Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

Ecological aspects of mosquitoes (Diptera: Culicidae) in an Atlantic forest area on the north coast of Rio Grande do Sul State, Brazil

Mosquito diversity was determined in an area located on the southern limit of the Atlantic Forest on the north coast of Rio Grande of Sul State. Our major objective was to verify the composition, diversity, and temporal distribution of the mosquito fauna, and the influence of temperature and rainfall. Samplings were performed monthly between December, 2006 and December, 2008, in three biotopes: forest, urban area, and transition area, using CDC light traps and a Nasci vacuum. A total of 2,376 specimens was collected, from which 1,766 (74.32%) were identified as 55 different species belonging to ten genera. Culex lygrus, Aedes serratus, and Aedes nubilus were dominant (eudominant) and constant throughout samplings. The forest environment presented the highest species dominance (D(S) = 0.20), while the transition area showed the highest values of diversity (H` = 2.55) and evenness (J` = 0.85). These two environments were the most similar, according to the Morisita-Horn Index (I(M-H) = 0.35). Bootstrap estimates showed that 87.3% of the species occurring in the region were detected. The seasonal pattern showed a greater abundance of mosquitoes between May and October, indicating the period to intensify entomological surveillance in that area. Journal of Vector Ecology 36 (1): 175-186. 2011.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

Placement of Kuhlmanniodendron Fiaschi & Groppo in Lindackerieae (Achariaceae, Malpighiales) confirmed by analyses of rbcL sequences, with notes on pollen morphology and wood anatomy

The phylogenetic placement of Kuhlmanniodendron Fiaschi & Groppo (Achariaceae) within Malpighiales was investigated with rbcL sequence data. This genus was recently created to accommodate Carpotroche apterocarpa Kuhlm., a poorly known species from the rainforests of Espirito Santo, Brazil. One rbcL sequence was obtained from Kuhlmanniodendron and analyzed with 73 additional sequences from Malpighiales, and 8 from two closer orders, Oxalidales and Celastrales, all of which were available at Genbank. Phylogenetic analyses were carried out with maximum parsimony and Bayesian inference; bootstrap analyses were used in maximum parsimony to evaluate branch support. The results confirmed the placement of Kuhlmanniodendron together with Camptostylus, Lindackeria, Xylotheca, and Caloncoba in a strongly supported clade (posterior probability = 0.99) that corresponds with the tribe Lindackerieae of Achariaceae (Malpighiales). Kuhlmanniodendron also does not appear to be closely related to Oncoba (Salicaceae), an African genus with similar floral and fruit morphology that has been traditionally placed among cyanogenic Flacourtiaceae (now Achariaceae). A picrosodic paper test was performed in herbarium dry leaves, and the presence of cyanogenic glycosides, a class of compounds usually found in Achariaceae, was detected. Pollen morphology and wood anatomy of Kuhlmanniodendron were also investigated, but both pollen (3-colporate and microreticulate) and wood, with solitary to multiple vessels, scalariform perforation plates and other features, do not seem to be useful to distinguish this genus from other members of the Achariaceae and are rather common among the eudicotyledons as a whole. However, perforated ray cells with scalariform plates, an uncommon wood character, present in Kuhlmanniodendron are similar to those found in Kiggelaria africana (Pangieae, Achariaceae), but the occurrence of such cells is not mapped among the angiosperms, and it is not clear how homoplastic this character could be.

Phylogenetic position of Dendropsophus gaucheri (Lescure and Marty 2000) highlights the need for an in-depth investigation of the phylogenetic relationships of Dendropsophus (Anura: Hylidae)

Dendropsophus gaucheri is a recently described species which inhabits open areas of the eastern part of the Guiana Shield and is currently assigned to the D. parviceps species group based on the presence of a subocular cream spot. Herein we investigate its phylogenetic position including material from the type locality and newly documented populations from Suriname and Brazil based on mtDNA sequences. The species, as well as D. riveroi which is assigned to the D. minimus species group, were recovered nested within the D. microcephalus species group which implies the paraphyly of the three Dendropsophus species groups. Such result, along with other evidences, highlights the need for a thorough revision of the genus. The genetic distances among D. gaucheri samples studied are low confirming their conspecificity and suggesting recent connections among populations from open areas currently isolated by rainforest in the lowlands of the Guiana Shield.

A new species of Cycloramphus Tschudi (Anura: Cycloramphidae) from the Parque Nacional da Serra dos Orgaos, Southeastern Brazil

We report here the discovery of a new species of frog associated to the open areas of the highlands of the Parque Nacional da Serra dos Orgaos. The new species, Cycloramphus organensis is characterized by a unique skin texture, medium size ( maximum male and female SVL 26.4 mm and 33.3 mm respectively), dorsal surfaces uniformly brick red colored, uniformly areolate skin on dorsum, pupil horizontal, iris with a menisc on upper margin; no fleshy tubercles on eyelid, tympanic annulus concealed beneath skin, macroglands not visible externally, fingers and toes without fringes and webs; supernumerary palmar and plantar tubercles absent, nuptial spines absent. Despite the presence of an iris menisc, a character shared by frogs of both genera Cycloramphus and Zachaenus Cope, the combination of morphological characters is so unique that the allocation of the species to any of these genera remains ambiguous. Consequently, we used additional molecular-based phylogenetic analyses to ascertain the position of the new taxon. The new species proved to be embedded within the genus Cycloramphus.

