However, it becomes challenging and often problematic in high and infinite dimensional models. related to this concept will be presented. CP COLT, volume 23, pp. An adaptation theory for nonparametric confidence intervals. Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems. Adaptive confidence sets for matrix completion. Bounds for the Fixed Budget Best Arm Identification Bandit Problem. CP COLT, volume 49, pp. On adaptive inference and confidence bands.
WIAS Berlin Mittwoch, 02. Universität zu Berlin Mittwoch, 02. Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. timation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network and derive optimal rates of convergence for this problem. Our results cover the important setting of sparse networks. max risk for graphon estimation when the probability matrix is sampled according to a graphon model.
The problem of estimation of the matrix of connection probabilities of a network can be viewed as a particular case of a general matrix sequence model. that is, it can be factorized using sparse factors. This model includes a number of interesting problems such as the mixture of Gaussian, sparse dictionary learning, stochastic block models and mixture membership models. In the second part of the talk, I will consider the problem of statistical estimation of the signal matrix for this model and derive optimal rates of estimation. Inhomogeneous random graph Networks Oracle inequality Sparse graphon.
Universität zu Berlin WIAS Berlin Dienstag, 01. as a model for a chaotic big bang cosmological singularity. conjectured that particle horizons form towards the big bang. cones remain spatially bounded, and spatially separate regions causally decouple. We prove this BKL conjecture, for almost every solution. More specifically, the answer to this question depends on the convergence speed towards the Mixmaster attractor. showed that this convergence occurs at all.
We introduce a novel expanding measure in order to prove that the convergence is fast enough to guarantee the formation of particle horizons for Lebesgue almost every solution. The talk is addressed at a nonspecialist audience. Freie Universität Berlin WIAS Berlin Dienstag, 01. Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics Dr. The definitions of these distances are based on specific optimization problems. The goal of the talk is to present new numerical methods for solution of these optimization problems. DFG Schwerpunktprogramm 1962 WIAS Berlin Mittwoch, 26. Universität zu Berlin Dienstag, 25. for an important problem of change point detection.
problem, which has applications in biostatistics and econometrics. The developed approach is essentially a significance testing procedure requiring a proper choice of a critical level. standard bootstrap scheme is proposed and theoretically justified under mild assumptions. The idea of the proof and the simulation study will be discussed as well. WIAS Berlin Dienstag, 25. Seminar Nichtlineare Optimierung und Inverse Probleme Dr. WIAS Berlin Freitag, 21. Seminar Nichtglatte Variationsprobleme und Operatorgleichungen Dr. posed problems in image processing.
As such, they rely heavily on appropriate regularization terms which render a stable recovery possible and strongly influence qualitative solution properties. In this talk, we consider regularization concepts for both static and dynamic data that are based on higher order differentiation. posedness results for standard inverse problems. We then consider the application of TGV in the context of a variational model for image decompression, being in particular applicable to JPEG or JPEG 2000 compressed images.
PET reconstruction that exploits structural similarities between the two modalities. After establishing essential analytical properties, we deal with applications to the reconstruction of highly subsampled dynamic MR data and the decompression of MPEG compressed movies. WIAS Berlin Mittwoch, 19. Universität zu Berlin Mittwoch, 19. Forschungsseminar Mathematische Statistik Dr. gy, chemistry, physics, medicine, and engineering.
differential equations are commonly used for the mathematical modeling of the rate of change of dynamic processes. However, modern dynamic systems are typically very complex: nonlinear, high dimensional and only partly measured. Moreover, data may be sparse and noisy. of dynamical systems is not a trivial task in practice. In this talk we will present some recent theoretical results and methodologies concerning identifiability and estimation of dynamic systems. We will also discuss real data examples coming from diverse areas such as infectious diseases and biology.
Universität zu Berlin SFB 649: Ökonomisches Risiko Universität Potsdam WIAS Berlin Dienstag, 18. WIAS Berlin Dienstag, 18. WIAS Berlin Mittwoch, 12. In this talk we consider a system of N coupled stochastic differential equations, which we interpret as a system of N particles evolving according to the dynamics given by the SDEs. We develop conditions on the interaction strength between the particles to ensure existence of solutions to the limiting stochastic PDE. time behaviour of the solution. This is joint work with Anton Bovier.
WIAS Berlin Dienstag, 11. Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics Dr. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 25. WIAS Berlin Dienstag, 11. WIAS Berlin Dienstag, 27. WIAS Berlin Donnerstag, 22. Forschungsseminar Mathematische Modelle der Photonik Dr. equation are obtained via a matrix version of the Darboux transformation, with a spectral matrix of the form of a Jordan block. We prove regularity of these solutions using properties of the Lyapunov equation. WIAS Berlin Donnerstag, 22. Seminar Numerische Mathematik Dr. When modelling semiconductor devices via the van Roosbroeck system one ofen uses statistical functions to describe the correspondence between carrier densities and chemical potentials.
case is still an open problem. Our main goal is to discretely preserve important properties from the continuous system such as existence and uniqueness of the solution, consistency with the thermodynamical equilibrium and unconditional stability. We also show how these new numerical schemes can be efciently implemented for 2D and 3D applications. WIAS Berlin Mittwoch, 21. Seminar Partielle Differentialgleichungen Prof. Problem solving at realistic complexities using the deal.
world problems has many levels of complexities. single method, or a single algorithm, is often not sufficient to address realistic problems from applied sciences and engineering. of data at each run. Codes at this level of complexity can no longer be written from scratch by a single person, and not even by a consistent group of well prepared PhD students.
However, over the past decade, many high quality libraries and tools have been developed that make writing advanced computational software simpler. In this talk I will briefly introduce the deal. life problems, with a focus on the lessons learned from developing this massively parallel library for the solution of complex problems. WIAS Berlin Dienstag, 20. whose natural frequencies are unimodally or bimodally distributed.
the hysteretic synchronization transition involves several states. SWs and finally arriving to a PS regime. The transition to the PS state from the SW occurs always at the same coupling, independently of the system size, while its value increases linearly with the inertia. On the other hand the critical coupling required to observe TWs and SWs increases with N suggesting that in the thermodynamic limit the transition from incoherence to PS will occur without any intermediate states.
Finally a linear stability analysis reveals that the system is hysteretic not only at the level of macroscopic indicators, but also microscopically as verified by measuring the maximal Lyapunov exponent. tions in the Kuramoto model with inertia? Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution? Springer International Publishing, 2016. WIAS Berlin Dienstag, 20. Accurate modeling and stochastic simulation of molecular reaction kinetics is a field of broad interest. Depending on the particles?
concentration, their mobility and reactivity, different mathematical models are appropriate. diffusion systems in which the space of motion naturally decomposes into sets of metastability and diffusion can be approximated by jumps between the sets. mixed such that the reaction dynamics can be described on the level of a chemical master equation. WIAS Berlin Donnerstag, 15. Seminar Numerische Mathematik Prof.
