An algorithm for counting circuits: application to real-world and random graphs

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world networks, it allows to estimate exponentially large numbers of circuits in polynomial time. We illustrate the method by studying a graph of the Internet structure.Comment: 7 pages, 3 figures, minor corrections, accepted versio

Ordinary Percolation with Discontinuous Transitions

Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a nontrivial critical point. There, the usual order parameter, describing the probability of any node to be part of the largest cluster, jumps instantly to a finite value. Here, we provide a simple example of this transition in form of a small-world network consisting of a one-dimensional lattice combined with a hierarchy of long-range bonds that reveals many features of the transition in a mathematically rigorous manner.Comment: RevTex, 5 pages, 4 eps-figs, and Mathematica Notebook as Supplement included. Final version, with several corrections and improvements. For related work, see http://www.physics.emory.edu/faculty/boettcher

Oscillations and dynamics in a two-dimensional prey-predator system

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbours, we conclude that temporal oscillations of these densities vanish in the thermodynamic limit. This result suggests that such oscillations do not exist in two-dimensional models, at least when driven by local dynamics. Depending on the control parameter, the model could be either in an active or in an absorbing phase, which are separated by the critical point. The critical behaviour of this model is studied using the dynamical Monte Carlo method. This model has two dynamically nonsymmetric absorbing states. In principle both absorbing states can be used for the analysis of the critical point. However, dynamical simulations which start from the unstable absorbing state suffer from metastable-like effects, which sometimes renders the method inefficient.Comment: 7 eps figures, Phys.Rev.E - in pres

Palaeoclimatic conditions in the Mediterranean explain genetic diversity of Posidonia oceanica seagrass meadows

Past environmental conditions in the Mediterranean Sea have been proposed as main drivers of the current patterns of distribution of genetic structure of the seagrass Posidonia oceanica, the foundation species of one of the most important ecosystems in the Mediterranean Sea. Yet, the location of cold climate refugia (persistence regions) for this species during the Last Glacial Maximum (LGM) is not clear, precluding the understanding of its biogeographical history. We used Ecological Niche Modelling together with existing phylogeographic data to locate Pleistocene refugia in the Mediterranean Sea and to develop a hypothetical past biogeographical distribution able to explain the genetic diversity presently found in P. oceanica meadows. To do that, we used an ensemble approach of six predictive algorithms and two Ocean General Circulation Models. The minimum SST in winter and the maximum SST in summer allowed us to hindcast the species range during the LGM. We found separate glacial refugia in each Mediterranean basin and in the Central region. Altogether, the results suggest that the Central region of the Mediterranean Sea was the most relevant cold climate refugium, supporting the hypothesis that long-term persistence there allowed the region to develop and retain its presently high proportion of the global genetic diversity of P. oceanica.Fundacao para a Ciencia e a Tecnologia (FCT, Portugal) [SFRH/BPD/85040/2012]; FCT [UID/Multi/04326/2013, FCT-BIODIVERSA/004/2015]; Pew foundation (USA)info:eu-repo/semantics/publishedVersio

Toxoplasma gondii Clonal Strains All Inhibit STAT1 Transcriptional Activity but Polymorphic Effectors Differentially Modulate IFN gamma Induced Gene Expression and STAT1 Phosphorylation

Host defense against the parasite Toxoplasma gondii requires the cytokine interferon-gamma (IFNγ). However, Toxoplasma inhibits the host cell transcriptional response to IFNγ, which is thought to allow the parasite to establish a chronic infection. It is not known whether all strains of Toxoplasma block IFNγ-responsive transcription equally and whether this inhibition occurs solely through the modulation of STAT1 activity or whether other transcription factors are involved. We find that strains from three North American/European clonal lineages of Toxoplasma, types I, II, and III, can differentially modulate specific aspects of IFNγ signaling through the polymorphic effector proteins ROP16 and GRA15. STAT1 tyrosine phosphorylation is activated in the absence of IFNγ by the Toxoplasma kinase ROP16, but this ROP16-activated STAT1 is not transcriptionally active. Many genes induced by STAT1 can also be controlled by other transcription factors and therefore using these genes as specific readouts to determine Toxoplasma inhibition of STAT1 activity might be inappropriate. Indeed, GRA15 and ROP16 modulate the expression of subsets of IFNγ responsive genes through activation of the NF-κB/IRF1 and STAT3/6 transcription factors, respectively. However, using a stable STAT1-specific reporter cell line we show that strains from the type I, II, and III clonal lineages equally inhibit STAT1 transcriptional activity. Furthermore, all three of the clonal lineages significantly inhibit global IFNγ induced gene expression

Stochastic dynamics and mean field approach in a system of three interacting species

The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on Lotka-Volterra equations. A correlated dichotomous noise acts on \beta, the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of each one of the three species. We study the time behaviour of the three species in single site for different values of the multiplicative noise intensity, finding noise-induced oscillations of the three species densities with an anticorrelated behaviour of the two preys. Afterwards, by considering a spatially extended system formed by a two-dimensional lattice with N sites and applying a mean field approach, we get the corresponding moment equations in Gaussian approximation. Within this formalism we obtain the time behaviour of the first and second order moments for different values of multiplicative noise intensity, with \beta(t) subject to the same dichotomous noise source. Finally, we compare our results with those obtained by using a coupled map lattice model, consisting of a time discrete version of the Lotka-Volterra equations.Comment: 21 pages, 7 figures. Submitted to Centr. Eur. J. Phy