搜索结果: 1-15 共查到“理学 polytopes”相关记录30条 . 查询时间(0.125 秒)
COUNTING FACES OF RANDOMLY-PROJECTED POLYTOPES WHEN THE PROJECTION RADICALLY LOWERS DIMENSION
RANDOMLY-PROJECTED RADICALLY LOWERS DIMENSION
2015/8/21
The modern trend in statistics and probability is to consider the case where both
the number of dimensions d and the sample size n are large [19, 21]. In that case, the
intuition fostered by the cla...
Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations
Centrosymetric Polytopes Centrally-Neighborly Polytopes
2015/8/21
Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is
underdetermined, and has many possible solutions (if there are any). In several fields it is
of interest to ...
High-Dimensional Centrally-Symmetric Polytopes With Neighborliness Proportional to Dimension
Centrosymmetric Polytopes Neighborly Polytopes
2015/8/21
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in
R
n
. It has recently been shown that properties of the centrosymmetric polytope P = AC are
of interest for ...
We show that the family of standard simplices and the family of Stasheff polytopes are dual to each other in the following sense.
The chain modules of the standard simplices, resp. the Stasheff poly...
Equivalence Classes of Full-Dimensional 0/1-Polytopes with Many Vertices
n-cube full-dimensional 0/1-polytope symmetry hyperplane Polya theory
2014/6/3
Let Qn denote the n-dimensional hypercube with the vertex set Vn = {0, 1}n. A 0/1-polytope of Qn is a convex hull of a subset of Vn. This paper is concerned with the enumeration of equivalence classes...
Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular ...
Approximations of convex bodies by polytopes and by projections of spectrahedra
convex body spectrahedron approximation computational complex-ity semidefinite programming
2012/4/18
We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d ...
We give a realization of the infinity crystal for affine sl(2) using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito's characterization of the infin...
Given positive integers $d$ and $n$ with $n \geq d+1$, the existence of a normal integral cyclic polytope of dimension $d$ with $n$ vertices is proved. In addition, we show that, for any integers $d \...
Abstract: We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cu...
Reflexive polytopes of higher index and the number 12
Reflexive polytopes higher index the number 12 Algebraic Geometry
2011/9/20
Abstract: We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension ...
On polyhedral approximations of polytopes for learning Bayes nets
polyhedral approximations of polytopes Statistics Theory Bayes nets
2011/9/19
Abstract: We review three vector encodings of Bayesian network structures. The first one has recently been applied by Jaakkola 2010, the other two use special integral vectors formerly introduced, cal...
Inscribing a regular octahedron into polytopes
inscribed polytopes spheric geometry Combinatorics
2011/9/19
Abstract: We prove that any simple polytope (and some non-simple polytopes) in $\mathbb R^3$ admits an inscribed regular octahedron.
On Arnold's Problem on the Classifications of Convex Lattice Polytopes
Arnold's Problem Classifications of Convex Lattice Polytopes Metric Geometry
2011/9/9
Abstract: In 1980, V.I. Arnold studied the classification problem for convex lattice polygons of given area. Since then this problem and its analogues have been studied by B'ar'any, Pach, Vershik, Liu...
Sherali-Adams Relaxations of Graph Isomorphism Polytopes
Sherali-Adams Relaxations Graph Isomorphism Polytopes Combinatorics
2011/8/24
Abstract: We investigate the Sherali-Adams lift & project hierarchy applied to a graph isomorphism polytope whose integer points encode the isomorphisms between two graphs. In particular, the Sherali-...