Still, for continuous limits, it is equivalent to locally uniform convergence, whereas under mild side conditions, it implies Lp convergence. Even in cases where uniform convergence fails, weak convergence with respect to the new metric is established for empirical copula and tail dependence processes. No additional assumptions are needed for tail dependence functions, and for copulas, the assumptions reduce to existence and continuity of the partial derivatives almost everywhere on the unit cube. tests and resampling procedures. Universität zu Berlin Universität Potsdam Dienstag, 28. Investigations of nonlinear dynamics in coupled systems have seen a huge increase in interest during the last years. synchronization is just the most prominent one.
The signal transmission between coupled elements is often not instantaneous. zero transmission times have to be taken into account as crucial quantities that influence the dynamics of network nodes to a large extent. In this presentation, I will discuss synchronization effects in the presence of delayed coupling for two excitable neural systems. coupling, the compound system exhibits different types of synchronized oscillations of variable period.
will present an analysis of this behavior based on the interplay of the different time delays. The numerical results are supported by analytical findings. like dynamics with two competing timescales on the basis of the autocorrelation function.
Schöll: Synchronization of coupled neural oscillators with heterogeneous delays Int. WIAS Berlin Freie Universität Berlin Dienstag, 28. based confidence sets with multiplier bootstrap. The procedure is attractive due to its clear interpretation and computational simplicity. which are stated for the case of finite samples and allow for model misspecification. WIAS Berlin Dienstag, 28. WIAS Berlin Montag, 27. in order to deal with certain classes of complex fluids dynamics.
In many cases indeed the resulting PDE systems dysplay high order nonlinearities due mainly to quadratic forcing terms. The main idea consists in replacing, in the weak formulation, these PDEs by an equality representing energy conservation complemented with a differential inequality describing production of entropy. In this way, the thermodynamical consistency is preserved, but the entropic formulation is more tractable mathematically. isothermal mixture of two different viscous incompressible fluids of the same density.
WIAS Berlin Donnerstag, 23. Depending on the specific method used to build a 3D structural model and on the exact purpose of this model, its mesh must be adapted so that it enforces criteria on element type, maximum number of elements, and mesh quality. Meshing methods developed for applications different from geomodeling forbid any modification of the input model. This may be desirable in geomodeling to better control the number of elements in the final mesh and their quality. The objective of my thesis is to develop meshing methods that fulfill this requirement to better manage the geometrical complexity of geological structural models. An analysis of the sources of geometrical complexity sources in those models is first proposed.
The introduced measures are a first step toward the definition of tools allowing objective comparisons of structural models and permit to characterize the model zones that are more complicated to mesh. We then introduce two original meshing methods based on Voronoï diagrams: one for surface remeshing and the second one for hybrid gridding. combinatorial considerations to locally build the final mesh while sometimes modifying the initial model. The surface remeshing method is automatic and permit to simplify a model at a given resolution.
The gridding method generates a hybrid volumetric mesh. Prisms and pyramids fill the very thin layers of the model while the remaining regions are filled with tetrahedra. WIAS Berlin Mittwoch, 22. Universität zu Berlin Mittwoch, 22. We discuss a fixed point method to obtain a local central limit theorem for distributions defined by certain renewal type equations. avoiding walks in continuous space.
The error bounds obtained are sharper that the ones obtained by other methods. WIAS Berlin Mittwoch, 22. Forschungsseminar Mathematische Statistik Prof. In this talk, we present a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. To enforce specific properties of the functional effects such as smoothness, informative multivariate Gaussian priors are assigned to the basis function coefficients.
specific iteratively weighted least squares approximations to the full conditionals. We provide detailed guidance on practical aspects of model choice including selecting an appropriate response distribution and predictor specification. The importance and flexibility of Bayesian structured additive distributional regression to estimate all parameters as functions of explanatory variables and therefore to obtain more realistic models, is exemplified in several applications with complex response distributions. We will also introduce extensions to multivariate distributional regression. Universität zu Berlin Universität Potsdam Dienstag, 21. Many types of neurons exhibit spike rate adaptation, a gradual decrease in spiking activity following a sudden increase in stimulus intensity. This phenomenon is typically produced by slowly deactivating transmembrane potassium currents, which effectively inhibit neuronal responses and can be controlled by neuromodulators.
how they contribute to spike synchronization as well as spike rate oscillations in recurrent networks of excitatory and inhibitory neurons. WIAS Berlin Freie Universität Berlin Mittwoch, 15. Universität zu Berlin Mittwoch, 15. WIAS Berlin Mittwoch, 15. dimensional inference has progressed rapidly in the last years. will give a brief introduction and show examples from biology, neuroscience and physics, while also mentioning theoretical underpinnings.
Some challenges of inference for large data sets will be discussed, including computational feasibility and inhomogeneity. will highlight some more recent developments about the feasibility of constructing confidence intervals for regression coefficients when the number of variables exceeds the number of observations. Universität zu Berlin Dienstag, 14. WIAS Berlin Dienstag, 14. WIAS Berlin Montag, 13. Some nonlocal aspects of partial differential equations and free boundary problems. We will discuss the notion of fractional, nonlocal diffusive operators and we will present some recent mathematical results with applications to different fields, such as: nonlocal phase transitions, nonlocal quantum mechanics, crystal dislocation, nonlocal free boundary problems. WIAS Berlin Mittwoch, 08. Universität zu Berlin Mittwoch, 08. new scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician.
optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Besides the classical minimax risk bounds at some xed point, new pointwise risk bounds along a shrinking neighborhood of lowest density regions are derived, which demonstrate the superiority of the new estimator as compared to classical adaptive estimators. Our bounds are complemented by a local minimax lower bound. This lower bound splits into three regimes depending on the value of the density. The new estimator adapts to the rst two regimes, and it is shown that simultaneous adaptation to the fastest regime is not possible in principal. in rules for support recovery based on the new estimator are worked out in detail.
optimal, up to some logarithmic factor. Universität zu Berlin Universität Potsdam Donnerstag, 19. Darcy Problem ist das gekoppelte Problem freier Strömung mit Strömung durch poröse Medien. Ein Anwendungsbeispiel ist etwa das Modell eines Flusses mit seinem Flussbett. Stokes Gleichungen für die freie Strömung und die Darcy Gleichungen für die Strömung durch poröse Medien koppeln kann. Einige der resultierenden Probleme werden besprochen und es werden Vorschläge zur Lösung dieser gemacht. Die generelle Idee zur numerischen Lösung des gekoppelten Problems ist die Betrachtung von getrennten Problemen, welche durch einen gemeinsamen Teil ihres Randes, genannt Interface, verbunden werden.
Diese getrennten Probleme können nun iterativ gelöst werden, wobei nach jedem Lösungsschritt die Randdaten am Interface des jeweils anderen Problems erneuert werden. Stokes Gleichungen machen es notwendig, sich mit ihrer Nichtlinearität zu beschäftigen, welche zusätzliche Fixpunktiterationen erforderlich macht. Stokes Gleichungen pro Iteration einschränken sollte, um beste Ergebnisse zu erzielen. Diese und andere Fragen werden anhand von zwei numerischen Beispielen diskutiert.
