complicated dynamics than those seen in the case where enzyme and substrate are distinct. We focus on the example of the enzyme Lck (lymphocyte-associated tyrosine kinase) which is of central importance in the function of immune cells. We study a model for the activation of Lck due to Kaimachnikov and Kholodenko and give a rigorous proof that it admits periodic solutions. We do so by showing that it exhibits a generic Bogdanov-Takens bifurcation. This is an example where this approach gives a simpler proof of the existence of periodic solutions than ones
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84203723799.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 20.04.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Caroline Geiersbach, WIAS Berlin:
Stochastic approximation with applications to PDE-constrained optimization under uncertainty (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 15.04.2021, 14:00 (Online Event)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Steven-Marian Stengl, WIAS Berlin:
Combined regularization and discretization of equilibrium problems and primal-dual gap estimators
more ... Location
Online Event
Abstract
In this talk, we address the treatment of finite element discretizations of a class of equilibrium problems involving moving constraints. Therefore, a Moreau-Yosida based regularization technique, controlled by a parameter, is discussed. A generalized Gamma-convergence concept is utilized to obtain a priori results. The same technique is applied to the discretization and the combination of both. In addition, a primal-dual gap technique is used for the derivation of error estimators and a strategy for balancing between a refinement of the mesh and an update of the regularization parameter is established. The theoretical findings are illustrated for the obstacle problem as well as numerical experiments are performed for two quasi-variational inequalities with application to thermoforming and biomedicine, respectively.
Further Informations
Seminar Mathematical Optimization / Non-smooth Variational Problems and Operator Equations
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 15.04.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Julia Novo, Universidad Autónoma de Madrid, Spanien:
Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows
more ... Location
Online Event
Abstract
Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are presented. We consider two cases: the case in which the snapshots are based on a non inf-sup stable method and the case in which the snapshots are based on an inf-sup stable method. For both cases we construct approximations to the velocity and the pressure. For the first case, we analyze a method in which the snapshots are based on a stabilized scheme with equal order polynomials for the velocity and the pressure with local projection stabilization (LPS) for the gradient of the velocity and the pressure. For the POD method we add the same kind of LPS stabilization for the gradient of the velocity and the pressure as the direct method, together with grad-div stabilization. In the second case, the snapshots are based on an inf-sup stable Galerkin method with grad-div stabilization and for the POD model we also apply grad-div stabilization. In this case, since the snapshots are discretely divergence-free, the pressure can be removed from the formulation of the POD approximation to the velocity. To approximate the pressure, needed in many engineering applications, we use a supremizer pressure recovery method. Error bounds with constants independent of inverse powers of the viscosity parameter are proved for both methods. Numerical experiments show the accuracy and performance of the schemes.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 14.04.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Flaviana Iurlano, Sorbonne Université Paris, Frankreich:
Shape optimization of light structures (online talk)
more ... Location
Online Event
Abstract
We prove rigorous results about the vanishing-mass limit of the classical problem to find a shape with minimal elastic compliance. Contrary to all previous results in the mathematical literature, which utilize a soft mass constraint by introducing a Lagrange multiplier, we here consider the hard mass constraint. Our results are the first to establish the convergence of approximately optimal shapes of (exact) size $varepsilonto 0$ to a limit generalized shape represented by a (possibly diffuse) probability measure. This limit generalized shape is a minimizer of the limit compliance, which involves a new integrand, namely the one conjectured by Bouchitté in 2001 and predicted heuristically before in works of Allaire & Kohn and Kohn & Strang from the 1980s and 1990s. This integrand gives the energy of the limit generalized shape understood as a fine oscillation of (optimal) lower-dimensional structures. Its appearance is surprising since the integrand in the original compliance is just a quadratic form and the non-convexity of the problem is not immediately obvious. In fact, it is the interaction of the mass constraint with the requirement of attaining the loading (in the form of a divergence-constraint) that gives rise to this new integrand. Our proofs rest on compensated compactness arguments applied to an explicit family of div-quasiconvex quadratic forms, computations involving the Hashin--Shtrikman bounds for the Kohn--Strang integrand, and the characterization of limit minimizers due to Bouchitté & Buttazzo.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 14.04.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Alexis Prevost, University of Cambridge, GB:
Cluster capacity functionals and isomorphism theorems for Gaussian free fields (online talk)
more ... Location
Online Event
Abstract
Various isomorphisms theorem relate Gaussian free fields to random walk models, through their local times. Among them, the second Ray-Knight theorem can be extended in an isomorphism between the Gaussian free field and random interlacements on transient graphs. Following the work of Lupu and Sznitman, we will explain how the cable system method let us make this isomorphism more explicit, and how it relates to a certain cluster capacity functional for the Gaussian free field. Finally, we will present applications to percolation for the Gaussian free field on the cable system. Joint work with Alexander Drewitz (Cologne) and Pierre-François Rodriguez (London)
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 13.04.2021, 16:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yangwen Sun, Humboldt-Universität zu Berlin:
Graph-spanning ratio test with application to change-point detection problem (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 30.03.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Simona Perotto, Politecnico di Milano, Italien:
Adaptive topology optimization in the design of structures and metamaterials (online talk)
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Monday, 29.03.2021, 15:00 (Online Event)
- Berlin Oberseminar: Optimization, Control and Inverse Problems
Prof. Serge Gratton, ENSEEIHT, Toulouse, France:
On a multilevel Levenberg--Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations (online talk)
more ... Location
Online Event
Abstract
We propose a new multilevel Levenberg--Marquardt optimizer for the training of artificial neural networks with quadratic loss function. When the least-squares problem arises from the training of artificial neural networks, the variables subject to optimization are not related by any geometrical constraints and the standard interpolation and restriction operators cannot be employed any longer. A heuristic, inspired by algebraic multigrid methods, is then proposed to construct the multilevel transfer operators. We test the new optimizer on an important application: the approximate solution of partial differential equations by means of artificial neural networks. The learning problem is formulated as a least-squares problem, choosing the nonlinear residual of the equation as a loss function, whereas the multilevel method is employed as a training method. Numerical experiments show encouraging results related to the efficiency of the new multilevel optimization method compared to the corresponding one-level procedure in this context.
Further Informations
Seminar on Optimization, Control and Inverse Problems
Host
WIAS Berlin
- Thursday, 25.03.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Benoît Gaudeul, Université de Lille, France:
Two entropic finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints
more ... Location
Online Event
Abstract
In this talk, I consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent electric field maintained by the ions and described by a Poisson equation.
I present two finite volume schemes based on different formulations of the fluxes. I will also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence result is proposed for non-degenerate solutions. Numerical experiments show the behavior of these schemes.
This is a joint work with Jürgen Fuhrmann.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Thursday, 18.03.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Leo Rebholz, Clemson University, USA:
Anderson acceleration and how it speeds up convergence in fixed point iterations
more ... Location
Online Event
Abstract
Anderson acceleration (AA) is an extrapolation technique originally proposed in 1965 that recombines the most recent iterates and update steps in a fixed point iteration to improve the convergence properties of the sequence. Despite being successfully used for many years to improve nonlinear solver behavior on a wide variety of problems, a theory that explains the often-observed accelerated convergence was lacking. In this talk, we give an introduction to AA, then present a proof of AA convergence which shows that it improves the linear convergence rate based on a gain factor of an underlying optimization problem, but also introduces higher order terms in the residual error bound. We then discuss improvements to AA based on our convergence theory, and show numerical results for the algorithms applied to several application problems including Navier--Stokes, Boussinesq, and nonlinear Helmholtz systems.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 17.03.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Daniel Heydecker, University of Cambridge, GB:
Large deviations of Kac's elastic particle system (online talk)
more ... Location
Online Event
Abstract
We consider Kac's stochastic model for a N-particle gas, with particles interacting by elastic collisions, and study the large deviations in the limit $Ntoinfty$ in the weak topology. There is a very natural candidate rate function, first proposed by Léonard, which amounts to the dynamic entropy of a flux measure plus an initial cost; with this rate function, we sketch the proof of an upper bound, and a lower bound restricted to a class of `sufficiently goods' paths. Perhaps surprisingly, we will see that the proposed rate function does not capture all of the possible large deviation behaviour. Lu and Wennberg showed that, even though the microscopic collisions preserve energy, there are solutions to the Boltzmann equation for which the energy is increasing, and these paths have 0 dynamic entropy. We will show that such paths can arise as large deviation limits with finite exponential cost, so cannot be excluded from large deviation analysis, but occur strictly more rarely than predicted by the rate function. At the level of the particle system, this occurs when a macroscopic proportion of the energy concentrates in $o(N)$ particles, which can happen with probability $e^-O(N)$.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 16.03.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Kostas Papafitsoros, WIAS Berlin:
Optimization with learning-informed differential equation constraints and its applications (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 16.03.2021, 13:30 (Online Event)
- Seminar Numerische Mathematik
Dr. Jürgen Fuhrmann, WIAS Berlin:
PDELib.jl: Towards software components for the numerical solution of partial differential equations in Julia
more ... Location
Online Event
Abstract
In recent years, in particular since the release of version 1.0, the Julia programming language gained significant momentum in fields related to scientific computing and data science. Taking advantage of accumulated experience and know-how in language design, designed around the just-in-time compilation paradigm, and featuring first class multidimensional array handling, it allows for the implementation of complex numerical algorithms without sacrificing efficiency. In recent years, in particular since the release of version 1..0, the Julia programming language gained significant momentum in fields related to scientific computing and data science.
In the talk, we will give a short overview on features of the Julia language which renders it well suited for the implementation of solvers for complex systems of partial differential equations, including multiple dispatch allowing for the implementation of automatic differentiation, interface oriented API design and its package manager supporting reusability and reproducibility.
We will report on the successful steps towards the implementation of software components for the numerical solution of PDEs.. Focus will be on the package VoronoiFVM.jl and supporting packages.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Tuesday, 09.03.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Caroline Geiersbach, WIAS Berlin:
Stochastic approximation with applications to PDE-constrained optimization under uncertainty (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 03.03.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Cecile Mailler, The University of Bath, GB:
The ants walk: finding geodesics in graphs using reinforcement learning
more ... Location
Online Event
Abstract
How does a colony of ants find the shortest path between its nest and a source of food without any means of communication other than the pheromones each ant leave behind itself? In this joint work with Daniel Kious (Bath) and Bruno Schapira (Marseille), we introduce a new probabilistic model for this phenomenon. In this model, the nest and the source of food are two marked nodes in a finite graph. Ants perform successive random walks from the nest to the food, and ths distribution of the n-th walk depends on the trajectories of the (n-1) previous walks through some linear reinforcement mechanism. Using stochastic approximation methods, couplings with Pólya urns, and the electric conductances method for random walks on graphs, we prove that, in this model, the ants indeed eventually find the shortest path(s) between their nest and the source food.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Tuesday, 02.03.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yunfei Huang, Ludwig-Maximilians-Universität München:
Advanced data analysis for traction force microscopy and data-driven discovery of physical equations (online talk)
more ... Location
Online Event
Abstract
The plummeting cost of collecting and storing data and the increasingly available computational power in the last decade have led to the emergence of new data analysis approaches in various scientific fields. Frequently, the new statistical methodology is employed for analyzing data involving incomplete or unknown information. In this thesis, new statistical approaches are developed for improving the accuracy of traction force microscopy (TFM) and data-driven discovery of physical equations. TFM is a versatile method for the reconstruction of a spatial image of the traction forces exerted by cells on elastic gel substrates. The traction force field is calculated from a linear mechanical model connecting the measured substrate displacements with the sought-for cell-generated stresses in real or Fourier space, which is an inverse and ill-posed problem. This inverse problem is commonly solved making use of regularization methods. Here, we systematically test the performance of new regularization methods and Bayesian inference for quantifying the parameter uncertainty in TFM. We compare two classical schemes, L1- and L2-regularization with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. We find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization.. We further combine the Bayesian L2 regularization with the computational speed of Fast Fourier Transform algorithms to develop a fully automated method for noise reduction and robust, standardized traction-force reconstruction that we call Bayesian Fourier transform traction cytometry (BFTTC). This method is made freely available as a software package with graphical user-interface for intuitive usage. Using synthetic data and experimental data, we show that these Bayesian methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Next, we employ our methodology developed for the solution of inverse problems for automated, data-driven discovery of ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). To find the equations governing a measured time-dependent process, we construct dictionaries of non-linear candidate equations. These candidate equations are evaluated using the measured data. With this approach, one can construct a likelihood function for the candidate equations. Optimization yields a linear, inverse problem which is to be solved under a sparsity constraint. We combine Bayesian compressive sensing using Laplace priors with automated thresholding to develop a new approach, namely automatic threshold sparse Bayesian learning (ATSBL). ATSBL is a robust method to identify ODEs, PDEs, and SDEs involving Gaussian noise, which is also referred to as type I noise. We extensively test the method with synthetic datasets describing physical processes. For SDEs, we combine data-driven inference using ATSBL with a novel entropy-based heuristic for discarding data points with high uncertainty. Finally, we develop an automatic iterative sampling optimization technique akin to Umbrella sampling. Therewith, we demonstrate that data-driven inference of SDEs can be substantially improved through feedback during the inference process if the stochastic process under investigation can be manipulated either experimentally or in simulations.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 26.02.2021, 13:00 (Online Event)
- AA2 - Materials, Light, Devices
Dr. Manuel Landstorfer, WIAS Berlin:
Modeling of concentration and electric field dependent susceptibilities in electrolytes (online talk)
more ... Location
Online Event
Host
Freie Universität Berlin
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 25.02.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Vojtěch Miloš, University of Chemistry and Technology Technická, Prag; Petr Vágner, WIAS Berlin:
Modelling of YSZ|LSM|O_2 electrode with experimental validation
more ... Location
Online Event
Abstract
A generalized Poisson-Nernst-Planck model of an yttria-stabilized zirconia (YSZ) electrolyte endowed with a lanthanum strontium manganite (LSM)--oxygen electrode interface is formulated with in the framework of non-equilibrium thermodynamics. The model takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a general reaction kinetic scheme capturing the oxygen reduction.
The model is fitted and compared to a large experimental dataset of electrochemical impedance spectra and cyclic voltammograms spanning temperatures from 700$^circ$ C to 850$^circ$ C. An apriori temperature dependenciies of the model parameters are introduced and the Nelder-Mead algorithm is employed to minimize a compound cost function. The compound cost function allows for different weights if the two types of experiments leading to interesting physical interpretations.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 24.02.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Torsten Hothorn, Universität Zürich, Switzerland:
Understanding and applying transformation models (online talk)
more ... Location
Online Event
Abstract
The mlt package implements maximum likelihood estimation in the class of conditional transformation models. Based on a suitable explicit parameterization of the unconditional or conditional transformation function using infrastructure from package basefun, we show how one can define, estimate, and compare a cascade of increasingly complex transformation models in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable are set up and estimated in the same computational framework simply by choosing an appropriate transformation function and parameterization thereof. As it is computationally cheap to evaluate the distribution function, models can be estimated by maximization of the exact likelihood, especially in the presence of random censoring or truncation. The relatively dense high-level implementation in the R system for statistical computing allows generalization of many established implementations of linear transformation models, such as the Cox model or other parametric models for the analysis of survival or ordered categorical data, to the more complex situations illustrated in this talk.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 23.02.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Dr. Alexandre Nolasco de Carvalho, University of São Paulo at São Carlos:
Gradient non-autonomous dynamics
more ... Location
Online Event
Abstract
In this lecture we present our approach for the study of the asymptotics of autonomous and non-autonomous dynamical systems. This unified approach shows how some different notions of attractors play a role in the description of the dynamics and enable us to address the gradient structure within non-autonomous attractors. As an application we characterize the gradient structure within the uniform attractor for a non-autonomous Chafee-Infante problem. A few, in our view, interesting and challenging problems, for future studies, are presented at the end of the lecture.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 23.02.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.-Doz. Dr. Christian Bayer, WIAS Berlin:
A pricing BSPDE for rough volatility (online talk)
more ... Location
Online Event
Abstract
In this talk, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic partial differential equation (BSPDE). The existence and uniqueness of weak solution is proved for general nonlinear BSPDEs with unbounded random leading coefficients whose connections with certain forward-backward stochastic differential equations are derived as well. These BSPDEs are then used to approximate American option prices. A deep leaning-based method is also investigated for the numerical approximations to such BSPDEs and associated non-Markovian pricing problems. Finally, the examples of rough Bergomi type are numerically computed for both European and American options.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 23.02.2021, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Thomas Nagel, Technische Universität Berlin:
Surface detection of clouds by using simple artificial neural networks
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Thursday, 18.02.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Derk Frerichs, WIAS Berlin:
On reducing spurious oscillations in discontinuous Galerkin methods for convection-diffusion equations
more ... Location
Online Event
Abstract
Among other desirable features, standard discontinuous Galerkin methods for discretizing steady-state convection-diffusion-reaction equations are able to produce sharp layers in the convection-dominated regime, but also show large spurious oscillations. A computationally cheap way to reduce nonphysical oscillations is to apply post-processing techniques that replace the solution in the vicinity of layers by linear or constant approximations. This talk presents known post-processing methods form the literature, and proposes several generalizations as well as novel modifications. Results for two numerical benchmark problems are shown indicating pros and cons of the methods.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 17.02.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Giovanni P. Galdi, University of Pittsburgh, USA:
On the self-propelled motion of a rigid body in a viscous liquid by time-periodic boundary data (online talk)
more ... Location
Online Event
Abstract
Consider a rigid body, B, constrained to move by translational motion in an unbounded viscous liquid. The driving mechanism is a given distribution of time-periodic velocity field, v, at the interface body-liquid, of magnitude (in appropriate function class). The main objective is to find conditions on v ensuring that B performs a non-zero net motion, namely, B can cover any given distance in a finite time. This study is mostly motivated by the self-propulsion of vibrating bodies in viscous liquids, where the vibration is generated by the oscillation of an internal mass. We show that the approach to the problem depends on whether the averaged value of v over a period of time is (case (b)) or is not (case (a)) identically zero. In case (a) we solve the problem in a relatively straightforward way, by showing that, for small , it reduces to the study of a suitable and well-investigated time-independent Stokes (linear) problem. In case (b), however, the question is much more complicated, because we show that it cannot be brought to the study of a linear problem. Therefore, in case (b), self-propulsion is a genuinely nonlinear issue that we solve directly on the nonlinear system by a contradiction argument. In this way, we are able to give, also in case (b), sufficient conditions for self-propulsion (for small ). Finally, we demonstrate, by means of counterexamples, that such conditions are, in general, also necessary.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 17.02.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Thorsten Lucke, Technische Universität Berlin:
Influence of mobility on telecommunication networks --- some thoughts (online talk)
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Online Event
Abstract
The Boolean model provides a nice framework for describing ad-hoc networks. It is well known that under certain assumptions on the distribution of the radii and the intensity of the Poisson process we can observe critical phenomena such as percolation or global connectivity. However, if we start in a subcritical regime, i.e., the intensity is below a critical threshold, can we manipulate the connectivity properties, if we allow the participants to move? This talk will provide a brief introduction to mobility models such as the random waypoint model.
