Comparative RH Maps of the River Buffalo and Bovine Y Chromosomes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Topological signatures in CMB temperature anisotropy maps

We propose an alternative formalism to simulate cosmic microwave background (CMB) temperature maps in Lambda CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature of the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulas might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show patterns of alignment, and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., T-1 topology.

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Betti number of the union of two generic map images

Let f: M --> N and g: K --> N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Development of environmental and natural vulnerability maps for Brazilian coastal at Sao Sebastiao in São Paulo State

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Colonization of a 'Lost World': Encrustation patterns in modern subtropical brachiopod assemblages.

The encrustation of Paleozoic rhynchonelliform brachiopods has been studied for decades, but modern brachiopods have not received similar scrutiny. The discovery of abundant subtropical brachiopods from the Southeast Brazilian Bight provides an unprecedented opportunity to assess epibiont abundance, diversity, and encrustation patterns in modern brachiopod assemblages. Across the outer shelf, encrustation frequencies vary among taxa, from mean values of 0.45% for Platidia to 9.3% for Argyrotheca. Encrustation frequencies for Bouchardia increase from 1.6% on the outer shelf to 84% on the inner shelf Larger valves are encrusted more frequently, and epibionts preferentially colonize valve interiors. Increased encrustation on the inner shelf may reflect the greater surface area of larger hosts, longer exposure of dead shells, water-mass characteristics, sedimentation rates, productivity, or other factors that vary with depth. Inner-shelf brachiopods exhibit encrustation frequencies comparable to those reported for epifaunal bivalves. The epibiont fauna is dominated by bryozoans and serpulids, with minor roles played by spirorbids, bivalves, barnacles, foraminifera, algae, and other taxa. Epibiont abundance at each site is highly variable, but sites are similar in rank importance of epibiont taxa. A different suite of epibionts colonized Paleozoic brachiopods, but similar patterns of encrustation have been observed, including preferential settlement according to valve morphology. These results provide a baseline for evaluating the encrustation of modern bivalves and ancient brachiopods, and may elucidate the macroevolutionary history of epibionts and their relationship to their hosts.

Platinum Group Minerals in Eastern Brazil GEOLOGY AND OCCURRENCES IN CHROMITITE AND PLACERS

Brazil does not have working platinum mines, nor even large reserves of the platinum metals, but there is platinum in Brazil. In this paper, four massifs (mafic/ultramafic complexes) in eastern Brazil, in the states of Minas Gerais and Ceara, where platinum is found will be described. Three of these massifs contain concentrations of platinum group minerals or platinum group elements, and gold, associated with the chromitite rock found there. In the fourth massif, in Minas Gerais State, the platinum group elements are found in alluvial deposits at the Bom Sucesso occurrence. This placer is currently being studied.

Simulation of electron density maps for two-dimensional crystal structures using Mathematica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.