Exchangeable Random Networks

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the degree distribution of the ensemble graphs, together with some features that are important for applications, such as subgraph distributions and kernel of the adjacency matrix. These results are used to compare to other models of simple and complex networks. A particular case of directed networks with power-law out--degree is studied in more detail, as an example of the flexibility of the model in applications.Comment: to appear on "Internet Mathematics

Random Networks Tossing Biased Coins

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with, asymptotically, scale-free outdegree and compact indegree. Entries in each row of the adjacency matrix are set to be zero or one according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n ~ 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs

Kinetic models with randomly perturbed binary collisions

We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases

Hierarchical Species Sampling Models

This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The proposed framework provides a general probabilistic foundation for hierarchical random measures with either atomic or mixed base measures and allows for studying their properties, such as the distribution of the marginal and total number of clusters. We show that hierarchical species sampling models have a Chinese Restaurants Franchise representation and can be used as prior distributions to undertake Bayesian nonparametric inference. We provide a method to sample from the posterior distribution together with some numerical illustrations. Our class of priors includes some new hierarchical mixture priors such as the hierarchical Gnedin measures, and other well-known prior distributions such as the hierarchical Pitman-Yor and the hierarchical normalized random measures

Complete characterization of convergence to equilibrium for an inelastic Kac model

Pulvirenti and Toscani introduced an equation which extends the Kac caricature of a Maxwellian gas to inelastic particles. We show that the probability distribution, solution of the relative Cauchy problem, converges weakly to a probability distribution if and only if the symmetrized initial distribution belongs to the standard domain of attraction of a symmetric stable law, whose index $\alpha$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $\alpha=\frac{2}{1+p}$. This result is then used: (1) To state that the class of all stationary solutions coincides with that of all symmetric stable laws with index $\alpha$. (2) To determine the solution of a well-known stochastic functional equation in the absence of extra-conditions usually adopted

Legionella Resources on the World Wide Web

Internet resources that focus on Legionella and legionnaires disease are presented. Web sites were selected on the basis of their content and adherence to suggested standards of medical Internet publishing. Free, accessible, English-language Web sites were categorized according to users' needs as follows: (1) those with comprehensive information on Legionella infection (including pathophysiologic characteristics, symptoms, and treatment of legionnaires disease), (2) those with information on outbreaks and epidemiology (including information for travelers), (3) those with information for researchers, (4) those about prevention, and (5) those with information for layperson

Error bounds for computing the expectation by Markov chain Monte Carlo

We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known asymptotical limit of the error is attained, i.e. there is no gap between the estimate and the asymptotical behavior. We discuss the dependence of the error on a burn-in of the Markov chain. Furthermore we suggest and justify a specific burn-in for optimizing the algorithm

Carriage of Staphylococcus aureus Among Injection Drug Users: Lower Prevalence in an Injection Heroin Maintenance Program Than in an Oral Methadone Program

Abstract Objectives: To compare the prevalence of Staphylococcus aureus and methicillin-resistant S. aureus (MRSA) carriage among injection drug users (IDUs) treated in an injection heroin maintenance program with that among IDUs treated in an oral methadone program, and to determine predictors of S. aureus carriage. Design: Survey. Setting: Two opiate maintenance programs at a psychiatrie university clinic. Participants: A volunteer sample consisting of 94 (74%) of 127 IDUs treated in an injection opiate maintenance program with at least twice daily injections of heroin, and 70 (56%) of 125 IDUs treated in an oral methadone program. Results: Addicts treated in the intravenous heroin substitution program had a significantly lower overall rate of S. aureus carriage (37 of 94 [39.4%] vs 42 of 70 [60%]; P = .009) and a significantly lower rate of nasal carriage (21 of 94 [22.3%] vs 30 of 70 [42.9%]; P = .005) than did addicts treated in the oral methadone program. Being treated in the oral methadone program was the only independent predictor of S. aureus carriage (odds ratio, 2.27; 95% confidence interval, 1.19-4.31; P=.012). All S. aureus isolates were susceptible to oxacillin. Conclusions: The regular use of needles under aseptic conditions did not increase the rate of S. aureus carriage among IDUs. Further studies are necessary to investigate whether the lower rate of S. aureus carriage among IDUs treated with intravenous heroin leads to a lower incidence of S. aureus infections in these patient

Structural Performance-Based Design Optimisation of a Secondary Mirror for a Concentrated Solar Power (CSP) Plant

Concentrated Solar Power (CSP) plants use mirrors to reflect and concentrate sunlight onto a receiver, to heat a fluid and store thermal energy, at high temperature and energy density, to produce dispatchable heat and/or electricity. The secondary mirror is a critical component in the optical system of certain Solar Power Tower plants (SPT), as it redirects the concentrated sunlight from the primary mirror onto the receiver, which can be arranged at ground level. In this study, we propose a design optimisation for the secondary mirror of a CSP plant. The design optimisation method consists of two steps. The first step involves the use of the finite element simulation software Abaqus 2022 to analyse the structural performance of the secondary mirror under thermal loads and wind. The second step consists of the use of simulation results to identify the combination of design parameters and best performances, with respect to both design constraints and structural safety. This is carried out by developing an algorithm that selects those configurations which satisfy the constraints by using safety coefficients. The proposed optimisation method is applied to the design of a potential configuration of a secondary mirror for the beam-down of the CSP Magaldi STEM® technology, although the methodology can be extended to other components of CSP plants, such as primary mirrors and receivers, to further enhance the structural performance of these systems