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...

The cyclic polytope C(n, d) is the convex hull of any n points on the moment curve {(t, t2, . . . , td ) : t ∈ R} in Rd . For d ′ > d , we consider the fiber polytope (in the sense of Billera and Sturmfels [6]) associated to the natural projection of cyclic polytopes π : C(n, d ) → C(n, d) which ‘forgets’ the last d ′ − d coordinates. It is known that this fiber polytope has face lattice indexe...

Approximating a given three-dimensional object in order to simplify its handling is a classical topic in computational geometry and related fields. A typical approach is based on incremental approximation algorithms, which start with a small and topologically correct polytope representation (the seed polytope) of a given sample point cloud or input mesh. In addition, a correspondence between th...

An extended formulation of a polytope is a linear description of this polytope using extra variables besides the variables in which the polytope is defined. The interest of extended formulations is due to the fact that many interesting polytopes have extended formulations with a lot fewer inequalities than any linear description in the original space. This motivates the development of methods f...

The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or, more generally, the complete k-partite graph. Lifting is a central tool to ...

The polytope of pointed pseudo triangulations was described in [RSS01]. This polytope is a combinatorial tool to observe all possible pseudo triangulations of a certain point set. Each point of the polytope refers to one possible pseudo triangulation of the point set. To polytope vertices are connected by an edge if their pseudo triangulations just differ in one edge-flip. Once we have a PPT-po...