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Monday, 27.06.2016, 14.00 Uhr (WIAS-ESH)
INSTITUTSKOLLOQUIUM
Prof. Dr. H. G. Matthies, TU Braunschweig, Institut für Wissenschaftliches Rechnen:
Probability, Analysis, and Numerics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract

Probability theory was axiomatically built on the concept of measure by A. Kolmogorov in the early 1930s, giving the probability measure and the related integral as primary objects and random variables, i.e. measurable functions, as secondary. Not long after Kolmogorov´s work, developments in operator algebras connected to quantum theory in the early 1940s lead to similar results in an approach where algebras of random variables and the expectation functional are the primary objects. Historically this picks up the view implicitly contained in the early probabilistic theory of the Bernoullis.

This algebraic approach allows extensions to more complicated concepts like non-commuting random variables and infinite dimensional function spaces, as it occurs e.g. in quantum field theory, random matrices, and tensor-valued random fields. It not only fully recovers the measure-theoretic approach, but can extend it considerably. For much practical and numerical work, which is often primarily concerned with random variables, expections, and conditioning, it offers an independent theoretical underpinning. In short words, it is "probability without measure theory".

This functional analytic setting has also strong connections to the spectral theory of linear operators, where analogies to integration are apparent if they are looked for. These links extend in a twofold way to the concept of weak distribution, which describes probability on infinite dimensional vector spaces. Here the random elements are represented by linear mappings, and factorisations of linear maps are intimately connected with representations and tensor products, as they appear in numerical approximations.

Taking this conceptual basis of vector spaces, algebras, linear functionals, and operators gives a fresh view on the concepts of expectation and conditioning, as it occurs in applications of Bayes´s theorem.

Host
WIAS Berlin
Tuesday, 28.06.2016, 10.15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
M. Piñeiro, University of Santiago de Compostela, Spanien:
MaxFEM: An open source software for numerical simulations in electromagnetism
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
MaxFEM is an open source software to numerically solve electromagnetic problems in the low-frequency regime by using the finite element method. The package brings together, under a single interface, different modules that can address problems in electrostatics, direct current, magnetostatics, transient magnetics and eddy currents, in two and/or three dimensions and in cartesian and/or cylindrical coordinates. MaxFEM also provides a powerful visualization tool to display the simulation results either in two or three dimensions.

MaxFEM users can perform internal changes to both the interface and the contained calculus programs in order to adapt the software to their needs. Moreover, thanks to the modular structure of the interface, it is possible to incorporate other models and even other types of simulations based on finite element techniques (e.g., thermal coupled electromagnetics). Under the GPL license, anyone can include its own application and redistribute the software.

MaxFEM was developed within the Research Group in Mathematical Engineering, Department of Applied Mathematics, University of Santiago de Compostela, in collaboration with the Supercomputing Center of Galicia (CESGA).

Host
WIAS Berlin

Tuesday, 28.06.2016, 13.30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. W. Huang, University of Kansas, USA:
A new implementation of the MMPDE moving mesh method and applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The MMPDE moving mesh method is a dynamic mesh adaptation method for use in the numerical solution of partial differential equations. It employs a partial differential equation (MMPDE) to move the mesh nodes continuously in time and orderly in space while adapting to evolving features in the solution of the underlying problem. The MMPDE is formulated as the gradient flow equation of a meshing functional that is typically designed based on geometric, physical, and/or accuracy considerations. In this talk, I will describe a new discretization of the MMPDE which gives the mesh velocities explicitly, analytically, and in a compact matrix form. The discretization leads to a simple, efficient, and robust implementation of the MMPDE method. In particular, it is guaranteed to produce nonsingular meshes. Some applications of the method will be discussed, including mesh smoothing (to improve mesh quality), generation of anisotropic polygonal meshes, and the numerical solution of the porous medium equation and the regularized long-wave equation.

