Quantitative Chemical Profile and Multivariate Statistical Analysis of Alembic Distilled Sugarcane Spirit Fractions

Concentrations of 39 organic compounds were determined in three fractions (head, heart and tail) obtained from the pot still distillation of fermented sugarcane juice. The results were evaluated using analysis of variance (ANOVA), Tukey's test, principal component analysis (PCA), hierarchical cluster analysis (HCA) and linear discriminant analysis (LDA). According to PCA and HCA, the experimental data lead to the formation of three clusters. The head fractions give rise to a more defined group. The heart and tail fractions showed some overlap consistent with its acid composition. The predictive ability of calibration and validation of the model generated by LDA for the three fractions classification were 90.5 and 100%, respectively. This model recognized as the heart twelve of the thirteen commercial cachacas (92.3%) with good sensory characteristics, thus showing potential for guiding the process of cuts.

Antimicrobial effect of endodontic solutions used as final irrigants on a dentine biofilm model

Aim To evaluate the residual biovolume of live bacterial cells, the mean biofilm thickness and the substratum coverage found in mixed biofilms treated with different endodontic irrigant solutions. Methodology Twenty-five bovine dentine specimens were infected intraorally using a removable orthodontic device. Five samples were used for each irrigant solution: 2% chlorhexidine, 1% sodium hypochlorite (NaOCl), 10% citric acid, 17% EDTA and distilled water. The solutions were used for 5 min. The samples were stained using the Live/Dead technique and evaluated using a confocal microscope. Differences in the amount of total biovolume (mu m3), number of surviving cells (mu m3), mean biofilm thickness (mu m) and substratum coverage (%) of the treated biofilms were determined using nonparametric statistical tests (P < 0.05). Results Similar values of biovolume total, biovolume of live subpopulations and substratum coverage were found in 2% chlorhexidine, 10% citric acid, 17% EDTA and distilled water-treated biofilms (P > 0.05). The lower values of the studied parameters were found in 1% NaOCl-treated dentine (P < 0.05) with the exception of the mean biofilm height criteria that did not reveal significant differences amongst the irrigant solutions (P > 0.05). Conclusions One per cent sodium hypochlorite was the only irrigant that had a significant effect on biofilm viability and architecture.

A log-Birnbaum-Saunders regression model with asymmetric errors

This paper introduces a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution proposed by Leiva et al. [A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426-443]. Some influence methods, such as the local influence and generalized leverage, are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p = -J(2)/J(1) where J(1) > 0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J(2) < 0 is associated with competing anti ferromagnetic interactions between second neighbours along m <= d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g = 0 space, with a Lifshitz point at p = 1/4, for d > 2, and closed-form expressions for the decay of the pair correlations in one dimension. In the T = 0 phase diagram, there is a critical border, g(c) = g(c) (p) for d >= 2, with a singularity at the Lifshitz point if d < (m + 4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p = 1/4. 2012 (C) Elsevier B.V. All rights reserved.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

The polysurvival model with long-term survivors

Long-term survival models have historically been considered for analyzing time-to-event data with long-term survivors fraction. However, situations in which a fraction (1 - p) of systems is subject to failure from independent competing causes of failure, while the remaining proportion p is cured or has not presented the event of interest during the time period of the study, have not been fully considered in the literature. In order to accommodate such situations, we present in this paper a new long-term survival model. Maximum likelihood estimation procedure is discussed as well as interval estimation and hypothesis tests. A real dataset illustrates the methodology.

A spatial stochastic model for rumor transmission

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate lambda. At rate alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders

We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of shape-disordered degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the shape-disordered degrees of freedom are quenched, we confirm the existence of a biaxial nematic structure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use a two-temperature formalism to mimic the presence of two distinct relaxation times, and show that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase.

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.