Further Informations
Seminar Interacting Random Systems (Online Event)
Host
WIAS Berlin
- Wednesday, 17.02.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Georg Keilbar, Humboldt-Universität zu Berlin:
Finite sample bounds for quantiles using SGD (online talk)
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 16.02.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Alexandre Pannier, Imperial College London , UK:
Large and moderate deviations for stochastic Volterra systems (online talk)
more ... Location
Online Event
Abstract
We provide a unified treatment of pathwise large and moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhiraja, Dupuis and Ellis. We show in particular how this framework encompasses most rough volatility models used in mathematical finance, yields pathwise moderate deviations for the first time and generalises many recent results in the literature. This is joint work with Antoine Jacquier.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Friday, 12.02.2021, 13:00 (Online Event)
- AA2 - Materials, Light, Devices
Dr. Benjamin Jurgelucks, Humboldt-Universität zu Berlin:
Material parameter identification and sensitivity optimization for piezoelectric ceramics (online talk)
more ... Location
Online Event
Abstract
Recent material parameter identification methods for piezoelectric ceramics rely on the solution of an inverse problem with the electrical impedance as the measurable quantity. A common complaint is that the sensitivity of impedance with respect to some material parameters is small or zero. Thus, some material parameters cannot be identified reliably. However, the sensitivity of impedance can be increased with the help of Algorithmic Differentiation by optimizing the shape of the electrodes attached to the ceramic. This greatly improves the accuracy of current material parameter identification methods for piezoelectrics. Furthermore, based on pre-optimized electrode shapes one can even achieve arbitrary sensitivity.
Further Informations
AA2 - Materials, Light, Devices
Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
WIAS Berlin
- Thursday, 11.02.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Dr. Ulrich Wilbrandt, WIAS Berlin:
Optimization of stabilization parameters for convection-dominated convection-diffusion equations
more ... Location
Online Event
Abstract
Solutions to convection-dominated convection-diffusion equations typically have spurious oscillations and other non-physical properties. To overcome these difficulties in the Finite Element context one often uses stabilizations, which are additional terms in the weak formulation. We will consider the streamline upwind Petrov-Galerkin (SUPG) and a spurious oscillations at layers diminishing (SOLD) method. These involve a user-chosen parameter on each cell and it is unknown how to choose these parameters exactly. The approach presented in this talk is to let an optimization algorithm decide on these parameters which leaves the choice of an appropriate objective to the user. We will show some objectives and their motivation and discuss a reduction of the rather larger control space.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 10.02.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. Eftychia Solea, École Nationale de la Statistique et de l'Analyse de l'Information (ENSAI), France:
Nonparametric and high-dimensional functional graphical models (online talk)
more ... Location
Online Event
Abstract
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear conditional means. In this article we provide a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The use of functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish concentration inequalities for the resulting estimators allowing both the number of predictors and the number of functional principal components to diverge to infinity with increasing sample size. We also investigate the empirical performance of our method through simulation studies and a real data application.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 09.02.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Svetlana Gurevich, Westfälische Wilhelms-Universität Münster:
Dynamics of temporal and spatio-temporal localized states in time-delayed systems
more ... Location
Online Event
Abstract
Time-delayed systems describe a large number of phenomena and exhibit a wealth of interesting dynamical regimes such as e.g., fronts, localized structures or chimera states. They naturally appear in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. In this talk, we review our recent theoretical results regarding the existence and the dynamics of temporal, spatial and spatio-temporal localized structures in the output of semiconductor mode-locked lasers. In particular, we discuss dispersive effects which are known to play a leading role in pattern formation. We show that they can appear naturally in delayed systems [1] and we exemplify our result by studying the influence of high order dispersion in a system composed of coupled optical microcavities.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 09.02.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Franz Besold, WIAS Berlin:
Adaptive weights community detection (online talk)
more ... Location
Online Event
Abstract
We study a likelihood-based approach for the stochastic block model proposed by Kirill Efimov, Larisa Adamyan and Vladimir Spokoiny. We propose a modification of the algorithm to improve the rate of consistency.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 04.02.2021, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Dr. Shalva Amiranashvili, WIAS Berlin:
Parallel splitting methods
more ... Location
Online Event
Host
WIAS Berlin
- Thursday, 04.02.2021, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Prof. Dr. Eberhard Bänsch, Friedrich-Alexander Universität Erlangen-Nürnberg:
The Buongiorno model for nanofluids (online talk)
more ... Location
Online Event
Abstract
We present a mathematical model for convective transport in nanofluids including thermophoretic effects that is very similar to the celebrated model of Buongiorno. Our model, however, is thermodynamically consistent and consequently an energy estimate can be shown. We show existence of weak solutions for the time-dependent as well as stationary problem. Moreover, an efficient numerical scheme for the time dependent problem is proposed. For the stationary system, regularity and subsequently optimal error estimates for finite element approximations can be shown under some smallness assumptions.
Further Informations
TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 03.02.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Petr Pelech, WIAS Berlin:
Separately global solutions to rate-independent systems - applications to large-strain deformations of damageable solids (online talk)
more ... Location
Online Event
Abstract
Rate-independent systems (RIS) are characterized by the lack of any internal time length scale: rescaling the input of the system in time leads to the very same rescaling of its solution. In continuum mechanics, rate-independent models represent a reasonable approximation whenever the external conditions change slowly enough so that the system can always reach its equilibrium. This applies if inertial, viscous, and thermal effects are neglected. RIS have proven to be useful in modeling of hysteresis, phase transitions in solids, elastoplasticity, damage, or fracture in small and large strain regimes. The talk introduces the notion of separately global solutions for RIS with non-convex functionals and describes an existence result for a model of bulk damage at large strains. The analysis covers non-convex energies blowing up for extreme compression, yields solutions excluding interpenetration of matter, and allows for handling nonlinear couplings of the deformation and the internal variable, which emerges e.g. from the interplay between Eulerian and Lagrangian description. It extends the theory developed so far in the small strain setting.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 03.02.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Elena Pulvirenti, Delft University of Technology, Niederlande:
The Widom-Rowlinson model: metastability, mesoscopic and microscopic fluctuations for the critical droplet (online talk)
more ... Location
Online Event
Abstract
We introduce the equilibrium Widom-Rowlinson model on a two-dimensional finite torus in which the energy of a particle configuration is attractive and determined by the union of small discs centered at the positions of the particles. We then discuss the metastable behaviour of a dynamic version of the WR model. This means that the particle configuration is viewed as a continuous time Markov process where particles are randomly created and annihilated as if the outside of the torus were an infinite reservoir with a given chemical potential. In particular, we start with the empty torus and are interested in the first time when the torus is fully covered by discs in the regime at low temperature and when the chemical potential is supercritical. In order to achieve the transition from empty to full, the system needs to create a sufficiently large droplet, called critical droplet, which triggers the crossover. We compute the distribution of the crossover time and identify the size and the shape of the critical droplet. The analysis relies on a mesoscopic and microscopic description of the surface of the critical droplet. It turns out that the critical droplet is close to a disc of a certain deterministic radius, with a boundary that is random and consists of a large number of small discs that stick out by a small distance. We will show how the analysis of surface fluctuations in the WR model allows us to derive the leading order term of the condensation time and also the correction order term. This is a joint work with Frank den Hollander (Leiden), Sabine Jansen (Munich) and Roman Kotecky (Prague & Warwick).
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Tuesday, 02.02.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
David Müller-Bender, Chemnitz University of Technology:
Laminar chaos in systems with time-varying delay
more ... Location
Online Event
Abstract
For many systems arising in nature and engineering, the influence of time-delays cannot be neglected. Due to environmental fluctuations that affect the delay generating processes such as transport processes, the delays are in general not constant but rather time-varying. Although it is known that variable delays can lead to interesting phenomena, their effect on the dynamics of systems is not completely understood. In this talk, it is demonstrated that a temporal delay variation can change the dynamics of a time-delay system drastically. A recently discovered type of chaos called laminar chaos is introduced, which can only be observed for a certain type of time-varying delays. It is characterized by nearly constant laminar phases with periodic duration, where the intensity of the laminar phases varies chaotically from phase to phase. In contrast to the high-dimensional turbulent chaos, which is also observed for constant delay, laminar chaos is low-dimensional. Furthermore, it is shown experimentally and theoretically that laminar chaos is a robust phenomenon. A time-series analysis toolbox for its detection is provided, which is benchmarked by experimental data and by time-series of a nonlinear delayed Langevin equation.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 02.02.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Moscow Institute of Physics and Technology, Russische Föderation:
Solving convex min-min problems with smoothness and strong convexity in one variable group and small dimension of the other(online talk)
more ... Location
Online Event
Abstract
Logistic regression with the prior on one of the parameter groups is an example of the convex min-min problem with strong convexity in only one of the two variable groups. The talk is devoted to approaches to such problems that achieve linear convergence. The outer minimization problem is solved using Vaidya?s cutting plane method, and the inner problem (smooth and strongly convex) is solved using Nesterov's fast gradient method. Due to the importance of machine learning applications, we also consider the case when the objective function is a sum of a large number of functions. In this case, the variance-reduced accelerated gradient algorithm is used instead of Nesterov's fast gradient method.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 02.02.2021, 13:30 (Online Event)
- Seminar Numerische Mathematik
Volker Kempf, Bundeswehr-Universität München:
Anisotropic and pressure-robust finite element discretizations for the Stokes equations
more ... Location
Online Event
Abstract
The incompressible Stokes equations show a fundamental invariance property, meaning that the velocity solution is not affected by a change of the right hand side data in form of a gradient field. Due to relaxation of the divergence constraint most common finite element discretizations, like the Taylor-Hood or Mini-element, are however not pressure-robust, i.e. they do not reproduce this property on the discrete level. The mentioned classical methods are also in general not inf-sup stable on anisotropic meshes with potentially unbounded aspect ratio, which are used e.g. when treating singularities caused by re-entrant edges.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Monday, 01.02.2021, 14:00 (Online Event)
- Oberseminar Nonlinear Dynamics
Bernold Fiedler, Freie Universtität Berlin:
Global attractors of scalar parabolic equations: The Thom--Smale complex
more ... Location
Online Event
Abstract
We consider the global attractors of scalar parabolic equations ut=uxx+f(x,u,ux) under Neumann boundary conditions. The Thom-Smale complex decomposes a global attractor into the unstable manifolds of its (hyperbolic) equilibria ut=0. In general this is not a topological cell complex ? not even in the presence of a gradient structure. For the above PDEs, however, the Thom-Smale complex turns out to be a signed regular topological cell complex: the boundaries of the unstable manifolds are topological spheres, each with a signed hemisphere decomposition. On the other hand, the equilibria ut=0 are characterized by a meander curve, which arises from a shooting approach to the ODE boundary value problem uxx+f(x,u,ux) =0. We explore a minimax characterization of boundary neighbors, along the meander. Specifically, we identify the precise geometric locations of these boundary neighbors in the signed Thom-Smale complex. This opens an approach to the construction of global attractors with prescribed Thom-Smale complex. Many examples will illustrate this joint work with Carlos Rocha, dedicated to the memory of Geneviève Raugel. See arxiv:1811.04206 and doi: 10.1007/s10884-020-09836-5.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Monday, 01.02.2021, 13:00 (Online Event)
- Oberseminar Nonlinear Dynamics
Carlos Rocha, Instituto Superior Técnico, Universidade de Lisboa, Portugal:
A minimax property for global attractors of scalar parabolic equations
more ... Location
Online Event
Abstract
We overview recent results on the geometric and combinatorial characterization of global attractors of semifl ows generated by scalar semilinear partial parabolic differential equations under Neumann boundary conditions. In special, we discuss a minimax property of the boundary neighbors of any specifi c unstable equilibrium. This property allows the identi fication of the equilibria on the cell boundary of any chosen equilibrium. This is a joint work with B. Fiedler.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Thursday, 28.01.2021, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Ass. Prof. Markus Hütter, Eindhoven University of Technology, Niederlande:
Finite-size effects in complex fluids: Phenomenology of fluctuations, stochastics, and statistical mechanics (online talk)
more ... Location
Online Event
Abstract
In general, in every system with dissipation there are also fluctuations; the fluctuation-dissipation theorem is a key result of nonequilibrium statistical mechanics, which is encoded e.g. in the GENERIC framework [1,2,3]. Correspondingly, also complex fluids, which contain the relaxation of the microstructure (e.g. polymer chains), must show behavior with fluctuations. Fluctuations are relevant particularly for the behavior on small scales, where they are not averaged out, e.g. in micro-/nano-fluidics and microrheology. To date, models for complex fluids do not include fluctuations systematically. In our recent work, we have extended conformation-tensor based models for complex fluids by including thermal fluctuations in a thermodynamically consistent way [4]. Furthermore, this work has been complemented by establishing a link between the fluctuating conformation-tensor models and the underlying description of polymer chains as bead-spring dumbbells [5]. To achieve this link, we follow two routes: (1) stochastic calculus, followed by averaging (direct approach); (2) nonequilibrium statistical mechanics, which includes the derivation of the coarse-grained relaxation tensor, the fluctuations, and the thermodynamic potential (particularly entropy). Denoting the number of polymer chains by N, it is shown that a finite (rather than infinite) value for N gives rise to a correction to the conventional entropy for the conformation tensor and leads to the fluctuations that vanish only in the thermodynamic limit (N to infinity). Finally, some subtleties are pointed out related to the appearance of the so-called spurious drift in the stochastic differential equation for the conformation tensor. References: [1] M. Grmela, H.C. Öttinger, Phys. Rev. E 56(6) (1997) 6620?6632 (http://dx.doi.org/10.1103/PhysRevE.56.6620) [2] H.C. Öttinger, M. Grmela, Phys. Rev. E 56(6) (1997) 6633?6655 (http://dx.doi.org/10.1103/PhysRevE.56.6633) [3] H.C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley, Hoboken, 2005. [4] M. Hütter, M.A. Hulsen, P.D. Anderson, J. Non-Newtonian Fluid Mech. 256 (2018) 42?56 (https://doi.org/10.1016/j.jnnfm.2018.02.012) [5] M. Hütter, P.D. Olmsted, D.J. Read, Eur. Phys. J. E 43 (2020) 71 (http://dx.doi.org/10.1140/epje/i2020-11999-x)
Further Informations
TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 27.01.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Sebastian Throm, Westfälische Wilhelms-Universität Münster:
Universal long-time asymptotics for coagulation equations (online talk)
more ... Location
Online Event
Abstract
In this talk, we will consider the long-time behaviour of coagulating systems. Clustering phenomenon can be observed in many processes in nature and industry and also on a broad range of scales. Our focus will be on Smoluchowski's coagulation equation and the question of universal scaling for large times - a problem which is known as scaling hypothesis. In particular, we will present a recent result proving this conjecture for perturbations of a constant rate kernel.
Further Informations
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 26.01.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Tibor Krisztin, University of Szeged, Hungary:
Periodic and connecting orbits for the Mackey--Glass equation
more ... Location
Online Event
Abstract
We consider the Mackey-Glass equation x' (t)=-ax(t)+b (x^k(t-1))/(1+x^n (t-1)) with positive parameters a,b,k,n. First, for the discontinuous limiting (n??) case, an orbitally asymptotically stable periodic orbit is constructed for some fixed parameter values a,b,k. Then it is shown that for large values of n and with the same parameters a,b,k, the Mackey-Glass equation also has an orbitally asymptotically stable periodic orbit near to the periodic orbit of the discontinuous equation. The shape of the obtained stable periodic solutions can be complicated. The existence of connecting orbits will be discussed as well.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 26.01.2021, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.-Doz. Dr. John Schoenmakers, WIAS Berlin:
From optimal martingales to randomized dual optimal stopping
more ... Location
Online Event
Abstract
In this talk we study and classify dual optimal martingales in the dualformulation of optimal stopping problems. In this respect it is distinguished between optimal and surely optimal martingales. It is shown that the family of optimal and surely optimal martingales may generally be quite large. On the other hand it is shown that the Doob-martingale, i.e. the martingale part of the Snell envelope, is in a certain sense the most robust surely optimal martingale under random perturbations. This new insight has led to a novel randomized dual martingale minimization algorithm that doesn't require nested simulation. As a main feature, in a possibly large family of optimal martingales the algorithm sorts out efficiently a martingale that is close to the Doob martingale. As a result, one obtains in an efficient way a dual estimate for the optimal stopping problem with low variance. (joint work with Denis Belomestny)
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 21.01.2021, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Dr. Pierre-Étienne Druet, Technische Universität Berlin WIAS Berlin:
The free energy of incompressible fluid mixtures: An asymptotic study (online talk)
more ... Location
Online Event
Abstract
The results presented in this talk are triggered by the modelling of multicomponent fluids at low Mach-number. We first perform the asymptotic of small compressibility for a globally stable phase, and we show that the Helmholtz free energy, which is the crucial constitutive quantity, tends to a limit in the sense of epi- or Gamma-convergence. The essential findings are: The limit model does not only prohibit thermal expansion - this is the well-known Mueller-paradox -, but it also excludes the phenomena of volume loss or excess due to mixing. In order to temper the latter unrealistic conclusion, we modify the basic scenario by performing the limit only inside of a bounded, stable phase. In this way we recover incompressible systems that are not volume additive. Moreover, the limit free energy depends continuously on the state variables. This research is joined work with D.Bothe (TU Darmstadt) and W.Dreyer (WIAS Berlin).
