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]

Synthesis, characterization, optical absorption, luminescence and defect centres in Er3+ and Yb3+ co-doped MgAl2O4 phosphors

The Er3+-Yb3+ co-doped MgAl2O4 phosphor powders have been prepared by the combustion method. The phosphor powders are well characterized by X-ray diffraction (XRD) and energy dispersive (EDX) techniques. The absorption spectrum of Er3+/Er3+-Yb3+ doped/co-doped phosphor powder has been recorded in the UV-Vis-NIR region of the electro-magnetic spectrum. The evidence for indirect pumping under 980 nm excitation of Er3+ from Yb3+ was observed in the MgAl2O4 matrix material. Electron spin resonance (ESR) studies were carried out to identify the defect centres responsible for the thermally stimulated luminescence (TSL) process in MgAl2O4:Er3+ phosphor. Three defect centres were identified in irradiated phosphor by ESR measurements which were carried out at room temperature and these were assigned to an O- ion and F+ centres. O- ion (hole centre) appears to correlate with the low temperature TSL peak at 210 A degrees C and one of the F+ centres (electron centre) is related to the high temperature peak at 460 A degrees C.

Synthesis, characterisation, luminescence and defect centres in solution combustion synthesised CaZrO3:Tb3+ phosphor

Tb3+ doped CaZrO3 has been prepared by an easy solution combustion synthesis method. The combustion derived powder was investigated by X-ray diffraction, Fourier-transform infrared spectrometry and scanning electron microscopy techniques. A room temperature photoluminescence study showed that the phosphors can be efficiently excited by 251 nm light with a weak emission in the blue and orange region and a strong emission in green light region. CaZrO3:Tb3+ exhibits three thermoluminescence (TL) glow peaks at 126 degrees C, 200 degrees C and 480 degrees C. Electron Spin Resonance (ESR) studies were carried out to study the defect centres induced in the phosphor by gamma irradiation and also to identify the centres responsible for the TL peaks. The room temperature ESR spectrum of irradiated phosphor appears to be a superposition of two distinct centres. One of the centres (centre I) with principal g-value 2.0233 is identified as an O- ion. Centre II with an axial symmetric g-tensor with principal values g(parallel to) = 1.9986 and g(perpendicular to) = 2.0023 is assigned to an F+ centre (singly ionised oxygen vacancy). An additional defect centre is observed during thermal annealing experiments and this centre (assigned to F+ centre) seems to originate from an F centre (oxygen vacancy with two electrons). The F centre and also the F+ centre appear to correlate with the observed high temperature TL peak in CaZrO3:Tb3+ phosphor. (c) 2012 Elsevier B.V. All rights reserved.

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.

Computed tomography to evaluate the association of fragmented heterolog cortical bone and methylmethacrylate to repare segmental bone defect produced in tibia of rabbits

A 6mm segmental defect was performed on the metaphyseal region of the tibia of 12 rabbits and the autoclaved fragmented heterolog cortical bone conserved in glycerin (98%) and methylmethacrylate was used as a bone graft for the reconstruction. The graft was placed in the receptor bed and its integration was evaluated by computed tomography after 30, 60 and 90 days. There was gradual bone graft incorporation in the receptor bed during the time in 100% of the cases. Fragmented cortical bone heterograft and methylmethacrylate was biologically compatible and promotes bone defect reparation without signs of infection, migration and or rejection, featuring a new option of osseous substitute to fill in bone defects.

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.