FLOWS WITHOUT WANDERING POINTS ON COMPACT CONNECTED SURFACES

Given a compact 2 dimensional manifold M we classify all continuous flows phi without wandering points on M. This classification is performed by finding finitely many pairwise disjoint open phi-invariant subsets {U(1), U(2), ..., U(n)} of M such that U(i=1)(n) (U(i)) over bar = M and each U(i) is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of phi.

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

TRANSITIVE CIRCLE EXCHANGE TRANSFORMATIONS WITH FLIPS

We study the existence of transit we exchange transformations with flips defined on the unit circle S(1). We provide a complete answer to the question of whether there exists a transitive exchange transformation of S(1) defined on a subintervals and having f flips.

Exchange transformations reversing orientation

University of Sao Paulo (USP)

Bacterial communities and biogeochemical transformations of iron and sulfur in a high saltmarsh soil profile

Microbial community structure in saltmarsh soils is stratified by depth and availability of electron acceptors for respiration. However, the majority of the microbial species that are involved in the biogeochemical transformations of iron (Fe) and sulfur (S) in such environments are not known. Here we examined the structure of bacterial communities in a high saltmarsh soil profile and discuss their potential relationship with the geochemistry of Fe and S. Our data showed that the soil horizons Ag (oxic-suboxic), Bg (suboxic), Cri (anoxic with low concentration of pyrite Fe) and Cr-2 (anoxic with high concentrations of pyrite Fe) have distinct geochemical and microbiological characteristics. In general, total S concentration increased with depth and was correlated with the presence of pyrite Fe. Soluble + exchangable-Fe, pyrite Fe and acid volatile sulfide Fe concentrations also increased with depth, whereas ascorbate extractable-Fe concentrations decreased. The occurrence of reduced forms of Fe in the horizon Ag and oxidized Fe in horizon Cr-2 suggests that the typical redox zonation, common to several marine sediments, does not occur in the saltmarsh soil profile studied. Overall, the bacterial community structure in the horizon Ag and Cr-2 shared low levels of similarity, as compared to their adjacent horizons, Bg and Cr-1, respectively. The phylogenetic analyses of bacterial 16S rRNA gene sequences from clone libraries showed that the predominant phylotypes in horizon Ag were related to Alphaproteobacteria and Bacteroidetes. In contrast, the most abundant phylotypes in horizon Cr-2 were related to Deltaproteo-bacteria, Chloroflexi, Deferribacteres and Nitrospira. The high frequency of sequences with low levels of similarity to known bacterial species in horizons Ag and Cr-2 indicates that the bacterial communities in both horizons are dominated by novel bacterial species. (c) 2008 Elsevier Ltd. All rights reserved.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.