Further Informations
TES-Seminar on Energy-based Mathematical Methods and Thermodynamics (online talk)
Host
Technische Universität Berlin
WIAS Berlin
- Thursday, 21.01.2021, 14:00 (Online Event)
- Seminar Numerische Mathematik
Felipe Galarce, INRIA, Paris:
Inverse problems in haemodynamics -- fast estimation of blood flows from medical data
more ... Location
Online Event
Abstract
We present a study at the interface between applied mathematics and biomedical engineering. The work's main subject is the estimation of blood flows and quantities of medical interest in diagnosing certain diseases concerning the cardiovascular system. We propose a complete pipeline, providing the theoretical foundations for state estimation from medical data using reduced-order models, and addressing inter-patient variability. Extensive numerical tests are shown in realistic 3D scenarios that verify the potential impact of the work in the medical community.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 20.01.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Lorenzo Taggi, University of Rome “La Sapienza”, Italien:
Exponential decay of correlations for O(N) spin systems
more ... Location
Online Event
Abstract
The Spin O(N) model is a classical statistical mechanics model whose configurations are collections of unit vectors, called spins, taking values on the surface of a N ?1 dimensional unit sphere, with each spin associated to the vertex of a graph. Some special cases of the spin O(N) model are the Ising model (N = 1), the XY model (N = 2), and the classical Heisenberg model (N = 3). Despite the fact that it is a very classical model, there remain important gaps in understanding, particularly in the case N > 2. This talk will provide an introduction on this class of models and present a new recent result about exponential decay of correlations for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N>1. The proof of this result employs a representation of the model as a system of coloured random paths and a sampling procedure, which allows us to bound from above the "typical lenght" of the open paths. The talk is based on a joint work with B. Lees.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 20.01.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Sven Wang, University of Cambridge:
On polynomial-time computation of high-dimensional posterior measures by Langevin-type algorithms
more ... Location
Online Event
Abstract
In this talk, we consider the task of generating random samples of high-dimensional posterior distributions. The main results consist of non-asymptotic computational guarantees for Langevin-type MCMC algorithms which scale polynomially in key quantities such as the dimension of the model, the desired precision level, and the number of statistical measurements. We also show that posterior mean vectors and maximum a posteriori (MAP) estimates are computable in polynomial time, with high probability under the distribution of the data. Those results are derived in a general non-linear regression setting where posterior measures are not necessarily log-concave. The main example is a non-linear PDE model involving the steady-state Schrödinger equation. The talk is based on the preprint https://arxiv.org/abs/2009.05298.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 19.01.2021, 16:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Dmitrii M. Ostrovskii, University of Southern California:
Near-optimal model discrimination with non-disclosure (online talk)
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 19.01.2021, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Michal Hadrava, Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic:
A dynamical systems approach to spectral music: Modeling the role of roughness and inharmonicity in perception of musical tension
more ... Location
Online Event
Abstract
Tension-resolution patterns seem to play a dominant role in shaping our emotional experience of music. Whereas in traditional Western music, these patterns are mainly expressed through harmony and melody, many contemporary musical compositions (e.g. so-called ?spectral music") employ sound materials lacking any perceivable pitch structure, rendering these two compositional devices useless. Motivated by recent advances in music-theoretical and neuroscientific research into the related phenomenon of dissonance, we propose a neurodynamical model of musical tension based on a spectral representation of sound and hence applicable to any kind of sound material, pitched or non-pitched.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Thursday, 14.01.2021, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Rostislav Arkhipov, St. Petersburg State University:
Dissipative self-induced transparency solitons and rogue waves in coherent mode-locking. Unipolar light
more ... Location
Online Event
Host
WIAS Berlin
- Thursday, 14.01.2021, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Dr. Denis Matignon, Université Fédérale Toulouse Midi-Pyrénées, Frankreich:
The Partitioned Finite Element Method for port-Hamiltonian systems: structure-preserving numerics for physics-based PDEs with boundary control (online talk)
more ... Location
Online Event
Abstract
The numerical simulation of complex open multiphysics systems in Computational Science and Engineering is a challenging topic. Based on energy exchanges, the port-Hamiltonian formalism aims at describing physics in a structured manner. One of the major interests of this approach is its versatility, allowing for coupling and interconnection that preserve this structure. We propose a Finite Element based technique for the structure-preserving discretization of a large class of port-Hamiltonian systems (pHs). Assuming a partitioned structure of the system associated to an integration-by-parts formula, it is possible to derive a consistent weak-formulation sharing the main features of the original boundary-controlled PDE. This allows using Galerkin approximations to obtain finite-dimensional systems that mimic the properties of the original distributed ones; these systems are either ODEs or Differential Algebraic Equations (DAEs). Moreover, the Partitioned Finite Element Method producing sparse matrices enables the use of dedicated algorithms in scientific computing. Indeed, this method can be easily implemented using well-established and robust libraries. This strategy is illustrated by means of physically motivated PDEs with boundary control and observation, either in 2D or in 3D, both linear and non-linear: acoustic waves, Mindlin and Kirchhoff plates, heat equation, Shallow Water equation, Maxwell's equation. Interactive Jupyter notebooks are available, relying on the FEniCS open-source software. Advanced applications include multiphysics problems, e.g. fluid-structure interactions, thermoelasticity, and modular modelling of complex systems, e.g. multibody dynamics.
Further Informations
TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 13.01.2021, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Anieza Maltsi, WIAS Berlin:
On the Darwin--Howie--Whelan equations for the scattering of fast electrons described by the Schrödinger equation (online talk)
more ... Location
Online Event
Abstract
The Darwin--Howie--Whelan (DHW) equations are widely used for the numerical simu-lation of transmission electron microscopy (TEM) images. They describe the propagation of the electron beam through crystalline solids and are formally stated as a system of infinitely many beam amplitudes?g. For the numerical simulation however only a finite set of beams is used, e.g. the two-beams approximation. In this talk we will address the accuracy of the approximation of this infinite system by suitable finite-dimensional ones.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 13.01.2021, 11:30 (Online Event)
- Seminar Interacting Random Systems
Sabine Jansen, Universität München:
Virial inversion and density functionals (online talk)
more ... Location
Online Event
Abstract
We present a novel inversion theorem for functionals that map measures to measures. Our main application is in statistical mechanics of inhomogeneous systems, in which the activity $z(x) = z_0 exp( - V_ext(x))$ is mapped to a density profile $rho(x)$ and one seeks to invert the density-activity relation. In probabilistic terms, the question is how to invert the relation between the intensity measure of an underlying Poisson point process and the intensity measure of a Gibbs point process, a question also of interest in spatial statistics. We apply the inversion theorem to the derivation of density functionals. The inversion theorem works in situations where the inverse function theorem in Banach spaces fails. Based on joint work with Tobias Kuna and Dimitrios Tsagkarogiannis (arXiv:1906.02322 [math-ph]).
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 13.01.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Bayesian inference in machine learning (online talk)
more ... Location
Online Event
Abstract
Statistical inference for binary data is one of the central problem in machine learning which can be treated within a nonparametric Bernoulli model. In many situations the underlying Bernoulli parameter may approach the edges zero or one that leads to inference for non-regular models. Properties like asymptotic normality of the MLE or of the posterior distribution are not valid in such irregular cases. The approach of this paper suggests to impose a Gaussian prior on the canonical Bernoulli parameter, or, analogously, to consider a penalized MLE with a quadratic penalty. A Gaussian prior can be viewed as a kind of a barrier preventing the canonical parameter to approach infinity and forcing it to stay within the region of regularity. The main results stay the classical results like asymptotic normality of the posterior distribution or asymptotic normality of the penalized MLE for any configuration of Bernoulli parameters under the assumption that the prior is strong enough in direction. We also demonstrate how the results can be applied to analysis of random graphs, ranking problems, and nonparametric binary classification.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- January 8, 2021 (Online Event)
- Workshop/Konferenz: Applied Probability Day
more ... Location
Online Event
Further Informations
Der Workshop findet bei Zoom statt: https://tu-berlin.zoom.us/j/69959389549?pwd=YWtnam1OSXNRRnVoWVJtUHJWdFpzZz09
Host
WIAS Berlin
Institute of Mathematical Statistics
- Wednesday, 06.01.2021, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Alexey Naumov, HSE University, Russische Föderation:
Finite time analysis of linear two-timescale stochastic approximation with Markovian noise (online talk)
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 17.12.2020, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Max Schiemangk, FBH Berlin:
Requirements on lasers for optical quantum metrology
more ... Location
Online Event
Host
WIAS Berlin
- Wednesday, 16.12.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Howard Bondell, University of Melbourne, Australien:
Bayesian regression for high-dimensional data using a prior on the model fit
more ... Location
Online Event
Abstract
We propose a new class of prior distributions for shrinkage regularization in sparse linear regression, particularly the high dimensional case. Instead of placing a prior on the coefficients themselves, we place a prior on the regression R-squared. This is then distributed to the coefficients in a suitable manner. We show that this framework induces a shrinkage prior that can obtain desirable theoretical properties. Compared to existing shrinkage priors, it can simultaneously achieve both high prior concentration at zero, as well as heavier tails. These two properties combine to provide a higher degree of shrinkage on the irrelevant coefficients, along with less bias in estimation of the larger signals. Both theoretical and practical aspects will be discussed.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
WIAS Berlin
Humboldt-Universität zu Berlin
- Friday, 11.12.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Judith Rousseau, University of Oxford, UK:
Bayesian nonparametric estimation in multivariate non linear Hawkes processes (online talk)
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://uni-potsdam.zoom.us/j/61627954803
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 10.12.2020, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Dr. Martin Kružík, Czech Academy of Sciences:
Equilibrium for multiphase solids with Eulerian interfaces (online talk)
more ... Location
Online Event
Abstract
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove the existence of energy minimizing equilibrium states and Gamma-convergence of diffuse-interface approximations to the sharp-interface limit. This is a joint work with D. Grandi, E. Mainini and U. Stefanelli.
Further Informations
Please register on this link: https://mathplus.de/topic-development-lab/tes-winter-2020-21/tes-seminar-on-energy-based-mathematical-methods-and-thermodynamics/
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 09.12.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Grigor Nika, WIAS Berlin:
Effective bulk-surface thermistor models for OLEDs (online talk)
more ... Location
Online Event
Abstract
We consider a thin-film OLED device placed on a flat surface, part of a bulk substrate material. The device is assumed to have N>2 layers and total thickness h>0. An effective electrothermal model is derived by considering the limit of vanishing thickness as it approaches zero under physically motivated scalings. The effective equations consist of two equations for the lateral current flow in the top and bottom electrodes and an iterative set of algebraic equations for the vertical flow in the organic layers posed on the flat surface where the OLED is placed and coupled to the heat equation in the bulk substrate material.
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
WIAS Berlin
- Wednesday, 09.12.2020, 11:30 (Online Event)
- Seminar Interacting Random Systems
Robert Patterson:
Large deviations for population growth from near zero concentration
more ... Location
Online Event
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Tuesday, 08.12.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Elisenda Feliu, University of Copenhagen, Denmark:
Understanding of bistability and Hopf bifurcations in biochemical reaction networks
more ... Location
Online Event
Abstract
In the context of (bio)chemical reaction networks, the dynamics of the concentrations of the chemical species over time are often modelled by a system of parameter-dependent ordinary differential equations, which are typically polynomial or described by rational functions. The polynomial structure of the system allows the use of techniques from algebra to study properties of the system around steady states, for arbitrary parameter values. In this talk I will present the formalism of the theory of reaction networks, and how applied algebra plays a role in the study of three main questions: determination of bistability, determination of Hopf bifurcations, and parameter regions for multistationarity. I will present new results tackling these questions by using a ubiquitous and challenging network from cell signaling (the dual futile cycle) as a case example. For this network, which is relatively small, several basic questions, such as the existence of oscillations, the parameter region of multistationarity, and whether multistationarity implies bistability, remain unresolved.
Host
Freie Universität Berlin
WIAS Berlin
- Wednesday, 02.12.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. Yegor Klochkov, University of Cambridge, UK:
Robust K-means clustering under two moments
more ... Location
Online Event
Abstract
We consider the robust algorithms for the k-means clustering problem where a quantizer is constructed based on N independent observations. Our main results are median of means based non-asymptotic excess distortion bounds that hold under the two bounded moments assumption in a general separable Hilbert space. In particular, our results extend the renowned asymptotic result of Pollard(1981) who showed that the existence of two moments is sufficient for strong consistency of an empirically optimal quantizer in R^d. In a special case of clustering in R^d, under two bounded moments, we prove matching (up to constant factors) non-asymptotic upper and lower bounds on the excess distortion, which depend on the probability mass of the lightest cluster of an optimal quantizer. Our bounds have the sub-Gaussian form, and the proofs are based on the versions of uniform bounds for robust mean estimators. This is joint work with Alexei Kroshnin and Nikita Zhivotovskiy.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- December 2 – 3, 2020 (Online Event)
- Workshop/Konferenz: ECMI Webinar “Math for Industry 4.0 - Models, Methods and Big Data”
more ... Location
Online Event
Host
WIAS Berlin
- Tuesday, 01.12.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Felix Kemeth, Johns Hopkins University, USA:
2-cluster fixed-point analysis of mean-coupled Stuart--Landau oscillators in the center manifold
more ... Location
Online Event
Abstract
Clustering in phase oscillator systems with long-range interactions has been subject to theoretical investigations for many years. By mapping the dynamics of mean-coupled Stuart-Landau oscillators onto the center manifold of the Benjamin-Feir instability, we aim to add to the theoretical understanding of clustering in systems beyond phase oscillator ensembles. In particular, we discuss the formation of 2-cluster states in this lower dimensional manifold and outline the resulting implications for the dynamics of the coupled oscillator ensemble.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 01.12.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Roman Kravchenko, Humboldt-Universität zu Berlin:
Distributed optimization with quantization for computing Wasserstein barycenters
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 26.11.2020, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Regina Finsterhölzl, TU Berlin:
Applying feedback control on quantum many-body systems within the matrix-product-state framework
more ... Location
Online Event
Host
WIAS Berlin
- Thursday, 26.11.2020, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Prof. Dr. Miroslav Grmela, Polytechnique Montréal:
Multiscale thermodynamics (online talk)
more ... Location
Online Event
Abstract
Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it is applicable to both static and time evolving processes in externally and internally driven macroscopic systems that are far from equilibrium and are investigated on microscopic, mesoscopic, and macroscopic levels. In this talk we formulate the multiscale thermodynamics, explain its origin, and illustrate it in mesoscopic dynamics that combines levels, see [1] for more details. [1] M. Grmela: Multiscale Thermodynamics. arxiv-preprint 2020.
Further Informations
Please register on this link: https://mathplus.de/topic-development-lab/tes-winter-2020-21/tes-seminar-on-energy-based-mathematical-methods-and-thermodynamics/
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 25.11.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Annika Bach, Technische Universität München:
Geometrically frustrated spin systems: The antiferromagnetic XY model on the triangular lattice (online talk)
more ... Location
Online Event
Abstract
Antiferromagnetic spin systems are magnetic lattice systems in which the exchange interaction between two spins (i.e., vectors in S1) favors anti-alignment. Such systems are said to be geometrically frustrated if, due to the geometry of the lattice, there is no orientation of spins that simultaneously minimizes all pairwise interactions. This is the case for the antiferromagnetic XY model on the two-dimensional triangular lattice. As a consequence, the system has two families of ground states which can be distinguished one from the other by what is called their chirality. In this talk we present a recent result obtained in collaboration with M. Cicales, L. Kreutz, and G. Orlando, where we characterise the discrete-to-continuum Gamma-limit of the XY-model energy in a regime which detects chirality transitions on one-dimensional interfaces between the two admissible chirality phases.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 25.11.2020, 11:30 (Online Event)
- Seminar Interacting Random Systems
Willem van Zuijlen:
Total mass asymptotics of the parabolic Anderson model
more ... Location
Online Event
Abstract
We consider the parabolic Anderson model with a white noise potential in two dimensions. This model is also called the stochastic heat equation with a multiplicative noise. We study the large time asymptotics of the total mass of the solution. Due to the irregularity of the white noise, in two dimensions the equation is a priori not well-posed. Using paracontrolled calculus or regularity structures one can make sense of the equation by a renormalisation, which can be thought of as “subtracting infinity of the potential”. To obtain the asymptotics of the total mass we use the spectral decomposition, an alternative Feynman-Kac type representation and heat-kernel estimates which come from joint works with Khalil Chouk, Wolfgang König and Nicolas Perkowski.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 25.11.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. Alexander Kreiß, KU Leuven:
Unbiased Markov chain Monte Carlo methods with couplings
more ... Location
Online Event
Abstract
We will consider multivariate stochastic processes indexed either by vertices or pairs of vertices of a dynamic network. Under a dynamic network we understand a network with a fixed vertex set and an edge set which changes randomly over time. We will assume that the spatial dependence-structure of the processes conditional on the network behaves in the following way: Close vertices (or pairs of vertices) are dependent, while we assume that the dependence decreases conditionally on that the distance in the network increases. We make this intuition mathematically precise by considering three concepts based on correlation, beta-mixing with time-varying beta-coefficients and conditional independence. These concepts allow proving weak-dependence results, e.g. an exponential inequality. These results will be useful for studying asymptotic regimes in which the network grows (i.e. the number of vertices tends to infinity) and we can expect that a growing network results in a larger distance between most vertices. Since the network is dynamic we allow that vertices move around the network and come close to different vertices. In order to demonstrate the use of these concepts in an application we study the asymptotics (for growing networks) of a goodness of fit test in a dynamic interaction network model based on a Cox-type model for counting processes. This model is then applied to bike-sharing data.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 24.11.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Giulia Ruzzene, Universitat Pompeu Fabra, Palma de Mallorca, Spain:
Control of chimera states in multilayer networks
more ... Location
Online Event
Abstract
Chimera states are one of the most intriguing and studied types of partial synchronization. In small systems, which are the most relevant for experimental situations, chimera states present various instabilities. Therefore, it is natural to investigate methods to control them. We propose a control mechanism based on the idea of a pacemaker oscillator, which allows to control the position of a chimera state within a network and to prevent its collapse to the fully synchronous state. We show how this mechanism developed for ring networks of phase oscillators can be applied to multilayer networks with more complex node dynamics, such as FitzHugh-Nagumo oscillator. In particular, we show that it allows to remotely control a chimera state in one layer via a pacemaker in the other layer.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/82815629022.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 24.11.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexander Gasnikov, WIAS Berlin:
Parallel and distributed algorithms for ML problems
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 24.11.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Sergey Nechayev, Ferdinand-Braun-Institut, Berlin:
Towards LDSL-based multiphysics modeling of semiconductor lasers: Ideals and challenges
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Thursday, 19.11.2020, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Dr. Konstantinos Mamis, Hellenic Naval Academy, Greece:
Formulating nonlinear Fokker--Planck equations for dynamical systems under coloured noise excitation
more ... Location
Online Event
Host
WIAS Berlin
- Thursday, 19.11.2020, 15:00 (Online Event)
- TES-Seminar on Energy-based Mathematical Methods and Thermodynamics
Prof. Dr. Christian Wieners, Karlsruher Institut für Technologie:
A discontinuous Galerkin method for phase field approximations of dynamic fracture (online talk)
more ... Location
Online Event
Abstract
We present a new numerical method for dynamic fracture at small strains which is based on a discontinuous Galerkin approximation of a first order formulation for elastic waves and where the fracture is approximated by a phase field driven by a stress based fracture criterion. The staggered algorithm in time combines the implicit midpoint rule for the wave propagation followed by an implicit Euler step for the phase field evolution. Then, driven by a stress based fracture criterion, the material is degradated, and the waves are reflected at the diffusive interface. Then method is evaluated in detail in one dimension, and then we demonstrate in a 2D application the fracture evolution with multiple fractures initiated by reflections. This is joint work with Kerstin Weinberg, Siegen.
