Recent advances and open challenges in percolation

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation

Variability of root traits in common bean genotypes at different levels of phosphorus supply and ontogenetic stages.

Selection of common bean (Phaseolus vulgaris L.) cultivars with enhanced root growth would be a strategy for increasing P uptake and grain yield in tropical soils, but the strong plasticity of root traits may compromise their inclusion in breeding programs. The aim of this study was to evaluate the magnitude of thegenotypic variability of root traits in common bean plants at two ontogenetic stages and two soil P levels. Twenty-four common bean genotypes, comprising the four growth habits that exist in the species and two wild genotypes, were grown in 4 kg pots at two levels of applied P (20 and 80 mg kg -1) and harvested at the stages of pod setting and early pod filling. Root area and root length were measured by digital image analysis. Significant genotype × P level and genotype × harvest interactions in analysis of variance indicate that the genotypic variation of root traits depended on soil nutrient availability and the stage at which evaluation was made. Genotypes differed for taproot mass, basal and lateral root mass, root area and root length at both P levels and growth stages; differences in specific root area and length were small. Genotypes with growth habits II (upright indeterminate) and III (prostrate indeterminate) showed better adaptation to limited P supply than genotypes of groups I (determinate) and IV (indeterminate climbing). Between the two harvests, genotypes of groups II and III increased the mass of basal and lateral roots by 40 and 50 %, respectively, whereas genotypes of groups I and IV by only 7 and 19 %. Values of the genotypic coefficient of determination, which estimates the proportion of phenotypic variance resulting from genetic effects, were higher at early pod filling than at pod setting. Correlations between shoot mass and root mass, which could indicate indirect selection of root systems via aboveground biomass, were higher at early pod filling than at pod setting. The results indicate that selection for root traits in common bean genotypes should preferentially be performed at the early pod-filling stage

Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges

One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions -- without, for instance, assuming that the universe is almost Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lema\^{i}tre-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations.Comment: 31 page

Contribuição dos efeitos de genearcas e de famílias sobre a probabilidade de permanência em rebanhos da raça Nelore.

Foram preditas diferenças esperadas na progênie para probabilidade de permanência no rebanho (stayability) de 4180 touros com filhas na base de dados do Programa de Melhoramento Genético da Raça Nelore, utilizando-se modelo de limiar unicaráter de touro-avô materno, sob metodologia bayesiana. Os touros foram classificados em ordem decrescente e aqueles com diferenças esperadas na progênie acima de 57,6%, considerados como TOP1%, foram analisados quanto à genealogia visando avaliar a existência de efeito de família, bem como a contribuição dos genearcas e ancestrais da raça Nelore para a característica considerada. Os principais fundadores, que juntos somaram 18,8% dos genes presentes nos touros TOP1%, foram Karvadi IMP (com 8,2% dos genes, essencialmente via seu filho Chummak), Godhavari IMP (com 6% de contribuição, via Kurupathy e Neófito), Rastã IMP e Falo da BV (2,5 e 2,1%, respectivamente, via materna, pois não apresentaram parentesco com touros ancestrais). O touro Rolex, da variedade mocha, esteve presente em 12 linhas (maternas ou paternas), via seu neto Cardeal. Dos sete ancestrais da raça Nelore com maiores contribuições genéticas (que somaram 15,3% dos genes), cinco foram da variedade mocha. Somente 28 animais aportaram 50% da variabilidade genética, evidenciando o baixo número de animais utilizados como reprodutores na raça Nelore

Biomassa e produtividade de cultivares de feijoeiro inoculadas com rizóbio em comparação à adubação nitrogenada.

Este trabalho teve o objetivo de avaliar o crescimento e a produção de grãos de oito cultivares de feijoeiro, comparando o desempenho das plantas inoculadas com rizóbio com as plantas adubadas com N mineral

Magnetic and superconducting instabilities in the periodic Anderson model: an RPA stud

We study the magnetic and superconducting instabilities of the periodic Anderson model with infinite Coulomb repulsion U in the random phase approximation. The Neel temperature and the superconducting critical temperature are obtained as functions of electronic density (chemical pressure) and hybridization V (pressure). It is found that close to the region where the system exhibits magnetic order the critical temperature T_c is much smaller than the Neel temperature, in qualitative agreement with some T_N/T_c ratios found for some heavy-fermion materials. In our study, all the magnetic and superconducting physical behaviour of the system has its origin in the fluctuating boson fields implementing the infinite on-site Coulomb repulsion among the f-electrons.Comment: 9 pages, 2 figure

Spin wave dispersion in La2CuO4

We calculate the antiferromagnetic spin wave dispersion in the half-filled Hubbard model for a two-dimensional square lattice and find it to be in excellent agreement with recent high-resolution inelastic neutron scattering performed on La2CuO4 [Phys. Rev. Lett. 86, 5377 (2001)].Comment: typos correcte

Local Moment Formation in the Periodic Anderson Model with Superconducting Correlations

We study local moment formation in the presence of superconducting correlations among the f-electrons in the periodic Anderson model. Local moments form if the Coulomb interaction U>U_cr. We find that U_cr is considerably stronger in the presence of superconducting correlations than in the non-superconducting system. Our study is done for various values of the f-level energy and electronic density. The smallest critical U_cr values occur for the case where the number of f- electrons per site is equal to one. In the presence of d-wave superconducting correlations we find that local moment formation presents a quantum phase transition as function of pressure. This quantum phase transition separates a region where local moments and d-wave superconductivity coexist from another region characterized by a superconducting ground state with no local moments. We discuss the possible relevance of these results to experimental studies of the competition between magnetic order and superconductivity in CeCu_2Si_2.Comment: 4 pages. accepted for publication in Phys. Rev.