ar X iv : 0 70 7 . 03 35 v 2 [ m at h . O C ] 2 9 Fe b 20 08 Label - setting methods for Multimode Stochastic Shortest Path problems on graphs

ar X iv : 0 70 7 . 03 35 v 1 [ m at h . O C ] 3 J ul 2 00 7 Label - setting methods for Multimode Stochastic Shortest Path problems on graphs

Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solutions to such a problem is typically computed using the value function, which can be found by solving the corresponding dynamic programming equations. In the deterministic case, these equations can be often solved by the highly efficient label-setting methods (such as Dijkstra’s an...

ar X iv : 0 80 2 . 38 39 v 1 [ m at h . G R ] 2 6 Fe b 20 08 Quadratic equations over free groups are NP - complete

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete

ar X iv : 0 70 7 . 03 09 v 2 [ q - bi o . N C ] 1 3 Fe b 20 08 Dynamic range of hypercubic stochastic excitable media

We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modelled either by a three-state stochastic susceptible-infected-recoveredsusceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h. The response function (mean density of active si...

ar X iv : h ep - p h / 03 02 12 9 v 1 1 7 Fe b 20 03 Scalar σ meson effects in radiative ρ 0 - meson decays

ar X iv : 0 71 2 . 09 14 v 2 [ m at h . FA ] 2 6 Fe b 20 08 CONTRACTION SEMIGROUPS ON METRIC GRAPHS

The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity preserving. Also we provide a characterization of generators of Feller semi-groups on metric graphs.