Further Informations
Please register on this link: https://mathplus.de/topic-development-lab/tes-winter-2020-21/tes-seminar-on-energy-based-mathematical-methods-and-thermodynamics/
Host
Technische Universität Berlin
WIAS Berlin
- Wednesday, 18.11.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Janusz Ginster, Humboldt-Universität zu Berlin:
On the motion of curved dislocations in three dimensions: Simplified linearized elasticity (online talk)
more ... Location
Online Event
Abstract
In this talk we discuss a simplified equilibrium problem for a curved dislocation line in a three-dimensional domain. As the core radius tends to zero, we derive an asymptotic expression to characterize the induced elastic energy. We then obtain the force on the dislocation line as the variation of thi sexpression and identify the highest order terms explicitly. As a main ingredient, we present an explicit asymptotic formula for the induced elastic strain which depends on the curvature of the dislocation line and thus highlights the difference to existing work on straight dislocation lines. Eventually, we present results on the corresponding dynamics. The presented methods area blueprint for the more physical setting of linearized isotropic elasticity. This is joint work with I. Fonseca and S. Wojtowytsch.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 18.11.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. Matthias Löffler, ETH Zürich:
Computationally efficient sparse clustering
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 17.11.2020, 13:30 (Online Event)
- Seminar Numerische Mathematik
Prof. Peter Berg, University of Alberta, Kanada:
From microscale to macroscale properties of polymer electrolyte membranes: A case for pore network models
more ... Location
Online Event
Abstract
We present the first attempt at describing the flow of water and protons through polymer electrolyte membranes (PEM) by use of an elastic pore network model. The main feature of our approach lies in the interplay between fluxes and pore structures, determined by randomized pore properties, the elasticity of the pores, and the liquid pressure distribution across the network.
Closed-form solutions of the Poisson-Nernst-Planck-Stokes equations along each bond (pore) are employed and coupled to a swelling model for the pores which are embedded in the elastic PEM backbone. All parameter values are taken from the literature, leaving little room for the fitting of model results to literature values.
The resulting nonlinear problem is solved computationally in an efficient manner. More importantly, computed PEM properties at different operating conditions, such as the specific conductivity and the electro-osmotic drag coefficient, compare favourably to values in the literature. In addition, the analysis reveals insights into the nonlinear couplings between transport processes and the structure of the elastic domain which motivates studies of other elastic, nanofluidic systems.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 11.11.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Charles University Prague, Czech Republic:
The old Stefan problem in a new mechanical context (online talk)
more ... Location
Online Event
Abstract
The Stefan problem historically describes melting of ice or freezing (solidification) of water as a mere heat-transfer problem with a latent heat. This solid-liquid phase transition however naturally occurs in a mechanical context: melted liquid can flow while frozen solid exhibits some elasticity or some visco-elasticity and even may undergo some inelastic processes as fracture. This needs also to cope with the fluid-solid (so-called fluid-structure) interaction and calls for a model in Eulerian description. Thermomechanical consistency is pursued, as well as a mathematical analysis outlined. The concepts of semi-compressible fluids, viscoelastic solids in Jeffreys' rheology, phase-field fracture, and nonsimple materials (known also as multipolar fluids) will be employed. Some enhancements of this basic thermomechanical scenario will be mentioned, too.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 11.11.2020, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Stein Andreas Bethuelsen:
Invariance principle for random walks on dynamically averaging random conductances
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on Z. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations decrease according to a typical diffusive scaling and eventually approach constant unit conductances. The proof relies on a coupling with the standard continuous time simple random walk. Based on joint work with Christian Hirsch (Groningen) and Christian Mönch (Mainz).
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Tuesday, 10.11.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Simon Breneis, WIAS Berlin:
Functions of bounded variation in one and multiple dimensions
more ... Location
Online Event
Abstract
We first recall univariate functions of bounded variation and treat a new result on the Hölder continuities of functions of bounded variation and their variation functions. Then, we discuss possible extensions of the concept of bounded variation to functions of several (though finitely many) variables, compare those generalizations and discuss their uses and shortcomings.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 04.11.2020, 11:30 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Pierre E. Jacob, Harvard University:
Unbiased Markov chain Monte Carlo methods with couplings
more ... Location
Online Event
Abstract
Various tasks in statistics involve numerical integration, for which Markov chain Monte Carlo (MCMC) methods are state-of-the-art. MCMC methods yield estimators that converge to integrals of interest in the limit of the number of iterations. This iterative asymptotic justification is not ideal; first, it stands at odds with current trends in computing hardware, with increasingly parallel architectures; secondly, the choice of "burn-in" and of the total number of iterations are dificult. This talk will describe recently proposed estimators that are exactly unbiased for the expectations of interest, while having an almost surely finite computing cost and a finite variance. They can thus be generated independently in parallel and averaged over. We argue that the removal of the "burn-in" bias can be done for many MCMC algorithms of practical interest without inflating the variance by much. The core idea is to use coupled pairs of Markov chains following the pathbreaking work of Peter Glynn & Chan-Han Rhee. The method also provides practical upper bounds on some distances between the marginal distribution of the chain at a finite step and its invariant distribution. This talk will provide an overview of this line of research, joint work with John O'Leary, Yves Atchade and many others.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 03.11.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Darina Dvinskikh, WIAS Berlin:
Improved complexity bounds in Wasserstein barycenter problem
more ... Location
Online Event
Abstract
We focus on computational aspects of Wasserstein barycenter problem. We provide two algorithms to compute Wasserstein barycenter. The first algorithm, based on mirror prox with some specific norm, meets the complexity of celebrated accelerated iterative Bregman projections (IBP), however, with no limitations unlike (accelerated) IBP, that is numerically unstable when regularization parameter is small. The second algorithm, based on area-convexity and dual extrapolation, improves the previously best-known convergence rates for Wasserstein barycenter problem.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 03.11.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Lasse Ermoneit, TU Berlin:
Semiconductor passively mode-locked lasers subject to opto-electronic feedback
more ... Location
Online Event
Host
WIAS Berlin
- November 2 – 4, 2020 (WIAS-405-406)
- Workshop/Konferenz: Workshop on Stochastic Geometry and Communications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Thursday, 29.10.2020, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Emil Cortes André, Technical University of Denmark:
An analysis of collective effects in nanolasers using minimally extended rate equations
more ... Location
Online Event
Host
WIAS Berlin
- Tuesday, 27.10.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Carsten Hartmann, Brandenburgische Technische Universität Cottbus-Senftenberg:
Convergence to equilibrium in underdamped Langevin dynamics: Fluctuation-dissipation relations, entropy production and optimal control
more ... Location
Online Event
Abstract
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin system at small noise (or low temperature) that is characterised by metastability and slow convergence to equilibrium. We follow an approach proposed by Pavon and co-workers [1] and consider a Langevin equation that is simulated at a high temperature, with the control playing the role of a friction that balances the additional noise so as to restore the original invariant measure at a lower temperature. We discuss different limits as the temperature ratio goes to infinity and prove convergence to a limit dynamics. It turns out that, depending on whether the lower (“target”) or the higher (“simulation”) temperature is fixed, the controlled dynamics converges either to the overdamped Langevin equation or to a deterministic gradient flow. This implies that (a) the ergodic limit and the large temperature separation limit do not commute in general, and that (b) it is not possible to accelerate the speed of convergence to the ergodic limit by making the temperature separation larger and larger. We discuss the implications of these observation from the perspective of stochastic optimisation algorithms and enhanced sampling schemes in molecular dynamics. This is joint work with Tobias Breiten, Lara Neureither and Upanshu Sharma [2]. [1] Y. Chen, T.T. Georgiou and M. Pavon. Fast cooling for a system of stochastic oscillators. J. Math. Phys. 56:113302, 2015. [2] T. Breiten, C. Hartmann, L. Neureither and U. Sharma. Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach. Preprint, 2020.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 22.10.2020, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Thorsten Svend Rasmussen, Technical University of Denmark:
Multi-purpose modelling of semiconductor Fano lasers: Switching, feedback, and non-linear dynamics
more ... Location
Online Event
Host
WIAS Berlin
- Wednesday, 21.10.2020, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Michiel Renger:
Variational structures beyond gradient flows: a macroscopic-fluctuation-theory perspective joint work with Rob Patterson (WIAS) and Upanshu Sharma (FU Berlin)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Variational formulations in physics are often related to probability via large deviations. Although the idea goes back to Onsager, modern work shows that the large deviations of reversible Markov processes are related to gradient flows. The challenge of non-equilibrium thermodynamics is now to uncover meaningful variational structures for irreversible Markov processes. In that case one can not rule out the occurrence of non-equilibrium steady states, which are best studied by taken particle fluxes into account; this is the approach of “macroscopic fluctuation theory” (MFT). Most literature on MFT study quadratic rate functionals exclusively. These come with a natural concept of orthogonality that allows the decomposition of the flux rate functional into reversible and irreversible parts. We generalise beyond the quadratic case, which is for example relevant for chemical reactions, biological fitness models and epidemiology. As a byproduct we derive a connection to so-called “FIR” inequalities, and we find that the gap is quantified by a large-deviation rate functional of a rather curious process that should be considered `purely irreversible'. Disclaimer: this talk will hardly be about probability, but it will be about analysis of large-deviation rate functionals of Markov processes.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Thursday, 08.10.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Dr. Yiannis Hadjimichael, WIAS Berlin:
Numeral approximations for spatial-dependent SIR models
more ... Location
Online Event
Abstract
One of the first models used to describe epidemic propagation phenomena is the SIR model, introduced by Kermack and McKendrick in 1927. SIR models split the population into three classes: a group of species susceptible to infection, a compartment of the ill species, and a class of recovered species. In this talk, we consider a generalization of the original model in which the populations' size differs in space. The use of local spatial dependence transforms the SIR model to a system of integro-differential equations. We analyze the uniqueness and stability of the continuous model and suggest suitable numerical approximations that preserve the qualitative properties of the spatial-dependent SIR model. Furthermore, we provide sufficient step-size restrictions under which high order numerical schemes preserve the model's discrete properties (population conservation, positivity, and monotonicity). Finally, computational experiments verify the convergence and accuracy of the numerical methods.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 07.10.2020, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Tal Orenshtein:
Aging in the Edwards-Wilkinson and KPZ universality classes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Aging is an asymptotic property of non-equilibrium dynamical systems that captures non-trivial relaxation time temporal change; a canonical formulation is expressed in terms of the correlations of the system at two large times with a fixed relation. It was conjectured in Dembo-Deuschel '06 that one-dimensional KPZ models satisfy aging. In line with the progress on the one-time asymptotic behavior of KPZ in the past decade, this challenging problem gained attention in both the physics and the mathematical communities; there has been some experimental evidence for the phenomenon as well as related non-rigorous predictions and partial results. In the talk we shall see that for stationary systems one can use methods that rely solely on the variance asymptotics to achieve aging with an explicit aging function. We shall then derive aging for stationary models in the Edwards-Wilkinson universality class, which is easier to tackle. Moreover, we will demonstrate how to apply the methods to compute a formula for the space-time correlation scaling function in this case. In the remaining part of the talk we shall discuss aging for several stationary models in the KPZ class, including the KPZ fixed point, with the same aging function, matching the stationary KPZ equation prediction in Ferrari-Spohn '16. The talk is based on a recent work with Jean-Dominique Deuschel (TU Berlin) and Gregorio Moreno Flores (PUC Chile).
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Thursday, 01.10.2020, 16:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Dr. Mindaugas Radziunas, WIAS Berlin:
Simulation of cascaded polarization-coupled systems of broad-area semiconductor lasers
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/89804229771.
Host
WIAS Berlin
- Tuesday, 29.09.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Tobias Breiten, Technische Universität Berlin:
Optimal feedback control and minimum energy estimation by value function approximations
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Wednesday, 23.09.2020, 11:30 (WIAS-405-406)
- Seminar Interacting Random Systems
Benedikt Jahnel:
The free energy of a grid version of the Bose gas
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
A rigorous derivation of the famous Bose-Einstein condensation in terms of statistical mechanics is widely considered as one of the outstanding open problems in statistical physics.. Starting from a microscopic description of the system as a Gibbs measure of interacting particles in continuous finite volumes, the conjecture is that, in the thermodynamic limit and when the system is forced to have a large particle density, the particles become delocalized and macroscopic components begin to emerge, a condensation phenomenon. One way to make this observation is to consider a reformulation of the problem in terms of a variational formula for the free energy, a strategy which has been successful applied for the non-interacting case. In the talk, I will present a slightly simplified version of the model which allows us to derive the variational description in a way that includes the microscopic and macroscopic parts of the model using large-deviation theory. This is joint work with Wolfgang König.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 09.09.2020, 11:15 (WIAS-HVP-3.13)
- Seminar Interacting Random Systems
Heide Langhammer:
Large deviations and the phase transition for the connected components of an inhomogeneous random graph
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 09.09.2020, 10:30 (WIAS-HVP-3.13)
- Seminar Interacting Random Systems
Alexandra Quitmann:
Macroscopic cycles in the random loop model
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Thursday, 03.09.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Andrea Walther, HU Berlin:
Algorithmic differentiation: Sensitivties, adjoints and nonsmooth optimization
more ... Location
Online Event
Abstract
The provision of exact and consistent derivative information is important for numerous applications arising from optimization purposes as for example optimal control problems. However, even the pure simulation of complex systems may require the computation of derivative information. Implicit integration methods are prominent examples for this case.
The talk will present the technique of algorithmic (or automatic) differentiation (AD) to compute exact derivative information for function evaluations given as computer programs. This includes a short overview of the history of AD and a description of the main variants of AD, namely the forward mode to compute sensitivities as well as the reverse mode for the provision of adjoints. A discussion of complexity estimates follows yielding the important cheap gradient result. Subsequently, I will sketch briefly the usage of our AD tool ADOL-C. Finally, an extension of AD to compute generalized derivatives for nonsmooth optimization is discussed.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Tuesday, 01.09.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Franziska Bielert, Humboldt-Universität zu Berlin:
Estimation of quadratic functionals in a non-parametric regression model and gaussian white noise model
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Thursday, 23.07.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Dr. Zahra Lakdawala, WIAS Berlin:
Supervised and unsupervised learning frameworks for fluid mechanics
more ... Location
Online Event
Abstract
This talk presents an overview of current developments and the future of deep learning for fluid mechanics. The fundamental methodologies for supervised and unsupervised learning will be outlined and the use for understanding, modeling, optimizing and controlling fluid flows will be discussed. For example, how does one incorporate the Navier--Stokes equations or Darcy equations into a deep learning algorithm using neural networks and infer velocity and pressure fields? A framework will be presented where these networks can be integrated within any flow simulation algorithm. We will focus on understanding what a neural network is, how is it trained and how to solve forward and inverse problems where unknown solutions are approximated by a neural network (or a Gaussian process).
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Tuesday, 14.07.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Rico Berner, TU Berlin:
From coherence to incoherence: Stability islands in adaptive neuronal networks
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/83552703765.
Host
Freie Universität Berlin
WIAS Berlin
Technische Universität Berlin
- Tuesday, 07.07.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Maria Barbarossa, Frankfurt Institute of Advanced Studies:
Modeling and simulating the early dynamics of COVID-19 in Germany
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/83552703765.
Host
Freie Universität Berlin
WIAS Berlin
Technische Universität Berlin
- Tuesday, 07.07.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Paul Hager, Technische Universität Berlin:
Reinforced optimal control
more ... Location
Online Event
Abstract
We extend the reinforced regression methodology from optimal stopping problems to a general class of optimal control problems. The prevailing idea is the reinforcement of the set of basis functions based on previous regressions in the backwards induction steps. Moreover, we propose an efficient modification of the algorithm, which overcomes cost limitations for problems with a high number of possible exercise dates and a high number of possible control states.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 30.06.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Nicolas Perkowski, FU Berlin:
Infinite regularization by noise
more ... Location
Online Event
Abstract
It is a very classical yet still surprising result that noise can have a regularizing effect on differential equations. For example, adding a Brownian motion to an ODE with bounded and measurable vector field leads to a well posed equation with Lipschitz continuous flow. While the equation without noise may have none or many solutions. Classical proofs of such results are based on stochastic analysis and on the close link between the Brownian motion and the heat equation. In that derivation it is not obvious which property of the noise gives the regularization. A more recent approach by Catellier and Gubinelli leads to pathwise conditions under which regularization occurs. I will present a simplified version of their approach and use it to construct (very irregular) paths which are infinitely regularizing: after adding them to an ODE we have a unique solution and an infinitely smooth flow - even if the vector field is only a tempered distribution. This is joint work with Fabian Harang.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/83552703765.
Host
Freie Universität Berlin
Technische Universität Berlin
WIAS Berlin
- Thursday, 25.06.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Holger Stephan, WIAS Berlin:
An overview of Lyapunov functions for linear continuous and discrete problems including some new results
more ... Location
Online Event
Abstract
Lyapunov functions are useful for studying the time behaviour of the solution of evolutionary equations. The classical example is the L_2 norm, which decays on the solution of a diffusion equation with Neumann boundary conditions. The corresponding operator is an operator in divergent form, which forms a symmetric positive definite Dirichlet form. This concept can be generalized to arbitrary linear evolution equations with Markov generators. These equations are exactly those which preserve the type of physical quantities describing them: Intensive quantities (Banach space of continuous functions) are averaged, extensive quantities (Banach space of Radon measures) conserve their mass and sign. It turns out that for Markov generators with real spectrum, there is always a Hilbert space whose norm is a Lyapunov function and whose corresponding Dirichlet form is symmetric and positive. This generalizes the concept of detailed balance. An analogous result applies to the normality of operators with complex spectrum. This is a joint result with Artur Stephan from RG1. Furthermore, an infinite sequence of positive Lyapunov functions -- like energy, dissipation rate and so on -- can be defined recursively. This can be understood as a generalization of the well-known Bakry-Emery theory for diffusion type equations. In the lecture both the finite dimensional discrete case and the infinite dimensional continuous case are considered. Depending on which case is better suited for understanding the nature of the problem, we switch between them in an appropriate manner.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 24.06.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Thomas Eiter, WIAS Berlin:
Spatially asymptotic structure of time-periodic Navier--Stokes flows (online talk)
more ... Location
Online Event
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 24.06.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Ingo Steinwart, Universität Stuttgart:
Some thoughts and questions towards a statistical understanding of DNNs
more ... Location
Online Event
Abstract
So far, our statistical understanding of the learning mechanisms of deep neural networks (DNNs) is rather limited. Part of the reasons for this lack of understanding is the fact that in many cases the tools of classical statistical learning theory can no longer be applied. In this talk, I will present some thoughts and possible questions that may be relevant for a successful end-to-end analysis of DNNs. In particular, I will discuss the role of initialization, over-parameterization, global minima, and optimization procedures.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 23.06.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Sara Mazzonetto, Universität Potsdam:
Threshold Ornstein-Uhlenbeck model: Parameters estimation
more ... Location
Online Event
Abstract
A threshold Ornstein-Uhlenbeck is a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed value, yet at this threshold its coefficients can be discontinuous. We discuss (quasi)-maximum likelihood estimation of the drift parameters, both assuming continuous and discrete time observations. In the ergodic case, we derive consistency and speed of convergence in long time and high frequency of these estimators. Based on these results, we develop a test for the presence of a threshold in the dynamics. Finally, we apply these statistical tools to the short term US interest rates. The talk is based on a joint work with Paolo Pigato.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 17.06.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. François Bachoc, Université Paul Sabatier, Toulouse:
Valid confidence intervals post-model-selection
more ... Location
Online Event
Abstract
In this talk, I will first introduce the post-model-selection inference setting, that has recently been subject to intensive investigation. In the case of Gaussian linear regression, I will review the post-model-selection confidence intervals suggested by Berk et al (2013). These intervals are meant to cover model-dependent regression coefficients, that depend on the selected set of variables. I will present some personal contributions on an adaptation of these confidence intervals to the case where the targets of inference are linear predictors. Then, I will present an extension of these confidence intervals to non-Gaussian and non-linear settings. The suggested more general intervals will be supported by asymptotic results and numerical comparisons with other intervals recently suggested in the literature.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 16.06.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Sindre W. Haugland, TU München:
A hierarchy of symmetries: Coexistence patterns of four (and more) Stuart--Landau oscillators with nonlinear global coupling
more ... Location
Online Event
Abstract
The symmetry of a system of globally coupled identical units is high: For any solution, interchanging the behavior of any two elements still guarantees a solution. A full N! permutations are possible in total, either not changing the current solution or producing a mirror-image equivalent in phase space. Together, these N! permutations form a symmetry group with many subgroups. Thus, a large number of different partially symmetric solutions might in principle exist. Here, we study N=4 Stuart-Landau oscillators with a particularly intriguing form of global coupling. Its solutions indeed exhibit symmetries corresponding to many of the subgroups of the group of all permutations. Moreover, the transitions between these solutions, together with additional bifurcations more subtly influcencing the symmetry, form an intriguing interconnected hierarchy of differentiated oscillator dynamics. We will also take a brief look at how this hierarchy develops if the ensemble size is scaled up.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/83893529850.
