The moment index of minima (II)

The moment index of a nonnegative random variable X has the property that the moment index of the minimum of two independent r.v.s X and Y is greater than or equal to the sum of the moment indices of X and Y. We characterize conditions under which equality holds for a given r.v. X and every independent nonnegative r.v. Y, and discuss extensions to related r.v.s and their distributions

Dynamics of Rumor Spreading in Complex Networks

We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allow us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer to peer communication networks and social spreading phenomena.Comment: Final version to appear in PR

Spreading of Persistent Infections in Heterogeneous Populations

Up to now, the effects of having heterogeneous networks of contacts have been studied mostly for diseases which are not persistent in time, i.e., for diseases where the infectious period can be considered very small compared to the lifetime of an individual. Moreover, all these previous results have been obtained for closed populations, where the number of individuals does not change during the whole duration of the epidemics. Here, we go one step further and analyze, both analytically and numerically, a radically different kind of diseases: those that are persistent and can last for an individual's lifetime. To be more specific, we particularize to the case of Tuberculosis' (TB) infection dynamics, where the infection remains latent for a period of time before showing up and spreading to other individuals. We introduce an epidemiological model for TB-like persistent infections taking into account the heterogeneity inherent to the population structure. This sort of dynamics introduces new analytical and numerical challenges that we are able to sort out. Our results show that also for persistent diseases the epidemic threshold depends on the ratio of the first two moments of the degree distribution so that it goes to zero in a class of scale-free networks when the system approaches the thermodynamic limit.Comment: 12 pages and 2 figures. Revtex format. Submitted for publication

On a method to calculate conductance by means of the Wigner function: two critical tests

We have implemented the linear response approximation of a method proposed to compute the electron transport through correlated molecules based on the time-independent Wigner function [P. Delaney and J. C. Greer, \prl {\bf 93}, 36805 (2004)]. The results thus obtained for the zero-bias conductance through quantum dot both without and with correlations demonstrate that this method is either quantitatively nor qualitatively able to provide a correct physical escription of the electric transport through nanosystems. We present an analysis indicating that the failure is due to the manner of imposing the boundary conditions, and that it cannot be simply remedied.Comment: 22 pages, 7 figur

Investigations into the Sarcomeric Protein and Ca2+-Regulation Abnormalities Underlying Hypertrophic Cardiomyopathy in Cats (Felix catus).

Hypertrophic cardiomyopathy (HCM) is the most common single gene inherited cardiomyopathy. In cats (Felix catus) HCM is even more prevalent and affects 16% of the outbred population and up to 26% in pedigree breeds such as Maine Coon and Ragdoll. Homozygous MYBPC3 mutations have been identified in these breeds but the mutations in other cats are unknown. At the clinical and physiological level feline HCM is closely analogous to human HCM but little is known about the primary causative mechanism. Most identified HCM causing mutations are in the genes coding for proteins of the sarcomere. We therefore investigated contractile and regulatory proteins in left ventricular tissue from 25 cats, 18 diagnosed with HCM, including a Ragdoll cat with a homozygous MYBPC3 R820W, and 7 non-HCM cats in comparison with human HCM (from septal myectomy) and donor heart tissue. Myofibrillar protein expression was normal except that we observed 20–44% MyBP-C haploinsufficiency in 5 of the HCM cats. Troponin extracted from 8 HCM and 5 non-HCM cat hearts was incorporated into thin filaments and studied by in vitro motility assay. All HCM cat hearts had a higher (2.06 ± 0.13 fold) Ca2+-sensitivity than non-HCM cats and, in all the HCM cats, Ca2+-sensitivity was not modulated by troponin I phosphorylation. We were able to restore modulation of Ca2+-sensitivity by replacing troponin T with wild-type protein or by adding 100 μM Epigallocatechin 3-gallate (EGCG). These fundamental regulatory characteristics closely mimic those seen in human HCM indicating a common molecular mechanism that is independent of the causative mutation. Thus, the HCM cat is a potentially useful large animal model

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

Global Versus Local Computations: Fast Computing with Identifiers

This paper studies what can be computed by using probabilistic local interactions with agents with a very restricted power in polylogarithmic parallel time. It is known that if agents are only finite state (corresponding to the Population Protocol model by Angluin et al.), then only semilinear predicates over the global input can be computed. In fact, if the population starts with a unique leader, these predicates can even be computed in a polylogarithmic parallel time. If identifiers are added (corresponding to the Community Protocol model by Guerraoui and Ruppert), then more global predicates over the input multiset can be computed. Local predicates over the input sorted according to the identifiers can also be computed, as long as the identifiers are ordered. The time of some of those predicates might require exponential parallel time. In this paper, we consider what can be computed with Community Protocol in a polylogarithmic number of parallel interactions. We introduce the class CPPL corresponding to protocols that use $O(n\log^k n)$, for some k, expected interactions to compute their predicates, or equivalently a polylogarithmic number of parallel expected interactions. We provide some computable protocols, some boundaries of the class, using the fact that the population can compute its size. We also prove two impossibility results providing some arguments showing that local computations are no longer easy: the population does not have the time to compare a linear number of consecutive identifiers. The Linearly Local languages, such that the rational language $(ab)^*$, are not computable.Comment: Long version of SSS 2016 publication, appendixed version of SIROCCO 201

Don't break a leg: Running birds from quail to ostrich prioritise leg safety and economy in uneven terrain

Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics