Related papers: Optimal Quantization of Finite Uniform Data on the…
The sum-of-squares hierarchy of semidefinite programs has become a common tool for algorithm design in theoretical computer science, including problems in quantum information. In this work we study a connection between a Hermitian version…
We consider regularised quadratic optimal transport with subquadratic polynomial or entropic regularisation. In both cases, we prove interior Lipschitz-estimates on a transport-like map and interior gradient Lipschitz-estimates on the…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the $L^r$-Kantorovich (or transport) distance, where either the locations or the weights of the approximations' atoms are…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
Sorted $L_1$ penalization estimator (SLOPE) is a regularization technique for sorted absolute coefficients in high-dimensional regression. By arbitrarily setting its regularization weights $\lambda$ under the monotonicity constraint, SLOPE…
The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…
The aim of this paper is to introduce a generalization of Steiner symmetrization in Euclidean space for spherical space, which is the dual of the Steiner symmetrization in hyperbolic space introduced by J. Schneider (Manuscripta Math. 60:…
We study numerical integration on the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by…
Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
We consider space-time tracking type distributed optimal control problems for the wave equation in the space-time domain $Q:= \Omega \times (0,T) \subset {\mathbb{R}}^{n+1}$, where the control is assumed to be in the energy space…
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…
We consider the problem of identifying the quantum spin states that are the optimal sensors of a given transformation averaged over all possible orientations of the spin system. Our geometric approach to the problem is based on a fidelity…
We establish a majorization-based theory for bounding observables of waves with varied coherence. For any measurement, exact bounds are attained by the maximal and minimal elements in the set of input coherence spectra. The set's supremum…
We prove a novel method for the embedding of a 3-fold rotationally symmetric sphere-type mesh onto a subset of the plane with 3-fold rotational symmetry. The embedding is free-boundary with the only additional constraint on the image set is…