Related papers: Normal polytopes: between discrete, continuous, an…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of…
I present a concise review of where we stand in particle physics today. First, I will discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model.
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A…
We give a self-contained introduction to the theory of secondary polytopes and geometric bistellar flips in triangulations of polytopes and point sets, as well as a review of some of the known results and connections to algebraic geometry,…
A very brief overview is presented on some of the current most active areas of research in formal aspects of High Energy Physics and Cosmology. Including the recent breakthrough on the black hole information paradox, developments on…
In this paper we present several results on the expected complexity of a convex hull of $n$ points chosen uniformly and independently from a convex shape. (i) We show that the expected number of vertices of the convex hull of $n$ points,…
We are on the way to obtaining multi-dimensional "pictures" of the proton. The field is bursting with activities, both from the theoretical and experimental side. A brief selection of important achievements of the last years and open…
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
Frequent itemsets form a polytope and can be found and analyzed with Linear Programming.
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last…
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…
We prove that for $n>3$ each generic simple polytope in $\mathbb{R}^n$ contains a point with at least $2n+4$ emanating normals to the boundary. This result is a piecewise-linear counterpart of a long-standing problem about normals to smooth…
The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…
A brief overview is given of some recent advances in charged-composite particle scattering. On the theoretical side, I address the three-charged particle wave function asymptotics, the nonperturbative investigation of the long-range…
In this paper we consider planar polygons with parallel opposite sides. This type of polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For this…
We present a concise review of where we stand in particle physics today. First we discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model.
We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the…