In 2010, M. Studený, R. Hemmecke, and S. Lindner explored a new algebraic description of graphical models, called characteristic imsets. Compared with standard imsets, characteristic imsets have several advantages: they are still unique vector representatives of conditional independence structures, 0-1 vectors, and more intuitive in terms of graphs than standard imsets. After defining a charact...

Let G be an n-node graph without two disjoint odd cycles. The algorithm of Artmann, Weismantel and Zenklusen (STOC’17) for bimodular integer programs can used to find a maximum weight stable set in strongly polynomial time. Building on structural results characterizing sufficiently connected graphs cycles, we construct size- $$O(n^2)$$ extended formulation the polytope G.

In this note we give the definition of the ”doubling operation” for simple polytopes, find the formula for the h-polynomial of new polytope. As an application of this operation we establish the relationship between moment-angle manifolds and their real analogues and prove the toral rank conjecture for moment-angle manifolds ZP . Let P be a simple n-dimensional polytope with m facets: P = {x ∈ R...

In the spirit of the Genetics of the Regular Figures, by L. Fejes Tóth [FT, Part 2], we prove the following theorem: If 2n points are selected in the n-dimensional Euclidean ball Bn so that the smallest distance between any two of them is as large as possible, then the points are the vertices of an inscribed regular cross-polytope. This generalizes a result of R.A. Rankin [R] for 2n points on t...

Polytope complexes are the generalisation of polygon meshes in geoinformation systems (GIS) to arbitrary dimension, and a natural concept for accessing spatio-temporal information. Complexes of each dimension have a straightforward dimension-independent database representation called Relational Complex. Accordingly, complex overlay is the corresponding generalisation of map overlay in GIS to ar...

polytope Abstract polytope November, 2013 – p. 2 Abstract polytope Abstract polytope −→ combinatorial generalization of convex polytopepolytope Abstract polytope −→ combinatorial generalization of convex polytope November, 2013 – p. 2 Abstract polytope Abstract polytope −→ combinatorial generalization of convex polytopepolytope Abstract polytope −→ combinatorial generalization of convex polytop...

Objective(s): The results of studies on vaccine development for foot-and-mouth disease (FMD) virus show that the use of inactivated vaccines for FMD virus is not completely effective. Novel vaccinations based on immuno-dominant epitopes have been shown to induce immune responses. Furthermore, for safety of immunization, access to efficient adjuvants against FMD virus seems to be critical.Materi...

The combinatorics of reduced words and their commutation classes plays an important role in geometric representation theory. For a semisimple complex Lie group $G$, string polytope is convex associated with each word the longest element $w_0$ Weyl $G$ encoding character certain irreducible $G$. In this paper, we deal case type $A$, i.e., $G = \mathrm{SL}_{n+1}(\mathbb{C})$. A Gelfand–⁠Cetlin on...

The definition of random polytope adopted in this paper restricts consideration to those probability measures satisfying two properties. First, the measure must induce an absolutely continuous distribution over the positions of the bounding hyperplanes of the random polytope; and second, it must result in every point in the space being equally as likely as any other point of lying within the ra...

One of the perennial difficulties in the representation of spatial data in database structures is that of the finite nature of the number representations. The vast majority of the mathematical analyses of the issue are based on the theory of real numbers, and metric space topology. The realization of this theory within a finite precision computer representation has been largely overlooked. Impl...