Host
WIAS Berlin
Tuesday, 28.06.2016, 15.15 Uhr (WIAS-ESH)
Oberseminar Nonlinear Dynamics
M. Field, Imperial College London:
Functional asynchronous networks: Factorization of dynamics and function
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional asynchronous networks gives a description of dynamics and function in terms of properties of constituent subnetworks. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network and thereby answer a question originally raised by Alon in the context of biological networks: ?Ideally, we would like to understand the dynamics of the entire network based on the dynamics of the individual building blocks.? (page 27, An Introduction to Systems Biology, Uri Alon.)

Host
WIAS Berlin
Freie Universität Berlin
Tuesday, 28.06.2016, 16.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. A. Sapozhnikov, Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig .:
Geometric aspects of random walks on large tori
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
In this talk, we consider the fragmentation of a discrete d-dimensional torus (d>=3) by a simple random walk, a basic mathematical model for the gel degradation by an enzyme. We overview recent results and open problems about geometric properties of the random walk trace and its complement on relevant time scales.

Host
WIAS Berlin
Wednesday, 29.06.2016, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. É. Moulines, École Polytechnique, Palaiseau, Frankreich:
Stochastic optimization and high-dimensional sampling
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Recently, the problem of designing MCMC samplers adapted to high-dimensional Bayesian inference with sensible theoretical guarantees has received a lot of interest. The applications are numerous, including large-scale inference in machine learning, Bayesian nonparametrics, Bayesian inverse problem, aggregation of experts among others. When the density is L-smooth (the log-density is continuously differentiable and its derivative is Lipshitz), we will advocate the use of a -Y´rejection-free¡ algorithm, based on the discretization of the Euler diffusion with either constant or decreasing stepsizes. We will present several new results allowing convergence to stationarity under different conditions for the log-density (from the weakest, bounded oscillations on a compact set and super-exponential in the tails to the strong concavity). When the log-density is not smooth (a problem which typically appears when using sparsity inducing priors for example), we still suggest to use a Euler discretization but of the Moreau envelope of the non-smooth part of the log-density. An importance sampling correction may be later applied to correct the target. Several numerical illustrations will be presented to show that this algorithm (named MYULA) can be practically used in a high dimensional setting. Finally, non-asymptotic bounds convergence bounds (in total variation and Wasserstein distances) are derived.

Further Informations
Forschungsseminar ``Mathematische Statistik''

Host
Humboldt-Universität zu Berlin
SFB 649: Ökonomisches Risiko
Universität Potsdam
WIAS Berlin
Wednesday, 29.06.2016, 15.15 Uhr (WIAS-ESH)
BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
Dr. P.-E. Druet, WIAS Berlin:
Existence of weak solutions for improved Nernst-Planck-Poisson models of compressible reacting electrolytes
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 30.06.2016, 10.00 Uhr (WIAS-ESH)
Seminar Nichtglatte Variationsprobleme und Operatorgleichungen
Dr. A. Alphonse, University of Warwick:
Parabolic PDEs on evolving spaces and some applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 30.06.2016, 10.00 Uhr (WIAS-406)
Analysis-Stochastik-Seminar
Dr. R. I. A. Patterson, WIAS Berlin:
Jump Process Convergence II
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Analysis-Stochastik-Seminar

Host
WIAS Berlin
Thursday, 30.06.2016, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
S. Pickartz, WIAS Berlin:
Numerical optimisation of all-optical switching
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Tuesday, 05.07.2016, 10.15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. A. Mantile, Université de Reims, Frankreich:
Selfadjoint operators with boundary conditions on not closed hypersurfaces and the direct scattering problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of Schrödinger-type operators with linear boundary/interface conditions on (a relatively open part of) a compact hypersurface in nD. Our approach allows to obtain Krein-like resolvent formulae where the reference operator coincides with the free operator corresponding to our model, i.e.: the Schrödinger operator defined on regular functions without interface conditions. This provides an useful tool for the scattering problem from a hypersurface. Schatten-von Neumann estimates for the difference of the powers of resolvents (of the free and the perturbed models) yield the existence and completeness of the wave operators of the associated scattering systems, while a limiting absorption principle for singular perturbations allows us to obtain the generalized eigenfunctions and the scattering matrix; both these objects are written in terms of operator-valued Weyl functions.

