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Dienstag, 27.10.2020, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Prof. Dr. Carsten Hartmann, Brandenburgische Technische Universität Cottbus-Senftenberg:
Convergence to equilibrium in underdamped Langevin dynamics: Fluctuation-dissipation relations, entropy production and optimal control
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Online Event

Abstrakt
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin system at small noise (or low temperature) that is characterised by metastability and slow convergence to equilibrium. We follow an approach proposed by Pavon and co-workers [1] and consider a Langevin equation that is simulated at a high temperature, with the control playing the role of a friction that balances the additional noise so as to restore the original invariant measure at a lower temperature. We discuss different limits as the temperature ratio goes to infinity and prove convergence to a limit dynamics. It turns out that, depending on whether the lower (“target”) or the higher (“simulation”) temperature is fixed, the controlled dynamics converges either to the overdamped Langevin equation or to a deterministic gradient flow. This implies that (a) the ergodic limit and the large temperature separation limit do not commute in general, and that (b) it is not possible to accelerate the speed of convergence to the ergodic limit by making the temperature separation larger and larger. We discuss the implications of these observation from the perspective of stochastic optimisation algorithms and enhanced sampling schemes in molecular dynamics. This is joint work with Tobias Breiten, Lara Neureither and Upanshu Sharma [2]. [1] Y. Chen, T.T. Georgiou and M. Pavon. Fast cooling for a system of stochastic oscillators. J. Math. Phys. 56:113302, 2015. [2] T. Breiten, C. Hartmann, L. Neureither and U. Sharma. Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach. Preprint, 2020.

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Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Donnerstag, 29.10.2020, 16:00 Uhr (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Emil Cortes André, Technical University of Denmark:
An analysis of collective effects in nanolasers using minimally extended rate equations
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Online Event

Veranstalter
WIAS Berlin
2. – 4. November 2020 (WIAS-ESH)
Workshop/Konferenz: Workshop on Stochastic Geometry and Communications
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
Dienstag, 03.11.2020, 10:00 Uhr (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Lasse Ermoneit, TU Berlin:
Semiconductor passively mode-locked lasers subject to opto-electronic feedback
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Online Event

Veranstalter
WIAS Berlin
Dienstag, 03.11.2020, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Darina Dvinskikh, WIAS Berlin:
Improved complexity bounds in Wasserstein barycenter problem
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Online Event

Abstrakt
We focus on computational aspects of Wasserstein barycenter problem. We provide two algorithms to compute Wasserstein barycenter. The first algorithm, based on mirror prox with some specific norm, meets the complexity of celebrated accelerated iterative Bregman projections (IBP), however, with no limitations unlike (accelerated) IBP, that is numerically unstable when regularization parameter is small. The second algorithm, based on area-convexity and dual extrapolation, improves the previously best-known convergence rates for Wasserstein barycenter problem.

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Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Mittwoch, 04.11.2020, 11:30 Uhr (Online Event)
Forschungsseminar Mathematische Statistik
Prof. Pierre E. Jacob, Harvard University:
Unbiased Markov chain Monte Carlo methods with couplings
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Abstrakt
Various tasks in statistics involve numerical integration, for which Markov chain Monte Carlo (MCMC) methods are state-of-the-art. MCMC methods yield estimators that converge to integrals of interest in the limit of the number of iterations. This iterative asymptotic justification is not ideal; first, it stands at odds with current trends in computing hardware, with increasingly parallel architectures; secondly, the choice of "burn-in" and of the total number of iterations are dificult. This talk will describe recently proposed estimators that are exactly unbiased for the expectations of interest, while having an almost surely finite computing cost and a finite variance. They can thus be generated independently in parallel and averaged over. We argue that the removal of the "burn-in" bias can be done for many MCMC algorithms of practical interest without inflating the variance by much. The core idea is to use coupled pairs of Markov chains following the pathbreaking work of Peter Glynn & Chan-Han Rhee. The method also provides practical upper bounds on some distances between the marginal distribution of the chain at a finite step and its invariant distribution. This talk will provide an overview of this line of research, joint work with John O'Leary, Yves Atchade and many others.

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Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Dienstag, 10.11.2020, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Simon Breneis, WIAS Berlin:
Functions of bounded variation in one and multiple dimensions
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Abstrakt
We first recall univariate functions of bounded variation and treat a new result on the Hölder continuities of functions of bounded variation and their variation functions. Then, we discuss possible extensions of the concept of bounded variation to functions of several (though finitely many) variables, compare those generalizations and discuss their uses and shortcomings.

