The present paper studies the \textit{approximate value iteration} (AVI) algorithm for the average cost criterion with bounded costs and Borel spaces. It is shown the convergence of the algorithm and provided a performance bound assuming that the model satisfies a standard continuity-compactness assumption and a uniform ergodicity condition. This is done for the class of approximation procedures that can be represented by linear positive operators which give exact representation of constant functions and also satisfy certain continuity property. The main point is that these operators define transition probabilities on the state space of the controlled system. This has the following important consequences: (a) the approximating function is the average value of the target function with respect to the induced transition probability; (b) the approximation step in the AVI algorithm can be seen as a perturbation of the original Markov model; (c) the perturbed model inherits the ergodicity properties imposed on the original Markov model. These facts allow to bound the AVI algorithm performance in terms of the accuracy of the approximations given by this kind of operators for the primitive data model, namely, the one-step reward function and the system transition law. The bounds are given in terms of the supremum norm of bounded functions and the total variation norm of finite-signed measures. The results are illustrated with numerical approximations for a class of single item inventory systems with linear order cost, no set-up cost and no back-orders.
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.
We have assessed the phylogenetic status of the Leishmania genome project Friedlin reference strain by MLEE and multiprimer RAPD including a set of 9 stocks representative of the main Leishmania species and of the whole genetic diversity of the Leishmania genus. To our knowledge, the detailed genetic characterization of the Friedlin strain has never been published before. As previously recorded (Tibayrenc et al. 1993), MLEE and RAPD data gave congruent phylogenetic results. The Friedlin reference strain was definitely attributed to Leishmania (Leishmania) major Yakimoff et Schokhor, 1914. Five specific RAPD patterns made it possible to distinguish between the Friedlin strain and the 2 other L. (L.) major stocks included in the study. Various specific MLEE and RAPD characters permitted to distinguish between the Leishmania species included in the study. All these characters are usable to detect accidental laboratory mix-ups involving the Friedlin reference strain. In confirmation with previous studies involving a more limited set of genetic markers, the general genetic diversity of the Leishmania genus proved to be considerable. It must be made clear that only one strain cannot be considered as representative of the whole genetic variability of the genus Leishmania. In the future, it is therefore advisable to complement the results obtained in the framework of the Leishmania genome project with data from other strains that should be selected on a criterion of important genetic differences with the Friedlin strain.
The parasitic caterpillars of Maculinea (Lepidoptera: Lycaenidae) need to be adopted and nursed by ants of the genus Myrmica (Hymenoptera: Formicidae). Each Maculinea species is locally associated with one or a few main and often several secondary host species. To determine whether the parasite-host associations bear marks of cophylogenetic constraints, we reconstructed phylogenies of Maculinea and Myrmica using DNA sequence data. We searched for evidence of cospeciation with a tree-independent (ParaFit) and tree-based (TreeFitter) method. This did not reveal any indication of phylogenetic host tracking in Maculinea. This agrees with earlier insights, which emphasise that as most of the potential host ant populations are never infested by Maculinea, the selective pressure of the butterflies on Myrmica is likely to be slight. Each Maculinea species also specialises on one or a few host plant species before adoption by ants. We suggest that Maculinea species have a substantial potential to accommodate evolutionarily to geographically changing ranges of potential Myrmica hosts, available at the oviposition sites of the butterflies. We use recently published evidence on geographically varying host ant species to discuss a suite of plausible scenarios of adaptive shifts to new Myrmica host species. and Gunther Jansen, Kari Vepsäläinen, Riitta Savolainen.