On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.

The relationship between hetero-oligomer formation and function of the topological specificity domain of the Escherichia coli MinE protein

MinE is an oligomeric protein that, in conjunction with other Min proteins, is required for the proper placement of the cell division site of Escherichia coli. We have examined the self-association properties of MinE by analytical ultracentrifugation and by studies of hetero-oligomer formation in non-denaturing polyacrylamide gets. The self-association properties of purified MinE predict that cytoplasmic MinE is likely to exist as a mixture of monomers and dimers. Consistent with this prediction, the C-terminal MinE(22-88) fragment forms hetero-oligomers with MinE(+) when the proteins are co-expressed. In contrast, the MinE(36-88) fragment does not form MinE(+)/MinE(36-88) hetero-oligomers, although MinE36-88 affects the topological specificity of septum placement as shown by its ability to induce minicell formation when co-expressed with MinE(+) in wild-type cells. Therefore, hetero-oligomer formation is not necessary for the induction of mini-celling by expression of MinE(36-88) in wild-type cells. The interference with normal septal placement is ascribed to competition between MinE(36-88),nd the corresponding domain in the complete MinE protein for a component required for the topological specificity of septal placement.

The dimerization and topological specificity functions of MinE reside in a structurally autonomous C-terminal domain

Correct placement of the division septum in Escherichia coli requires the co-ordinated action of three proteins, MinC, MinD and MinE. MinC and MinD interact to form a non-specific division inhibitor that blocks septation at all potential division sites. MinE is able to antagonize MinCD in a topologically sensitive manner, as it restricts MinCD activity to the unwanted division sites at the cell poles, Here, we show that the topological specificity function of MinE residues in a structurally autonomous, trypsin-resistant domain comprising residues 31-88, Nuclear magnetic resonance (NMR) and circular dichroic spectroscopy indicate that this domain includes both alpha and beta secondary structure, while analytical ultracentrifugation reveals that it also contains a region responsible for MinE homodimerization. While trypsin digestion indicates that the anti-MinCD domain of MinE (residues 1-22) does not form a tightly folded structural domain, NMR analysis of a peptide corresponding to MinE(1-22) indicates that this region forms a nascent helix in which the peptide rapidly interconverts between disordered (random coil) and alpha-helical conformations, This suggests that the N-terminal region of MinE may be poised to adopt an alpha-helical conformation when it interacts with the target of its anti-MinCD activity, presumably MinD.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Coexistence of Universal and Topological Anomalous Hall Effects in Metal CrO2 Thin Films in the Dirty Limit

The scaling exponent of 1.6 between anomalous Hall and longitudinal conductivity, characteristic of the universal Hall mechanism in dirty-metal ferromagnets, emerges from a series of CrO2 films as we systematically increase structural disorder. Magnetic disorder in CrO2 increases with temperature and this drives a separate topological Hall mechanism. We find that these terms are controlled discretely by structural and magnetic defect populations, and their coexistence leads to apparent divergence from exponent 1.6, suggesting that the universal term is more prevalent than previously realized.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Copper-organic frameworks assembled from in situ generated 5-(4-pyridyl) tetrazole building blocks: synthesis, structural features, topological analysis and catalytic oxidation of alcohols

Two new metal- organic compounds {[Cu-3(mu(3)-4-(p)tz)(4)(mu(2)-N-3)(2)(DMF)(2)](DMF)(2)}(n) (1) and {[Cu(4ptz) (2)(H2O)(2)]}(n) (2) {4-ptz = 5-(4-pyridyl)tetrazolate} with 3D and 2D coordination networks, respectively, have been synthesized while studying the effect of reaction conditions on the coordination modes of 4-pytz by employing the [2 + 3] cycloaddition as a tool for generating in situ the 5-substituted tetrazole ligands from 4-pyridinecarbonitrile and NaN3 in the presence of a copper(II) salt. The obtained compounds have been structurally characterized and the topological analysis of 1 discloses a topologically unique trinodal 3,5,6-connected 3D network which, upon further simplification, results in a uninodal 8-connected underlying net with the bcu (body centred cubic) topology driven by the [Cu-3(mu(2)-N-3)(2)] cluster nodes and mu(3)-4-ptz linkers. In contrast, the 2D metal-organic network in 2 has been classified as a uninodal 4-connected underlying net with the sql [Shubnikov tetragonal plane net] topology assembled from the Cu nodes and mu(2)-4-ptz linkers. The catalytic investigations disclosed that 1 and 2 act as active catalyst precursors towards the microwave-assisted homogeneous oxidation of secondary alcohols (1-phenylethanol, cyclohexanol, 2-hexanol, 3-hexanol, 2-octanol and 3-octanol) with tert-butylhydroperoxide, leading to the yields of the corresponding ketones up to 86% (TOF = 430 h(-1)) and 58% (TOF = 290 h(-1)) in the oxidation of 1-phenylethanol and cyclohexanol, respectively, after 1 h under low power ( 10 W) microwave irradiation, and in the absence of any added solvent or additive.

Invariant integrals applied to nematic liquid crystals with small Ericksen number and topological defects

Invariant integrals are derived for nematic liquid crystals and applied to materials with small Ericksen number and topological defects. The nematic material is confined between two infinite plates located at y = -h and y = h (h is an element of R+) with a semi-infinite plate at y = 0 and x < 0. Planar and homeotropic strong anchoring boundary conditions to the director field are assumed at these two infinite and semi-infinite plates, respectively. Thus, a line disclination appears in the system which coincides with the z-axis. Analytical solutions to the director field in the neighbourhood of the singularity are obtained. However, these solutions depend on an arbitrary parameter. The nematic elastic force is thus evaluated from an invariant integral of the energy-momentum tensor around a closed surface which does not contain the singularity. This allows one to determine this parameter which is a function of the nematic cell thickness and the strength of the disclination. Analytical solutions are also deduced for the director field in the whole region using the conformal mapping method. (C) 2013 Elsevier Ltd. All rights reserved.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Testing native speakers of German and Portuguese on the understanding of topological operators-line-region relations in gvSIG

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

A qualitive reasoning approach for improving query results for sketch based queries by topological analysis of spatial aggregation

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.