Critical exponents for the long-range Ising chain using a transfer matrix approach

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance $r^\alpha$, $1<\alpha<2$, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and the number of interaction constants can be independently increased. Systems with interactions between spins up to 18 sites apart and up to 2500 spins in the chain are considered. We obtain data for the critical exponents $\nu$ associated with the correlation length based on the Finite Range Scaling (FRS) hypothesis. FRS expressions require the evaluation of derivatives of the thermodynamical properties, which are obtained with the help of analytical recurrence expressions obtained within the TM framework. The Van den Broeck extrapolation procedure is applied in order to estimate the convergence of the exponents. The TM procedure reduces the dimension of the matrices and circumvents several numerical matrix operations.Comment: 10 pages, 2 figures, Conference NEXT Sigma Ph

On the random neighbor Olami-Feder-Christensen slip-stick model

We reconsider the treatment of Lise and Jensen (Phys. Rev. Lett. 76, 2326 (1996)) on the random neighbor Olami-Feder-Christensen stik-slip model, and examine the strong dependence of the results on the approximations used for the distribution of states p(E).Comment: 6pages, 3 figures. To be published in PRE as a brief repor

Abrupt transitions from reinfections in social contagions

The study of social contagion processes is of utmost importance for understanding the emergence of collective social states. Here we introduce reinfections in the Susceptible-Infected-Recovered (SIR) model so to incorporate the possibility that an individual that ceases its activity (recovered) can resume it due to secondary infections from its active (infected) peers. We show that, when primary infection is less frequent than secondary ones, a typical situation in many social contagion processes, the epidemic transition turns from smooth to abrupt. As a consequence, macroscopic collective states can be triggered from the inactive (healthy) regime by a small increment of the primary contagion rate

Pair approximation for a model of vertical and horizontal transmission of parasites.

We apply Stochastic Dynamics method for a differential equations model, proposed by Marc Lipsitch and collaborators (Proc. R. Soc. Lond. B 260, 321, 1995), for which the transmission dynamics of parasites occurs from a parent to its offspring (vertical transmission), and by contact with infected host (horizontal transmission). Herpes, Hepatitis and AIDS are examples of diseases for which both horizontal and vertical transmission occur simultaneously during the virus spreading. Understanding the role of each type of transmission in the infection prevalence on a susceptible host population may provide some information about the factors that contribute for the eradication and/or control of those diseases. We present a pair mean-field approximation obtained from the master equation of the model. The pair approximation is formed by the differential equations of the susceptible and infected population densities and the differential equations of pairs that contribute to the former ones. In terms of the model parameters, we obtain the conditions that lead to the disease eradication, and set up the phase diagram based on the local stability analysis of fixed points. We also perform Monte Carlo simulations of the model on complete graphs and Erdös-Rényi graphs in order to investigate the influence of population size and neighborhood on the previous mean-field results; by this way, we also expect to evaluate the contribution of vertical and horizontal transmission on the elimination of parasite. Pair Approximation for a Model of Vertical and Horizontal Transmission of Parasites

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

Um modelo matemático em quimioterapia

The mathematical modeling of cancer progression is considered in order to understand the causes that lead to unsuccessful antineoplastic chemotherapy. With regard to the implications of oncological treatment, numerical simulations made possible the comparison of different treatment schedules, specifically examining dose administered and time interval between doses. As clinically expected, the results indicate that low doses and large time intervals between doses are related to unsuccessful clinical outcomes.Modelo matemático aplicado em câncer é considerado para entender os motivos que levam a tratamentos quimioterápicos mal sucedidos. Frente às implicações do tratamento oncológico, as simulações numéricas possibilitaram a comparação de diferentes protocolos de tratamento, quanto a dose administrada e intervalo de tempo entre as doses. Conforme esperado clinicamente, nossos resultados indicam que a administração de baixas doses e longos intervalos de tempo entre as dosagens estão relacionados ao fracasso terapêutico.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq