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Thursday, 21.11.2019, 16:00 (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. Markus Kantner, WIAS Berlin:
t. b. a.
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Thursday, 21.11.2019, 11:00 (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Jo 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