Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

Neotropical termites: revision of Armitermes Wasmann (Isoptera, Termitidae, Syntermitinae) and phylogeny of the Syntermitinae

We present a comprehensive phylogenetic analysis of Syntermitinae, including representatives of all genera of the subfamily, along with all 12 species assigned formerly to the genus Armitermes Wasmann (Termitidae, Syntermitinae), and 4 new species described herein. Syntermitinae was recovered as a natural group and the hypothesis that the frontal tube indicates convergence between Syntermitinae and Nasutitermitinae was corroborated. Also, several diagnostic characters proposed in the original description of Syntermitinae are discussed. Alongside the phylogenetic study, a taxonomic revision of the Neotropical genus Armitermes was carried out, resulting in division of the genus into four genera. Taxonomic novelties are: Armitermes now includes A. armiger (Motschulsky), A. bidentatus Rocha & Cancello sp.n. and A. spininotus Rocha & Cancello sp.n.; Silvestritermes Rocha & Cancello gen.n. includes S. euamignathus (Silvestri) comb.n., S. lanei (Canter) comb.n., S. gnomus (Constantino) comb.n., S. duende Rocha & Cancello sp.n., S. minutus (Emerson) comb.n., S. almirsateri Rocha & Cancello sp.n. and S. holmgreni (Snyder) comb.n.; Uncitermes Rocha & Cancello gen.n. includes U. teevani (Emerson) comb.n.; Mapinguaritermes Rocha & Cancello gen.n. includes M. peruanus (Holmgren) comb.n. and M. grandidens (Emerson) comb.n. A new synonymy is proposed for A. cerradoensis Mathews under S. euamignathus. All soldiers are described and illustrated, as are the mandibles and digestive tract of the worker and the imago caste, when available. We provide a dichotomous key, based on soldiers, for all genera of Syntermitinae, and distribution maps and dichotomous keys, based on soldiers, for the species of Armitermes and all the new genera described herein.

Spatial analysis of leprosy incidence and associated socioeconomic factors

OBJECTIVE: To identify clusters of the major occurrences of leprosy and their associated socioeconomic and demographic factors. METHODS: Cases of leprosy that occurred between 1998 and 2007 in Sao Jose do Rio Preto (southeastern Brazil) were geocodified and the incidence rates were calculated by census tract. A socioeconomic classification score was obtained using principal component analysis of socioeconomic variables. Thematic maps to visualize the spatial distribution of the incidence of leprosy with respect to socioeconomic levels and demographic density were constructed using geostatistics. RESULTS: While the incidence rate for the entire city was 10.4 cases per 100,000 inhabitants annually between 1998 and 2007, the incidence rates of individual census tracts were heterogeneous, with values that ranged from 0 to 26.9 cases per 100,000 inhabitants per year. Areas with a high leprosy incidence were associated with lower socioeconomic levels. There were identified clusters of leprosy cases, however there was no association between disease incidence and demographic density. There was a disparity between the places where the majority of ill people lived and the location of healthcare services. CONCLUSIONS: The spatial analysis techniques utilized identified the poorer neighborhoods of the city as the areas with the highest risk for the disease. These data show that health departments must prioritize politico-administrative policies to minimize the effects of social inequality and improve the standards of living, hygiene, and education of the population in order to reduce the incidence of leprosy.