The Frank-Wolfe algorithm is a method for constrained optimization relying on linear minimizations, as opposed to projections. Therefore, motivation put forward in large body of work the computational advantage solving minimizations instead However, discussions supporting this are often incomplete. We review complexity bounds both tasks several sets commonly used optimization. Projection method...

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...

There are two positive, absolute constants c1 and c2 so that the volume of the difference set of the d-dimensional Euclidean ball and an inscribed polytope with n vertices is larger than c2 d n − 2 d−1 vold(B d 2 ) for n ≥ (c1 d) d−1 2 . 1991 Mathematics Subject Classification. 52A22. Yehoram Gordon was partially supported by the Fund for the Promotion of Research at the Technion Carsten Schütt...

We prove that all combinatorial diierential manifolds involving only Euclidean oriented matroids are PL manifolds. In doing so we introduce a new notion of triangulations of oriented matroids, and show that any triangulation of a Euclidean oriented matroid is a PL sphere. In Section 5 we adapt these results to get a new deenition of tri-angulations of oriented matroid polytopes, and show that a...

A Helly-type theorem for diameter provides a bound on the of intersection finite family convex sets in $\mathbb{R}^d$ given some information all sufficiently small subfamilies. We prove fractional and colorful versions long-standing conjecture by Bárány, Katchalski, Pach. also show that Minkowski norm admits an exact if only its unit ball is polytope version those do. Finally, we theorems prope...

A periodic graph in dimension d is a directed graph with a free action of Z with only finitely many orbits. It can conveniently be represented in terms of an associated finite graph with weights in Z. Here we use the weight sums along cycles in this associated graph to construct a certain polytope in R, which we regard as a geometrical invariant associated to the periodic graph. It is the unit ...