Geodesic languages for rational subsets and conjugates in virtually free groups

We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that the language of geodesics representing conjugates of elements in a rational subset of a virtually free group is context-free. As a corollary, the doubly generalized conjugacy problem is decidable for rational subsets of finitely generated virtually free groups: there is an algorithm taking as input two rational subset...

On a pseudovariety of finite supersolvable groups

We introduce the pseudovariety of finite groups U =boolean OR(p is an element of & Popf;)Ab(p) & lowast;Ab(p - 1), where & Popf; is the set of all primes. We show that U consists of all finite supersolvable groups with elementary abelian derived subgroup and abelian Sylow subgroups, and so U has decidable membership problem. We prove that it is decidable whether or not a finitely generated subgroup of a free group is closed or dense for the pro-U topology. We consider also the pseudovariety o...

Maximum-expectation matching under recourse

This paper addresses the problem of maximizing the expected size of a matching in the case of unreliable vertices and/or edges. The assumption is that the solution is built in several steps. Ina given step, edges with successfully matched vertices are made permanent; but upon edge or vertex failures, the remaining vertices become eligible for reassignment. This process maybe repeated a given number of times, and the objective is to end with the overall maximum number of matched vertices. An a...

Modeling the Effect of Intravenous Anesthetics: A Path Toward Individualization

The path from complex pharmacokinetic/pharmacodynamic (PK/PD) models to reduced models that allow for runtime parameter estimation and provide good runtime prediction capabilities in the closed-loop cyber-physical system (CPSs) delivering the anesthesia is reported. The path from the administered amount of drug to the measured effect is hence divided into two parts, the pharmacokinetics (PK) and the pharmacodynamics (PD). Due to the fact that the majority of the PK of the drugs can be capture...