# Upcoming Events

- Friday, 21.10.2016, 15.00 Uhr (WIAS-ESH)
- Seminar Nichtglatte Variationsprobleme und Operatorgleichungen

Dr. M. Holler, Karl-Franzens-Universität Graz, Österreich:

Higher order regularization and applications to medical image processing and data decompression

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Abstract**

Variational methods are a powerful tool for tackling ill-posed problems in image processing. As such, they rely heavily on appropriate regularization terms which render a stable recovery possible and strongly influence qualitative solution properties. In this talk, we consider regularization concepts for both static and dynamic data that are based on higher order differentiation. Beginning with the static setting, we first discuss analytical properties of Total Generalized Variation (TGV) regularization which allow for well-posedness results for standard inverse problems. We then consider the application of TGV in the context of a variational model for image decompression, being in particular applicable to JPEG or JPEG 2000 compressed images. As second application, we introduce a nuclear-norm-based vectorial TGV functional for joint MR-PET reconstruction that exploits structural similarities between the two modalities. Moving to the dynamic setting, we motivate and introduce a suitable extension of derivative based regularization for spatio-temporal data. After establishing essential analytical properties, we deal with applications to the reconstruction of highly subsampled dynamic MR data and the decompression of MPEG compressed movies.**Host**

WIAS Berlin

- Tuesday, 25.10.2016, 10.15 Uhr (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme

Dr. W. Iff, Université Jean Monnet, Frankreich:

Rigorous and extremely fast electromagnetic methods for diffraction problems

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)**Host**

WIAS Berlin

- Tuesday, 25.10.2016, 15.00 Uhr (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

V. Avanesov, WIAS Berlin:

Bootstrap for high-dimentional online multiscale covariance matrix change-point detection

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)**Abstract**

During this talk I will present a novel approach (arXiv:1610.03783 [math.ST]) for an important problem of change point detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which has applications in biostatistics and econometrics. The developed approach is essentially a significance testing procedure requiring a proper choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. The idea of the proof and the simulation study will be discussed as well.**Host**

WIAS Berlin

- Wednesday, 26.10.2016, 15.15 Uhr (WIAS-ESH)
- BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)

Prof. Dr. A. Mielke, WIAS Berlin:

Global entropy entropy-production estimates for energy-reaction-diffusion systems

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

- October 27 – 28, 2016 (WIAS-ESH)
- Workshop/Konferenz: Kick-off Meeting of the DFG Priority Programme 1962

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Host**

DFG Schwerpunktprogramm 1962

WIAS Berlin

- Tuesday, 01.11.2016, 15.00 Uhr (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

Dr. P. Dvurechensky, WIAS Berlin:

Numerical aspects of Wasserstein distance, Wasserstein barycenters, and Hellinger-Kantorovich distance

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)**Abstract**

In this talk, we will consider Wasserstein and Hellinger-Kantorovich distances. The definitions of these distances are based on specific optimization problems. The goal of the talk is to present new numerical methods for solution of these optimization problems.**Host**

WIAS Berlin

- Wednesday, 02.11.2016, 10.00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik

O. Klopp, Universtité Paris-Ouest Nanterre:

Network models and sparse graphon estimation

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Abstract**

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical es- timation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network and derive optimal rates of convergence for this problem. Our results cover the important setting of sparse networks. We also establish upper bounds on the mini- max risk for graphon estimation when the probability matrix is sampled according to a graphon model. The problem of estimation of the matrix of connection probabilities of a network can be viewed as a particular case of a general matrix sequence model. In this model, we observe the noisy entries of a matrix and assume that the signal matrix is ßtructured", that is, it can be factorized using sparse factors. This model includes a number of interesting problems such as the mixture of Gaussian, sparse dictionary learning, stochastic block models and mixture membership models. In the second part of the talk, I will consider the problem of statistical estimation of the signal matrix for this model and derive optimal rates of estimation. Keywords. Inhomogeneous random graph; Networks; Oracle inequality; Sparse graphon.**Host**

SFB 649: Ökonomisches Risiko

Universität Potsdam

Humboldt-Universität zu Berlin

WIAS Berlin

- Wednesday, 09.11.2016, 14.00 Uhr (WIAS-ESH)
- INSTITUTSKOLLOQUIUM

Prof. Dr. M. Kohlhase, Friedrich-Alexander-Universität Erlangen/Nürnberg, Germany:

FrameIT: From Serious Games to Modeling and Applying Mathematical Models

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Abstract**

Mathematical modeling is the key tool that drives modern science, technology engineering, and medicine (STEM). It comprises data about the respective situations & phenomena and models (e.g. differential equations) that allow to draw inferences and make predictions from the data.

STEM data has seen a lot of attention to support its collection, storage, curation, and presentation by computers, and large public and private data repositories have been established. The models themselves have largely remained in the pen-and-paper world of mathematics, and have been transformed into programs on a case-by-case basis. In particular, the question on how to model the models declaratively for computer support is largely unresolved, and as a consequence we do not have collections of models as a resource.

In this talk we will present the knowledge-based FrameIT method, which represents mathematical models and the knowledge backing it in a theory graph whose nodes (theories) are logic-based representations of the mathematical objects, their assumptions, and properties and whose edges (theory morphisms) are meaning-preserving mappings. The critical realization utilized by the FrameIT method is that the application of a mathematical model can be represented as an extension of the model theory graph by special theories representing the situation and phenomena and that the application mapping naturally becomes a theory morphism. This gives an abstract framework for modelling mathematical modelling and makes the models into represented objects that can be collected, curated, presented, and reused.