Infant mortality model for lifetime data

In this paper we introduce a parametric model for handling lifetime data where an early lifetime can be related to the infant-mortality failure or to the wear processes but we do not know which risk is responsible for the failure. The maximum likelihood approach and the sampling-based approach are used to get the inferences of interest. Some special cases of the proposed model are studied via Monte Carlo methods for size and power of hypothesis tests. To illustrate the proposed methodology, we introduce an example consisting of a real data set.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Cross-situational and supervised learning in the emergence of communication

Scenarios for the emergence or bootstrap of a lexicon involve the repeated interaction between at least two agents who must reach a consensus on how to name N objects using H words. Here we consider minimal models of two types of learning algorithms: cross-situational learning, in which the individuals determine the meaning of a word by looking for something in common across all observed uses of that word, and supervised operant conditioning learning, in which there is strong feedback between individuals about the intended meaning of the words. Despite the stark differences between these learning schemes, we show that they yield the same communication accuracy in the limits of large N and H, which coincides with the result of the classical occupancy problem of randomly assigning N objects to H words.

Tectonic fabric revealed by AARM of the proterozoic mafic dike swarm in the Salvador city (Bahia state): Sao Francisco Craton, NE Brazil

Magnetic fabric and rock magnetism studies were performed on 25 unmetamorphosed mafic dikes of the Meso-Late Proterozoic (similar to 1.02 Ga) dike swarm from Salvador (Bahia State, NE Brazil). This area lies in the north-eastern part of the Sao Francisco Craton, which was dominantly formed/reworked during the Transamazonian orogeny (2.14-1.94 Ga). The dikes crop out along the beaches and in quarries around Salvador city, and cut across both amphibolite dikes and granulites. Their widths range from a few centimeters up to 30 m with an average of similar to 4 m, and show two main trends N 140-190 and N 100-120 with vertical dips. Magnetic fabrics were determined using both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetization (AARM). The magnetic mineralogy was investigated by many experiments including remanent magnetization measurements at variable low temperatures (10-300 K), Mossbauer spectroscopy, high temperature magnetization curves (25-700 degrees C) and scanning electron microscopy (SEM). The rock magnetism study suggests pseudo-single-domain magnetite grains carrying the bulk magnetic susceptibility and AARM fabrics. The magnetite grains found in these dikes are large and we discard the presence of single-domain grains. Its composition is close to stoichiometric with low Ti substitution, and its Verwey transition occurs around 120 K. The main AMS fabric recognized in the swarm is so-called normal, in which the K(max)-K(int) plane is parallel to the dike plane and the magnetic foliation pole K(min)) is perpendicular to it. This fabric is interpreted as due to magma flow, and analysis of the K m inclination permitted to infer that approximately 80% of the dikes were fed by horizontal or sub-horizontal flows (K(max) < 30 degrees). This interpretation is supported by structural field evidence found in five dikes. In addition, based on the plunge of K(max), two mantle sources could be inferred; one of them which fed about 80% of the swarm would be located in the southern part of the region, and the other underlied the Valeria quarry. However, for all dikes the AARM tensors are not coaxial with AMS fabrics and show a magnetic lineation (AARM(max)) oriented to N30-60E, suggesting that magnetite grains were rotated clockwise from dike plane. The orientation of AARM lineation is similar to the orientation of a system of faults in which the Salvador normal fault is the most important. These faults were formed during Cretaceous rifting in the Reconcavo-Tucano-jatoba assemblage that corresponds to an aborted intra-continental rift formed during the opening of the South Atlantic. Therefore, the AARM fabric found for the Salvador dikes is probably tectonic in origin and suggests that the dike swarm was affected by the important tectonic event responsible for the break-up of the Gondwanaland. (C) 2008 Elsevier B.V. All rights reserved.

Inferring Contagion in Regulatory Networks

Several gene regulatory network models containing concepts of directionality at the edges have been proposed. However, only a few reports have an interpretable definition of directionality. Here, differently from the standard causality concept defined by Pearl, we introduce the concept of contagion in order to infer directionality at the edges, i.e., asymmetries in gene expression dependences of regulatory networks. Moreover, we present a bootstrap algorithm in order to test the contagion concept. This technique was applied in simulated data and, also, in an actual large sample of biological data. Literature review has confirmed some genes identified by contagion as actually belonging to the TP53 pathway.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.