Host
Freie Universität Berlin
Technische Universität Berlin
WIAS Berlin
- Tuesday, 16.06.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Valeriy Avanesov, WIAS Berlin:
Data-driven confidence bands for distributed nonparametric regression
more ... Location
Online Event
Abstract
Gaussian Process Regression and Kernel Ridge Regression are popular nonparametric regression approaches. Unfortunately, they suffer from high computational complexity rendering them inapplicable to the modern massive datasets. To that end a number of approximations have been suggested, some of them allowing for a distributed implementation. One of them is the divide and conquer approach, splitting the data into a number of partitions, obtaining the local estimates and finally averaging them. In this paper we suggest a novel computationally efficient fully data-driven algorithm, quantifying uncertainty of this method, yielding frequentist L_2- confidence bands. We rigorously demonstrate validity of the algorithm. Another contribution of the paper is a minimax-optimal high-probability bound for the averaged estimator, complementing and generalizing the known risk bounds.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Wednesday, 10.06.2020, 15:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. Jonathan Niles-Weed, New York University:
Minimax estimation of smooth densities in Wasserstein distance
more ... Location
Online Event
Abstract
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates for this problem for general Wasserstein distances, and show that, unlike classical nonparametric density estimation, these rates depend on whether the densities in question are bounded below. Motivated by variational problems involving the Wasserstein distance, we also show how to construct discretely supported measures, suitable for computational purposes, which achieve the minimax rates. Our main technical tool is an inequality giving a nearly tight dual characterization of the Wasserstein distances in terms of Besov norms. Joint work with Q. Berthet.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 09.06.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Peter Koltai, FU Berlin:
Reaction coordinates (order parameters) for metastable systems
more ... Location
Online Event
Abstract
We consider non-deterministic dynamical systems showing complex metastable behavior but no local separation in fast and slow coordinates. We raise the question whether and when such systems exhibit a low-dimensional parametrization supporting their effective statistical dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates (or order parameters), such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus less prone to the curse of dimension with respect to the state space of the dynamics than global methods. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as?but not only?molecular dynamics.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/84070311127.
Host
Freie Universität Berlin
WIAS Berlin
Technische Universität Berlin
- Tuesday, 09.06.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Rinaldo Mario Colombo, University of Brescia, Italien:
A hyperbolic-parabolic system to model and control parasites through parasitoids
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- June 8 – 10, 2020 (Online Event)
- Workshop/Konferenz: 13th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Online Event
Host
Technische Universität Berlin
WIAS Berlin
- Thursday, 04.06.2020, 11:00 (Online Event)
- Seminar Numerische Mathematik
Prof. Volker John, WIAS Berlin:
On the provable convergence order for the kinetic energy of FEMs for the incompressible Navier--Stokes equations
more ... Location
Online Event
Abstract
The kinetic energy of a flow is proportional to the square of the L2(Ω) norm of the velocity. Given a sufficient regular velocity field u and a velocity finite element space with polynomials of degree r, then the best approximation error in L2(Ω) is of order r+1. This talk will discuss which order of convergence for the kinetic energy can be proved with robust error estimates, i.e., with estimates where the constant does not depend on inverse powers of the viscosity. To fix ideas, the first part of the talk is devoted to evolutionary scalar convection-diffusion equations. In the second part, results for robust discretizations of the time-dependent incompressible Navier--Stokes equations will be surveyed. This survey covers as well inf-sup stable pairs of finite element spaces as pressure-stabilized discretizations.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 03.06.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Ingrid van Keilegom, KU Leuven:
On a semiparametric estimation method for AFT mixture cure models
more ... Location
Online Event
Abstract
When studying survival data in the presence of right censoring, it often happens that a certain proportion of the individuals under study do not experience the event of interest and are considered as cured. The mixture cure model is one of the common models that take this feature into account. It depends on a model for the conditional probability of being cured (called the incidence) and a model for the conditional survival function of the uncured individuals (called the latency). This work considers a logistic model for the incidence and a semiparametric accelerated failure time model for the latency part. The estimation of this model is obtained via the maximization of the semiparametric likelihood, in which the unknown error density is replaced by a kernel estimator based on the Kaplan-Meier estimator of the error distribution. Asymptotic theory for consistency and asymptotic normality of the parameter estimators is provided. Moreover, the proposed estimation method is compared with a method proposed by Lu (2010), which uses a kernel approach based on the EM algorithm to estimate the model parameters. Finally, the new method is applied to data coming from a cancer clinical trial.
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 02.06.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Sebastian Riedel, WIAS Berlin:
Runge-Kutta methods for rough differential equations
more ... Location
Online Event
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Thursday, 28.05.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Dr. Hang Si, WIAS Berlin:
Detri2, a 2D constrained Delaunay-Voronoi mesh generator
more ... Location
Online Event
Abstract
Detri2 is a C++ program to generate triangular meshes from arbitrary polygonal domains.It uses constrained Delaunay algorithms to conform the input line segments and maintain the locally Delaunay property of the mesh toplogy. It uses Delaunay refinement algorithms to generate meshes with good angle bounds. It can generate adaptive meshes corresponding to input mesh sizing functions. In this talk, I will give a brief tutorial of the basic functionalites of Detri2. I will demonstrate the aglorithms and many of the features of Detri2 using a graphic user interface - Detri2Qt. The source code of Detri2 and Detri2Qt are available at http://www.wias-berlin.de/people/si/detri2.html
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 27.05.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Martin Heida, WIAS Berlin:
Stochastic homogenization on randomly perforated domains (online talk)
more ... Location
Online Event
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 26.05.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Eckehard Schöll, TU Berlin:
Partial synchronization patterns in the brain
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/89795202774.
Host
Freie Universität Berlin
WIAS Berlin
Technische Universität Berlin
- Tuesday, 26.05.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
Analysis of 3D chromatin structure using Bures-Wasserstein distance
more ... Location
Online Event
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Wednesday, 20.05.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Chiara Amorino, Université d'Evry Paris-Saclay, France:
Invariant adaptive density estimation for ergodic SDE with jumps over anisotropic classes
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 19.05.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Priv.- Doz. Dr. John G. M. Schoenmakers, WIAS Berlin:
Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 19.05.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Robert Lasarzik, WIAS Berlin:
Dissipative solutions-or-a short crusade against weak solutions
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Thursday, 14.05.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Derk Frerichs, WIAS Berlin:
Basic concepts of virtual element methods and a really pressure-robust virtual element method for the Stokes problem
more ... Location
Online Event
Abstract
Virtual element methods (VEM) can be seen as a modern approach to extend finite element methods to polygonal and polyhedral meshes. This talk has two aims. First, basic ideas, concepts and advantages of VEM are presented using the well known Poisson problem. The second part concerns a VEM for the Stokes problem. For the Stokes problem exactly divergence-free VEM fail when it comes to small viscosity parameters or when the continuous pressure is complicated. In this talk a modification of the VEM is presented based on Raviart--Thomas approximations of the testfunctions which renders the method really pressure-robust, i.e. locking free for very small viscosities. The construction is also interesting for hybrid hyigh-order methods on polygonal or polyhedral meshes. Numerical results round up the theoretical findings.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Wednesday, 13.05.2020, 11:00 (Online Event)
- Seminar Interacting Random Systems
Sam Baguley, Universität Mannheim:
Perpetual Integrals for stable SDEs
more ... Location
Online Event
Abstract
The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and completely understood for many several decades. For stochastic differential equations with jumps the picture is different, and even the most basic questions are only partially understood. We study the question of existence and uniqueness of weak solutions to $$dZ_t=sigma(Z_t-)dint X_t$$ driven by $$alpha$$-stable Lévy processes.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/86368292467.
Host
WIAS Berlin
- Tuesday, 12.05.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Kostya Blyuss, University of Sussex, England:
Mathematical models of epidemics: Insight for control of COVID-19
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/89675974271.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 12.05.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. César A. Uribe, Massachusetts Institute of Technology:
Distributed inference for cooperative learning
more ... Location
Online Event
Abstract
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior density, and its relation to the stochastic mirror descent algorithm, to propose a new distributed learning algorithm. We show that, under appropriate assumptions, the beliefs generated by the proposed algorithm concentrate around the true parameter exponentially fast. We provide explicit non-asymptotic bounds for the convergence rate. Moreover, we develop explicit and computationally efficient algorithms for observation models belonging to exponential families.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 12.05.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Robert Gruhlke, WIAS Berlin:
Domain decomposition for random partial differential equations
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Thursday, 07.05.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Dilara Abdel, WIAS Berlin:
Comparison of modified Scharfetter-Gummel schemes for generalized drift-diffusion systems
more ... Location
Online Event
Abstract
The standard model for the description of semi-classical transport of free electrons and holes in a self-consistent electric field in a semiconductor device is the van Roosbroeck system of equations. For the discretization of this system Voronoi finite volume schemes based on different choices of flux approximations are considered. The classical Scharfetter--Gummel scheme yields a thermodynamically consistent numerical flux, but cannot be used for general charge carrier statistics. This talk aims to give an impression of the comparison and analysis of modified Scharfetter--Gummel schemes to simulate generalized drift-diffusion systems.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Thursday, 07.05.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Modelle der Photonik
Dr. Matthias Wolfrum, WIAS Berlin:
Temporal dissipative solitons in delay-differential equations
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/81751744679.
Host
WIAS Berlin
- Wednesday, 06.05.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Boris Zaltzman, Ben Gurion University of the Negev, Israel:
Equilibrium electro-convective instability in electrodeposition with Butler--Volmer kinetics (online talk)
more ... Location
Online Event
Abstract
Isaak Rubinstein and Boris Zaltzman. In this presentation we report that equilibrium electro-convective instability is possible in concentration polarization in the course of cathodic electrodeposition. The cathode is modelled as an ideally perm-selective interface with infinite lateral conductivity. The cation transfer across the cathode/solution interface is assumed to obey the Butler--Volmer kinetics with parameters typical of copper deposition. It is shown that deviation from the local reaction equilibrium due to the final deposition reaction rate renders possible the equilibrium electro-convective instability with a critical wavelength on the scale of diffusion layer width. This scaling may be recognized as a characteristic signature of equilibrium instability as opposed to the non-equilibrium one, related to the extended space charge. This latter instability, owning to its shortwave character, is characterized by origination of critical small vortices with a wavelength considerably shorter that the width of the diffusion layer. Interaction of these small scale vortices yields their fusion through which they evolve until reach a size comparable to the width of the diffusion layer.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 06.05.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Dr. Julia Schaumburg, VU Amsterdam, Netherlands:
Dynamic clustering of multivariate panel data
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 05.05.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Prof. Carlos Rocha, Instituto Superior Tecnico, Lisboa, Portugal:
Meanders, zero numbers and the cell structure of Sturm global attractors
more ... Location
Online Event
Abstract
We overview recent results on the geometric and combinatorial characterization of global attractors of semiflows generated by scalar semilinear partial parabolic differential equations under Neumann boundary conditions. This is joint work with B. Fiedler.
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/83594452457.
Host
GAMM (AG UQ)
WIAS Berlin
- Tuesday, 05.05.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Stochastic sewing with controls and skew fractional Brownian motion
more ... Location
Online Event
Abstract
I will explain how sewing with controls developed by Peter Friz & Huilin Zhang can be extended to the stochastic setup and show how this can be used to establish existence of skew fractional brownian motion and related SDEs with iregular drift.
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 05.05.2020, 14:00 (Online Event)
- Seminar Numerische Mathematik
Dr. Christian Merdon, WIAS Berlin:
A novel gradient-robust, well-balanced discretisation for the compressible Stokes problem
more ... Location
Online Event
Abstract
This talk suggests a novel well-balanced discretisation of the stationary compressible isothermal Stokes problem based on the concept of gradient-robustness. Gradient-robustness means that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient - if there is enough mass in the system to compensate the force. The scheme is provably convergent and asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust modified Bernardi--Raugel finite element method for the incompressible Stokes equations. All properties are demonstrated in numerical examples.
Further Informations
For zoom login details please contact Alexander Linke linke@wias-berlin.de
Host
WIAS Berlin
- Tuesday, 05.05.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Andreas Rathsfeld, WIAS Berlin:
Scatterometry and rough surfaces
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Wednesday, 29.04.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Boris Zaltzman, Ben-Gurion University of the Negev, Israel:
Orientation effects in hydrodynamic instability in concentration polarization (online talk)
more ... Location
Online Event
Abstract
Pramoda Kumar, Isaak Rubinstein and Boris Zaltzman. One dimensional steady state passage of the electric current from an aqueous electrolyte solution into a charge selective (perm-selective) solid, such as a metal electrode or ion exchange membrane, is hydro-dynamically unstable, [1]-[3]. For a long time this instability has been attributed to electro-convection related to the extended space charge which forms at the outer edge of the electric double layer at the limiting current, [4]-[10]. For the perfectly perm-selective solid with infinite conductivity this mechanism is the only possible one. Recently, it has been shown that for a non-perfectly perm-selective membrane, or for a perfectly perm-selective membrane with finite conductivity (commercial ion-exchange membranes are practically perfectly perm-selective), additional electro-convective instability mechanisms non-related to the extended space charge are possible, [11]-[13]. All of the afore mentioned studies focused on electro-convective instability mechanisms because it was recognized the gravitational mechanism could not yield instability for most practical situations (sub-millimeter electrolyte systems with concentration below one centimolar and without a forced stirring). In such systems, the passage of electric current results in formation of concentration variations near the perm-selective solid known as concentration polarization (CP). The expression of CP is a characteristic voltage current dependence with a current saturation at the limiting value (limiting current, corresponding to a nearly vanishing interface electrolyte concentration) followed by a current increase with voltage known as the over-limiting conductance regime. For some systems, transition to the over-limiting conductance is accompanied by the appearance of excessive electric noise. Commonly, over-limiting conductance sets on due to the mechanical stirring of the interface diffusion layer resulting from a hydrodynamic electroconvective instability of quiescent electric conduction. In relation to possible gravitational mechanisms, the CP-induced density stratification results both from direct concentration variation and its related non-uniform Joule heating.The temperature variations related to the latter usually do not exceed one degree Kelvin. As a result, for gravitationally unstable orientation with the depleted interface at the bottom, the Rayleigh number related to the thermally induced density stratification is usually smaller than that related to concentration variation, whereas the latter is lower than the Rayleigh--Benard instability threshold. For this reason, electro-convective mechanisms have been invoked to explain the instability, and no systematic study of the Joule heating effects in CP has been undertaken until recently (not long ago, the effect of density stratification related to concentration variation upon the electroconvective instability in CP has been addressed in Ref. [14]). Lately, this shortcoming has been remedied in the theoretical studies by Demekhin and his group, [15]. They discovered a very interesting possibility of a Joule heating related instability expected to occur for overall stable density stratification (depleted interface on the top). In this presentation we investigate this possibility both experimentally and theoretically. References 1. G. Yossifon and H. C. Chang, Phys. Rev. Lett.101, 254501 (2008). 2. S. M. Rubinstein, G. Manukyan, A. Staicu, I. Rubinstein, B. Zaltzman, R. G. H. Lammertink, F. Mugele, and M. Wessling, Phys. Rev. Lett. 101, 236101 (2008). 3. J.C. de Valenc, R. M.Wagterveld, R. G. H. Lammertink, and P.A.Tsai, Phys.Rev.E 92, 031003(R) (2015). 4. I. Rubinstein and L. Shtilman, J. Chem. Soc. Faraday Trans. II 75, 231 (1979). 5. A.V.Listovnichy, Elektrokhimia 25, 1651 (1989). 6. V. V. Nikonenko, V. I. Zabolotsky, and N. P. Gnusin, Sov. Electrochem. 25, 262 (1989). 7. I. Rubinstein and B. Zaltzman, Phys. Rev. E62, 2238 (2000). 8. I. Rubinstein and B. Zaltzman, Math. Mod. Meth. Appl. Sci. 11, 263 - 300 (2001). 9. B. Zaltzman and I. Rubinstein, J. Fluid Mech. 579, 173 (2007). 10. C.L.Druzgalski, M.B.Andersen,and A. Mani, Phys. Fluids 25, 110804 (2013). 11. I. Rubinstein and B. Zaltzman, Phys. Rev. Lett.114, 114502 (2015). 12. R. Abu-Rjal, I. Rubinstein, and B. Zaltzman, Phys. Rev. Fluids 1, 023601 (2016). 13. I. Rubinstein and B. Zaltzman, Phys.Rev. Fluids 2, 093702 (2017). 14. E. Karatay, M.B.Andersen, M.Wessling, and A. Mani, Phys. Rev. Lett.116, 194501 (2016). 15. E. A. Demekhin, S. Amiroudine, G. S. Ganchenko, and N. Y. Khasmatulina, Phys. Rev. E91, 063006 (2015).
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 29.04.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Thorsten Dickhaus, Universität Bremen:
How many null hypotheses are false?
