A single-walker approach for studying quasi-nonergodic systems.

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-nonergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down.

Explosive Contagion in Networks.

The spread of social phenomena such as behaviors, ideas or products is an ubiquitous but remarkably complex phenomenon. A successful avenue to study the spread of social phenomena relies on epidemic models by establishing analogies between the transmission of social phenomena and infectious diseases. Such models typically assume simple social interactions restricted to pairs of individuals; effects of the context are often neglected.

Effects of local and global network connectivity on synergistic epidemics.

Epidemics in networks can be affected by cooperation in transmission of infection and also connectivity between nodes. An interplay between these two properties and their influence on epidemic spread are addressed in the paper. A particular type of cooperative effects (called synergy effects) is considered, where the transmission rate between a pair of nodes depends on the number of infected neighbors.

Effect of disorder on condensation in the lattice gas model on a random graph.

The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to exhibit two phase transitions as a function of chemical potential in a certain temperature range. Heterogeneity in interaction strengths is demonstrated to reduce the critical temperature and, for large-enough degreeS of disorder, divides the cells into ones which are either on average occupied or unoccupied.

Effects of variable-state neighborhoods for spreading synergystic processes on lattices.

A theoretical framework for the description of susceptible-infected-removed (SIR) spreading processes with synergistic transmission of infection on a lattice is developed. The model incorporates explicitly the effects of time-dependence of the state of the hosts in the neighborhood of transmission events. Exact solution of the model shows that time-dependence of the state of nearest neighbors of recipient hosts is a key factor for synergistic spreading processes.

Zero-temperature random-field Ising model on a bilayered Bethe lattice.

The zero-temperature random-field Ising model is solved analytically for magnetization versus external field for a bilayered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established. The effects of variable interlayer interaction strengths on infinite avalanches are investigated.

Capillary condensation in one-dimensional irregular confinement.

A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis.

Mechanisms of evolution of avalanches in regular graphs.

A mapping of avalanches occurring in the zero-temperature random-field Ising model to life periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for the occurrence of an infinite avalanche in a q-regular graph to be determined. A key factor for an avalanche of spin flips to become infinite is that it interacts in an optimal way with previously flipped spins.

Prominent effect of soil network heterogeneity on microbial invasion.

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks.

Prediction of invasion from the early stage of an epidemic.

Predictability of undesired events is a question of great interest in many scientific disciplines including seismology, economy and epidemiology. Here, we focus on the predictability of invasion of a broad class of epidemics caused by diseases that lead to permanent immunity of infected hosts after recovery or death. We approach the problem from the perspective of the science of complexity by proposing and testing several strategies for the estimation of important characteristics of epidemics, such as the probability of invasion.

The effect of heterogeneity on invasion in spatial epidemics: from theory to experimental evidence in a model system.

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established "percolation paradigm" to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased.

Mass distribution and rotational inertia of "microtype" and "freely mobile" middle ear ossicles in rodents.

The middle ears of seven species of rodents, including four hamster species, were examined under light microscopy and through micro-CT imaging. Hamsters were found to possess a spectrum of ossicular morphologies ranging from something approaching "freely mobile" (Mesocricetus) to something nearer the "microtype" (Cricetulus), although no hamster has an orbicular apophysis of the malleus. Rats, mice and Calomyscus were found to have typically microtype ossicles.

Synergy in spreading processes: from exploitative to explorative foraging strategies.

An epidemiological model which incorporates synergistic effects that allow the infectivity and/or susceptibility of hosts to be dependent on the number of infected neighbors is proposed. Constructive synergy induces an exploitative behavior which results in a rapid invasion that infects a large number of hosts. Interfering synergy leads to a slower and sparser explorative foraging strategy that traverses larger distances by infecting fewer hosts.

The two-mutant problem: clonal interference in evolutionary graph theory.

