Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Semantic Equivalence of the Brazilian Portuguese version of the "Body Change Inventory"

With the increase in research on the components of Body Image, validated instruments are needed to evaluate its dimensions. The Body Change Inventory (BCI) assesses strategies used to alter body size among adolescents. The scope of this study was to describe the translation and evaluation for semantic equivalence of the BCI in the Portuguese language. The process involved the steps of (1) translation of the questionnaire to the Portuguese language; (2) back-translation to English; (3) evaluation of semantic equivalence; and (4) assessment of comprehension by professional experts and the target population. The six subscales of the instrument were translated into the Portuguese language. Language adaptations were made to render the instrument suitable for the Brazilian reality. The questions were interpreted as easily understandable by both experts and young people. The Body Change Inventory has been translated and adapted into Portuguese. Evaluation of the operational, measurement and functional equivalence are still needed.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

QUASI-TOPOLOGICAL QUANTUM FIELD THEORIES AND Z(2) LATTICE GAUGE THEORIES

We consider a two-parameter family of Z(2) gauge theories on a lattice discretization T(M) of a three-manifold M and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space Gamma. We show that there is a region Gamma(0) subset of Gamma where the partition function and the expectation value h < W-R(gamma)> i of the Wilson loop can be exactly computed. Depending on the point of Gamma(0), the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of M. The Wilson loop on the other hand, does not depend on the topology of gamma. However, for a subset of Gamma(0), < W-R(gamma)> depends on the size of gamma and follows a discrete version of an area law. At the zero temperature limit, the spin-gauge model approaches the topological and the quasi-topological regions depending on the sign of the coupling constant.

Assessment of Pharmaceutical Equivalence: Difference Test or Equivalence Test?

Pharmaceutical equivalence is an important step towards the confirmation of similarity and Interchangeability among pharmaceutical products, particularly regarding those that win not be tested for bioequivalence. The aim of this paper is to compare traditional difference testing to two one-side equivalence tests in the assessment of pharmaceutical equivalence, by means of equivalence studies between similar, generic and reference products of acyclovir cream, atropine sulfate injection, meropenem for injection, and metronidazole injection. All tests were performed in accordance with the Brazilian Pharmacopeia or the United States Pharmacopeia. All four possible combinations of results arise in these comparisons of difference testing and equivalence testing. Most of the former did not show significant difference, whereas the latter presented similarity. We concluded that equivalence testing is more appropriate than difference testing, what can make it a useful tool to assess pharmaceutical equivalence in products that will not be tested for bioequivalence.

Predicting the connectivity of primate cortical networks from topological and spatial node properties

Abstract Background The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked together, in an attempt to recover the original network structure. Results Inferring primate cortical connectivity from the properties of the nodes, remarkably good reconstructions of the global network organization could be obtained, with the topological features allowing slightly superior accuracy to the spatial ones. Analogous reconstruction attempts for the C. elegans neuronal network resulted in substantially poorer recovery, indicating that cortical area interconnections are relatively stronger related to the considered topological and spatial properties than neuronal projections in the nematode. Conclusion The close relationship between area-based features and global connectivity may hint on developmental rules and constraints for cortical networks. Particularly, differences between the predictions from topological and spatial properties, together with the poorer recovery resulting from spatial properties, indicate that the organization of cortical networks is not entirely determined by spatial constraints.