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).

Conformational differences between the wild type and V30M mutant transthyretin modulate its binding to genistein: Implications to tetramer stability and ligand-binding

Transthyretin (TTR) is a tetrameric beta-sheet-rich transporter protein directly involved in human amyloid diseases. It was recently found that the isoflavone genistein (GEN) potently inhibits TTR amyloid fibril formation (Green et al., 2005) and is therefore a promising candidate for TTR amyloidosis treatment. Here we used structural and biophysical approaches to characterize genistein binding to the wild type (TTRwt) and to its most frequent amyloidogenic variant, the V30M mutant. In a dose-dependent manner, genistein elicited considerable increases in both mutant and TTRwt stability as demonstrated by high hydrostatic pressure (HHP) and acid-mediated dissociation/denaturation assays. TTR:GEN crystal complexes and isothermal titration calorimetry (ITC) experiments showed that the binding mechanisms of genistein to the TTRwt and to V30M are different and are dependent on apoTTR structure conformations. Furthermore, we could also identify potential allosteric movements caused by genistein binding to the wild type TTR that explains, at least in part, the frequently observed negatively cooperative process between the two sites of TTRwt when binding ligands. These findings show that TTR mutants may present different ligand recognition and therefore are of value in ligand design for inhibiting TTR amyloidosis. (C) 2010 Elsevier Inc. All rights reserved.

Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Genome-wide association mapping in a wild avian population identifies a link between genetic and phenotypic variation in a life-history trait

Understanding the genetic basis of traits involved in adaptation is a major challenge in evolutionary biology but remains poorly understood. Here, we use genome-wide association mapping using a custom 50 k single nucleotide polymorphism (SNP) array in a natural population of collared flycatchers to examine the genetic basis of clutch size, an important life-history trait in many animal species. We found evidence for an association on chromosome 18 where one SNP significant at the genome-wide level explained 3.9% of the phenotypic variance. We also detected two suggestive quantitative trait loci (QTLs) on chromosomes 9 and 26. Fitness differences among genotypes were generally weak and not significant, although there was some indication of a sex-by-genotype interaction for lifetime reproductive success at the suggestive QTL on chromosome 26. This implies that sexual antagonism may play a role in maintaining genetic variation at this QTL. Our findings provide candidate regions for a classic avian life-history trait that will be useful for future studies examining the molecular and cellular function of, as well as evolutionary mechanisms operating at, these loci.

Is there a price puzzle in Brazil? An application of Bias-Corrected Bootstrap

Using data from the United States, Japan, Germany , United Kingdom and France, Sims (1992) found that positive innovations to shortterm interest rates led to sharp, persistent increases in the price level. The result was conÖrmed by other authors and, as a consequence of its non-expectable nature, was given the name "price puzzle" by Eichenbaum (1992). In this paper I investigate the existence of a price puzzle in Brazil using the same type of estimation and benchmark identiÖcation scheme employed by Christiano et al. (2000). In a methodological improvement over these studies, I qualify the results with the construction of bias-corrected bootstrap conÖdence intervals. Even though the data does show the existence of a statistically signiÖcant price puzzle in Brazil, it lasts for only one quarter and is quantitatively immaterial

Desempenho animal em sistema silvipastoril com acácia-negra (Acacia mearnsii De Wild.) e rendimento de matéria seca de cultivares de Panicum maximum Jacq. sob dois regimes de luz solar

Esse estudo foi compreendido por dois experimentos de campo, no período de outubro/2003 a abril/2004, na Fundação Estadual de Pesquisa Agropecuária (FEPAGRO), localizado em Tupanciretã, no Planalto Médio, região ecoclimática do RS. O principal objetivo do primeiro experimento foi avaliar o desempenho de novilhas de corte e a dinâmica de três pastos constituídos por Panicum maximum cvs. Gatton e Aruana e por Digitaria diversinervis em um sistema silvipastoril (SSP), associadas com acácia-negra (Acacia mearnsii De Wild.) sob duas densidades arbóreas (833 e 500 árvores/ha). Os resultados mostraram que não houve efeito da densidade arbórea com relação à dinâmica dos pastos e no desempenho animal. As cvs. de P. maximum apresentaram maiores resultados de massa de forragem residual do que a D. diversinervis. A taxa de acúmulo diário de MS, forragem total, oferta de forragem real e relação folha/colmo não diferiram entre as espécies. A cv. Gatton obteve maior resultado de forragem disponível quando comparado com a D. diversinervis. O ganho médio diário, ganho por área, animais.dia/ha, lotação animal e carga animal média também não diferiram com relação as forrageiras. O objetivo do segundo experimento foi avaliar o rendimento de matéria seca total de cinco cultivares de Panicum maximum, crescendo dentro e fora de um bosque de Eucalyptus sp. de 17 anos de idade, estabelecido na densidade de 1111 árvores/ha. A produção media de MS e a taxa de crescimento diário foram significativamente menores (P≤0.05) na condição de sombra (5.529 kg/ha) do que em pleno sol (22.346 kg/ha). Na condição de sombra, os resultados das cvs. não diferiram, enquanto que os resultados em pleno sol apresentaram diferenças significativas (P≤0,01), onde a cv. Tanzânia apresentou menores resultados no rendimento de matéria seca e taxa de crescimento e a cv. Mombaça os maiores resultados Pode-se concluir que as cvs. Mombaça, Tobiatã, Gatton e Vencedor são boas promissoras para o uso em SSP. Esse estudo indicou claramente altos níveis de desempenho animal sob pastejo em SSP com algumas cvs. de P. maximum selecionadas ou D. diversinervis usando Acacia-Negra no Sul do Brasil.

Is there a price puzzle in Brazil? an application of bias- corrected bootstrap

Using data from the United States, Japan, Germany , United Kingdom and France, Sims (1992) found that positive innovations to shortterm interest rates led to sharp, persistent increases in the price leveI. The result was confirmed by other authors and, as a consequence of its non-expectable nature, was given the name "price puzzle" by Eichenbaum (1992). In this paper I investigate the existence of a price puzzle in Brazil using the same type of estimation and benchmark identification scheme employed by Christiano et aI. (2000). In a methodological improvement over these studies, I qualify the results with the construction of bias-corrected bootstrap confidence intervals. Even though the data does show the existence of a statistically significant price puzzle in Brazil, it lasts for .only one quarter and is quantitatively immaterial.

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

Inference in differences-in-differences with few treated groups and heteroskedasticity

Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment periods. We extend our inference methods to linear factor models when there are few treated groups. We also derive conditions under which a permutation test for the synthetic control estimator proposed by Abadie et al. (2010) is robust to heteroskedasticity and propose a modification on the test statistic that provided a better heteroskedasticity correction in our simulations.