Thierry Corrêa Petit Lobão

Some properties of deformed q-numbers

Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of q-operations on the construction of q-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the q-sum. Finally, we present different patterns of q-Pascals triangles, based on q-sum, whose elements are q-numbers.

Neighborhood properties of complex networks.

A concept of neighborhood in complex networks is addressed based on the criterion of the minimal number of steps to reach other vertices. This amounts to, starting from a given network R1, generating a family of networks Rl, l = 2, 3,... such that, the vertices that are l steps apart in the original R1, are only 1 step apart in Rl. The higher order networks are generated using Boolean operations among the adjacency matrices Ml that represent Rl. The families originated by the well known linear and the Erdös-Renyi networks are found to be invariant, in the sense that the spectra of Ml are the same, up to finite size effects. A further family originated from small world network is identified.

Detecting Network Communities: An Application to Phylogenetic Analysis

This paper proposes a new method to identify communities in generally weighted complex networks and apply it to phylogenetic analysis. In this case, weights correspond to the similarity indexes among protein sequences, which can be used for network construction so that the network structure can be analyzed to recover phylogenetically useful information from its properties. The analyses discussed here are mainly based on the modular character of protein similarity networks, explored through the Newman-Girvan algorithm, with the help of the neighborhood matrix . The most relevant networks are found when the network topology changes abruptly revealing distinct modules related to the sets of organisms to which the proteins belong. Sound biological information can be retrieved by the computational routines used in the network approach, without using biological assumptions other than those incorporated by BLAST. Usually, all the main bacterial phyla and, in some cases, also some bacterial classes corresponded totally (100%) or to a great extent (>70%) to the modules. We checked for internal consistency in the obtained results, and we scored close to 84% of matches for community pertinence when comparisons between the results were performed. To illustrate how to use the network-based method, we employed data for enzymes involved in the chitin metabolic pathway that are present in more than 100 organisms from an original data set containing 1,695 organisms, downloaded from GenBank on May 19, 2007. A preliminary comparison between the outcomes of the network-based method and the results of methods based on Bayesian, distance, likelihood, and parsimony criteria suggests that the former is as reliable as these commonly used methods. We conclude that the network-based method can be used as a powerful tool for retrieving modularity information from weighted networks, which is useful for phylogenetic analysis.

Nondistributive algebraic structures derived from nonextensive statistical mechanics

We propose a two-parametric nondistributive algebraic structure that follows from (q,q′)-logarithm and (q,q′)-exponential functions. Properties of generalized (q,q′)-operators are analyzed. We also generalize the proposal into a multiparametric structure (generalization of logarithm and exponential functions and the corresponding algebraic operators). All n-parameter expressions recover (n−1)-generalization when the corresponding qn→1. Nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures, in which this work is a consequence.

Comparative protein analysis of the chitin metabolic pathway in extant organisms: A complex network approach

Chitin is a structural endogenous carbohydrate, which is a major component of fungal cell walls and arthropod exoskeletons. A renewable resource and the second most abundant polysaccharide in nature after cellulose, chitin is currently used for waste water clearing, cosmetics, medical, and veterinary applications. This work comprises data mining of protein sequences related to the chitin metabolic pathway of completely sequenced genomes of extant organisms pertaining to the three life domains, followed by meta-analysis using traditional sequence similarity comparison and complex network approaches. Complex networks involving proteins of the chitin metabolic pathway in extant organisms were constructed based on protein sequence similarity. Several usual network indices were estimated in order to obtain information on the topology of these networks, including those related to higher order neighborhood properties. Due to the assumed evolutionary character of the system, we also discuss issues related to modularity properties, with the concept of edge betweenness playing a particularly important role in our analysis. Complex network approach correctly identifies clusters of organisms that belong to phylogenetic groups without any a priori knowledge about the biological features of the investigated protein sequences. We envisage the prospect of using such a complex network approach as a high-throughput phylogenetic method.

IDENTIFICATION OF COMMUNITY STRUCTURE IN NETWORKS USING HIGHER ORDER NEIGHBORHOOD CONCEPTS

The identification of community structures in networks is investigated within a framework based on the concepts of higher order neighborhoods and neighborhood matrix

What are the Evolutionary Origins of Mitochondria? A Complex Network Approach

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Comparison of complex networks and tree-based methods of phylogenetic analysis and proposal of a bootstrap method

. This procedure is of relevance especially for networks representing evolutionary situations, since several evidences show that they are assembled from pre-existing smaller structures, rather than by the mere adhesion of individual nodes. We proceed within the successive elimination of the links with largest betweenness degree. The effect of erasing a link at step k is quantified by the distance between

The Isomorphism Problem for Integral Group Rings of a Complete Monomial Group

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SCANNET: A Software for Identifying Network Communities

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