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Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Mittwoch, 11.11.2020, 11:30 Uhr (WIAS-405-406)
Seminar Interacting Random Systems
Stein Andreas Bethuelsen:
Invariance principle for random walks on dynamically averaging random conductances
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on Z. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations decrease according to a typical diffusive scaling and eventually approach constant unit conductances. The proof relies on a coupling with the standard continuous time simple random walk. Based on joint work with Christian Hirsch (Groningen) and Christian Mönch (Mainz).

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Mittwoch, 11.11.2020, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Charles University Prague, Czech Republic:
The old Stefan problem in a new mechanical context
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Abstrakt
The Stefan problem historically describes melting of ice or freezing (solidification) of water as a mere heat-transfer problem with a latent heat. This solid-liquid phase transition however naturally occurs in a mechanical context: melted liquid can flow while frozen solid exhibits some elasticity or some visco-elasticity and even may undergo some inelastic processes as fracture. This needs also to cope with the fluid-solid (so-called fluid-structure) interaction and calls for a model in Eulerian description. Thermomechanical consistency is pursued, as well as a mathematical analysis outlined. The concepts of semi-compressible fluids, viscoelastic solids in Jeffreys' rheology, phase-field fracture, and nonsimple materials (known also as multipolar fluids) will be employed. Some enhancements of this basic thermomechanical scenario will be mentioned, too.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 18.11.2020, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Janusz Ginster, Humboldt-Universität zu Berlin:
On the motion of curved dislocations in three dimensions: Simplified linearized elasticity
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Abstrakt
In this talk we discuss a simplified equilibrium problem for a curved dislocation line in a three-dimensional domain. As the core radius tends to zero, we derive an asymptotic expression to characterize the induced elastic energy. We then obtain the force on the dislocation line as the variation of thi sexpression and identify the highest order terms explicitly. As a main ingredient, we present an explicit asymptotic formula for the induced elastic strain which depends on the curvature of the dislocation line and thus highlights the difference to existing work on straight dislocation lines. Eventually, we present results on the corresponding dynamics. The presented methods area blueprint for the more physical setting of linearized isotropic elasticity. This is joint work with I. Fonseca and S. Wojtowytsch.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 25.11.2020, 15:15 Uhr (Online Event)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Annika Bach, Technische Universität München:
Geometrically frustrated spin systems: The antiferromagnetic XY model on the triangular lattice
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Abstrakt
Antiferromagnetic spin systems are magnetic lattice systems in which the exchange interaction between two spins (i.e., vectors in S1) favors anti-alignment. Such systems are said to be geometrically frustrated if, due to the geometry of the lattice, there is no orientation of spins that simultaneously minimizes all pairwise interactions. This is the case for the antiferromagnetic XY model on the two-dimensional triangular lattice. As a consequence, the system has two families of ground states which can be distinguished one from the other by what is called their chirality. In this talk we present a recent result obtained in collaboration with M. Cicales, L. Kreutz, and G. Orlando, where we characterise the discrete-to-continuum Gamma-limit of the XY-model energy in a regime which detects chirality transitions on one-dimensional interfaces between the two admissible chirality phases.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 26.11.2020, 16:00 Uhr (Online Event)
Forschungsseminar Mathematische Modelle der Photonik
Regina Finsterhölzl, TU Berlin:
Applying feedback control on quantum many-body systems within the matrix-product-state framework
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Online Event

Veranstalter
WIAS Berlin
Dienstag, 08.12.2020, 15:00 Uhr (Online Event)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Accelerated alternating minimization methods
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Abstrakt
We combine alternating minimization (AM) and Nesterov-type momentum acceleration and propose a generic accelerated alternating minimization method with a $1/k^2$ convergence rate in terms of the objective for convex problems and $1/k$ in terms of the squared gradient norm for non-convex problems, where $k$ is the iteration counter. Our method does not require any knowledge of neither convexity of the problem nor function parameters such as smoothness constant, i.e. it is adaptive to convexity and smoothness. Further, we develop its primal-dual modification for convex problems with linear constraints. We consider two applications of our methods to highlight their properties. The first one is the non-convex collaborative filtering problem, and the second one is optimal transport, where our primal-dual method takes a form of accelerated Sinkhorn's algorithm or accelerated Iterative Bregman Projections algorithm. In both applications, we show numerically that our methods outperform the baselines. In the second application, we also obtain state-of-the-art complexity results for optimal transport problems.

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin