On the Isotropy Constant of Projections of Polytopes
نویسنده
چکیده
The isotropy constant of any d-dimensional polytope with n vertices is bounded by C p n/d where C > 0 is a numerical constant.
منابع مشابه
Linear Programming, the Simplex Algorithm and Simple Polytopes
In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
متن کاملPixel selection by successive projections algorithm method in multivariate image analysis for a QSAR study of antimicrobial activity for cephalosporins and design new cephalosporins
Thirty-one Cephalosporin compounds were modeled using the multivariate image analysis and applied to the quantitative structure activity relationship (MIA-QSAR) approach. The acid dissociation constants (pKa) of cephalosporins play a fundamental role in the mechanism of activity of cephalosporins. The antimicrobial activity of cephalosporins was related to their first pKa by different models. B...
متن کاملPixel selection by successive projections algorithm method in multivariate image analysis for a QSAR study of antimicrobial activity for cephalosporins and design new cephalosporins
Thirty-one Cephalosporin compounds were modeled using the multivariate image analysis and applied to the quantitative structure activity relationship (MIA-QSAR) approach. The acid dissociation constants (pKa) of cephalosporins play a fundamental role in the mechanism of activity of cephalosporins. The antimicrobial activity of cephalosporins was related to their first pKa by different models. B...
متن کاملVisualizing 3D Projections of Higher Dimensional Polytopes: An Approach Linking Art and Computers
Visualizing higher dimensional polytopes through computer graphics offers a way to understand and to analyze these interesting objects. Such advantages can be improved by considering polytopes’ three-dimensional projections which are embedded in our space. In this work we will describe basic methodologies for polytopes’ visualization and the way such procedures assist the creation of sculptures...
متن کاملBanach-Mazur Distances and Projections on Random Subgaussian Polytopes
We consider polytopes in Rn that are generated by N vectors in Rn whose coordinates are independent subgaussian random variables. (A particular case of such polytopes are symmetric random ±1 polytopes generated by N independent vertices of the unit cube.) We show that for a random pair of such polytopes the Banach-Mazur distance between them is essentially of a maximal order n. This result is a...
متن کامل