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 28.04.2020, 15:15 (Online Event)
- Oberseminar Nonlinear Dynamics
Dr. Markus Kantner, WIAS Berlin:
Beyond just ,,flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions
more ... Location
Online Event
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 28.04.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Darina Dvinskikh, WIAS Berlin:
SA vs SAA for population Wasserstein barycenter calculation
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 28.04.2020, 10:15 (Online Event)
- Seminar Nichtlineare Optimierung und Inverse Probleme
David Sommer, WIAS Berlin:
A variable transformation for the Hamilton Jacobi Bellman equation
more ... Location
Online Event
Further Informations
Diesen Vortrag können Sie mit Zoom verfolgen unter: https://zoom.us/j/98493865627.
Host
WIAS Berlin
- Wednesday, 22.04.2020, 15:15 (Online Event)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Boris Zaltzman, Ben Gurion University of the Negev, Israel:
Artifact of “Breakthrough” osmosis or what may be wrong with local Spiegler--Kedem--Katchalsky equations with constant coefficients (online talk)
more ... Location
Online Event
Abstract
Isaak Rubinstein and Boris Zaltzman. Osmosis - solution (solvent) flow through non-perfectly (perfectly) semipermeable membranes - is a fundamental classical phenomenon of major practical importance. One of its potentially useful technological applications is the Pressure Retarded Osmosis employed for energy harvesting from salinity variations. In this process the flow resulting from the osmotic pressure drop between fresh and saline water is used to drive a turbine. Unfortunately, at the current stage, in spite of its extreme simplicity and conceptual beauty, this process does not appear to be practically viable due to insufficient power efficiency. This assessment could be radically changed by operating pressure retarded osmosis the recently theoretically predicted “Breakthrough” operation mode. In this mode, the solute concentration at the interface between the porous support and the dense selective barrier layer of a non-perfect (“leaky”) asymmetric membrane employed in process decreases with the increase of draw concentration, and, thus, the impeding effect of internal concentration polarization is eliminated. The existence of this mode was predicted based on the analysis of the system of classical local Spiegler--Kedem--Katchalsky equations of membrane transport in the barrier layer employing three constant coefficients: solute permeability, solute reflection coefficient and hydraulic permeability. In a still more recent study the physical feasibility of “Breakthrough” mode was contested and doubt was casted upon the suitability of Spiegler--Kedem--Katchalsky equations with constant coefficients for modeling of Pressure Retarded Osmosis. We re-derive the Spiegler--Kedem--Katchalsky equations based on a simple capillary friction model of membrane transport in the dense barrier layer and identify the problem with the constant coefficients' assumption resulting in the occurrence of “Breakthrough” mode. Our derivation recovers the Spiegler--Kedem--Katchalsky equations in the dilute solution limit, albeit with hydraulic permeability dependent on the local solute concentration in the barrier layer. Taking into account this dependence, necessary for preserving the detailed force balance in the barrier layer, eliminates the existence of the “Breakthrough” mode.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 22.04.2020, 10:00 (Online Event)
- Forschungsseminar Mathematische Statistik
Gabriel Peyré, Ecole Normale Supérieure Paris:
Scaling optimal transport for high dimensional learning
more ... Location
Online Event
Further Informations
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 21.04.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Nikita Zhivotovskiy, Google Research:
Fast classification rates in online and statistical learning with abstention
more ... Location
Online Event
Further Informations
Dieser Vortrag findet bei Zoom statt: http://zoom.us/j/492088715
Host
WIAS Berlin
- Tuesday, 21.04.2020, 14:00 (Online Event)
- Seminar Materialmodellierung/ Seminar Numerische Mathematik
Dr. Alfonso Caiazzo, WIAS Berlin:
Modeling of biological flows and tissues
more ... Location
Online Event
Abstract
The talk shows results of ongoing research in RG 3 related to modeling of blood flows and biological tissues. After a brief introduction on medical imaging techniques - especially magnetic resonance elastography - the first part of the talk wil discuss multiscale models for the simulation of vascularized tissues, using immersed methods. As next, we will introduce the equations and the challenges in computational hemodynamics, recent results and recently started collaborations.
Further Informations
For zoom login details please contact Dirk Peschka http://www.wias-berlin.de/ peschka/?lang=1
Host
WIAS Berlin
- Tuesday, 14.04.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexandra Suvorikova, WIAS Berlin:
On some general pricniples behind the results on the bootstrap validity in Bures-Wasserstein space
more ... Location
Online Event
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Tuesday, 14.04.2020, 11:00 (Online Event)
- Seminar Interacting Random Systems
Prof.Dr. Wolfgang König, WIAS Berlin:
Condensation in the interacting Bose gas in the semi-classical mean-field setting
more ... Location
Online Event
Further Informations
online seminar
Host
WIAS Berlin
- Tuesday, 07.04.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Bayesian inference for nonlinear inverse problems
more ... Location
Online Event
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Tuesday, 07.04.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Vladimir Spokoiny, WIAS Berlin:
Bayesian inference for nonlinear inverse problems
more ... Location
Online Event
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Tuesday, 31.03.2020, 15:00 (Online Event)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Karsten Tabelow, WIAS Berlin:
Model-based geometry reconstruction (MGBR) from TEM
more ... Location
Online Event
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Thursday, 12.03.2020, 13:00 (WIAS-406)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Olivier Huber, HU Berlin:
Topics in gas transport: Nash equilibrium and constrained exact boundary controllability
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
We present two results related to the transport of gas: the existence of a solution to a Generalized Nash Equilibrium Problem (GNEP) arising from the modeling of the gas market as an oligopoly, that is only the producers are players, and the consumers just react to the quantity of gas available. In a second part, the constrained exact boundary controllability of a semilinear hyperbolic PDE is investigated. The existence of an absolutely continuous solution and boundary control will be shown, under appropriate assumptions.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- March 12 – 13, 2020 (WIAS-ESH)
- Workshop/Konferenz: International Workshop: Uncertainty and Fluctuations in Thermodynamics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 05.03.2020, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Alexander Linke, WIAS Berlin:
Gradient-robustness: A new concept assuring accurate spatial discretizations for vector-valued PDEs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Vector-valued PDEs like the incompressible Navier--Stokes equations (in primitive variables velocity and pressure) describe the time evolution of a vector-valued quantity like the momentum density. For vector-valued PDEs it is quite natural to derive formally on the continuous level a derived time evolution of the vorticity and the divergence. Accordingly, any space discretization for a vector-valued PDE (implicitly) delivers a discrete vorticity and discrete divergence equation.
While the celebrated inf-sup stability will be shown to assure an accurate discrete divergence equation, the talk will actually focus on the question, which structural properties allow for an implicitly defined accurate discrete vorticity equation. The key observation is that the L^2-orthogonality of divergence-free vector fields and gradient fields is the weak equivalent to the vector calculus identity $nabla times nabla psi = mathbf0$ for arbitrary smooth scalar fields $psi$.
In the context of the incompressible Navier-Stokes equations, the concept of pressure-robustness was introduced in 2016, in order to discriminate between space discretizations with accurate and inaccurate discrete vorticity equations. H(div)-conforming finite element spaces have been found as an important means to realize the L^2-orthogonality between discretely divergence-free vector fields and (arbitrary) gradient fields. Further, it is shown that spatial discretizations that are not pressure-robust may suffer from i) a degradation of the (preasymptotic) convergence rate, and ii) large, parameter-dependent constants in error estimates. Typical flows that benefit from pressure-robustness are quasi-hydrostatic flows, quasi-geostrophic flows and vortex-dominated high Reynolds number flows.
Last but not least, the talk shows how to extend the concept of pressure-robustness to more general vector-valued PDEs, leading to the concept of gradient-robustness. Gradient robustness assures that dominant and extreme gradient fields in a vector-valued PDE will not lead to inaccuracies in the discretization. The talk will show examples from linear elasticity and compressible (Navier--)Stokes flows at low Mach numbers and in stratified flows. Thus, connections to well-balanced schemes and WENO schemes will be drawn.
Host
WIAS Berlin
- Thursday, 27.02.2020, 15:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Anton Stephan, Institut für Physik der Atmosphäre:
Modeling Navier--Stokes equations for high Reynolds number flows and complex geometries in aerodynamic applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The flight of an aircraft through a turbulent environment presents a difficult numerical problem. Though it can be easily described by the Navier-Stokes equations, it is impossible to perform a direct numerical simulation resolving all physically relevant scales. For several decades, numerous different models have been developed which perform very well for very specific problems. However, since the aircraft flight includes complex geometries as well as large spatial dimensions these models fail to capture all important features of the problem.
The vision of establishing a simulation system for virtual flight in a realistic environment is addressed by the coupling of two separate flow solvers in a bi-directional manner. This enables for example the simulation of a flight through gusts, trailing vortices and clear air turbulence, including the effects on the aircraft and the roll-up of trailing vortices and their further development until final decay. A compressible Reynolds-Averaged Navier-Stokes (RANS) solver resolves the near-field around an aircraft model. An incompressible Large-Eddy Simulation (LES) solver is used to model the atmosphere around the aircraft with its wake footprint in the LES domain. This hybrid simulation setup is used to investigate complex physical problems occurring in different flight scenarios.
Host
WIAS Berlin
- Thursday, 27.02.2020, 15:00 (WIAS-HVP-3.13)
- Seminar Laserdynamik
Maksymilian-Gregor Siwik, TU Berlin:
Calculation of Andronov--Hopf-Bifurcations of a PDE using the continuation and bifurcation software Auto-07P
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Host
WIAS Berlin
- Thursday, 27.02.2020, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Philip Lederer, TU Wien, Österreich:
Divergence-free tangential finite element methods for incompressible flows on surfaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this work we consider the numerical solution of incompressible flows on twodimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning H1-conformity allows us to construct finite elements which are -- due to an application of the Piola transformation -- exactly tangential. To reintroduce continuity (in a weak sense) we make use of (hybrid) discontinuous Galerkin techniques. To further improve this approach, H(div Γ)-conforming finite elements can be used to obtain exactly divergence-free velocity solutions. We present several new finite element discretizations. On a number of numerical examples we examine and compare their qualitative properties and accuracy.
Host
WIAS Berlin
- Thursday, 27.02.2020, 11:00 (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Axel Kröner, WIAS Berlin:
Optimal control of a semilinear heat equation subject to state and control constraints
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Tuesday, 25.02.2020, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Håkon Hoel, RWTH Aachen:
Multilevel ensemble Kalman filtering algorithms
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Host
WIAS Berlin
- Thursday, 20.02.2020, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Prof. Wolfgang Dreyer, WIAS Berlin:
Classical tests of electro-chemistry
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Volume changes, heat of dilution, osmosis, saturation pressure decrease and boiling temperature increase of electrolytes are classical phenomena that can be used to test and adjust parameter of electrochemical modeling. In this lecture we apply the electrolyte model developed at WIAS to these phenomena in order to critically examine the underlying assumptions. The observations require generalizations of the notions of incompressibility and surface tension.
Host
WIAS Berlin
- Tuesday, 18.02.2020, 13:30 (WIAS-ESH)
- Seminar Numerische Mathematik
Ondřej Pártl, WIAS Berlin:
Mathematical modeling of non-isothermal compositional compressible fluid flow in zeolite bed and above its surface
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
I will present a mathematical model and numerical scheme for the simulation of non-isothermal compositional compressible fluid flow in a heterogeneous porous medium and in the coupled atmospheric boundary layer above the surface of this porous medium, where one of the flowing components adsorbs on the porous matrix. I will discuss the application of this model to the simulation of the hydration of a zeolite bed.
My model is based on the two-domain approach, i.e., the domain in which the flow occurs is divided into the porous medium subdomain and the free flow subdomain. In each subdomain, the flow is described by the corresponding balance equations for mass, momentum and energy. On the interface between the subdomains, coupling conditions are prescribed.
In both subdomains, the spacial discretization of the governing equations is carried out via the finite volume method. For time integration, we use a special time stepping procedure.
Host
WIAS Berlin
- Thursday, 13.02.2020, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Gabriel R. Barrenechea, University of Strathclyde, Scotland:
Low-order divergence-free finite element methods
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk I will review results on a divergence-free reconstruction of the lowest order pair for the Navier-Stokes equation. More precisely, from a stabilised P1xP0 scheme, a divergence-free velocity field is built as the result of a lift of the pressure jumps, and it is then plugged in the convective term of the momentum equation. This process provides a method that can be proven stable without the need to suppose the mesh refined enough. We first apply this idea to the transient Navier-Stokes equations, where estimates independent of the viscosity are derived. Then, the applicability of this idea is extended to a steady-state generalised Boussinesq system.
Host
WIAS Berlin
- Wednesday, 12.02.2020, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Fredi Tröltzsch, Technische Universität Berlin:
Optimal and feedback control of some reaction-diffusion equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The optimal control of some systems of nonlinear reaction-diffusion equations is considered including the Nagumo and FitzHugh--Nagumo equations. These equations are known to develop traveling wave fronts, spiral waves or scroll rings as solutions. Well-posedness of the system, differentiability of the control-to-state mapping, and optimality conditions of first order are briefly sketched. In particular, the case of sparse optimal control is addressed. Moreover, the optimization of time-delays in local and nonlocal Pyragas type feedback control up to the control by measures is discussed. Various numerical examples illustrate the great diversity of geometrical patterns and their control.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 12.02.2020, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Alexandra Carpentier, Universität Magdeburg:
Adaptive inference and its relations to sequential decision making
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Adaptive inference - namely adaptive estimation and adaptive confidence statements - is particularly important in high of in nite dimensional models in statistics. Indeed whenever the dimension becomes high or infinite, it is important to adapt to the underlying structure of the problem. While adaptive estimation is often possible, it is often the case that adaptive and honest con dence sets do not exist. This is known as the adaptive inference paradox. And this has consequences in sequential decision making. In this talk, I will present some classical results of adaptive inference and discuss how they impact sequential decision making. (based on joint works with Andrea Locatelli, Matthias Loeffler, Olga Klopp and Richard Nickl)
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 11.02.2020, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Peter Szmolyan, Technische Universität Wien, Austria:
Advances in GSPT -- Teaching new tricks to an old dog
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Abstract
Due to the efforts of many people geometric singular perturbation theory (GSPT) has developed into a very successful branch of applied dynamical systems. GSPT has proven to be very useful in the analysis of an impressive collection of diverse problems from natural sciences, engineering and life sciences. Fenichel theory for normally hyperbolic critical manifolds combined with the blow-up method at non-hyperbolic points is often able to provide remarkably detailed insight into complicated dynamical phenomena, often even in a constructive way. Much of this work has been carried out in the framework of slow-fast systems in standard form, i.e. for systems with an a priori splitting into slow and fast variables. More recently GSPT turned out to be useful for systems for which the slow-fast structures and the resulting applicability of GSPT are somewhat hidden. Problems of this type include singularly perturbed systems in nonstandard form, problems depending singularly on more than one parameter and smooth systems limiting on non-smooth systems as a parameter tends to zero. Often several distinct scalings must be used to cover the dynamics of interest and matching of these different scaling regimes is carried out by the blow-up method.. In this talk I will survey these developments and highlight some ongoing activities.
Host
Freie Universität Berlin
WIAS Berlin
- Thursday, 06.02.2020, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Holger Stephan, WIAS Berlin:
A general concept of majorization and a corresponding Robin Hood method
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The Robin Hood method is a numerical method for constructing a double-stochastic matrix that maps a given vector to another vector that is also given. This is possible if the preimage majorizes the image. The majorization of vectors is a special order sometimes called the Lorentz order. A double-stochastic matrix is a special case of a Markov (or stochastic) matrix. In the case of a general Markov matrix, it is not yet clear when such a construction is possible, what kind of condition similar to the majorization must be fulfilled by the given vectors, nor is a numerical method for determining the matrix known (regardless some heuristic iterative versions of the Robin-Hood method).
In the talk, we give a complete solution to all these problems, including a general direct Robin Hood method. It turns out that the construction of a Markov matrix from two given pairs of two vectors is possible if and only if the pairs satisfy a certain order condition. If one interprets the vectors as states of a physical system, then this order is exactly the order known as the natural time order or the second law of thermodynamics.
Host
WIAS Berlin
- Wednesday, 05.02.2020, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Riccardo Cristoferi, Heriot-Watt University:
Epitaxial crystal growth with adatoms
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Surface diffusion is one of the most important mechanisms driving crystal growth. When bulk diffusion is much faster than the surface one, the evolution of the profile of the crystal is described by the so called Einstein--Nernst relation. According to this law, the normal velocity of the profile is related to the chemical potential. This evolution equation has a variational flavor, in that it can be obtained as a gradient flow of a suitable free energy. Albeit usually neglected, adatoms (atoms freely diffusing on the surface of the crystal) seem to play a fundamental role in the description of the behaviour of a solid-vapor interfaces. For this reason, some years ago Fried and Gurtin introduced a system of evolution equations to describe such a situation, where adatoms are treated as a separate variable of the problem. Also such system of evolution equations can be seen as the gradient flow of an energy. In this talk a first step in the programme of studying the above mentioned evolution equations from a variational point of view is presented. In particular, the focus is on the static problem in the small mass regime, where the elastic energy is negligible. Ground states, effective energy, and phase filed approximation suitable for numerical purposes are discussed. This latter is embedded in a general framework that allows to treat similar problems for a large class of functionals. The talk is based on works in collaboration with Marco Caroccia (Roma Tor Vergata), and Laurent Dietrich (Lycée Fabert).
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 05.02.2020, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Richard Pymar, Birkbeck University of London:
Mixing times of exclusion processes on regular graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Place k black particles and n-k white particles on the vertices of an n vertex graph, with one per vertex. Suppose each edge rings at rate 1 independently, and when an edge rings particles at the end-points switch positions. Oliveira conjectured that this "k-particle exclusion process" has mixing time of order at most that of k independent particles. Together with Jonathan Hermon we prove a bound for regular graphs which is in general within a log log n factor from this conjecture when k>n^c and which, in certain cases, verifies the conjecture. As a result we obtain new mixing time bounds for the exclusion process on expanders and the hypercube.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 05.02.2020, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Tim Sullivan, Freie Universität Berlin:
A rigorous theory of conditional mean embeddings
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Conditional mean embeddings (CME) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert spaces (RKHSs) by providing a linear-algebraic relation for the kernel mean embeddings of the respective probability distributions. Both centered and uncentered covariance operators have been used to define CMEs in the existing literature. In this talk, we develop a mathematically rigorous theory for both variants, discuss the merits and problems of either, and significantly weaken the conditions for applicability of CMEs. In the course of this, we demonstrate a beautiful connection to Gaussian conditioning in Hilbert spaces.
