29 research outputs found
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 , , 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 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 matemĂĄtico 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 matemĂĄtico aplicado em cĂąncer Ă© considerado para entender os motivos que levam a tratamentos quimioterĂĄpicos mal sucedidos. Frente Ă s implicaçÔes do tratamento oncolĂłgico, as simulaçÔes numĂ©ricas 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 estĂŁo relacionados ao fracasso terapĂȘutico.Coordenação de Aperfeiçoamento de Pessoal de NĂvel Superior (CAPES)Fundação de Amparo a Pesquisa do Estado de SĂŁo Paulo (FAPESP)Conselho Nacional de Desenvolvimento CientĂfico e TecnolĂłgico (CNPq