A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons.

This study developed a method to approximate the covariance matrix associated with the simulation of water molecular diffusion inside the brain tissue. The computation implements the Discontinuous Galerkin method of the diffusion equation. A physically consistent numerical flux is applied to model the interaction between the axon walls and extracellular regions. This numerical flux yields an efficient GPU-CUDA implementation. We consider the two-dimensional case of high axon pack density, valid, for instance, in the brain's corpus callosum region.

Invariant Quantum States of Quadratic Hamiltonians.

The problem of finding covariance matrices that remain constant in time for arbitrary multi-dimensional quadratic Hamiltonians (including those with time-dependent coefficients) is considered. General solutions are obtained.

Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States.

In the differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and momentum operators or quadrature components. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state, unitarily evolving according to a Hamiltonian H ^ . We also present the corresponding differential equations, which describe the nonunitary evolution of the subsystems. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schrödinger equation. The formalism elaborated allows us to define new specific invariant and quasi-invariant states, as well as states with invariant covariance matrices, i.e., states were only the mean values evolve according to the classical Hamilton equations. By using density matrices in the position and in the tomographic-probability representations, we study examples of these properties. As examples, we present novel invariant states for the two-mode frequency converter and quasi-invariant states for the bipartite parametric amplifier.

Mixed nonlinear models in ruminal in situ degradability trials / Modelos não lineares mistos em ensaios de degradabilidade ruminal in situ

Classical methods of analysis of nonlinear models are widely used in studies of ruminal degradation kinetics. As this type of study involves repeated measurements in the same experimental unit, the use of mixed nonlinear models (MNLM) is proposed, in order to solve problems of heterogeneity of variances of the responses, correlation among repeated measurements and consequent lack of sphericity in the covariance matrix. The aims of this work are to present an evaluation of the applicability of MNLM in the estimation of parameters to describe the in situ ruminal degradation kinetics of the dry matter of Tifton 85 hay and to compare the results with those obtained from the usual analysis in two-phases. The steers used in the trial were fed diets composed of three different combinations of roughage and concentrate and two hays with different nutritional qualities. The proposed approach was proven as effective as the traditional one for estimating model parameters. However, it adequately models the correlation among the longitudinal data, which can affect the estimates obtained, the standard error associated with them and potentially change the results of the inferences. It is quite attractive when the research seeks to understand the behavior of the process of food degradation throughout the incubation times.(AU)

Métodos clássicos de análise de modelos não lineares são amplamente utilizados em estudos da cinética de degradação ruminal. Como esse tipo de estudo envolve medidas repetidas na mesma unidade experimental, propõe-se o uso de modelos não lineares mistos (MNLM), buscando resolver os problemas de heterogeneidade de variâncias das respostas, de correlação entre as medidas repetida se a consequente falta de esfericidade da matriz de covariâncias. Os objetivos deste trabalho envolvem apresentar uma avaliação da aplicabilidade dos MNLM na estimação de parâmetros para descrever a cinética de degradação ruminal in situ da matéria seca de fenos de capim-Tifton 85 e comparar os seus resultados com os obtidos da análise usual realizada em duas fases. Os novilhos utilizados no ensaio foram alimentados com rações compostas por três diferentes combinações de volumoso e concentrado e dois fenos com diferentes qualidades nutricionais. A abordagem proposta mostrou-se tão efetiva quanto à tradicional para a estimação dos parâmetros do modelo. Contudo, ela modela de forma adequada a correlação entre os dados longitudinais, o que pode afetar as estimativas obtidas, o erro padrão associado a elas e, potencialmente, alterar os resultados das inferências. É bastante atraente quando a pesquisa busca entender o comportamento do processo da degradação dos alimentos ao longo dos tempos de incubação.(AU)

Learning genetic and environmental graphical models from family data.

Many challenging problems in biomedical research rely on understanding how variables are associated with each other and influenced by genetic and environmental factors. Probabilistic graphical models (PGMs) are widely acknowledged as a very natural and formal language to describe relationships among variables and have been extensively used for studying complex diseases and traits. In this work, we propose methods that leverage observational Gaussian family data for learning a decomposition of undirected and directed acyclic PGMs according to the influence of genetic and environmental factors. Many structure learning algorithms are strongly based on a conditional independence test. For independent measurements of normally distributed variables, conditional independence can be tested through standard tests for zero partial correlation. In family data, the assumption of independent measurements does not hold since related individuals are correlated due to mainly genetic factors. Based on univariate polygenic linear mixed models, we propose tests that account for the familial dependence structure and allow us to assess the significance of the partial correlation due to genetic (between-family) factors and due to other factors, denoted here as environmental (within-family) factors, separately. Then, we extend standard structure learning algorithms, including the IC/PC and the really fast causal inference (RFCI) algorithms, to Gaussian family data. The algorithms learn the most likely PGM and its decomposition into two components, one explained by genetic factors and the other by environmental factors. The proposed methods are evaluated by simulation studies and applied to the Genetic Analysis Workshop 13 simulated dataset, which captures significant features of the Framingham Heart Study.

