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.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

An extinction-survival-type phase transition in the probabilistic cellular automaton p182-q200

We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram`s enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction-survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

Critical behavior of a contact process with aperiodic transition rates

We performed Monte Carlo simulations to investigate the steady-state critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

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.

The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

Differential Antitumor Effects of IgG and IgM Monoclonal Antibodies and Their Synthetic Complementarity-Determining Regions Directed to New Targets of B16F10-Nex2 Melanoma Cells

Malignant melanoma has increased incidence worldwide and causes most skin cancer-related deaths. A few cell surface antigens that can be targets of antitumor immunotherapy have been characterized in melanoma. This is an expanding field because of the ineffectiveness of conventional cancer therapy for the metastatic form of melanoma. In the present work, antimelanoma monoclonal antibodies (mAbs) were raised against B16F10 cells (subclone Nex4, grown in murine serum), with novel specificities and antitumor effects in vitro and in vivo. MAb A4 (IgG2ak) recognizes a surface antigen on B16F10-Nex2 cells identified as protocadherin beta(13). It is cytotoxic in vitro and in vivo to B16F10-Nex2 cells as well as in vitro to human melanoma cell lines. MAb A4M (IgM) strongly reacted with nuclei of permeabilized murine tumor cells, recognizing histone 1. Although it is not cytotoxic in vitro, similarly with mAb A4, mAb A4M significantly reduced the number of lung nodules in mice challenged intravenously with B16F10-Nex2 cells. The V(H) CDR3 peptide from mAb A4 and V(L) CDR1 and CDR2 from mAb A4M showed significant cytotoxic activities in vitro, leading tumor cells to apoptosis. A cyclic peptide representing A4 CDR H3 competed with mAb A4 for binding to melanoma cells. MAb A4M CDRs L1 and L2 in addition to the antitumor effect also inhibited angiogenesis of human umbilical vein endothelial cells in vitro. As shown in the present work, mAbs A4 and A4M and selected CDR peptides are strong candidates to be developed as drugs for antitumor therapy for invasive melanoma.

Site-directed mutagenesis and structural modeling of Coq10p indicate the presence of a tunnel for coenzyme Q6 binding

Coq10p is a protein required for coenzyme Q function, but its specific role is still unknown. It is a member of the START domain superfamily that contains a hydrophobic tunnel implicated in the binding of lipophilic molecules. We used site-directed mutagenesis, statistical coupling analysis and molecular modeling to probe structural determinants in the Coq10p putative tunnel. Four point mutations were generated (coq10-K50E, coq10-L96S, coq10-E105K and coq10-K162D) and their biochemical properties analysed, as well as structural consequences. Our results show that all mutations impaired Coq10p function and together with molecular modeling indicate an important role for the Coq10p putative tunnel. (C) 2010 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Oriented Percolation in One-dimensional 1/vertical bar x-y vertical bar(2) Percolation Models

We consider independent edge percolation models on Z, with edge occupation probabilities. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104: 547, 1986). The proof is based on multi-scale analysis.

Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P = p/d(s), where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s = 2. The percolation threshold of networks with s < 2 decreases with increasing system size L, while the percolation threshold for networks with s > 2 converges to a finite value. We speculate that s < 2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions, cells originating from more deformable tissues show longer F-actin cytoskeletal filaments. (C) 2008 Elsevier B.V. All rights reserved.

NeXSPheRIO results on elliptic flow and directed flow for Au plus Au and Cu plus Cu collisions at RHIC

Hydrodynamics has been rather successful at describing results obtained in relativistic nuclear collisions at RHIC. Here we show results obtained with NeXSPheRIO on Au+Au collisions and the less studied Cu+Cu collisions. We study elliptic flow and its connection with eccentricity suggested by PHOBOS, as well as present elliptic flow fluctuations. We also show results for directed flow and compare with PHOBOS and STAR data.

Engineering of 3D self-directed quantum dot ordering in multilayer InGaAs/GaAs nanostructures by means of flux gas composition

Lateral ordering of InGaAs quantum dots on the GaAs (001) surface has been achieved in earlier reports, resembling an anisotropic pattern. In this work, we present a method of breaking the anisotropy of ordered quantum dots (QDs) by changing the growth environment. We show experimentally that using As(2) molecules instead of As(4) as a background flux is efficient in controlling the diffusion of distant Ga adatoms to make it possible to produce isotropic ordering of InGaAs QDs over GaAs (001). The control of the lateral ordering of QDs under As(2) flux has enabled us to improve their optical properties. Our results are consistent with reported experimental and theoretical data for structure and diffusion on the GaAs surface.

Directed self-assembly of quantum structures by nanomechanical stamping using probe tips

We demonstrate that nanomechanically stamped substrates can be used as templates to pattern and direct the self-assembly of epitaxial quantum structures such as quantum dots. Diamond probe tips are used to indent or stamp the surface of GaAs( 100) to create nanoscale volumes of dislocation-mediated deformation, which alter the growth surface strain. These strained sites act to bias nucleation, hence allowing for selective growth of InAs quantum dots. Patterns of quantum dots are observed to form above the underlying nanostamped template. The strain state of the patterned structures is characterized by micro-Raman spectroscopy. The potential of using nanoprobe tips as a quantum dot nanofabrication technology are discussed.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

FROM TRISECTIONS IN MODULE CATEGORIES TO QUASI-DIRECTED COMPONENTS

In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander-Reiten components.