Sep. Oktober 2017 Nov.
Filtereinstellungen ändern

Kategorien-Filter ist aus: keine Filterung nach Kategorien.


17.10.2017 14:15 Prof. Steffen Lauritzen (Humboldt Awardee; University of Copenhagen):
Maximum likelihood estimation in Gaussian models under total positivityBC1 2.01.10 (Parkring 11, 85748 Garching)

The problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2) is investigated. The maximum likelihood estimator (MLE) for such distributions exists based on just two observations, irrespective of the underlying dimension. It is further demonstrated that the MTP2 constraint serves as an implicit regularizer and leads to sparsity in the estimated inverse covariance matrix, determining what we name the ML graph. We show that the maximum weight spanning forest (MWSF) of the empirical correlation matrix is a spanning forest of the ML graph. In addition, we show that we can find an upper bound for the ML graph by adding edges to the MSWF corresponding to correlations in excess of those explained by the forest. We provide globally convergent coordinate descent algorithms for calculating the MLE under the MTP2 constraint which are structurally similar to iterative proportional scaling. The lecture is based on recent joint work with Caroline Uhler and Piotr Zwiernik.

19.10.2017 16:30 Aiso Heinze:
Mathematische Lernvoraussetzungen für MINT-Studiengänge - Eine Delphi-Studie mit HochschullehrendenA 027 (Theresienstr. 39, 80333 München)

In MINT-Studiengängen stellen insbesondere die Mathematikveranstaltungen große Hürden für Erstsemesterstudierende dar. Trotz hoher Studienabbruchquoten gibt es von Hochschulseite keine einheitlichen Vorgaben, welche mathematischen Lernvoraussetzungen für den Einstieg in MINT-Studiengänge als notwendig angesehen werden. Auch zeigen die Vorkurse der Hochschulen in Deutschland kein homogenes Bild. Erste Ansätze zur Beschreibung erwarteter mathematischer Lernvoraussetzungen bilden Empfehlungen, die von Arbeitsgruppen für einige Studiengänge entwickelt wurden. Im Vortrag wird eine Delphi-Studie vorgestellt, in der knapp 1000 Hochschullehrenden der Mathematik nach den mathematischen Mindestlernvoraussetzungen für einen erfolgreichen Einstieg in MINT-Studiengänge befragt wurden. Dabei wurden 179 mathematische Lernvoraussetzungen identifiziert; für 144 Lernvoraussetzungen lässt sich ein Konsens der befragten Hochschullehrenden uüber MINT-Studiengänge feststellen. Im Vortrag werden exemplarische Ergebnisse vorgestellt und Implikationen für den Uuml;bergang Schule-Hochschule diskutiert.

23.10.2017 14:15 Marita Holtmannspötter, University of Duisburg:
Optimal control of mechanical damage processesMI 02.06.011 (Boltzmannstr. 3, 85748 Garching)

In this talk a numerical solution method for an optimal control problem of a specific viscous two-field gradient damage model will be presented. The mechanical damage model features two damage variables which are coupled by a penalty term in the gradient enhanced free energy functional. The minimization of the free energy as well as the consideration of the evolution of the damage in time result in state equations which are nonlinear and nonsmooth in general. Therefore necessary optimality conditions are difficult to obtain. Under certain assumptions it is possible to derive an approximate gradient which is used to apply a gradient based optimization algorithm. We focus on solving the discretized problem and present supporting test results.

23.10.2017 15:00 Cinzia Soresina (CNR IMATI, Mailand, Italien):
About predator-prey reaction cross-diffusion systems derived by time scale argumentsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

We consider predator-prey reaction-diffusion systems, incorporating the dynamics of searching and handling predators, together with active and hidden prey. Reaction cross-diffusion systems involving a Holling-type II or a Beddington-DeAngelis functional response are obtained by suitable scaling and asymptotics. The Turing instabilty is then investigated, by characterizing the instability domains of the systems and comparing them to those obtained when cross-diffusion terms are replaced by a standard diffusion.

23.10.2017 16:30 Katja Miller:
Random walks on oriented percolation and in recurrent random environments 2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

TBA

25.10.2017 13:15 Dr. Ercan Sönmez (Heinrich-Heine-Universität, Düsseldorf):
Hausdorff dimension of multivariate operator-self-similar random fields BC1 2.01.10 (Parkring 11, 85748 Garching)

The notion of Hausdorff dimension has been introduced in order to characterize sets which do possess a fractional pattern, commonly referred to as fractals. A typical feature of fractals is that they exhibit reappearing patterns, i.e. many fine details of the set resemble the whole set, a phenomenon which is called self-similarity. In case of multivariate self-similar random fields self-similarity means that a time-scaling corresponds statistically to a scaling in the state space, where the scaling relation is with respect to suitable matrices. This talk provides the first results on the sample paths and fractal dimensions of such fields, including quite general scaling matrices. A short introduction to the notion of Hausdorff dimension will also be given.