Mixed nonlinear models in ruminal in situ degradability trials / Modelos não lineares mistos em ensaios de degradabilidade ruminal in situ

Classical methods of analysis of nonlinear models are widely used in studies of ruminal degradation kinetics. As this type of study involves repeated measurements in the same experimental unit, the use of mixed nonlinear models (MNLM) is proposed, in order to solve problems of heterogeneity of variances of the responses, correlation among repeated measurements and consequent lack of sphericity in the covariance matrix. The aims of this work are to present an evaluation of the applicability of MNLM in the estimation of parameters to describe the in situ ruminal degradation kinetics of the dry matter of Tifton 85 hay and to compare the results with those obtained from the usual analysis in two-phases. The steers used in the trial were fed diets composed of three different combinations of roughage and concentrate and two hays with different nutritional qualities. The proposed approach was proven as effective as the traditional one for estimating model parameters. However, it adequately models the correlation among the longitudinal data, which can affect the estimates obtained, the standard error associated with them and potentially change the results of the inferences. It is quite attractive when the research seeks to understand the behavior of the process of food degradation throughout the incubation times.

Métodos clássicos de análise de modelos não lineares são amplamente utilizados em estudos da cinética de degradação ruminal. Como esse tipo de estudo envolve medidas repetidas na mesma unidade experimental, propõe-se o uso de modelos não lineares mistos (MNLM), buscando resolver os problemas de heterogeneidade de variâncias das respostas, de correlação entre as medidas repetida se a consequente falta de esfericidade da matriz de covariâncias. Os objetivos deste trabalho envolvem apresentar uma avaliação da aplicabilidade dos MNLM na estimação de parâmetros para descrever a cinética de degradação ruminal in situ da matéria seca de fenos de capim-Tifton 85 e comparar os seus resultados com os obtidos da análise usual realizada em duas fases. Os novilhos utilizados no ensaio foram alimentados com rações compostas por três diferentes combinações de volumoso e concentrado e dois fenos com diferentes qualidades nutricionais. A abordagem proposta mostrou-se tão efetiva quanto à tradicional para a estimação dos parâmetros do modelo. Contudo, ela modela de forma adequada a correlação entre os dados longitudinais, o que pode afetar as estimativas obtidas, o erro padrão associado a elas e, potencialmente, alterar os resultados das inferências. É bastante atraente quando a pesquisa busca entender o comportamento do processo da degradação dos alimentos ao longo dos tempos de incubação.

Evolution of morphological integration in the skull of Carnivora (Mammalia): Changes in Canidae lead to increased evolutionary potential of facial traits.

Morphological integration refers to the fact that different phenotypic traits of organisms are not fully independent from each other, and tend to covary to different degrees. The covariation among traits is thought to reflect properties of the species' genetic architecture and thus can have an impact on evolutionary responses. Furthermore, if morphological integration changes along the history of a group, inferences of past selection regimes might be problematic. Here, we evaluated the stability and evolution of the morphological integration of skull traits in Carnivora by using evolutionary simulations and phylogenetic comparative methods. Our results show that carnivoran species are able to respond to natural selection in a very similar way. Our comparative analyses show that the phylogenetic signal for pattern of integration is lower than that observed for morphology (trait averages), and that integration was stable throughout the evolution of the group. That notwithstanding, Canidae differed from other families by having higher integration, evolvability, flexibility, and allometric coefficients on the facial region. These changes might have allowed canids to rapidly adapt to different food sources, helping to explain not only the phenotypic diversification of the family, but also why humans were able to generate such a great diversity of dog breeds through artificial selection.

Error Covariance Penalized Regression: A novel multivariate model combining penalized regression with multivariate error structure.

A new multivariate regression model, named Error Covariance Penalized Regression (ECPR) is presented. Following a penalized regression strategy, the proposed model incorporates information about the measurement error structure of the system, using the error covariance matrix (ECM) as a penalization term. Results are reported from both simulations and experimental data based on replicate mid and near infrared (MIR and NIR) spectral measurements. The results for ECPR are better under non-iid conditions when compared with traditional first-order multivariate methods such as ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLS).

EvolQG - An R package for evolutionary quantitative genetics.

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

Phenotypic integration in flowers of neotropical lianas: diversification of form with stasis of underlying patterns.

Phenotypic integration is essential to the understanding of organismal evolution as a whole. In this study, a phylogenetic framework is used to assess phenotypic integration among the floral parts of a group of Neotropical lianas. Flowers consist of plant reproductive organs (carpels and stamens), usually surrounded by attractive whorls (petals and sepals). Thus, flower parts might be involved in different functions and developmental constraints, leading to conflicting selective forces. We found that Bignonieae flowers have very similar patterns of variance/covariance among traits and that such patterns are uncorrelated with the phylogenetic relationships between species. However, in spite of pattern stasis, our results also indicate that diversification of floral morphology in this group has occurred throughout the evolution of magnitudes of correlation among traits. Thus, we suggest that stabilizing selection has played an important role in phenotypic integration, resulting in the long-term stasis of covariance patterns underlying flower diversification during the ca. 50 Myr of evolution of Bignonieae. This is the first report of long-term stasis in the phenotypic integration of angiosperms, suggesting that patterns of floral morphology can be recognizable as specific attributes of distinct botanical families.

