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Monday, 26.06.2017, 15.15 Uhr (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. M. Hanss, Universität Stuttgart:
Fuzzy arithmetic and probability theory in uncertainty analysis -- Unity in diversity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 27.06.2017, 10.15 Uhr (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
M. Mäck, Universität Stuttgart:
Numerical implementation of Fuzzy arithmetic in uncertainty analysis
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 27.06.2017, 15.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
C. Uebel, Humboldt-universtiät zu Berlin:
Variable selection with hamming loss
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Tuesday, 27.06.2017, 15.15 Uhr (WIAS-ESH)
Oberseminar Nonlinear Dynamics
I. Franovic, University of Belgrade, Serbia:
Bistability, rate oscillations and slow rate fluctuations in networks of noisy neurons with coupling delay
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Spontaneous activity of cortical neurons is typically characterized as a doubly-stochastic process, underlying two distinct forms of variability. While the local spike-train variability is reflected on the fast timescale, the variability associated with much longer timescales involves macroscopic irregular fluctuations of the firing rate. The latter fluctuations apparently emerge by coherent switching of neurons between the ?up? and ?down? states of membrane potential, and are believed to play important functional roles. In order to gain qualitative insight into the mechanisms behind such switching phenomena, we consider a random network of rate-based neurons influenced by external and internal noise, as well as the coupling delay. The network behavior is analyzed by deriving the second-order stochastic mean-field model, which describes the network dynamics in terms of the mean-rate and the associated variance. The mean-field model is used to study the stability and bifurcations in the thermodynamic limit, as well as the fluctuations due to the finite-size effect. For the thermodynamic limit, it is established that (i) the network may exhibit coexistence between two stationary levels in a wide range of parameters, whereby the two types of noise affect the levels in a fundamentally different fashion, and (ii) coupling delay may give rise to oscillations of the mean-rate. The slow rate fluctuations are demonstrated to emerge via two distinct scenarios. In the delay-free case, the leading mechanism can be seen as noise-induced transitions between two metastable states, quite reminiscent to fluctuations of a particle in a double-well potential. In the second scenario, which involves the cooperative action of noise and delay, the fluctuations can be interpreted as stochastic mixing between two different oscillatory regimes.

Further Informations
Oberseminar Nonlinear Dynamics

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 28.06.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. B. Sturmfels, Max Planck Institute for Mathematics in the Sciences Leipzig, Germany:
Geometry of log-concave density estimation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We present recent work with Elina Robeva and Caroline Uhler that establishes a new link between geometric combinatorics and nonparametric statistics. It concerns shape-constrained densities on d-space that are log-concave, with focus on the maximum likelihood estimator (MLE) for weighted samples. Cule, Samworth, and Stewart showed that the logarithm of the optimal log-concave density is piecewise linear and supported on a regular subdivision of the samples. This defines a map from the space of weights to the set of regular subdivisions of the samples, i.e. the face poset of their secondary polytope. We prove that this map is surjective. In fact, every regular subdivision arises in the MLE for some set of weights with positive probability, but coarser subdivisions appear to be more likely to arise than finer ones. To quantify these results, we introduce a continuous version of the secondary polytope, whose dual we name the Samworth body.

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Universität Potsdam
Thursday, 29.06.2017, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
Dr. A. Pimenov, WIAS Berlin:
Efficient simulation and analysis of multi-mode laser dynamics using time-delay models
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 11.07.2017, 10.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Ch. Ben Hammouda, King Abdullah University of Science and Technology - KAUST, Saudi-Arabien, Königreich:
Multilevel hybrid split-step implicit tau-leap
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Tn this talk, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method.

Further Informations
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

Host
WIAS Berlin
Wednesday, 12.07.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. W. Polonik, University of California at Davis, USA:
Statistical topological data analysis: Rescaling the persistence diagram
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
A persistence diagram (PD) is one of the basic objects underlying topological data analysis. It is used to analyze topological and geometric features of an underlying space M, assuming availability of a random sample from M. Existing approaches for such analyses will be reviewed brie y, and their bene ts and shortcomings will be discussed. Then we introduce ideas for rescaling PDs, which enables the derivation of novel limit theorems for the total k persistence, and other functionals of PDs. The long-term goal of studying the rescaling of PDs is to develop novel types of statistical analysis of persistence diagrams.

Further Informations
Forschungsseminar ``Mathematische Statistik''

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin