Oberseminar "Numerische Mathematik, Optimierung und dynamische Systeme"

Oberseminar , Nummer im Vorlesungsverzeichnis: 10525

SWS: 2

Dozenten

Mario Bebendorf, Kurt Chudej, Lars Grüne, Anton Schiela

Allgemeines

gemeinsames Oberseminar der Lehrstühle für Angewandte Mathematik und Ingenieurmathematik

Vortragsankündigungen für das Oberseminar

Im Rahmen unseres gemeinsamen Oberseminars finden folgende Vorträge statt:


Am Montag, dem 3. Juli 2017, um 16:15 Uhr im S 80, Gebäude NW II, spricht

Herr Prof. Dr. Joachim Krug
Institut für Theoretische Physik
Mathematisch-Naturwissenschaftliche Fakultät
Universität zu Köln

im Rahmen des Oberseminars und des „Forschungszentrums für Modellierung und Simulation (MODUS)”
über das Thema
"Mathematical aspects of biological fitness landscapes"

Abstract:

Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. The relationship between genotype and fitness is generally complex, as it is mediated by the multidimensional organismic phenotype that interacts with the environment and thereby determines reproductive success. Two modeling strategies have been devised to deal with this situation. One is to shortcut the intermediate phenotypic level by assigning fitness directly to genotypes. This leads to probabilistic models that define ensembles of random functions on Hamming spaces or (in the standard case of binary sequences) on the hypercube. An alternative and biologically more realistic approach is provided by Fisher's geometric model (FGM), which describes the phenotype as a vector in an n-dimensional Euclidean trait space with a unique fitness optimum. Genetic mutations are encoded as random phenotypic displacements, and complexity arises from the difficulty of optimizing a smooth function by a finite number of random vectors. After a historical introduction and an overview of the current understanding of real fitness landscapes that is available from empirical studies, I will survey quantitative measures of fitness landscape complexity and present the results of a recent analytical study of the fitness landscape generated by FGM.

Am Freitag, dem 2. Juni 2017, um 13:00 Uhr im S 80, Gebäude NW II, spricht

Herr Prof. Dr. Sigurður Hafstein
Professor for Applied Mathematics
Faculty of Physical Sciences
School of Engineering and Natural Sciences
University of Iceland in Reykjavík, Island

über das Thema
"Computational methods for Lyapunov functions and estimation of basins of attraction"

Abstract:

We discuss several different numerical methods for the computation of Lyapunov functions and the corresponding estimation of basins of attraction for nonlinear systems in different settings. We discuss how some of these methods can be combined and/or adapted to compute approximations to complete Lyapunov functions, which are Lyapunov functions defined on the whole state-space and subdivide it into two disjunct sets with very different dynamical properties. Namely the chain-recurrent part and the gradient-like part, where solutions pass through.

Am Montag, dem 29. Mai 2017, um 16:15 Uhr im S 80, Gebäude NW II, spricht

Herr Dr. Tobias Breiten
Arbeitsgruppe "Optimierung, Optimal Control und Inverse Probleme"
Naturwissenschaftliche Fakultät
Institut für Mathematik und Wissenschaftliches Rechnen
Karl-Franzens-Universität Graz in Graz, Österreich

über das Thema
"“Feedback stabilization of the Fokker-Planck equation"

Abstract:

The probability distribution function of a dragged Brownian particle can be characterized by the Fokker-Planck equation. By means of an optical tweezer, interaction with the particle is possible and leads to a bilinear control system. It is known that the uncontrolled system converges to the stationary distribution. However, depending on the parameters of the system, this convergence can be inadequately slow. Projection-based decoupling of the Fokker-Planck equation allows to design certain feedback control laws that locally increase the rate of convergence to the stationary distribution. Different strategies based on a projected Riccati equation and approximations of the Hamilton-Jacobi-Bellman equation are discussed.
This is joint work with Karl Kunisch and Laurent Pfeiffer (University of Graz).

Am Montag, dem 22. Mai 2017, um 16:15 Uhr im S 80, Gebäude NW II, spricht

Herr Dr. Kevin Sturm
Research Group "Optimization and optimal control"
Johann Radon Institute for Computational and Applied Mathematics (RICAM) in Linz, Österreich

über das Thema
"Weakly-normal basis vector fields in RKHS with an application to shape Newton methods"

Abstract:

In this talk I discuss the approximation of normal vector fields defined on the boundary of a domain in the plane. For this purpose we introduce so-called weakly normal basis functions with the help of reproducing kernels. These normal functions enjoy several nice properties and are tailored to shape optimisation problems. This is joint work with Alberto Paganini.

Einladende:

Prof. Dr. Mario Bebendorf
Prof. Dr. Kurt Chudej
Prof. Dr. Lars Grüne
Prof. Dr. Anton Schiela