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Tuesday, 20.06.2017, 10.15 Uhr (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. U. Römer, Technische Universität Darmstadt:
Stochastic collocation with adjoint error control for uncertainty quantification in computational electromagnetics
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 20.06.2017, 10.45 Uhr (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
D. Loukrezis, Technische Universität Darmstadt:
Low-rank tensor decompositions for high-dimensional uncertainty quantification in electromagnetic field problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Wednesday, 21.06.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. D. Chetverikov, University of California, Los Angeles, USA:
On cross-validated lasso
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this paper, we derive a rate of convergence of the Lasso estimator when the penalty parameter $lambda$ for the estimator is chosen using $K$-fold cross-validation; in particular, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of $lambda$, the prediction norm of the estimation error of the cross-validated Lasso estimator is with high probability bounded from above up to a constant by $(slog p /n)^1/2cdot log^7/8(p n)$, where $n$ is the sample size of available data, $p$ is the number of covariates, and $s$ is the number of non-zero coefficients in the model. Thus, the cross-validated Lasso estimator achieves the fastest possible rate of convergence up to a small logarithmic factor $log^7/8(p n)$. In addition, we derive a sparsity bound for the cross-validated Lasso estimator; in particular, we show that under the same conditions as above, the number of non-zero coefficients of the estimator is with high probability bounded from above up to a constant by $slog^5(p n)$. Finally, we show that our proof technique generates non-trivial bounds on the prediction norm of the estimation error of the cross-validated Lasso estimator even if the assumption of the Gaussian noise fails; in particular, the prediction norm of the estimation error is with high-probability bounded from above up to a constant by $(slog^2(p n)/n)^1/4$ under mild regularity conditions.(The authors are Denis Chetverikov, Zhipeng Liao, and Victor Chernozhukov.)

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Wednesday, 21.06.2017, 15.15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. J. Prüß, Martin-Luther-Universität Halle-Wittenberg:
Critical spaces for quasilinear evolution equations and applications
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In the last decades, considerable effort in pde's has been put into finding the most general spaces of Initial data such that a given nonlinear pde is well-posed. So far, this has been achieved with case studies, each equation has ist own theory. Moreover, the available proofs in the literature are usually arkwardly involved, sometimes going even into the miscroscopic theory of the relevant spaces, in most cases Besov spaces. In my talk, I present an abstract approach in the framework of parabolic evolution equations relying on maximal Lp-regularity in time weighted Lp-spaces. This approach easily recovers many known results in applications, for example for the Navier-Stokes equation, the Keller-Segal equations, quasi-geostrophic equations, and many others, but also leads in a direct, smooth way to new results, e.g. for the vorticity equations.

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

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Wednesday, 21.06.2017, 15.30 Uhr (WIAS-HVP-4.13)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
M. Bongini, Barcelona Graduate School of Economics:
Optimal Control Problems in Transport Dynamics
more ... Location
Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 4. Etage, Raum: 4.13

Abstract
In this talk we shall discuss several results concerning the "indirect control of populations", i.e., how to influence a group of individuals by means of external agents with a directly controlled dynamics. By using the general theory of functionals defined on spaces of measures, we give sufficient conditions for the existence of optimal control strategies and then we present a Pontryagin Maximum Principle for such controls in the form of an Hamiltonian flow in the Wasserstein space of probability measure. Finally, we present an application of the above framework to the evacuation problem of a crowd from an unknown environment with the help of undercover stewards.

Host
WIAS Berlin
Thursday, 22.06.2017, 09.30 Uhr (HU Berlin in Adlershof RUD25 Raum 2.417)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
C. Löbhard, WIAS:
An adaptive space-time discretization for parabolic optimal control problem with state constraints
more ... Location
Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Johann-von-Neumann-Haus, Raum 2.417

Abstract
We present a space-time discretization which is based on a reformulation of the stationarity conditions of a Moreau-Yosida regularized parabolic optimal control problem, which involves only the state variable. The resulting nonlinear partial differential equation is of fourth order in space, and of second order in time. In order to cope with the disbalance of regularity of the respective solutions, we develop a taylored discontinuous Galerkin scheme and derive convergence rates in the mesh size as well as an integrated update strategy for the regularization parameter related to the state constraints. We also propose an adaptive mesh refinement strategy and illustrate the performance of our method in numerical test cases.

Further Informations
Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations

Host
Humboldt-Universität zu Berlin
WIAS Berlin
Thursday, 22.06.2017, 10.00 Uhr (WIAS-ESH)
Seminar Laserdynamik
S. Eydam, WIAS Berlin:
Phase oscillator mode-locking
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Seminar Laserdynamik

Host
WIAS Berlin
Thursday, 22.06.2017, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. C. Brée, WIAS:
Feedback-operator for a photonic crystal in the external cavity of a broad area laser diode
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin