Related papers: Some Ideas to Test if a Polyhedron is Empty
In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…
We propose a novel generalized method for mass measurements based on phase space singularity structures that can be applied to any event topology with missing energy. Our method subsumes the well-known end-point and transverse mass methods…
Given a deterministic finite automaton and its implementation with at most one single fault, that we can test on a set of inputs, we provide an algorithm to find a test set that guarantees finding whether the fault exists.
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. For example, we develop an algorithm that takes two cubic forms $f, g\in…
The aim of this paper is to present a symbolic computational algorithm that will allow us to deal with the feedback stabilization problem for continuous nonlinear polynomial systems. The overall approach is based on a methodology that…
Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial…
This work explores the potential of spatial model checking of polyhedral models on a number of selected examples. In computer graphics polyhedral models can be found in the form of triangular surface meshes of tetrahedral volume meshes…
A group $G$ has cube-free order if no prime to the third power divides $|G|$. We describe an algorithm that given two cube-free groups $G$ and $H$ of known order, decides whether $G\cong H$, and, if so, constructs an isomorphism $G\to H$.…
We show how to determine if a given simple rectilinear polygon can be tiled with rectangles, each having an integer side.
A simple apparatus to demonstrate free fall weightlessness is given. This can be easily constructed from readily available materials and can be used for the demonstration purpose to an audidence with all the details of the apparatus…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
This paper describes implementation and computational results of a polynomial test of total unimodularity. The test is a simplified version of a prior method. The program also decides two related unimodularity properties. The software is…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
We study anisotropic geometric energy functionals defined on a class of k-dimensional surfaces in a Euclidean space. The classical notion of ellipticity, coming from Almgren, for such functionals is investigated. We prove a variant of a…
We present a simple null test of a dimension of a quantum system, using a single repeated operation in the method of delays, assuming that each instance is identical and independent. The test is well-suited to current feasible quantum…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely,…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
We give an exposition of White's characterization of empty lattice tetrahedra. In particular, we describe the second author's proof of White's theorem that appeared in her doctoral thesis.
The aim of this note is to give an effective criterion to verify whether a cubic polynomial over a non-Archimedean field has a weak N\'{e}ron model or not.