相关论文: Exact Volume of Zonotopes Generated by a Matrix Pa…

Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…

We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting…

Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…

We develop a method to compute the vacuum polarization energy for coupled scalar fields with different masses scattering off a background potential in one space dimension. As an example we consider the vacuum polarization energy of a…

We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show…

The proliferation of neural networks in safety-critical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…

Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…

We consider a classical system of $N$ particles confined in a box $\Lambda\subset\mathbb{R}^d$ interacting via a finite range pair potential. Given the validity of the cluster expansion in the canonical ensemble we compute the error between…

The effects of a finite system volume on thermodynamic quantities, such as the pressure, energy density, specific heat, speed of sound, conserved charge susceptibilities and correlations, in hot and dense strongly interacting matter are…

This note is a comment to the paper by D.R.Heath-Brown and B.Z.Moroz (Math Proc. Camb. Phil. Soc. 125 (1999)). That paper concerns with the projective surface $S$ in $\mathbb{P}^{3}$ defined by the equation $x_{1}x_{2}x_{3}=x_{4}^{3}$. It…

We discuss various properties of the variational class of continuous matrix product states, a class of ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful…

In these notes, we explain residue formulae for volumes of convex polytopes, and for Ehrahrt polynomials based on the notion of total residue. We apply this method to the computation of the volume of the Chan-Robbins polytope. The final…

Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…

We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…

In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…

We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and prove related results on the critical points of the diameter…

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…