Let $(X, D)$ be a log variety with an effective holomorphic torus action, and $\Theta$ closed positive $(1,1)$-current. For any smooth function $g$ defined on the moment polytope of we study Monge-Amp\`{e}re equations that correspond to generalized twisted K\"{a}hler-Ricci $g$-solitons. We prove version Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing existence solutions...

Let S be a convex polytope. The set of all valid inequalities carries the structure of a convex polytope S, called the polar (polytope) of S. The facial structure of the polar provides information for each of its points: two points a and b are in the same face of S if and only if the faces of S obtained by intersecting it with the hyperplanes given respectively by a and b coincide. Suppose now ...

This theoretical paper is inspired by an integer linear programming (ILP) approach to learning the structure of decomposable models. We intend to represent decomposable models by special zeroone vectors, named characteristic imsets. Our approach leads to the study of a special polytope, defined as the convex hull of all characteristic imsets for chordal graphs, named the chordal graph polytope....

The monomial initial ideals of a graded polynomial ideal are in bijection with the vertices of a convex polytope known as the state polytope of the ideal. The Grr obner fan of the ideal is the normal fan of its state polytope. In this paper we present a software system called TiGERS (Toric Grr obner bases Enumeration by Reverse Search) for computing the Grr obner fan of a toric ideal by enumera...

We study the problem of how to obtain an integer realization of a 3d polytope when an integer realization of its dual polytope is given. We focus on grid embeddings with small coordinates and develop novel techniques based on Colin de Verdière matrices and the Maxwell–Cremona lifting method. We show that every truncated 3d polytope with n vertices can be realized on a grid of size O(n). Moreove...

Compelling evidence now suggests that alphabeta CD8 cytotoxic T lymphocytes (CTL) have an important role in preventing human immunodeficiency virus (HIV) infection and/or slowing progression to AIDS. Here, we describe an HIV type 1 CTL polyepitope, or polytope, vaccine comprising seven contiguous minimal HLA A2-restricted CD8 CTL epitopes conjoined in a single artificial construct. Epitope-spec...

For n 2, the boolean quadric polytope P n is the convex hull in d := ? n+1 2 dimensions of the binary solutions of x i x j = y ij , for all i < j in N := f1; 2; :::; ng. The polytope is naturally modeled by a somewhat larger polytope; namely, Q n the solution set of y ij x i , y ij x j , x i + x j 1 + y ij , y ij 0, for all i; j in N. In a rst step toward seeing how well Q n approximates P n , ...

human cytomegalovirus is one of the most common pathogenic viruses all over the world. in congenital infection leads to neurologic severe disorders and even death of fetus and in individuals with immunosuppression may also cause severe clinical symptoms. multiple evidence indicate that among several strategies, epitope-based vaccine (evs) that can induce both humoral and cellular immunity respo...

Let G be a finite graph allowing loops, having no multiple edge and no isolated vertex. We associate G with the edge polytope PG and the toric ideal IG. By classifying graphs whose edge polytope is simple, it is proved that the toric ideals IG of G possesses a quadratic Gröbner basis if the edge polytope PG of G is simple. It is also shown that, for a finite graph G, the edge polytope is simple...

The topic of our research is unconstrained 0-1 quadratic programming. We find some properties of the Boolean Quadric Polytope, which is obtained from the standard linearization of the given 0-1 quadratic function. By using a result obtained by Deza and Laurent on a class of hypermetric inequalities for the Cut Polytope, we find a necessary and sufficient condition for a class of inequalities to...