This is a joint work with A. Posilicano and M. Sini

Host
WIAS Berlin

Tuesday, 05.07.2016, 16.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. J. Serra, WIAS Berlin:
American option pricing with Lévy diffusion: an introduction to nonlocal equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
In the last decade, there has been an explosion of papers studying nonlocal equations within the PDE community. Some of the main applied motivations come from mathematical finance. Many outstanding mathematicians have updated the old PDE tools, and developed new ones when necessary, in order to study in depth nonlinear elliptic and parabolic nonlocal equations. In this talk, I would like to present, from a very broad perspective, some recent results in collaboration with L. Caffarelli and X. Ros-Oton on the optimal regularity of the solutions and the regularity of the free boundaries (near regular points) for nonlocal obstacle problems. These problems arise in pricing of American options under non-Gaussian diffusion of the underlying stock price. The talk will be oriented to a broad audience with expertise and interest in modeling and not necessarily in regularity theory.. The previous research results will serve more as a context rather that being the main goal of the talk. I would like to introduce the basics on nonlocal equations, and to briefly explain its theoretical interest ---also discussing with the audience its applied interest. Last, I would like to discuss with the audience, in a very open way, what are the best current models (arising from data analysis) for option pricing. The true goal of the talk will be to raise the following (very ambitious perhaps) question: What is The Equation to be studied, now that we have very flexible methods?

Host
WIAS Berlin
Wednesday, 06.07.2016, 15.15 Uhr (WIAS-ESH)
BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
Prof. Dr. L. Pestov, Immanuel Kant Baltic Federal University, Kaliningrad/Russische Föderation:
On determining an absorption coefficient and a speed of sound in the wave equation by the boundary control method
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider the inverse multidimensional problem for the wave equation with unknown variable speed and absorption. A linear procedure based on the boundary control method for determining both coffcients is proposed.

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 07.07.2016, 10.00 Uhr (WIAS-ESH)
Seminar Laserdynamik
Dr. S. Bialonski, Max-Planck-Institut für Physik komplexer Systeme:
Predicting and preventing extreme events in a spatially extended excitable system
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Extreme events occur in many spatially extended systems and can threaten human life. Their reliable prediction and prevention is thus highly desirable. We study the prediction and prevention of extreme events in a spatially extended system, a network of FitzHugh-Nagumo units, in which events occur in a spatially and temporally irregular way. Despite being challenged by the rareness of events and without knowing the governing equations of motion, we can predict - with a data-driven method - the beginning, propagation, and termination of extreme events in this system remarkably well. We suppress extreme events via tiny and spatiotemporally localized perturbations which are guided by our predictions. We discuss how symmetries in the system could be exploited for better forecast performance.

Host
WIAS Berlin
Thursday, 07.07.2016, 10.00 Uhr (WIAS-406)
Analysis-Stochastik-Seminar
Dr. R. I. A. Patterson, WIAS Berlin:
Jump Process Convergence III
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Analysis-Stochastik-Seminar

Host
WIAS Berlin
Thursday, 07.07.2016, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
M. Kantner, WIAS Berlin:
Modeling and simulation of injection dynamics for quantum dot based single-photon sources
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Tuesday, 12.07.2016, 10.15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. M. Heinkenschloss, Rice University, USA:
A parallel-in-time gradient-type method for optimal control problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
A new parallel-in-time gradient type method for the solution of time dependent optimal control problems is introduced. Each iteration of the classical gradient method requires the solution of the forward-in-time state equation followed by the solution of the backward-in-time adjoint equation to compute the gradient. To introduce parallelism, the time steps are split into N groups corresponding to time subintervals. At the time subinterval boundaries state and adjoint information from the previous iteration is used. On each time subinterval the forward-in-time state equation is solved, the backward-in-time adjoint equation is solved, gradient-type information is generated, and the control are updated. These computations can be performed in parallel across time subintervals. State and adjoint information at time subinterval boundaries is then exchanged with neighboring subintervals and the process is repeated. Applied to a finite dimensional convex linear quadratic discrete time optimal control (DTOC) problem, this method can be interpreted as a so-called (2N-1)-part iteration scheme. Convergence of this new method applied to convex linear quadratic DTOC problems is proven for sufficiently small step sizes. Numerical examples on a 3D parabolic advection diffusion control problem and on a well rate optimization problem for a two-phase immiscible reservoir show good speed-up of the new method.