25.10.2017 13:15 Dr. Ercan Sönmez (Heinrich-Heine-Universität, Düsseldorf):
Hausdorff dimension of multivariate operator-self-similar random fields2.01.10 (Parkring 11, 85748 Garching-Hochbrück)

The notion of Hausdorff dimension has been introduced in order to characterize sets which do possess a fractional pattern, commonly referred to as fractals. A typical feature of fractals is that they exhibit reappearing patterns, i.e. many fine details of the set resemble the whole set, a phenomenon which is called self- similarity. In case of multivariate self-similar random fields self-similarity means that a time-scaling corresponds statistically to a scaling in the state space, where the scaling relation is with respect to suitable matrices. This talk provides the first results on the sample paths and fractal dimensions of such fields, including quite general scaling matrices. A short introduction to the notion of Hausdorff dimension will also be given.

26.10.2017 15:00 Katrin Wendland (Universität Freiburg):
From the heat equation to conformal field theoryRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

The classical Jacobi theta function may be obtained as fundamental solution of the heat equation with certain periodic initial data. Its main properties can be motivated by this approach, and they enter crucially in the applications of Jacobi theta functions in conformal field theory. We use this as a bridge from the heat equation to conformal field theory, in this talk, assuming no background knowledge in these special quantum field theories.

26.10.2017 16:30 Mario Santilli (Max-Planck-Institut, Golm):
A notion of curvature for closed subsets of Euclidean space with applications to generalized minimal submanifolds of arbitrary codimensionRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

A second fundamental form is introduced for arbitrary closed subsets of Euclidean space, extending the same notion introduced by J. Fu for sets of positive reach. We extend well known integral-geometric formulas to this general setting and we provide a structural result in terms of second fundamental forms of submanifolds of class 2 that is new even for sets of positive reach. For a large class of minimal submanifolds, which include viscosity solutions of the minimal surface system and rectifiable stationary varifolds of arbitrary codimension and higher multiplicities, we prove the area formula for the generalized Gauss map in terms of the discriminant of the second fundamental form and, adapting techniques from the theory of viscosity solutions of elliptic equations to our geometric setting, we conclude a natural second-order-differentiability property almost everywhere.

26.10.2017 16:30 Nam Phan:
On the Thomas-Fermi approximation and Lieb-Thirring inequality (Antrittsvorlesung)A 027 (Theresienstr. 39, 80333 München)

In the Thomas-Fermi theory, the kinetic energy of a many-electron wave function is conveniently expressed in terms of its one-body density functional. This semiclassical approximation goes back to the early days of quantum mechanics and has been used widely in computational physics and chemistry. However, many questions on the validity of the approximation remain open from a mathematical point of view. I will prove that the Thomas-Fermi approximation is a rigorous lower bound for the many-body kinetic energy, up to a gradient term of lower order. This is an improved version of the Lieb-Thirring inequality.

26.10.2017 17:00 Christof Haubner (UniBw):
Finite element approximation of a sharp interface model for tumour growthGebäude 33, Raum 1401 (Werner-Heisenberg-Weg 39, 85577 Neubiberg)

In this talk we consider two sharp interface models based on [Garcke, Lam, Sitka, Styles, 2016] that describe tumour growth: one without fluid flow while the second includes Darcy-flow. We work on an open, bounded domain that is divided into a tumour and a healthy region by an interface. The task is to find the evolution of the interface, the concentration of nutrients for the tumour, a chemical potential on the tumour region (and the pressure in the model with Darcy-flow). We note that the model accounts for transport mechanisms such as chemotaxis and active transport which causes discontinuity across the interface for the nutrients (and the pressure). We present a finite element approximation where we discretize the time, domain and interface independently, introduce finite element spaces and approximate inner products to get a discrete system. Under some mild assumptions we show existence of a unique solution.

30.10.2017 15:00 Stefania Ottaviano (Universität Trient, Italien):
The influence of the population contact network and stochasticity on the epidemics transmissionMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Networks represent the backbone of many complex systems and they appear for a large variety of real-world systems in ecology, epidemiology and neuroscience. In particular, there is a close relationship between epidemiology and network theory, since viral propagation between interacting agents strongly depends on intrinsic characteristics of the population contact network. With regard to this, in the first part of the talk, we investigate how a particular network structure, can impact on the long-term behavior of epidemics. Specifically, we consider networks that are partitioned into local communities. The rationale of this approach is that the epidemic spreads at a different rate within communities with respect to the rate at which it spreads across the communities. We describe the epidemic process as a continuous-time individual-based susceptible–infected–susceptible (SIS) model using a first-order mean-field approximation. We give conditions in order to decide whether the overall healthy-state defines a globally asymptotically stable or an unstable equilibrium. Moreover, we show that above the epidemic threshold another steady-state exists, that can be computed using a lower-dimensional system, in the case of a certain structural regularity of the graph connectivity.

In the second part of the talk, we consider the inclusion of stochasticity, modeling the infection rates in the form of independent stochastic processes. This allows us to get stochastic differential equations for the probability of infection in each node. We report on the existence of the solution for all times. Moreover, we show that there exist two regions, given in terms of the coefficients of the model, one where the system goes to extinction almost surely, and the other where it is stochastic permanent.