Generating Scale-free Networks with Adjustable Clustering Coefficient Via Random Walks

This paper presents an algorithm for generating scale-free networks with adjustable clustering coefficient. The algorithm is based on a random walk procedure combined with a triangle generation scheme which takes into account genetic factors; this way, preferential attachment and clustering control are implemented using only local information. Simulations are presented which support the validity of the scheme, characterizing its tuning capabilities.

Exploring the random genesis of co-occurrence networks

Using the network random generation models from Gustedt (2009)[23], we simulate and analyze several characteristics (such as the number of components, the degree distribution and the clustering coefficient) of the generated networks. This is done for a variety of distributions (fixed value, Bernoulli, Poisson, binomial) that are used to control the parameters of the generation process. These parameters are in particular the size of newly appearing sets of objects, the number of contexts in which new elements appear initially, the number of objects that are shared with `parent` contexts, and, the time period inside which a context may serve as a parent context (aging). The results show that these models allow to fine-tune the generation process such that the graphs adopt properties as can be found in real world graphs. (C) 2011 Elsevier B.V. All rights reserved.

Optimization of random amplified polymorphic DNA techniques for use in genetic studies of Cuban triatominae

Random amplified polymorphic DNA (RAPD) technique is a simple and reliable method to detect DNA polymorphism. Several factors can affect the amplification profiles, thereby causing false bands and non-reproducibility of assay. In this study, we analyzed the effect of changing the concentration of primer, magnesium chloride, template DNA and Taq DNA polymerase with the objective of determining their optimum concentration for the standardization of RAPD technique for genetic studies of Cuban Triatominae. Reproducible amplification patterns were obtained using 5 pmoL of primer, 2.5 mM of MgCl2, 25 ng of template DNA and 2 U of Taq DNA polymerase in 25 µL of the reaction. A panel of five random primers was used to evaluate the genetic variability of T. flavida. Three of these (OPA-1, OPA-2 and OPA-4) generated reproducible and distinguishable fingerprinting patterns of Triatominae. Numerical analysis of 52 RAPD amplified bands generated for all five primers was carried out with unweighted pair group method analysis (UPGMA). Jaccard's Similarity Coefficient data were used to construct a dendrogram. Two groups could be distinguished by RAPD data and these groups coincided with geographic origin, i.e. the populations captured in areas from east and west of Guanahacabibes, Pinar del Río. T. flavida present low interpopulation variability that could result in greater susceptibility to pesticides in control programs. The RAPD protocol and the selected primers are useful for molecular characterization of Cuban Triatominae.

Identification and differentiation of Candida species from pediatric patients by random amplified polymorphic DNA

Thirty-four Candida isolates were analyzed by random amplified polymorphic DNA using the primer OPG-10:24 Candida albicans; 4 Candida tropicalis; 2 Candida parapsilosis; 2 Candida dubliniensis; 1 Candida glabrata and 1 Candida krusei. The UPGMA-Pearson correlation coefficient was used to calculate the genetic distance between the different Candida groupings. Samples were classified as identical (correlation of 100%); highly related samples (90%); moderately related samples (80%) and unrelated samples (< 70%). The results showed that the RAPD proposed was capable of classifying the isolates coherently (such that same species were in the same dendrogram), except for two isolates of Candida parapsilosis and the positive control (Netherlands, 1973), probably because they are now recognized as three different species. Concerning the only fluconazole-resistant Candida tropicalis isolate with a genotype that was different to the others, the data were insufficient to affirm that the only difference was the sensitivity to fluconazole. We concluded that the Random Amplified Polymorphic DNA proposed might be used to confirm Candida species identified by microbiological methods.