This is joint work with Xiaodi Deng.

Host
WIAS Berlin

Wednesday, 13.07.2016, 15.15 Uhr (WIAS-ESH)
BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
H. Meinlschmidt, Technische Universität Darmstadt:
The Keller-Segel model is well-posed
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
July 14 – 15, 2016 (WIAS-ESH)
Workshop/Konferenz: New Methods in Extension Theory applied to Quantum Mechanics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 14.07.2016, 10.00 Uhr (WIAS-406)
Analysis-Stochastik-Seminar
Dr. R. I. A. Patterson, WIAS Berlin:
Jump Process Convergence IV
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Analysis-Stochastik-Seminar

Host
WIAS Berlin
Thursday, 14.07.2016, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
M. Hofmann, WIAS Berlin:
Adiabatisches Floquet-Resonanz-Modell für die Licht-Materie-Wechselwirkung in Femtosekundenfilamenten
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Tuesday, 19.07.2016, 16.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
S. Boeckel, Humboldt-Universität zu Berlin:
High-dimensional nonparametric hypothesis testing using Monge-Kantorovich-depth
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
How to talk about quantiles, ranks and signs of a measure in R^d with d>1? Monge-Kantorovich-depth is a proposal for the generalization of these concepts to higher dimensions. It is proposed to evaluate the optimal transport map (wrt. to quadratic risk) of the measure into the uniform distribution of the unit ball. It can be shown, that these notions specialize to their usual counterparts in d=1 and for elliptic families and that it can be empirically evaluated. As an application it is proposed to test nonparametric hypothesis in a high-dimensional setting.

Host
WIAS Berlin
Wednesday, 20.07.2016, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. F. Bach, INRIA, Paris, Frankreich:
Beyond stochastic gradient descent for large-scale machine learning
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Many machine learning and statistics problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are O(1/sqrtn) for general convex functions and reaches O(1/n) for strongly-convex functions. In this talk, I will show how the smoothness of loss functions may be used to design novel simple algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-basedstochastic approximation algorithm leads to a convergence rate of O(1/n) without strong convexity assumptions. (joint work with Alexandre Defossez, Aymeric Dieuleveut, Nicolas Flammarion, and Eric Moulines)

Host
Humboldt-Universität zu Berlin
SFB 649: Ökonomisches Risiko
Universität Potsdam
WIAS Berlin
Wednesday, 20.07.2016, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. F. Bach, INRIA, Paris, Frankreich:
Beyond stochastic gradient descent for large-scale machine learning
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Many machine learning and statistics problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are O(1/sqrtn) for general convex functions and reaches O(1/n) for strongly-convex functions. In this talk, I will show how the smoothness of loss functions may be used to design novel simple algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-basedstochastic approximation algorithm leads to a convergence rate of O(1/n) without strong convexity assumptions. (joint work with Alexandre Defossez, Aymeric Dieuleveut, Nicolas Flammarion, and Eric Moulines)

Further Informations
Forschungsseminar ``Mathematische Statistik''

Host
Humboldt-Universität zu Berlin
SFB 649: Ökonomisches Risiko
Universität Potsdam
WIAS Berlin
July 25 – 29, 2016 (ZIB-SEM)
Workshop/Konferenz: Patterns of Dynamics
more ... Location
Zuse-Zentrum für Informationstechnik (ZIB), Takustr. 7, 14195 Berlin, Seminarraum

Host
Freie Universität Berlin
Technische Universität Berlin
WIAS Berlin
SFB 910 ``Control of self-organizing nonlinear systems: Theoretical methods and concepts of application''
Humboldt-Universität zu Berlin
August 12 – 15, 2016 (WIAS-ESH)
Workshop/Konferenz: 5th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
European Research Council
WIAS Berlin
September 8 – 9, 2016 (WIAS-ESH)
Workshop/Konferenz: 1st Leibniz MMS Mini Workshop on CFD & GFD
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin