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]

Reliability and construct validity of the karate-specific aerobic test

Chaabene, H, Hachana, Y, Franchini, E, Mkaouer, B, Montassar, M, and Chamari, K. Reliability and construct validity of the karate-specific aerobic test. J Strength Cond Res 26(12): 3454-3460, 2012-The aim of this study was to examine absolute and relative reliabilities and external responsiveness of the Karate-specific aerobic test (KSAT). This study comprised 43 male karatekas, 19 of them participated in the first study to establish test-retest reliability and 40, selected on the bases of their karate experience and level of practice, participated in the second study to identify external responsiveness of the KSAT. The latter group was divided into 2 categories: national-level group (G(n)) and regional-level group (Gr). Analysis showed excellent test-retest reliability of time to exhaustion (TE), with intraclass correlation coefficient ICC(3,1) >0.90, standard error of measurement (SEM) <5%: (3.2%) and mean difference (bias) +/- the 95% limits of agreement: -9.5 +/- 78.8 seconds. There was a significant difference between test-retest session in peak lactate concentration (Peak [La]) (9.12 +/- 2.59 vs. 8.05 +/- 2.67 mmol.L-1; p < 0.05) but not in peak heart rate (HRpeak) and rating of perceived exertion (RPE) (196 +/- 9 vs. 194 +/- 9 b.min(-1) and 7.6 +/- 0.93 vs. 7.8 +/- 1.15; p > 0.05), respectively. National-level karate athletes (1,032 +/- 101 seconds) were better than regional level (841 +/- 134 seconds) on TE performance during KSAT (p < 0.001). Thus, KSAT provided good external responsiveness. The area under the receiver operator characteristics curve was >0.70 (0.86; confidence interval 95%: 0.72-0.95). Significant difference was detected in Peak [La] between national- (6.09 +/- 1.78 mmol.L-1) and regional-level (8.48 +/- 2.63 mmol.L-1) groups, but not in HRpeak (194 +/- 8 vs. 195 +/- 8 b.min(-1)) and RPE (7.57 +/- 1.15 vs. 7.42 +/- 1.1), respectively. The result of this study indicates that KSAT provides excellent absolute and relative reliabilities. The KSAT can effectively distinguish karate athletes of different competitive levels. Thus, the KSAT may be suitable for field assessment of aerobic fitness of karate practitioners.

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.

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.

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.