Related papers: Hyper-ideal circle patterns with cone singularitie…
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six intersection points with neighboring circles is equal to -1.…
This paper develops a method to learn optimal controls from data for bilinear systems without a priori knowledge of the system dynamics. Given an unknown bilinear system, we first characterize when the available data is suitable to solve…
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…
We generalize the study of higher-form-symmetries to theories with supersymmetry. Using a supergeometry formulation, we find that ordinary higher-form-symmetries nicely combine with supersymmetry to give rise to a much larger spectrum of…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…
This paper investigates a generalized hyperbolic circle packing (including circles, horocycles or hypercycles) with respect to the total geodesic curvatures on the surface with boundary. We mainly focus on the existence and rigidity of…
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
We study mixtures of decomposable graphical models, focusing on their ideals and dimensions. For mixtures of clique stars, we characterize the ideals in terms of ideals of mixtures of independence models. We also give a recursive formula…
In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their…
We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…
We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information…
We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.
The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems.…
A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, including triangulations, integer programming and Groebner bases.…