Lindelof spaces which are indestructible, productive, or D

We discuss relationships in Lindelof spaces among the properties "indestructible". "productive", "D", and related properties. (C) 2011 Elsevier B.V. All rights reserved.

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]

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.

Motor learning, retention and transfer after virtual-reality-based training in Parkinson's disease - effect of motor and cognitive demands of games: a longitudinal, controlled clinical study

Objectives To evaluate the learning, retention and transfer of performance improvements after Nintendo Wii Fit (TM) training in patients with Parkinson's disease and healthy elderly people. Design Longitudinal, controlled clinical study. Participants Sixteen patients with early-stage Parkinson's disease and 11 healthy elderly people. Interventions Warm-up exercises and Wii Fit training that involved training motor (shifts centre of gravity and step alternation) and cognitive skills. A follow-up evaluative Wii Fit session was held 60 days after the end of training. Participants performed a functional reach test before and after training as a measure of learning transfer. Main outcome measures Learning and retention were determined based on the scores of 10 Wii Fit games over eight sessions. Transfer of learning was assessed after training using the functional reach test. Results Patients with Parkinson's disease showed no deficit in learning or retention on seven of the 10 games, despite showing poorer performance on five games compared with the healthy elderly group. Patients with Parkinson's disease showed marked learning deficits on three other games, independent of poorer initial performance. This deficit appears to be associated with cognitive demands of the games which require decision-making, response inhibition, divided attention and working memory. Finally, patients with Parkinson's disease were able to transfer motor ability trained on the games to a similar untrained task. Conclusions The ability of patients with Parkinson's disease to learn, retain and transfer performance improvements after training on the Nintendo Wii Fit depends largely on the demands, particularly cognitive demands, of the games involved, reiterating the importance of game selection for rehabilitation purposes. (C) 2012 Chartered Society of Physiotherapy. Published by Elsevier Ltd. All rights reserved.

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.