In large asexual populations, clonal interference, whereby different beneficial mutations compete to fix in the population simultaneously, may be the norm. Results extrapolated from the spread of individual mutations in homogeneous backgrounds are found to be misleading in such situations: clonal interference severely inhibits the spread of beneficial mutations. In contrast with results gained in systems with just one mutation striving for fixation at any one time, the spatial structure of the population is found to be an important factor in determining the fixation probability when there are two beneficial mutations.

Unveiling the neuromorphological space.

This article proposes the concept of neuromorphological space as the multidimensional space defined by a set of measurements of the morphology of a representative set of almost 6000 biological neurons available from the NeuroMorpho database. For the first time, we analyze such a large database in order to find the general distribution of the geometrical features. We resort to McGhee's biological shape space concept in order to formalize our analysis, allowing for comparison between the geometrically possible tree-like shapes, obtained by using a simple reference model, and real neuronal shapes.

Epidemics in networks of spatially correlated three-dimensional root-branching structures.

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected-recovered ('SIR') epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection.

Heterogeneity in susceptible-infected-removed (SIR) epidemics on lattices.

The percolation paradigm is widely used in spatially explicit epidemic models where disease spreads between neighbouring hosts. It has been successful in identifying epidemic thresholds for invasion, separating non-invasive regimes, where the disease never invades the system, from invasive regimes where the probability of invasion is positive. However, its power is mainly limited to homogeneous systems.

Assortative mating and mutation diffusion in spatial evolutionary systems.

The influence of spatial structure on the equilibrium properties of a sexual population model defined on networks is studied numerically. Using a small-world-like topology of the networks as an investigative tool, the contributions to the fitness of assortative mating and of global mutant spread properties are considered. Simple measures of nearest-neighbor correlations and speed of spread of mutants through the system have been used to confirm that both of these dynamics are important contributory factors to the fitness.

Complexity and anisotropy in host morphology make populations less susceptible to epidemic outbreaks.

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model.

Scaling behavior of the disordered contact process.

The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasistationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical scaling, conventional or activated, as well as of universality of critical exponents by employing a scaling analysis of the distribution of lifetimes and the quasistationary density of infection. We find activated scaling to be the appropriate description for intermediate to strong disorder.

Contact process in disordered and periodic binary two-dimensional lattices.

The critical behavior of the contact process (CP) in disordered and periodic binary two-dimensional (2D) lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory. Phase-separation lines calculated numerically are found to agree well with analytical predictions around the homogeneous point. For the disordered case, values of static scaling exponents obtained via quasistationary simulations are found to change with disorder strength.

Simulating the contact process in heterogeneous environments.

The one-dimensional contact process (CP) in a heterogeneous environment-a binary chain consisting of two types of site with different recovery rates-is investigated. It is argued that the commonly used random-sequential Monte Carlo simulation method which employs a discrete notion of time is not faithful to the rates of the contact process in a heterogeneous environment. Therefore, a modification of this algorithm along with two alternative continuous-time implementations are analyzed.

Infrared absorption in glasses and their crystalline counterparts.

It is demonstrated by means of numerical analysis that absorption of light in glasses in the IR region, [Formula: see text], can be understood in terms of light absorption in their crystalline counterparts. This signifies the important role of local structural motifs (units) present both in glasses and crystals. Decomposition of the coupling coefficient into coherent and incoherent contributions gives insight into the origin of the spectral features of IR absorption.

Supercritical series expansion for the contact process in heterogeneous and disordered environments.

The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents beta . The heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates. Two analytical approaches based on nested Padé approximants and partial differential approximants were used in the case of expansions with respect to two variables (two recovery rates) for the evaluation of the critical values and critical exponents.

Temporal and dimensional effects in evolutionary graph theory.

The spread in time of a mutation through a population is studied analytically and computationally in fully connected networks and on spatial lattices. The time t* for a favorable mutation to dominate scales with the population size N as N(D+1)/D in D-dimensional hypercubic lattices and as NlnN in fully-connected graphs. It is shown that the surface of the interface between mutants and nonmutants is crucial in predicting the dynamics of the system.