Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators

We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general setting features stochastic approximations of the cocoercive operator and stochastic perturbations in the evaluation of the resolvents of the set-valued operator. In addition, relaxations and not necessarily vanishing proximal parameters are allowed. Weak and strong almost sure convergence properties of the iterates is established under mild conditions on the underlying stochastic processes. Leveraging these results, we also establish the almost sure convergence of the iterates of a stochastic variant of a primal-dual proximal splitting method for composite minimization problems

The Role of Monotonicity in the Epistemic Analysis of Strategic Games

It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski's Fixpoint Theorem.Comment: 20 page

First report of caprine abortions due to Chlamydia abortus in Argentina.

Infectious abortions of goats in Argentina are mainly associated with brucellosis and toxoplasmosis. In this paper, we describe an abortion outbreak in goats caused by Chlamydia abortus. Seventy out of 400 goats aborted. Placental smears stained with modified Ziehl-Neelsen stain showed many chlamydia-like bodies within trophoblasts. One stillborn fetus was necropsied and the placenta was examined. No gross lesions were seen in the fetus, but the inter-cotyledonary areas of the placenta were thickened and covered by fibrino-suppurative exudate. The most consistent microscopic finding was found in the placenta and consisted of fibrinoid necrotic vasculitis, with mixed inflammatory infiltration in the tunica media. Immunohistochemistry of the placenta was positive for Chlamydia spp. The results of polymerase chain reaction targeting 23S rRNA gene performed on placenta were positive for Chlamydia spp. An analysis of 417 amplified nucleotide sequences revealed 99% identity to those of C. abortus pm225 (GenBank AJ005617) and pm112 (GenBank AJ005613) isolates. To the best of our knowledge, this is the first report of abortion associated with C. abortus in Argentina