Symmetric edge polytopes are a class of lattice constructed from finite simple graphs. In the present paper we highlight their connections to Kuramoto synchronization model in physics -- where they called adjacency and Kantorovich--Rubinstein metric space theory. Each these motivates study symmetric particular classes We focus on such apply algebraic-combinatorial methods investigate invariants...

Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone C and its dual C∗. We show that whether some one-way communication complexity problems can be solved within a GPT is equivalent to the recently introduced cone factorisation of the corresponding communication matrix M . We also prove an analogue of Holevo’...

The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last these, for which least is known, in particular understanding polytopes psd-minimal. prove existence an obstruction psd-minimality efficiently computable lattice membership...

We consider the decidability of state-to-state reachability in linear time-invariant control systems, with control sets defined by boolean combinations of linear inequalities. Decidability of the sub-problem in which control sets are linear subspaces is a fundamental result in control theory. We first show that reachability is undecidable if the set of controls is a finite union of affine subsp...

No part of this Journal may be reproduced in any form, by print, photoprint, mi-croolm or any other means without written permission from Faculty of Technical : Abstract We devise a new simplex pivot rule which has interesting theoretical properties. Beginning with a basic feasible solution, and any nonbasic variable having a negative reduced cost, the pivot rule produces a sequence of pivots s...

Ever since Valiant and Vazirani [VV86] showed that there exists a random reduction from SAT to USAT, the complexity of USAT has been cited as “USAT is complete for DP under randomized reductions.” However, the definition of the randomized reduction was never quite satisfying because the probability of a “correct” reduction can approach zero as the length of the formula increases. The discrepanc...