Viability of using multidimensional graphics in epidemiological data analysis: case study with respiratory diseases / Viabilidade do uso gráfico multidimensional para análise de dados epidemiológicos: estudo de caso com doenças respiratórias

The statistical methodology to be used in epidemiological data analysis is extremely important for obtaining reliable and plausible results that can be interpreted in the epidemiological context. In order to carry out a case study about the incidence of the main respiratory diseases in some cities with different climatic seasons, the present work aimed at studying the viability for applying the multidimensional graphic technique known as "h-plot" to identify the main variables that resulted in a higher contribution to the data dispersal. In accordance with the results obtained and discussed, we state that the h-plot graphics are viable to be applied as an alternative method as regards to the identification and collection of the variables.

A metodologia estatística a ser utilizada na análise dos dados epidemiológicos é de suma importância para que os resultados obtidos sejam confiáveis e plausíveis de serem interpretados no contexto epidemiológico. Com o propósito de realizar um estudo de caso sobre a incidência das principais doenças respiratórias em algumas cidades com estações climáticas bem diferenciadas, o presente trabalho tem por objetivo estudar a viabilidade da aplicação da técnica gráfica multidimensional conhecida por "h-plot" para identificar principais variáveis que resultaram em maior contribuição na dispersão dos dados. Em consonância com os resultados obtidos e discutidos neste trabalho, recomendou-se que os gráficos h-plots são viáveis de serem aplicados como um método alternativo no que se refere à identificação e agrupamento das variáveis.

Obtención de la matriz de varianzas y covarianzas a través de los productos Kronecker en modelos balanceados de dos y tres vías con aplicaciones en R / Obtenção da matriz de variância-covariância através dos produtos Kronecker em modelos balanceados de duas e três vias com aplicações em R / Obtainment of the variance-covariance matrix through Kronecker products for balanced models of two and three ways with applications in R

Objetivo. Presentar una metodología basada en el concepto de productos Kronecker que facilita la construcción de la matriz de varianzas y covarianzas para diseños con estructura balanceada de datos a 2 y 3-vías y una aplicación realizada en R para facilitar su cálculo y aplicación en diferentes áreas. Materiales y métodos. Se proporciona un punto de partida para personas interesadas en utilizar R en el análisis de varianza. Resultados. Se utiliza una aplicación realizada en R donde se desarrolla la metodología basada en productos Kronecker mediante la cual se construye la matriz de varianzas y covarianzas cuando se trabaja en diseños con estructura balanceada de datos desarrollada por Moya 2003. De igual forma se presenta una aplicación del método con datos reales. Conclusiones. La metodología expuesta permite agilizar el desarrollo y solución de algunos problemas prácticos. El método propuesto puede ser aplicado a modelos mixtos con efectos fijos o aleatorios con cualquier número de factores...

Obtainment of the variance-covariance matrix through Kronecker products for balanced models of two and three ways with applications in R. Objective. To present a methodology based on the concept of Kronecker products that facilitates the construction of the variance and covariance matrix for designs with balanced data structure for 2 and 3 ways, and an application in R to facilitate its calculation and application in different areas. Materials and methods. We provide a starting point for people interested in using R in the analysis of variance. Results. We use an application made in R for a methodology based on Kronecker products through which we build the covariance matrix for working with designs with balanced data structure developed by Moya (2003). We also present an application of the method with real data. Conclusions. With this methodology we can accelerate the development and solution of some practical problems. The proposed methodology can be applied to mixed models with fixed or random effects with any number of factors...

Obtenção da matriz de variância-covariância através dos produtos Kronecker em modelos balanceados de duas e três vias com aplicações em R. Objetivo. Apresentar uma metodologia baseada no conceito de produtos de Kronecker para facilitar a construção da matriz de variância-covariância para desenhos com estrutura balanceada de dados em 2 e 3 vias e uma aplicação realizada em R para o cálculo fácil e aplicação em diferentes áreas. Materiais e métodos. É fornecido um ponto de partida para as pessoas interessadas em utilizar R na análise de variância. Resultados. Usa-se uma aplicação realizada em R, onde é desenvolvida a metodologia baseada nos produtos de Kronecker com a qual se constrói a matriz de variância-covariância quando se trabalha em desenhos com estrutura balanceada de dados segundo Moya (2003). Da mesma forma, se apresenta uma aplicação do método com dados reais. Conclusões. A metodologia descrita pode acelerar o desenvolvimento e solução de alguns problemas práticos. O método proposto pode ser aplicado a modelos mistos com efeitos fixos ou aleatórios com qualquer número de fatores...