A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

An asymmetric sandpile model with height restriction

We analyze by numerical simulations and mean-field approximations an asymmetric version of the stochastic sandpile model with height restriction in one dimension. Each site can have at most two particles. Single particles are inactive and do not move. Two particles occupying the same site are active and may hop to neighboring sites following an asymmetric rule. Jumps to the right or to the left occur with distinct probabilities. In the active state, there will be a net current of particles to the right or to the left. We have found that the critical behavior related to the transition from the active to the absorbing state is distinct from the symmetrical case, making the asymmetry a relevant field.

Glassy states in the stochastic Potts model

We have studied by numerical simulations the relaxation of the stochastic seven-state Potts model after a quench from a high temperature down to a temperature below the first-order transition. For quench temperatures just below the transition temperature the phase ordering occurs by simple coarsening under the action of surface tension. For sufficient low temperatures however the straightening of the interface between domains drives the system toward a metastable disordered state, identified as a glassy state. Escaping from this state occurs, if the quench temperature is nonzero, by a thermal activated dynamics that eventually drives the system toward the equilibrium state. (C) 2009 Elsevier B.V. All rights reserved.

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Culture-area relation in Axelrod`s model for culture dissemination

Axelrod`s model for culture dissemination offers a nontrivial answer to the question of why there is cultural diversity given that people`s beliefs have a tendency to become more similar to each other`s as they interact repeatedly. The answer depends on the two control parameters of the model, namely, the number F of cultural features that characterize each agent, and the number q of traits that each feature can take on, as well as on the size A of the territory or, equivalently, on the number of interacting agents. Here, we investigate the dependence of the number C of distinct coexisting cultures on the area A in Axelrod`s model, the culture-area relationship, through extensive Monte Carlo simulations. We find a non-monotonous culture-area relation, for which the number of cultures decreases when the area grows beyond a certain size, provided that q is smaller than a threshold value q (c) = q (c) (F) and F a parts per thousand yen 3. In the limit of infinite area, this threshold value signals the onset of a discontinuous transition between a globalized regime marked by a uniform culture (C = 1), and a completely polarized regime where all C = q (F) possible cultures coexist. Otherwise, the culture-area relation exhibits the typical behavior of the species-area relation, i.e., a monotonically increasing curve the slope of which is steep at first and steadily levels off at some maximum diversity value.

The n-site approximation for the triplet-creation model

The nonequilibrium phase transition of the one-dimensional triplet-creation model is investigated using the n-site approximation scheme. We find that the phase diagram in the space of parameters (gamma, D), where gamma is the particle decay probability and D is the diffusion probability, exhibits a tricritical point for n >= 4. However, the fitting of the tricritical coordinates (gamma(t), D(t)) using data for 4 <= n <= 13 predicts that gamma(t) becomes negative for n >= 26, indicating thus that the phase transition is always continuous in the limit n -> infinity. However, the large discrepancies between the critical parameters obtained in this limit and those obtained by Monte Carlo simulations, as well as a puzzling non-monotonic dependence of these parameters on the order of the approximation n, argue for the inadequacy of the n-site approximation to study the triplet-creation model for computationally feasible values of n.

Molecular Basis of the Thermostability and Thermophilicity of Laminarinases: X-ray Structure of the Hyperthermostable Laminarinase from Rhodothermus marinus and Molecular Dynamics Simulations

Glycosyl hydrolases are enzymes capable of breaking the glycosidic linkage of polysaccharides and have considerable industrial and biotechnological applications. Driven by the later applications, it is frequently desirable that glycosyl hydrolases display stability and activity under extreme environment conditions, such as high temperatures and extreme pHs. Here, we present X-ray structure of the hyperthermophilic laminarinase from Rhodothermus marinus (RmLamR) determined at 1.95 angstrom resolution and molecular dynamics simulation studies aimed to comprehend the molecular basis, for the thermal stability of this class of enzymes. As most thermostable proteins, RmLamR contains a relatively large number of salt bridges, which are not randomly distributed on the structure. On the contrary, they form clusters interconnecting beta-sheets of the catalytic domain. Not all salt bridges, however, are beneficial for the protein thermostability: the existence of charge-charge interactions permeating the hydrophobic core of the enzymes actually contributes to destabilize the structure by facilitating water penetration into hydrophobic cavities, as can be seen in the case of mesophilic enzymes. Furthermore, we demonstrate that the mobility of the side-chains is perturbed differently in each class of enzymes. The side-chains of loop residues surrounding the catalytic cleft in the mesophilic laminarinase gain mobility and obstruct the active site at high temperature. By contrast, thermophilic laminarinases preserve their active site flexibility, and the active-site cleft remains accessible for recognition of polysaccharide substrates even at high temperatures. The present results provide structural insights into the role played by salt-bridges and active site flexibility on protein thermal stability and may be relevant for other classes of proteins, particularly glycosyl hydrolases.

PACKMOL: A Package for Building Initial Configurations for Molecular Dynamics Simulations

Adequate initial configurations for molecular dynamics simulations consist of arrangements of molecules distributed in space in such a way to approximately represent the system`s overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different molecules Must keep safe pairwise distances. Obtaining Such a molecular arrangement can be considered it packing problem: Each type molecule must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different molecules Must be greater than some specified tolerance. We have developed a code able to pack millions of atoms. grouped in arbitrarily complex molecules, inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one molecule of each type and the geometrical constraints that each type of molecule must satisfy. Building complex mixtures, interfaces, solvating biomolecules in water, other solvents, or mixtures of solvents, is straight forward. In addition. different atoms belonging to the same molecule may also be restricted to different spatial regions, in Such a way that more ordered molecular arrangements call be built, as micelles. lipid double-layers, etc. The packing time for state-of-the-art molecular dynamics systems varies front a few seconds to a few Minutes in a personal Computer. The input files are simple and Currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and call be downloaded front http://www.ime.unicamp.br/similar to martinez/packmol/. (C) 2009 Wiley Periodicals. Inc. J Comput Chem 30: 2157-2164, 2009

Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

The shoving model for the glass-former LiCl center dot 6H(2)O: A molecular dynamics simulation study

Molecular dynamics (MD) simulations of LiCl center dot 6H(2)O Showed that the diffusion coefficient D, and also I lie structural relaxation time , follow a power law at high temperatures, D(-1) proportional to (T - T(0))(-mu), with the same experimental parameters for viscosity (T(0) = 207 K, mu = 2.08). Decoupling between D and occurs at T(x) similar to 1.1 T(0). High frequency acoustic excitations for the LiCl center dot 6H(2)O model were obtained by the calculation of time correlation functions of mass current fluctuations. The temperature dependence of the instantaneous shear modulus, G,(T), was considered in the shoving model for supercooled liquids [J.C. Dyre, T. Christensen, N.B. Olsen, J. Non-Cryst. Solids 352 (2006) 4635] resulting in a linear relationship log (D(-1)) vs. G root T. (C) 2009 Elsevier B.V. All rights reserved.