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Wednesday, 29.03.2017, 13.15 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Prof. Ch. Clason, Universität Duisburg-Essen:
Convex relaxation of hybrid discrete-continuous control problems
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Wednesday, 29.03.2017, 15.15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. M. Demuth, Technische Universität Clausthal:
On eigenvalues of non-selfadjoint operators: A comparison of two approaches
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, 30.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. J.H.M. ten Thije Boonkkamp, Eindhoven University of Technology, Netherlands:
Complete flux schemes fOR conservation laws of advection-diffusion-reaction typ
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Complete flux schemes are recently developed numerical flux approximation schemes for conservation laws of advection-diffusion-reaction type; see e.g. [1, 2]. The basic complete flux scheme is derived from a local one-dimensional boundary value problem for the entire equation, including the source term. Consequently, the integral representation of the flux contains a homogeneous and an inhomogeneous part, corresponding to the advection-diffusion operator and the source term, respectively. Suitable quadrature rules give the numerical flux. For time-dependent problems, the time derivative is considered a source term and is included in the inhomogeneous flux, resulting in an implicit semi-discretisation. The implicit system proves to have much smaller dissipation and dispersion errors than the standard semidiscrete system, especially for dominant advection. Just as for scalar equations, for coupled systems of conservation laws, the complete flux approximation is derived from a local system boundary value problem, this way incorporating the coupling between the constituent equations in the discretization. Also in the system case, the numerical flux (vector) is the superpostion of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term vector, respectively. The scheme is applied to multispecies diffusion and satisfies the mass constraint exactly.
References:
[1] J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen, ``The finite volume-complete flux scheme for advection-diffusion-reaction equations'', J. Sci. Comput., 46, 47--70, (2011).
[2] J.H.M. ten Thije Boonkkamp, J. van Dijk, L. Liu and K.S.C. Peerenboom, ``Extension of the complete flux scheme to systems of comservation laws'', J. Sci. Comput., 53, 552?568, (2012).

Host
WIAS Berlin
Tuesday, 04.04.2017, 15.15 Uhr (WIAS-ESH)
Seminar Laserdynamik
Prof. E. Knobloch, University of California, USA:
Geostrophic turbulence and the formation of large scale structure
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Low Rossby number convection is studied using an asymptotically reduced system of equations valid in the limit of strong rotation. The equations describe four regimes as the Rayleigh number $Ra$ increases: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger $Ra$, followed for yet larger $Ra$ by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced heat transport efficiency, and finally by geostrophic turbulence. The Nusselt number--Rayleigh number scaling in the ültimate" regime of geostrophic turbulence is predicted and confirmed using direct numerical simulations of the reduced equations. These simulations reveal that geostrophic turbulence is unstable to the formation of large scale barotropic vortices, via a process known as spectral condensation. The details of this process are quantified and its implications explored.

Further Informations
Seminar Laserdynamik

Host
WIAS Berlin
Thursday, 06.04.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. D. Silvester, University of Manchester, GB:
Accurate time-integration strategies for modelling incompressible flow bifurcations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbations. In this study, we show that an approach similar to pseudo-spectral analysis can be performed inexpensively using stochastic collocation methods and the results can be used to provide quantitive information about the nature and probability of instability.

Host
WIAS Berlin
Wednesday, 19.04.2017, 18.15 Uhr (WIAS-ESH)
Berliner Kolloquium Wahrscheinlichkeitstheorie/GK ''Stochastische Analysis''
Prof. Dr. F. den Hollander, Leiden University, Niederlande:
Random walks on dynamic random graphs
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The mixing time of a Markov chain is the time it needs to approach its stationary distribution. For random walks on graphs, the characterisation of the mixing time has been the subject of intensive study. One of the motivations is the fact that the mixing time gives information about the geometry of the graph. In the last few years, much attention has been devoted to the analysis of mixing times for random walks on emphrandom graphs, which poses interesting challenges. Many real-world networks are dynamic in nature. It is therefore natural to study random walks on emphdynamic random graphs. In this talk we consider a random walk on the configuration model, i.e., a random graph with prescribed degrees. We investigate what happens when at each unit of time a fraction $alpha_n$ of the edges is randomly relocated, where $n$ is the number of nodes. We identify emphthree regimes for the mixing time in the limit as $n to infty$, depending on the choice of $alpha_n$. These regimes exhibit surprising behaviour. Joint work with Luca Avena (Leiden), Hakan Guldas (Leiden) and Remco van der Hofstad (Eindhoven)

Host
Humboldt-Universität zu Berlin
Technische Universität Berlin
Universität Potsdam
WIAS Berlin
Tuesday, 25.04.2017, 15.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
N. Zhivotovskiy, IITP RAS, SkolTech:
Towards minimax optimal rates in classification and regression
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
In this talk, we consider two approaches that allow (in some cases) to obtain minimax rates of the prediction risk up to absolute constants. Classification problems will be considered under small noise conditions for an arbitrary distribution of objects, as well as cases of certain special distributions. In contrast to several standard results in the learning theory, our bounds are simultaneously optimal for entire families of classes.

Host
WIAS Berlin
Wednesday, 26.04.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
J. Weed, Massachusetts Institute of Technology, USA:
Optimal rates of estimation for the multi-reference alignment problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal.. These bounds show a striking dependence on the signal-to-noise ratio of the problem. Joint work with Afonso Bandeira and Philippe Rigollet.

Further Informations
Forschungsseminar ``Mathematische Statistik''

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
International Research Training Group 1792
Wednesday, 14.06.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. J.-M. Loubes, Université Toulouse Paul Sabatier, Frankreich:
Kantorovich distance based kernel for Gaussian processes : Estimation and forecast
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. Here, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Universität Potsdam