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Monday, 03.02.2020, 14:00 (WIAS-ESH)
- INSTITUTSKOLLOQUIUM
Prof. Dr.-Ing. Georg Duda, Charité Berlin, Julius Wolff Institute for Biomechanics and Musculoskeletal Regeneration:
From Mechanical Forces to Tissue Straining - How to Employ Biophysical Cues to Guide Regeneration
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Conceptually, our research aims at understanding endogenous cascades of tissue formation, cytokine signaling and cellular self-organization especially in bone. Mechanical straining and adaptation due to mechanical cues plays a central role in all these tissues. The aim of our work is to understand the mechano-biological cues of regeneration and adaptation and how they can be employed to enable healing even in tissues with impaired regenerative capacity such as muscle, cartilage or tendon. All approaches are motivated by clinical challenges, are based on in vivo patient measurements, employ basic research principles and aim at being translated into daily clinical routine. Examples of translation include innovative concepts for joint replacement procedures, angle stable fixation of implants or cell therapies for immune-modulation to empower tissue regeneration.
Further Informations
Presentation slides
Host
WIAS Berlin
- Wednesday, 29.01.2020, 10:00 (WIAS-405-406)
- Forschungsseminar Mathematische Statistik
Nadja Klein, Humboldt-Universität zu Berlin:
Bayesian regression copulas
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 28.01.2020, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Martin Brokate, TU München:
Sensitivity results for rate independent evolutions
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Abstract
Rate independent evolutions are evolutions whose solution operators commute with time transformations. They are inherently nonlinear and nonsmooth. We present some introduction, outlining various mathematical approaches as well as relations to other fields. We then address sensitivity, in particular the question whether the solution operators possess weak differentiability properties.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 28.01.2020, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Anastasia Ivanova, Moscow Institute of Physics and Technology (MIPT), Russische Föderation:
Optimization methods for resource allocation problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Further Informations
Forschungsseminar “Mathematische Statistik”
Host
WIAS Berlin
- January 28 – 30, 2020 (WIAS-ESH)
- Workshop/Konferenz: Workshop on PDE Constrained Optimization under Uncertainty and Mean Field Games
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Wednesday, 22.01.2020, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
The numerical range of Dirichlet forms
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 22.01.2020, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Jorge Mateu, Universitat Jaume I, Valencia, Spain:
Complex spatial and spatio-temporal point process dependencies: Linear ANOVA-type models, metrics and barycenters and predictive stochastic models of crime
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 21.01.2020, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr Pavel Dvurechensky, WIAS Berlin:
On the complexity of optimal transport problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Friday, 17.01.2020, 14:00 (WIAS-ESH)
- INSTITUTSKOLLOQUIUM
Prof. Stefan Heinrich, Universität Kaiserslautern, Germany:
Quantum computing for numerical problems - algorithms and complexity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
After a brief introduction into quantum computation we survey results on the speedup quantum algorithms can reach over classical (i.e. non-quantum) deterministic and randomized algorithms. We focus on basic numerical problems including integration, approximation and the solution of PDEs. We compare optimal convergence rates in the quantum setting with those in the deterministic and randomized classical setting. Upper bounds are obtained by suitable algorithms and their analysis, lower bounds by using the framework of information-based complexity theory.
Host
WIAS Berlin
- January 17, 2020 (WIAS-ESH)
- Workshop/Konferenz: Workshop on the occasion of the retirement of Peter Mathé
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Wednesday, 15.01.2020, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Marcel Fenzl, Universität Zürich, Schweiz:
Asymptotic results for stabilizing geometric statistics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Even though global in nature, many geometric statistics like the germ-grain model or the $k$-nearest neighbour model can be realized as a sum of local contributions. This idea can be formalized by using the concept of stabilizing score functions. In this talk, we investigate geometric statistics arising from such stabilizing score functions for randomly chosen input points. More specifically, we analyse the asymptotic behaviour of such a statistic for general point processes with fast decaying correlation functions.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 15.01.2020, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Sven Wang, University of Cambridge, UK:
Convergence rates for penalised least squares estimators in PDE-constrained regression problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 14.01.2020, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Frits Veerman, University of Heidelberg:
Toll roads and freeways: Defects in bilayer interfaces in the multi-component functionalised Cahn--Hilliard equation
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Abstract
We study a multi-component extension of the functionalised Cahn-Hilliard equation, which provides a framework for the formation of patterns in fluid systems with multiple amphiphilic molecules. The assumption of a length scale dichotomy between two amphiphilic molecules allows the application of geometric techniques for the analysis of patterns in singularly perturbed reaction-diffusion systems. For a generic two-component system, we show that solutions to the four-dimensional connection problem provide the leading order approximation for solutions to the full eight-dimensional barrier problem, which can be obtained through a perturbative expansion in the layer width. Moreover, we show that a saddle-node bifurcation of bilayer solutions in the four-dimensional connection problem acts as a source of so-called defect solutions, i.e. solutions to the barrier problem that are not also solutions to the connection problem. The analysis combines geometric singular perturbation theory with centre manifold theory in an infinite-dimensional context.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 14.01.2020, 15:00 (WIAS-ESH)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexander Gasnikov, Moscow Institute of Physics and Technology:
An overview of distributed optimization
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 09.01.2020, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Lia Strenge, Technische Universität Berlin:
A multilayer, multi-timescale model approach for economic and frequency control in power grids using Julia
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Power systems are subject to fundamental changes due to the increasing infeed of decentralized renewable energy sources and storage. The decentral nature of the new actors in the system requires new concepts for structuring the power grid, and achieving a wide range of control tasks ranging from seconds to days. Here we introduce a multilayer dynamical network model covering a wide range of control time scales. Crucially we combine a decentralized, self-organized low-level control and a smart grid layer of devices that can aggregate information from remote sources. The stability critical task of frequency control is performed by the former, the economic objective of demand matching dispatch by the latter. Having both aspects present in the same model allows us to study the interaction between the layers. Remarkably we find that adding communication in the form of aggregation does not improve the performance in the cases considered. Instead the self-organised state of the system already contains the information required to learn the demand structure in the entire power grid. The model introduced here is highly flexible, and can accommodate a wide range of scenarios relevant to future power grids. We expect that it will be especially useful in the context of low-energy microgrids with distributed generation. All simulations and numerical experiments for control design and analysis with sampling-based methods are performed in Julia 1.1.0. The overall model is implemented as stiff nonlinear ordinary differential equation (ODE) with periodic callbacks for the control actions. The ODE has dimension 4 N, where N is the number of edges of the graph representing the power grid (i.e., N feed-in/load connections). It is planned to use automatic differentiation to learn more about the overall nonlinear model.
Host
WIAS Berlin
- Wednesday, 08.01.2020, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michiel Renger, WIAS Berlin:
Fast reaction limits via Gamma-convergence of the flux rate functional
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We consider a system of linear ODEs on a finite graph with multiple time scales, and revisit the classical problem of deriving effective equations for the evolution. If solutions of the ODEs minimise an action functional, one can study Γ-convergence of that functional, and find the effective equations as the minimiser of the limit functional. In this work we use a natural action functional that is related to the large deviations of a random particle system; the value at each vertex can then be interpreted as a particle density. Our central idea is to study densities as well as particle fluxes through each edge. This additional information allows a full decomposition of the graph into separate components, which simplifies the Γ-convergence considerably.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 08.01.2020, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Dr. Dominik Liebl, Universität Bonn:
Fast and fair simultaneous confidence bands for functional parameters
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in Functional Data Analysis are underdeveloped compared to estimation and hypothesis testing. This work represents a major leap forward in this area by presenting a new methodology for constructing simultaneous confidence bands for functional parameter estimates. These bands possess a number of striking qualities: (1) they have a nearly closed-form expression, (2) they give nearly exact coverage, (3) they have a finite sample correction, (4) they do not require an estimate of the full covariance of the parameter estimate, and (5) they can be constructed adaptively according to a desired criteria. One option for choosing bands we find especially interesting is the concept of fair bands which allows us to do fair (or equitable) inference over subintervals and could be especially useful in longitudinal studies over long time scales. Our bands are constructed by integrating and extending tools from Random Field Theory, an area that has yet to overlap with Functional Data Analysis. Authors: Dominik Liebl (University Bonn) and Matthew Reimherr (Penn State University).
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Wednesday, 18.12.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Jürgen Sprekels, WIAS Berlin, Humboldt-Universität zu Berlin:
Optimal control of a Cahn--Hilliard--Darcy system with mass source modeling tumor growth
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Further Informations
Berliner Oberseminar “Nichtlineare partielle Differentialgleichungen”
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 18.12.2019, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Siragan Gailus, Hausdorff Institute for Mathematics/Boston University:
Homogenization of multiscale diffusion processes with small noise
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
Dynamical systems exhibiting multiple characteristic scales in space or time arise naturally as models in a great variety of applied fields. It is moreover common to incorporate random perturbations into these models in order to account for imperfect information or to capture random phenomena. We will discuss homogenization and fluctuations limit theorems for a model of diffusion type. Results on statistical inference will be introduced if time permits.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Monday, 16.12.2019, 14:00 (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
André Uschmajew, MPI Leipzig:
Optimization on low-rank manifolds
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Low-rank matrix and tensor models are important in many applications for representing and embedding high-dimensional data or functions. They typically lead to non-convex optimization problems on sets of matrices or tensors of given rank. In this talk, we give a basic introduction to the geometry of such sets and how it can be used to derive and study optimization algorithms. Compared to direct optimization of the factors in the model, the geometric approach is more intrinsic and can lead to improved methods. For a class of quadratic cost functions on matrices we also discuss how the geometric viewpoint is useful for studying the non-convex optimization landscape under low-rank constraints.
Further Informations
Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 12.12.2019, 16:00 (WIAS-ESH)
- Seminar Laserdynamik
Denis S. Goldobin, Perm State University, Russia:
Dynamics of oscillator populations beyond the Ott--Antonsen ansatz
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 12.12.2019, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Nancy Hitschfeld Kahler, Universdad de Chile, Santiago:
GPU computing and meshing
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
GPUs are an efficient and low cost alternative to CPU clusters for solving problems that are data-parallel or close to data parallel, but there are some restrictions in the current GPU hardware that must be taken into account in order to get efficient solutions. In this talk, fundamental concepts of GPU computing will be first introduced along with relevant techniques to make optimal use of GPU hardware, such as thread branching, coalesced memory, effective use of shared memory, thread mappings onto a triangular mesh, dynamic memory allocation, thread-safe exclusion mechanisms for neighboring triangles, and indeterminate decisions and traversals over the discrete graph structure of unstructured meshes. Then, an algorithm to transform any triangulation into a Delaunay triangulation and an implementation of a particle tracking algorithm that uses previous algorithm will be discussed. Finally, other relevant aspects to take into account such as gpu-mapping techniques and the ongoing work will be mentioned.
Host
WIAS Berlin
- Wednesday, 11.12.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Laura Lauerbach, Universität Würzburg:
Fracture and stochastic homogenization in the passage from discrete to continuous systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We consider a one dimensional particle system, interacting through nearest-neighbour Lennard--Jones potentials. The non-standard growth conditions and the convex-concave structure of the Lennard-Jones interactions allow for fracture. The interaction potentials are assumed to be randomly distributed. We study the variational limit in the framework of Γ-convergence of this chain of particles which leads to a homogenized energy density. Further, we rescale our model which results in a limiting energy of Griffith's type, consisting of an elastic part and a jump contributions. In a further approach, we study fracture at the level of the discrete energies. This is joint work with S. Neukamm (TU Dresden), M. Schäffner (Leipzig), A. Schlömerkemper (Würzburg).
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 11.12.2019, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Benjamin Lees, University of Bristol:
The phase transition for random loop models on trees
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
We show the existence of a sharp phase transition from non-existence to existence of infinite loops for a random loop model on d-regular trees, for all dimensions d ≥ 3. The loop model is built up by randomly placed 'crosses' and 'bars' whose relative intensity is controlled by a parameter u. We give a recursive scheme to obtain an expansion of the critical parameter in powers of 1/d, which in principle is explicit but whose combinatorial complexity grows very quickly. We were able to explicitly obtain the first 6 terms (the first two were previously found by Ueltschi and Bjornberg for the limit d → ∞), and observed that (as functions of u) they seem to have a very interesting structure. This is a joint work with Volker Betz and Johannes Ehlert.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Tuesday, 10.12.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Valeriy Avanesov, WIAS Berlin:
How to gamble with non-stationary X-armed bandits and have no regrets
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In X-armed bandit problem an agent sequentially interacts with environment which yields a reward based on the vector input the agent provides. The agent's goal is to maximise the sum of these rewards across some number of time steps. The problem and its variations have been a subject of numerous studies, suggesting sub-linear and sometimes optimal strategies. The given paper introduces a new variation of the problem. We consider an environment, which can abruptly change its behaviour an unknown number of times. To that end we propose a novel strategy and prove it attains sub-linear cumulative regret. Moreover, the obtained regret bound matches the best known bound for GP-UCB for a stationary case, and approaches the minimax lower bound in case of highly smooth relation between an action and the corresponding reward. The theoretical result is supported by experimental study.
Host
WIAS Berlin
- Wednesday, 04.12.2019, 10:00 (WIAS-405-406)
- Forschungsseminar Mathematische Statistik
Prof. Nils Bertschinger, Goethe Universität Frankfurt a. M.:
Systemic Greeks: Measuring risk in financial networks
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
Since the latest financial crisis, the idea of systemic risk has received considerable interest. In particular, contagion effects arising from cross-holdings between interconnected financial firms have been studied extensively. Drawing inspiration from the field of complex networks, these attempts are largely unaware of models and theories for credit risk of individual firms. Here, we note that recent network valuation models extend the seminal structural risk model of Merton (1974). Furthermore, we formally compute sensitivities to various risk factors -- commonly known as Greeks -- in a network context. In the end, we present some numerical illustrations and discuss possible implications for measuring systemic risk as well as insurance pricing.
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 03.12.2019, 13:30 (WIAS-406)
- Seminar Materialmodellierung
Prof. Michal Pavelka, Charles University, Prague, Tschechische Republik:
Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations within GENERIC
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Further Informations
Seminar Materialmodellierung
Host
WIAS Berlin
- December 3 – 5, 2019 (WIAS-ESH)
- Workshop/Konferenz: Workshop on Mathematics of Deep Learning
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 28.11.2019, 16:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Dr. Markus Kantner, WIAS Berlin:
Modeling of semiconductor devices: From quantum mechanics to non-equilibrium thermodynamics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Wednesday, 27.11.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Charles University Prague, Tschechische Republik:
Fully convective models of some processes in the Earth
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Devised towards geophysical applications for modeling of the solid Earth, a model of poro-elastodynamics with inelastic strains and with convection/diffusion of water will be formulated fully in the Eulerian setting. There, concepts of gradient of the total strain rate as well as the additive splitting of the total strain rate are used, eliminating the displacement from the formulation. It relies on that the elastic strain is small while the inelastic and the total strains can be large. The energetics behind this model is derived and used for analysis as far as the existence of global weak energy-conserving solutions concerns. In some aspects, it improves a model of V. Lyakhovsky at al. to make it thermodynamically consistent and amenable for analysis. Coupling with the fluidic parts of the Earth is also possible while using the concept of elastic (so-called semi-compressible) fluids. Also magnetic phenomena will be discussed both in the solid and the fluidic parts, i.e. paleomagnetism and Earth dynamo, respectively. The talk reflects a collaboration with Giuseppe Tomassetti (Univ. Roma Tre).
Further Informations
Berliner Oberseminar Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
Host
WIAS Berlin
Humboldt-Universität zu Berlin
- Wednesday, 27.11.2019, 14:00 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Johannes Zimmer, University of Bath, GB:
Regularisation and analysis of Dean--Kawasaki-type equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The Dean--Kawasaki-model consists of a nonlinear stochastic partial differential equation describing the evolution of the density function for a system of finitely many particles governed by Langevin dynamics. This equation is formally obtained, in a Schwartz distribution setting, on the hydrodynamic scale. As motivation for the study of this class of equations, we will show that the fluctuations they describe can, in the purely diffusive case, be linked to macroscopic diffusion operators of Wasserstein type. We then derive and analyse a suitably regularised Dean--Kawasaki-model for noninteracting particles obeying a second order Langevin equation, in one space dimension. We prove a high-probability result for the existence and uniqueness of mild solutions to this regularised Dean--Kawasaki-model. Extensions to the case of weakly interacting particles will also be described. This is joint work with Federico Cornalba and Tony Shardlow.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 27.11.2019, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Alain Celisse, University of Lille, France:
Kernelized change-points detection procedure
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 26.11.2019, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Jia-Yuan Dai, National Center for Theoretical Sciences, Taiwan:
Hyperbolicity of Ginzburg--Landau vortex solutions
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Abstract
We prove that each equilibrium of the Ginzburg-Landau equation restricted on the invariant subspace of vortex solutions is hyperbolic, that is, its associated linearization possesses nonzero eigenvalues. This result completely describes the global attractor of vortex solutions, and also yields the Ginzburg-Landau spiral waves of nodal type. This result is a joint work with Dr. Lappicy.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 26.11.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Franz Besold, WIAS Berlin:
Manifold clustering
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Thursday, 21.11.2019, 11:00 (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Jo Andrea Brüggemann, WIAS:
On the existence of solutions and solution methods for elliptic obstacle-type quasi-variational inequalities with volume constraints
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
In this talk, an elliptic obstacle-type quasi-variational inequality (QVI) with volume constraints is studied. This type of QVI is motivated by the reformulation of a compliant obstacle problem, where two elastic membranes are subject to external forces while enclosing a constant volume. The existence of solutions to this QVI is established building on fixed-point arguments and partly on the concept of Mosco-convergence. Since Mosco-convergence of the considered feasible sets usually requires complete continuity or compactness properties of the obstacle map, a two-fold approach is explored towards generalising the available existence results for the considered QVI. Based on the analytical findings, the solution of the QVI is approached by solving a sequence of variational inequalities (VIs). Each of these VIs is tackled in function space via a path-following semismooth Newton method. An a posteriori error estimator is derived towards enhancement of the algorithm's numerical performance by using adaptive finite element methods.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 20.11.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Antonius Frederik Maria ter Elst, The University of Auckland, Neuseeland:
The Dirichlet-to-Neumann operator on C 1+κ -domains
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We present some recent results on kernel bounds for the semigroup generated by the Dirichlet-to-Neumann operator when the underlying operator has Hölder continuous coefficients and the domain has a C 1+κ-boundary. The proof depends on Gaussian bounds for derivatives of the semigroup kernel of an elliptic operator with Dirichlet boundary conditions. As a consequence the Dirichlet-to-Neumann semigroup is holomorphic on the right half-plane on L¹. Moreover, it is also strongly continuous on the space of continuous functions on the boundary and holomorphic on the right half-plane.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 20.11.2019, 11:30 (WIAS-HVP-3.13)
- Seminar Interacting Random Systems
D. R. Michiel Renger:
Dynamical Phase Transitions on Finite Graphs
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstract
We consider systems where particles jump through edges of a finite graph with nonlinear intensities, and study time-averaged particle fluxes as both the number of particles and the end time go to infinity. The corresponding large-deviation rate functional involve a minimisation over trajectories with a given time-averaged flux. The minimisation can often be restricted to constant paths, resulting in a very simple expression for the rate functional. However, for specific models and specific regimes of the average flux, such expression overshoot the large-deviation rate functional, which typically happens if small oscillations in the trajectories are more profitable. In that case we say that a dynamical phase transition occurs. The literature on dynamical phase transition is almost exclusively restricted to models where the graph becomes continuous in the limit, yielding quadratic rate functionals. In our work we focus on graphs that remain discrete in the limit, which leads to entropic rate functionals. We present conditions that rule out dynamical phase transition, and for zero-range processes on a discrete ring, we give sufficient conditions under which a dynamical phase transition can be constructed. (Joint work with Davide Gabrielli, l'Aquila)
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 20.11.2019, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Nikita Zhivotowskii, Google Zürich, Switzerland:
Robust covariance estimation for vectors with bounded kurtosis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Let X be a centered random vector and assume that we want to estimate its covariance matrix. In this talk I will discuss the following result: if the random X satisfies the bounded kurtosis assumption, there is a covariance matrix estimator that given a sequence of n independent random vectors distributed according to X exhibits the optimal performance one would expect had X been a gaussian vector. The procedure also improves the current state-of-the-art regarding high probability bounds in the sub-gaussian case (sharp results were only known in expectation or with constant probability). In both scenarios the new bound does not depend explicitly on the dimension, but rather on the effective rank of the covariance matrix of X. The talk is based on the joint work with S. Mendelson "Robust covariance estimation under L4-L2 moment equivalence", to appear in AoS 2019.