The FrameIT method has been implemented and tested in the context of serious games for mathematics. We will present that work in the talk and discuss how the very simple models (highschool math) used there can be scaled to realistic models in the STEM fields. We also discuss the OMDoc/MMT infrastructure for collection, storage, curation, and presentation of theory graphs and how this can serve as a basis for a repository of mathematical models.**Host**

WIAS Berlin

- Thursday, 10.11.2016, 16.00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Modelle der Photonik

Prof. R. Čiegis, Vilnius Gediminas Technical University, Litauen:

On stability analysis of some non-classical schemes for the Schrodinger equation

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Abstract**

In this talk we consider the stability and efficiency of numerical algorithms for the solution of the Schrodinger problem and some modifications of this equation. The first problem deals with local approximations of the exact nonlocal transparent boundary conditions. The family of rational functions is investigated and optimal values of coefficients are computed by solving global optimization problems with different objective functions. In the second part, the 1D Schrodinger problem is approximated by Numerov's type finite difference scheme but non-uniform meshes are used. The obtained finite difference scheme is non-conservative and the spectral stability analysis is done in order to show that the non-classical restriction $h_x <= C h_t$ is required to regularize the scheme and to prove $rho$-stability estimates. In the last part, some parallel numerical algorithms are analyzed for efficient computation of fractional powers of elliptic type operators.**Host**

Humboldt-Universität zu Berlin

WIAS Berlin

- November 14 – 16, 2016 (WIAS-ESH)
- Workshop/Konferenz: Probabilistic Methods in Telecommunication

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Host**

WIAS Berlin

- Tuesday, 15.11.2016, 10.15 Uhr (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme

Dr. K. Sturm, RICAM, Linz, Österreich:

Convergence of Newon's method in shape optimisation

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)**Host**

WIAS Berlin

- Wednesday, 16.11.2016, 10.00 Uhr (WIAS-HVP-4.13)
- Forschungsseminar Mathematische Statistik

Prof. Th. Dickhaus, Universität Bremen:

Statistical properties of Bernstein copulae with applications in multiple testing

more ...**Location**

Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 4. Etage, Raum: 4.13**Abstract**

A general way to estimate continuous functions consists of approximations by means of Bernstein polynomials. Sancetta and Satchell (2004) proposed to apply this technique to the problem of approximating copula functions. The resulting so-called Bernstein copulae are nonparametric copula estimates with some desirable mathematical features like smoothness. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family-wise error rate (FWER) of simultaneous test procedures which are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. This extends a similar approach by Stange, Bodnar and Dickhaus (2015) in the parametric case. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power which can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or the Sidak correction. Finally, we demonstrate an application of the proposed methodology to real-life data from insurance. (joint work with André Neumann, Taras Bodnar and Dietmar Pfeifer)**Further Informations**

Forschungsseminar ``Mathematische Statistik''**Host**

WIAS Berlin

Universität Potsdam

SFB 649: Ökonomisches Risiko

Humboldt-Universität zu Berlin

- Thursday, 17.11.2016, 14.00 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik

Prof. J. Novo, Universidad Autónoma de Madrid, Spain:

Non inf-sup stable mixed finite element approximations to the evolutionary Stokes equations

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Abstract**

In the first part of the talk we will consider the pressure stabilized Petrov Galerkin (PSPG) method in space to approximate the evolutionary Stokes equations with non inf-sup stable mixed finite elements. The analytical results are based on an appropriate approach for computing the initial velocity, which we suggest. We clarify the so called instability of the discrete pressure for small time steps reported in the literature and show that this instability does not occur for our proposed initial condition. In the second part of the talk we study the approximation of the same equations by means of a projection scheme with non inf-sup stable mixed finite elements. The projection scheme we propose has a stability parameter analogous to the stability parameter of the PSPG method. As a consequence of our analysis we prove the pressure stability of the Chorin--Temam method for non inf-sup stable elements. This property was known in the literature but to our knowledge had not yet been proved.**Host**

WIAS Berlin

- Thursday, 17.11.2016, 15.15 Uhr (WIAS-ESH)
- Seminar Numerische Mathematik

Dr. S. Weißer, Universität des Saarlandes:

Convection-adapted BEM-based finite element method on tetrahedral and polyhedral meshes

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Abstract**

A new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D is presented that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements, see [1]. The element stiffness matrices are constructed by means of local boundary element techniques. The method, which is referred to as a BEM-based FEM, can therefore be considered a local Trefftz method with element-wise (locally) PDE-harmonic shape functions. The current research combines the results of [2] with the hierarchical construction of shape functions presented in [3]. The Dirichlet boundary data for these shape functions is chosen according to a convection-adapted procedure which solves projections of the PDE onto the edges and faces of tetrahedral and polyhedral elements, respectively. This improves the stability of the discretization method for convection-dominated problems both when compared to a standard FEM and to previous BEM-based FEM approaches, as we demonstrated in several numerical experiments. Our experiments also show an improved resolution of the exponential layer at the outflow boundary for our proposed method when compared to the SUPG method.

[1] C. Hofreither, U. Langer and S. Weißer. Convection-adapted BEM-based FEM. Z. Angew. Math. Mech. doi:10.1002/zamm.201500042 (2016).

[2] C. Hofreither, U. Langer and C. Pechstein. A non-standard finite element method for convection-diffusion-reaction problems on polyhedral meshes. AIP Conference Proceedings 1404(1):397404 (2011).

[3] S. Rjasanow and S. Weier. FEM with Trefftz trial functions on polyhedral elements. J. Comput. Appl. Math. 263:202217 (2014).**Host**

WIAS Berlin

- Monday, 28.11.2016, 10.00 Uhr (WIAS-ESH)
- INSTITUTSKOLLOQUIUM

Dr. F. Hildebrand, Robert Bosch GmbH, Germany:

Technological challenges and chances of Li-metal solid state batteries

more ...**Location**

Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal**Host**

WIAS Berlin