相关论文: Asymptotic optimality of the triangular lattice fo…

Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully…

We investigate the asymptotic behavior, as $N$ grows, of the largest minimal pairwise distance of $N$ points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal…

This paper is concerned with the rigorous analysis of a recently proposed model of Zheng et. al. for describing nematic liquid crystals within the dense regime, with the orientation distribution function as the variable. A key feature of…

We investigate numerically the optimal constants in Lieb-Thirring inequalities by studying the associated maximization problem. We use a monotonic fixed-point algorithm and a finite element discretization to obtain trial potentials which…

We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…

We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…

It is well-known that any Lennard-Jones type potential energy must have a periodic ground state given by a triangular lattice in dimension 2. In this paper, we describe a computer-assisted method that rigorously shows such global minimality…

In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth…

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of…

We study optimal estimation when the likelihood may be misspecified. Building on tools from the theory of decision-making under uncertainty, we analyze a class of axiomatically grounded optimality criteria which nests several existing…

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…

We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the…

In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method…

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

Tensor parameters that are amortized or regularized over large tensor powers, often called "asymptotic" tensor parameters, play a central role in several areas including algebraic complexity theory (constructing fast matrix multiplication…

We study periodic tessellations of the Euclidean space with unequal cells arising from the minimization of perimeter functionals. Existence results and qualitative properties of minimizers are discussed for different classes of problems,…

Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…

High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…

Dense packings have served as useful models of the structure of liquid, glassy and crystal states of matter, granular media, heterogeneous materials, and biological systems. Probing the symmetries and other mathematical properties of the…