24.04.2019 um 17:15 Uhr in 69/125
Prof. Dr. Marcel Campen (Universität Osnabrück)
Beyond Simplicial: Advanced Discretizations of 3D Domains for Visualization and Simulation
A key component in computational applications that operate on three-dimensional domains, such as digitized real-world objects or virtually designed assets, are techniques for the discretization of these domains and of data defined over these. Goal is the representation or approximation by a finite number of compactly representable elements, enabling efficient processing using practical algorithms. Drawing from solid theoretical results, discretizations based on simplicial complexes (called triangular or tetrahedral meshes in this context) have been prevalent in practice for decades. However, non-simplicial discretizations are known to be beneficial for a variety of use cases. In this talk recent advances in the field of algorithmic generation and optimization of non-simplicial complexes for the representation and approximation of three-dimensional domains will be discussed. We will consider the case of elements which are non-simplicial combinatorially (e.g. complexes of quadrilateral or hexahedral elements) as well as the case of elements being non-simplicial geometrically (i.e. non-linear elements). We will touch upon a variety of questions and problems that still are open in this field — from a theoretical perspective (e.g. existence conditions, quality bounds) as well as a practical point of view (numerical robustness, efficiency).
02.05.2019 um 17:15 Uhr in 69/125 Achtung: Donnerstag!
Prof. Dr. Adrian Röllin (National University of Singapore)
From Berry-Esseen to Stein
Starting from the classical Berry-Esseen theorem and characteristic functions, we give a gentle introduction to Stein’s method along with recent applications to central limit theorems with dependence arising in random graph theory
30.04.2019 um 12:00 Uhr in Raum 69/E15
Random Spatial Networks
23.04.2019 um 16:15 Uhr in 69/125:
Marcin Wnuk (Universität Osnabrück)
Negative Dependence in Numerical Integration and Discrepancy Theory
Intuitively, a randomized point set in a d-dimensional unit cube is said to be negatively dependent if the points tend not to cluster. In my talk I will present a few notions of negative dependence, as well as their applications: it turns out that negatively dependent point sets yield good quadrature nodes, and in some sense (measured by the so-called discrepancy) are highly regular.
In the end I will discuss concrete constructions of negatively dependent point sets.