Host
WIAS Berlin
Universität Potsdam
Humboldt-Universität zu Berlin
- Tuesday, 19.11.2019, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Ralf Toenjes, University of Potsdam:
The constructive role of noise in the dynamics on network hubs for network synchronization
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Abstract
We describe and analyze a coherence resonance phenomenon for synchronization in bipartite networks of well connected hubs and followers when the hubs are subjected to noise. Using the Ott-Antonsen ansatz for globally coupled phase oscillators the dynamics of the mean fields is described by a low-dimensional system of Langevin equations. Averaging over the fast stochastic dynamics of the hubs yields ordinary differential equations which predict the coherence resonance reasonably well.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 19.11.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Yangwen Sun, Humboldt-Universität zu Berlin:
Online change-point detection for high-dimensional data using graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 13.11.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michael Kniely, Institute of Science and Technology Austria (IST Austria) , Österreich:
On the large-time behavior of a class of semiconductor equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
This talk will be concerned with the exponential convergence to equilibrium of solutions to some semiconductor models arising from different modeling perspectives. The resulting PDE systems typically include drift-diffusion terms for electrons and holes as well as reaction terms describing the underlying electron-hole recombination mechanism. Including also the self-consistent electrostatic potential is often desired from a physical point of view. The main goal of the talk is the derivation of functional entropy-entropy dissipation inequalities in a constructive way for a set of semiconductor equations with and without potential and including different reaction processes. To this end, we will revisit nowadays classical calculations for prototype systems, and we shall also investigate more elaborate strategies necessary to deal with more complex models. Some parts of the talk are based on joint work with Klemens Fellner.
Further Informations
Berliner Oberseminar Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 13.11.2019, 10:00 (WIAS-405-406)
- Forschungsseminar Mathematische Statistik
Merle Behr, University of California, Berkeley:
Learning compositional structures
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 12.11.2019, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Prof. Dr. Nicolas Perkovski, Freie Universität Berlin:
From hopping particles to stochastic PDEs
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Abstract
I will try to give an overview of some of my research interests, focusing on certain a priori ill posed stochastic PDEs and their derivation. An important task in stochastics is to find and construct üniversal" models that describe a given phenomenon. For example, any random variable that is given by the superposition of many small independent influences is approximately Gaussian, independently of the concrete nature of the small influences, and therefore we call the Gaussian distribution universal. When trying to derive universal models for phenomena that evolve in space and time, formal calculations often suggest that we should consider nonlinear stochastic PDEs driven by space-time white noise. This is a problem because due to the irregularity of the noise the solution might be too irregular to make sense of the nonlinearities in the equation. But in recent years we found new ways of overcoming these problems, making sense of the equations, and proving their universality in some cases.
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 12.11.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Olga Krivorotko, Russian Academy of Sciences Novosibirsk:
Regularization of multi-parametric inverse problems for differential equations arising in immunology, epidemiology and economy
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Thursday, 07.11.2019, 14:00 (WIAS-405-406)
- Seminar Numerische Mathematik
Benoît Gaudeul, Université de Lille , Frankreich:
Some numerical schemes for a reduced case of a Nernst--Planck--Poisson model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
We compare several di erent numerical strategies to simulate a Nernst--Planck--Poisson model introduced in [1]. Different equivalent formulations are exploited based either on concentrations or activities [2]. As a first step, we focus on a simplified model for ionic liquid, for which four different schemes are discussed. A particular attention is given to the preservation at the discrete level of key features of the continuous problem, that are the positivity of the concentrations and the dissipation of the energy along time. The existence and convergence of a discrete solutions to the nonlinear system corresponding to each scheme is then established. Finally, numerical comparisons between the schemes are provided.
References
[1] Wolfgang Dreyer, Clemens Guhlke, and Rüdiger Müller. Overcoming the shortcomings of the Nernst--Planck model. Physical Chemistry Chemical Physics, 15, 2013.
[2] Jürgen Fuhrmann. Comparison and numerical treatment of generalised Nernst--Planck models. Computer Physics Communications, 6, 2015.
Host
WIAS Berlin
- November 6 – 8, 2019 (WIAS-ESH)
- Workshop/Konferenz: Foundations of Modern Statistics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
Humboldt-Universität zu Berlin
DFG Research Unit 1735
International Research Training Group 1792
- Wednesday, 06.11.2019, 11:30 (WIAS-HVP-3.13)
- Seminar Interacting Random Systems
Tal Orenshtein, WIAS:
Random walks in random environment as rough paths
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstract
Random walk in random environment (RWRE) is a model to describe propagation of heat or diffusion of matter through a highly irregular medium. The latter is expressed locally in the model in terms of a random environment according to which the process evolves randomly in time. In a few fundamental classes the phenomenon of homogenization of the media takes place. One way this can be expressed is in the fact that on large scales, the RWRE looks like a Brownian motion with a deterministic covariance matrix given in terms the (law of the) environment. Rough path theory enables the construction of solutions to SDEs so that the solution map is continuous with respect to the noise. One important application guarantees that if the approximation converges to the noise in the rough path topology, the SDEs driven by the noise approximations converge, in an appropriate sense, to a well-defined SDE different than the original one, so that the correction term is explicit in terms of the noise approximation. In this talk we shall present our current program, in which one lifts RWRE in various classes to the rough path space and shows a convergence to an enhanced Brownian motion in the rough path topology. Interestingly, the limiting second level of the lifted RWRE may have a linear correction, called area anomaly, which we identify. Except for the immediate application to approximations of SDEs (and potentially of SPDEs), this adds some new information on the RWRE limiting path. Time permitted, we shall elaborate on the tools to tackle these problems. Based on joint works with Olga Lopusanschi, with Jean-Dominique Deushcel and Nicolas Perkowski and with Johaness Bäumler, Noam Berger, and Martin Slowik.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Wednesday, 06.11.2019, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Charles Manski, North Western University, USA:
Patient care under uncertainty (Hermann Otto Hirschfeld Lecture 2019)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 05.11.2019, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Phillipo Lappicy, Universidade de Sao Paulo, FU Berlin:
Hořava--Lifshitz gravity: Bifurcations and chaos
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 05.11.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Roman Kravchenko, WIAS und HU Berlin:
Optimal transport for imaging
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Monday, 04.11.2019, 14:00 (WIAS-ESH)
- Seminar Numerische Mathematik
Dr. Christopher Rackauckas, Massachusetts Institute of Technology/University of Maryland, USA:
Neural differential equations as a basis for scientific machine learning
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Scientific Machine Learning (SciML) is an emerging discipline which merges the mechanistic models of science and engineering with non-mechanistic machine learning models to solve problems which were previously intractable. Recent results have showcased how methods like Physics Informed Neural Networks (PINNs) can be utilized as a data-efficient learning method, embedding the structure of physical laws as a prior into a learnable structures so that small data and neural networks can sufficiently predict phenomena. Additionally, deep learning embedded within backwards stochastic differential equations has been shown to be an effective tool for solving high-dimensional partial differential equations, like the Hamilton-Jacobian-Bellman equation with 1000 dimensions. In this talk we will introduce the audience to these methods and show how these diverse methods are all instantiations of a neural differential equation, a differential equation where all or part of the equation is described by a latent neural network. Once this is realized, we will show how a computational tool, DiffEqFlux.jl, is being optimized to allow for efficient training of a wide variety of neural differential equations, explaining how the performance properties of these equation differ from more traditional uses of differential equations and some of the early results of optimizing for this domain. The audience will leave knowing how neural differential equations and DiffEqFlux.jl may be a vital part of next-generation scientific tooling.
Host
WIAS Berlin
- Friday, 01.11.2019, 14:00 (WIAS-ESH)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Ana Djurdjevac, FU Berlin, Institut für Mathematik:
Random PDEs on moving hypersurfaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
It is well-known that in a variety of applications, especially in the biological modeling, PDEs that appear can be better formulated on evolving curved domains. Most of these equations contain various parameters and often there is a degree of uncertainty regarding the given data. We investigate the uncertainty which comes from unknown parameters or geometry. In the first part we study the advection-diffusion equation with random coefficients that is posed on an evolving hypersurface. We consider both cases, uniformly bounded and log-normal distributions of the coefficient. We introduce the solution space and prove the well-posedness using Banach - Nechas - Babushka theorem. Furthermore, we will introduce and analyse the evolving surface finite element discretization of the equation, introduced by Dziuk and Elliott. In the uniformly bounded case, we show unique solvability of the resulting semi-discrete problem and prove optimal error bounds for the semi-discrete solution and Monte Carlo of its expectation. In the second part we study PDEs that evolve with a given random velocity. Utilizing the domain mapping method, we transfer the problem into a PDE with random coefficients on a fixed domain and analyse this equation. Our theoretical convergence rates are confirmed by numerical experiments. This work is supported by DFG through project AA1-3 of MATH+
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Thursday, 31.10.2019, 16:00 (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik
Jan-Philipp Köster, Ferdinand-Braun-Institut Berlin:
Traveling wave model based simulation of tunable multi-wavelength diode laser and MOPA systems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 31.10.2019, 14:00 (WIAS-ESH)
- INSTITUTSKOLLOQUIUM
Prof. Max Gunzburger, Florida State University, USA:
Four “better” ways to solve the Navier--Stokes equations: Simulation of Richardson pair dispersion, ensemble discretization methods, an auxiliary equation approach for UQ, and filtered regularizations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
The facetious and self-serving title refers to four approaches for Navier-Stokes simulations. The first involves the analysis, numerical analysis, and an efficient implementation strategy for a recently proposed fractional Laplacian closure model that accounts for Richardson pair dispersion observed in turbulent flows. The second is the exploitation of accurate and widely applicable ensemble methods in settings in which multiple inputs need to be processed, as may be the case for uncertainty quantification, reduced-order modeling, and control and optimization. The third addresses the lack of regularity of solutions and the resultant loss of accuracy of approximations in the case of white or weakly correlated additive noise forcing. The fourth involves filtered spectral viscosity and hierarchical finite element methods for regularized Navier-Stokes equations.
Further Informations
Institutskolloquium
Host
WIAS Berlin
- Thursday, 31.10.2019, 10:15 (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. Grigor Nika, WIAS Berlin:
Optimal design of 3D-printed microarchitectured polymer materials exhibiting a negative Poisson's ratio
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Host
WIAS Berlin
- Wednesday, 30.10.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Katharina Hopf, WIAS Berlin:
On the singularity formation and relaxation to equilibrium in 1D Fokker--Planck model with superlinear drift
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 30.10.2019, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Dr. Niccolo Torri, Université Paris Nanterre, Frankreich:
Directed polymer in a heavy-tail random environment
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
A classical problem in the field of disordered systems is to understand the behaviour of a directed polymer in interaction with a random environment. Mathematically, the directed polymer is modeled by a directed random walk and the random environment is a sequence of random variables which can interact with the random walk perturbing its behaviour, giving rise to super-diffusive transversal fluctuations and localisation phenomena. Understanding the typical trajectories of the the walk is a very challenging issue and several results have been obtained when the random environment has exponential moments. In this talk we consider the case of a heavy-tail random environment, that is, the environment?s distribution function decades polynomially with exponent $alpha >0$. We mainly focus on the case in which the random environment has no second moment ($alphain (0,2)$), finding the super-diffusive transversal fluctuations of the polymer as function of the parameter $alpha$. Joint work with Quentin Berger (Sorbonne Université).
Further Informations
Seminar Interacting Random Suystems
Host
WIAS Berlin
- Tuesday, 29.10.2019, 15:15 (FU Berlin)
- Oberseminar Nonlinear Dynamics
Pavel Gurevich and Hannes Stuke, Freie Universität Berlin:
Reinforcement learning
more ... Location
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130
Host
Freie Universität Berlin
WIAS Berlin
- Tuesday, 29.10.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Tim Jahn, Universität Frankfurt am Main:
Beyond the Bakushinskii veto
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 23.10.2019, 14:00 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Ansgar Jüngel, Technische Universität Wien, Österreich:
Cross-diffusion systems: from spin semiconductors to biological populations with stochastic forcing
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
Many real-world applications consist of multiple components, leading on the macroscopic scale to cross-diffusion systems which consist of strongly coupled parabolic equations. The applications may be very diverse and range from spin-polarized transport in semiconductors and ion transport in cell membranes to population dynamics. In this talk, some existence results for global-in-time weak solutions is proved, based on entropy methods. This technique was already used by Herbert Gajewski, and we detail some of his ideas to prove the large-time behavior and uniqueness of weak solutions, followed by some extensions like boundedness-by-entropy and martingale solutions to stochastic cross-diffusion systems.
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 23.10.2019, 11:00 (WIAS-HVP-3.13)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Martin Holler, Universität Graz, Österreich:
A variational model for learning convolutional image atoms from incomplete data
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstract
Using lifting and relaxation strategies, we present a convex variational model for learning a convolutional sparse representation of image data via a few basic atoms. Such a representation provides a model for repeating patterns, but is also of interest for classification or as structural prior. We ensure well-posedness results for the proposed model in a general inverse problems setting and provide numerical experiments, where an atom-based representation is computed from incomplete, noisy and blurry data.
Further Informations
Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 23.10.2019, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Prof. Vladimir Spokoiny, WIAS Berlin, HU Berlin:
Bayesian inference for nonlinear inverse problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstract
We discuss the properties of the posterior for a wide class of statistical models including nonlinear generalised regression and deep neuronal networks, nonlinear inverse problems, nonparametric diffusion, error-in-operator and IV models. The new calming approach helps to treat all such problems in a unified manner and to obtain tight finite sample results about Gaussian approximation of the posterior with an explicit error bound in term of so called effective dimension.
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 22.10.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Oleg Butkovsky, WIAS Berlin:
Regularization by noise for SDEs and SPDEs with applications to numerical methods
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 16.10.2019, 15:15 (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Joachim Rehberg, WIAS Berlin:
Explicit and uniform estimates for second order divergence operators on Lp spaces
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
WIAS Berlin
- Wednesday, 16.10.2019, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Dr. Christian Mönch, Johannes-Gutenberg-Universität:
Universality of persistence exponents for self-similar processes with stationary increments
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
n 1999, G. Molchan showed that for a centered fractional Brownian motion X on the real line Prob[X(t) <1, 1 <t<T]=TH-1+o(1), where H is the index of self-similarity of X. Furthermore, he showed that the same tail exponent occurs for sevaral other path functionals of X and conjectured that it also governs the tail of Prob[L(t)<1, 1<t<T], where L is the local time at 0 of X, but was only able to prove a lower bound. In this talk, I present an entirely novel approach to persistence problems for self-similar processes with stationary increments based on Palm theory. The technique is not limited to Gaussian processes, allows us to resolve Molchan's conjecture for ANY H-self-similar process with stationary increments that admits a sufficiently smooth local time and provides a better error estimate even for the known lower bound of Prob[L(t)<1, 1<t<T] in the fractional Brownian case. Furhermore, I will discuss some work in progress concerning fractional variants of Brownian excursion-type processes.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
DFG Research Center MATHEON
- Wednesday, 16.10.2019, 10:00 (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Alexey Onatskiy, Cambridge University:
Cointegration the modern way
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Tuesday, 15.10.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Alexandra Suvorikova, Universität Potsdam:
Shape-based domain adaptation
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Host
WIAS Berlin
- Wednesday, 09.10.2019, 11:30 (WIAS-406)
- Seminar Interacting Random Systems
Dr. Lorenzo Taggi, WIAS:
Phase transition in random lattice permutations
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
We consider the model of random lattice permutations, whose realisations are permutations of the vertices of Z^d and can be viewed as a system of oriented self-avoiding loops interacting via mutual exclusion, with parameter beta (”inverse temperature”) which rewards the number ”jumps”. This model attracts interest from different perspectives: it is related to the interacting quantum Bose gas through a representation which is due to Feynman, it can be viewed as representation of the dimer model (when the inverse temperature is infinite) and it is a variant of loop O(N) models. A central question for all these models is whether a regime of ”macroscopic loops” and uniformly positive "two point correlations" occurs when the inverse temperature is large enough and d > 2. This talk presents the results and the proof techniques of a recent paper where a positive answer to this question is provided.
Further Informations
Seminar Interacting Random Systems
Host
WIAS Berlin
- Tuesday, 08.10.2019, 15:00 (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Alexander Gasnikov, Moscow Institute of Physics and Technology:
Introduction lecture in non convex optimization
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstract
In this talk we try to observe the modern numerical methods for non convex optimization problems. In particular, we concentrate on gradient type methods, high-order methods and randomization of sum type methods. Most of the results are taken from the papers that were published in the last 2-3 years.
Host
WIAS Berlin
- Monday, 07.10.2019, 14:00 (WIAS-ESH)
- Colloquium on the occasion of the 70th birthday of Dr. Johannes Elschner
Prof. Dr. Masahiro Yamamoto (University of Tokyo):
Inverse problems for first-order transport equations by Carleman estimatesProf. Dr. Guang-Hui Hu (Beijing Computational Science Research Center):
Corner scattering theory and data-driven inversion schemes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Host
WIAS Berlin
- Thursday, 26.09.2019, 15:00 (WIAS-406)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Prof. Dr. Martin Brokate, Technische Universität München:
Sensitivity in rate independent evolutions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstract
As a topic in science, rate independent evolutions have appeared more than 100 years ago; their study as a mathematical subject in its own began in the 1960's. We will present some basic issues and