Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co) variances with age adequately and larger breeding value accuracies can be expected using this model.

Can type of school be used as an alternative indicator of socioeconomic status in dental caries studies? A cross-sectional study

Background: Despite the importance of collecting individual data of socioeconomic status (SES) in epidemiological oral health surveys with children, this procedure relies on the parents as respondents. Therefore, type of school (public or private schools) could be used as an alternative indicator of SES, instead of collecting data individually. The aim of this study was to evaluate the use of the variable type of school as an indicator of socioeconomic status as a substitute of individual data in an epidemiological survey about dental caries in Brazilian preschool children. Methods: This study followed a cross-sectional design, with a random sample of 411 preschool children aged 1 to 5 years, representative of Catalao, Brazil. A calibrated examiner evaluated the prevalence of dental caries and parents or guardians provided information about several individual socioeconomic indicators by means of a semi-structured questionnaire. A multilevel approach was used to investigate the association among individual socioeconomic variables, as well as the type of school, and the outcome. Results: When all significant variables in the univariate analysis were used in the multiple model, only mother's schooling and household income (individual socioeconomic variables) presented significant associations with presence of dental caries, and the type of school was not significantly associated. However, when the type of school was used alone, children of public school presented significantly higher prevalence of dental caries than those enrolled in private schools. Conclusions: The type of school used as an alternative indicator for socioeconomic status is a feasible predictor for caries experience in epidemiological dental caries studies involving preschool children in Brazilian context.

Random X Inactivation and Extensive Mosaicism in Human Placenta Revealed by Analysis of Allele-Specific Gene Expression along the X Chromosome

Imprinted inactivation of the paternal X chromosome in marsupials is the primordial mechanism of dosage compensation for X-linked genes between females and males in Therians. In Eutherian mammals, X chromosome inactivation (XCI) evolved into a random process in cells from the embryo proper, where either the maternal or paternal X can be inactivated. However, species like mouse and bovine maintained imprinted XCI exclusively in extraembryonic tissues. The existence of imprinted XCI in humans remains controversial, with studies based on the analyses of only one or two X-linked genes in different extraembryonic tissues. Here we readdress this issue in human term placenta by performing a robust analysis of allele-specific expression of 22 X-linked genes, including XIST, using 27 SNPs in transcribed regions. We show that XCI is random in human placenta, and that this organ is arranged in relatively large patches of cells with either maternal or paternal inactive X. In addition, this analysis indicated heterogeneous maintenance of gene silencing along the inactive X, which combined with the extensive mosaicism found in placenta, can explain the lack of agreement among previous studies. Our results illustrate the differences of XCI mechanism between humans and mice, and highlight the importance of addressing the issue of imprinted XCI in other species in order to understand the evolution of dosage compensation in placental mammals.

Disordered ensembles of random matrices

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Levy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdos-Renyi and the scale free models.

A study of disorder effects in random (Al(x)Ga(1-x)As)(n)(Al(y)Ga(1-y)As)(m) superlattices embedded in a wide parabolic potential

A photoluminescence (PL) study of the individual electron states localized in a random potential is performed in artificially disordered superlattices embedded in a wide parabolic well. The valence band bowing of the parabolic potential provides a variation of the emission energies which splits the optical transitions corresponding to different wells within the random potential. The blueshift of the PL lines emitted by individual random wells, observed with increasing disorder strength, is demonstrated. The variation of temperature and magnetic field allowed for the behavior of the electrons localized in individual wells of the random potential to be distinguished.

Delocalization-localization transition of plasmons in random (GaAs)(m)(Al(0.3)Ga(0.7)As)(6) superlattices

The transition of plasmons from propagating to localized state was studied in disordered systems formed in GaAs/AlGaAs superlattices by impurities and by artificial random potential. Both the localization length and the linewidth of plasmons were measured by Raman scattering. The vanishing dependence of the plasmon linewidth on the disorder strength was shown to be a manifestation of the strong plasmon localization. The theoretical approach based on representation of the plasmon wave function in a Gaussian form well accounted for by the obtained experimental data.

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

Exceptional times for the dynamical discrete web

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter tau. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed tau. In this paper, we study the existence of exceptional (random) values of tau where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of such exceptional tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by Haggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in the DyDW is rather different from the situation for the dynamical random walks of Benjamini, Haggstrom, Peres and Steif. For example, we prove that the walk from the origin S(0)(tau) violates the law of the iterated logarithm (LIL) on a set of tau of Hausdorff dimension one. We also discuss how these and other results should extend to the dynamical Brownian web, the natural scaling limit of the DyDW. (C) 2009 Elsevier B.V. All rights reserved.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Survival time of random walk in random environment among soft obstacles

We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the survival time in the general d-dimensional case. We then consider a simplified one-dimensional model (where transition probabilities and obstacles are independent and the RWRE only moves to neighbour sites), and obtain finer results for the tail of the survival time. In addition, we study also the ""mixed"" probability measures (quenched with respect to the obstacles and annealed with respect to the transition probabilities and vice-versa) and give results for tails of the survival time with respect to these probability measures. Further, we apply the same methods to obtain bounds for the tails of hitting times of Branching Random Walks in Random Environment (BRWRE).

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

Gibbs random graphs on point processes

Consider a discrete locally finite subset Gamma of R(d) and the cornplete graph (Gamma, E), with vertices Gamma and edges E. We consider Gibbs measures on the set of sub-graphs with vertices Gamma and edges E` subset of E. The Gibbs interaction acts between open edges having a vertex in common. We study percolation properties of the Gibbs distribution of the graph ensemble. The main results concern percolation properties of the open edges in two cases: (a) when Gamma is sampled from a homogeneous Poisson process; and (b) for a fixed Gamma with sufficiently sparse points. (c) 2010 American Institute of Physics. [doi:10.1063/1.3514605]

An oracle approach for interaction neighborhood estimation in random fields

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

Depressive symptoms in old age: relations among sociodemographic and self-reported health variables

Background: Depression in old age is a complex multifactorial phenomenon that is influenced by several biopsychosocial variables. Depressive symptoms are associated with the presence of chronic diseases, with being female, with low education and low income levels, and with poor perceived health assessment. In impoverished areas, older adults may have more physical disability, as they may have less access to health services. Therefore, they may be more likely to report depressive symptoms. Methods: Population-based cross-sectional research was undertaken using data from the FIBRA study conducted in Ermelino Matarazzo, a poor subdistrict of the city of Sao Paulo, Brazil. The participants comprised 303 elderly people, aged 65 years and over, who attended a single-session data collection effort carried out at community centers. The protocol comprised sociodemographic and self-reported health variables, and the Geriatric Depression Scale. Results: The majority of the subjects reported five or fewer symptoms of depression (79.21%), reported one or two self-reported chronic diseases (56.86%), declared themselves to have one or two self-reported health problems (46.15%), and had good perceived health assessment (40.27%). The presence of depressive symptoms was associated with a higher number of self-reported health problems, poor perceived health assessment, and lower schooling levels, in the total sample and in analyses including men only. For women, depressive symptoms were associated with the number of self-reported health problems and family income. Conclusion: The presence of health problems, such as falls and memory problems, lower perceived health, and low education (and low family income for women) were associated with a higher presence of depressive symptoms among elderly people in this poor area of Sao Paulo.