Tuning clustering in random networks with arbitrary degree distributions

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

Tarification logit dans un réseau

Le problème de tarification qui nous intéresse ici consiste à maximiser le revenu généré par les usagers d'un réseau de transport. Pour se rendre à leurs destinations, les usagers font un choix de route et utilisent des arcs sur lesquels nous imposons des tarifs. Chaque route est caractérisée (aux yeux de l'usager) par sa "désutilité", une mesure de longueur généralisée tenant compte à la fois des tarifs et des autres coûts associés à son utilisation. Ce problème a surtout été abordé sous une modélisation déterministe de la demande selon laquelle seules des routes de désutilité minimale se voient attribuer une mesure positive de flot. Le modèle déterministe se prête bien à une résolution globale, mais pèche par manque de réalisme. Nous considérons ici une extension probabiliste de ce modèle, selon laquelle les usagers d'un réseau sont alloués aux routes d'après un modèle de choix discret logit. Bien que le problème de tarification qui en résulte est non linéaire et non convexe, il conserve néanmoins une forte composante combinatoire que nous exploitons à des fins algorithmiques. Notre contribution se répartit en trois articles. Dans le premier, nous abordons le problème d'un point de vue théorique pour le cas avec une paire origine-destination. Nous développons une analyse de premier ordre qui exploite les propriétés analytiques de l'affectation logit et démontrons la validité de règles de simplification de la topologie du réseau qui permettent de réduire la dimension du problème sans en modifier la solution. Nous établissons ensuite l'unimodalité du problème pour une vaste gamme de topologies et nous généralisons certains de nos résultats au problème de la tarification d'une ligne de produits. Dans le deuxième article, nous abordons le problème d'un point de vue numérique pour le cas avec plusieurs paires origine-destination. Nous développons des algorithmes qui exploitent l'information locale et la parenté des formulations probabilistes et déterministes. Un des résultats de notre analyse est l'obtention de bornes sur l'erreur commise par les modèles combinatoires dans l'approximation du revenu logit. Nos essais numériques montrent qu'une approximation combinatoire rudimentaire permet souvent d'identifier des solutions quasi-optimales. Dans le troisième article, nous considérons l'extension du problème à une demande hétérogène. L'affectation de la demande y est donnée par un modèle de choix discret logit mixte où la sensibilité au prix d'un usager est aléatoire. Sous cette modélisation, l'expression du revenu n'est pas analytique et ne peut être évaluée de façon exacte. Cependant, nous démontrons que l'utilisation d'approximations non linéaires et combinatoires permet d'identifier des solutions quasi-optimales. Finalement, nous en profitons pour illustrer la richesse du modèle, par le biais d'une interprétation économique, et examinons plus particulièrement la contribution au revenu des différents groupes d'usagers.

Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model I assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2. (C) 2007 Elsevier B.V. All rights reserved.

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Coherence characteristics of random lasing in a dye doped hybrid powder

The photon statistics of the random laser emission of a Rhodamine B doped di-ureasil hybrid powder is investigated to evaluate its degree of coherence above threshold. Although the random laser emission is a weighted average of spatially uncorrelated radiation emitted at different positions in the sample, a spatial coherence control was achieved due to an improved detection configuration based on spatial filtering. By using this experimental approach, which also allows for fine mode discrimination and timeresolved analysis of uncoupled modes from mode competition, an area not larger than the expected coherence size of the random laser is probed. Once the spectral and temporal behavior of nonoverlapping modes is characterized, an assessment of the photon-number probability distribution and the resulting second-order correlation coefficient as a function of time delay and wavelength was performed. The outcome of our single photon counting measurements revealed a high degree of temporal coherence at the time of maximum pump intensity and at wavelengths around the Rhodamine B gain maximum.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.

Evaluation of a Bayesian MCMC Random Effects Inference Methodology for Capture-Mark-Recapture Data

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean μ and variance σ2 . Marginal prior distributions on logit(p) and μ were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for μ ; hence minimally informative. Marginal prior distribution on σ2 was placed on τ2=1/σ2 as a gamma distribution with α=β=0.001 . The study design has 432 points spread over 5 factors: occasions (t) , new releases per occasion (u), p, μ , and σ . At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n=10,000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on μ , and σ based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter μ , but under the conditions used here, MCMC inference performance for σ was mixed: poor for sparse data (i.e., only 7 occasions) or σ=0 , but good when there were sufficient data and not small σ .