Related papers: On Euclidean designs and the potential energy
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
A spherical $t$-design is a finite subset $X$ of the unit sphere such that every polynomial of degree at most $t$ has the same average over $X$ as it does over the entire sphere. Determining the minimum possible size of spherical designs,…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
Let $V$ be a $n$-dimensional real vector space. In this paper we introduce the concept of \emph{euclidean} Clifford algebra $\mathcal{C\ell}(V,G_{E})$ for a given euclidean structure on $V,$ i.e., a pair $(V,G_{E})$ where $G_{E}$ is a…
The hyperoctahedral group $H$ in $n$ dimensions (the Weyl group of Lie type $B_n$) is the subgroup of the orthogonal group generated by all transpositions of coordinates and reflections with respect to coordinate hyperplanes. A finite set…
In this paper, we propose a practical Bayesian framework for the calibration and validation of a computer code, and apply it to a case study concerning the energy consumption forecasting of a building. Validation allows to quantify…
We define a metric on $\mathbb{F}_q^n$ using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound and we will give constructions of subspaces of…
The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time,…
The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical significance. In this paper, we construct several new…
The interplay between coding theory and $t$-designs started many years ago. While every $t$-design yields a linear code over every finite field, the largest $t$ for which an infinite family of $t$-designs is derived directly from a linear…
A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known…
We are going to use the nickname "Das Budapester Programm" for a large class of finite combinatorial problems to be posed below. Following Klein's original idea, they concern various dimensional Euclidean spaces and several groups of…
The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…