Properties of highly clustered networks

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study SIR-type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.Comment: 7 pages, 2 figures, 1 tabl

The Initial Mass Function in the Nearest Strong Lenses from SNELLS: Assessing the Consistency of Lensing, Dynamical, and Spectroscopic Constraints

We present new observations of the three nearest early-type galaxy (ETG) strong lenses discovered in the SINFONI Nearby Elliptical Lens Locator Survey (SNELLS). Based on their lensing masses, these ETGs were inferred to have a stellar initial mass function (IMF) consistent with that of the Milky Way, not the bottom-heavy IMF that has been reported as typical for high-σ ETGs based on lensing, dynamical, and stellar population synthesis techniques. We use these unique systems to test the consistency of IMF estimates derived from different methods. We first estimate the stellar M */L using lensing and stellar dynamics. We then fit high-quality optical spectra of the lenses using an updated version of the stellar population synthesis models developed by Conroy & van Dokkum. When examined individually, we find good agreement among these methods for one galaxy. The other two galaxies show 2–3σ tension with lensing estimates, depending on the dark matter contribution, when considering IMFs that extend to 0.08 M ⊙. Allowing a variable low-mass cutoff or a nonparametric form of the IMF reduces the tension among the IMF estimates to <2σ. There is moderate evidence for a reduced number of low-mass stars in the SNELLS spectra, but no such evidence in a composite spectrum of matched-σ ETGs drawn from the SDSS. Such variation in the form of the IMF at low stellar masses (m lesssim 0.3 M ⊙), if present, could reconcile lensing/dynamical and spectroscopic IMF estimates for the SNELLS lenses and account for their lighter M */L relative to the mean matched-σ ETG. We provide the spectra used in this study to facilitate future comparisons

Fate of Zero-Temperature Ising Ferromagnets

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe ``defect''. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically ``blinking'' metastable states.Comment: 4 pages in column format, 6 figure

Growing Scale-Free Networks with Small World Behavior

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases logartihmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive expressions for the clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure

Introducing Small-World Network Effect to Critical Dynamics

We analytically investigate the kinetic Gaussian model and the one-dimensional kinetic Ising model on two typical small-world networks (SWN), the adding-type and the rewiring-type. The general approaches and some basic equations are systematically formulated. The rigorous investigation of the Glauber-type kinetic Gaussian model shows the mean-field-like global influence on the dynamic evolution of the individual spins. Accordingly a simplified method is presented and tested, and believed to be a good choice for the mean-field transition widely (in fact, without exception so far) observed on SWN. It yields the evolving equation of the Kawasaki-type Gaussian model. In the one-dimensional Ising model, the p-dependence of the critical point is analytically obtained and the inexistence of such a threshold p_c, for a finite temperature transition, is confirmed. The static critical exponents, gamma and beta are in accordance with the results of the recent Monte Carlo simulations, and also with the mean-field critical behavior of the system. We also prove that the SWN effect does not change the dynamic critical exponent, z=2, for this model. The observed influence of the long-range randomness on the critical point indicates two obviously different hidden mechanisms.Comment: 30 pages, 1 ps figures, REVTEX, accepted for publication in Phys. Rev.

Evolution of the Corticotropin-releasing Hormone Signaling System and Its Role in Stress-induced Phenotypic Plasticity

Developing animals respond in variation in their habitats by altering their rules of development and/or their morphologies (i.e., they exhibit phenotypic plasticity). In vertebrates, one mechanism by which plasticity is expressed is through activation of the neuroendocrine system, which transduces environmental information into a physiological response. Recent findings of ours with amphibians and of others with mammals show that the primary vertebrate stress neuropeptide, corticotropin-releasing hormone (CRH), is essential for adaptive developmental responses to environmental stress. For instance, CRH-dependent mechanisms cause accelerated metamorphosis in response to pond-drying in some amphibian species, and intrauterine fetal stress syndromes in humans precipitate preterm birth. CRH may be a phylogenetically ancient developmental signaling molecule that allows developing organisms to escape deleterious changes in their larval/fetal habitat. The response to CRH is mediated by at least two different receptor subtypes and may also be modulated by a secreted binding protein.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73287/1/j.1749-6632.1999.tb07877.x.pd

Random Networks with given Rich-club Coefficient

In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density within a set of nodes. This density is measure by the rich-club coefficient. We present a method to generate surrogates networks with a given rich-club coefficient. We show that by choosing a suitable local linking term, the generated random networks can reproduce the degree distribution and the mixing pattern of real networks. The method is easy to implement and produces good models of real networks.Comment: revised version, new figure

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality

We show that the generating functions of avalanche observables in SOC models exhibits a Lee-Yang phenomenon. This establishes a new link between the classical theory of critical phenomena and SOC. A scaling theory of the Lee-Yang zeroes is proposed including finite sampling effects.Comment: 33 pages, 19 figures, submitte