Related papers: polyDB: A Database for Polytopes and Related Objec…

Tadao Oda conjectured that every smooth polytope has the Integer Decomposition Property. In this paper, we show this result for a subclass of polytopes: smooth combinatorial cubes of any dimension.

We present two exact implementations of efficient output-sensitive algorithms that compute Minkowski sums of two convex polyhedra in 3D. We do not assume general position. Namely, we handle degenerate input, and produce exact results. We…

There are (at least) two reasons to study random polytopes. The first is to understand the combinatorics and geometry of random polytopes especially as compared to other classes of polytopes, and the second is to analyze average-case…

Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…

Stochastic dynamic matching problems have recently gained attention in the stochastic-modeling community due to their diverse applications, such as supply-chain management and kidney exchange programs. In this paper, we study a matching…

We present a dynamical systems approach for geometric matchings in an ensemble of polytopes along rigid-body motions. Each polytope can be characterized by a vertex set and edge or faces determined by vertices, and polygons and simplexes…

SOSOPT is a Matlab toolbox for formulating and solving Sum-of-Squares (SOS) polynomial optimizations. This document briefly describes the use and functionality of this toolbox. Section 1 introduces the problem formulations for SOS tests,…

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct…

A short note describing the development of a database providing factual and numerical data on the spectral properties of diatomic molecules. This database is available online for the overall scientific community at the following adress:…

This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…

Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…

Complementarity polytope is a geometric structure that exists in N2-1 dimensional space for an N dimensional Hilbert space. The existence of N + 1 mutually unbiased bases(MUBs) is possible, if such a polytope can be shown to be a subset of…

We present a database created within the project on studying edge-on galaxies. These galaxies provide a unique opportunity to study the three-dimensional distribution of the matter in galaxy disks, which is extremely important for analyzing…

Modern telescopes generate increasingly large and diverse datasets, often consisting of complex and morphologically rich structures. To efficiently explore such data requires automated methods that can extract and organize physically…

Conventionally, high-throughput computational materials searches start from an input set of bulk compounds extracted from material databases, and this set is screened for candidate materials for specific applications. In contrast, many…

We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than…

The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree…

Factorised databases are relational databases that use compact factorised representations at the physical layer to reduce data redundancy and boost query performance. This paper introduces FDB, an in-memory query engine for…

This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…

In this study, the distributions of protein structure classes (or folding types) of experimentally determined structures from a legacy dataset and a comprehensive database (SCOP) are modeled precisely with geometric constructs such as…