Scaling limit for a drainage network model

We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.Comment: 15 page

Analytical results for a Bessel function times Legendre polynomials class integrals

When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make unnecessary numerical quadrature techniques or localized approximations. The solution is presented using the properties of the Bessel and associated Legendre functions.Comment: 4 page

Aplicação de geoestatística na produção integrada de frutas no nordeste do Brasil.

A competitividade dos produtos agrícolas na economia globalizada direciona o setor da fruticultura em busca de alternativas tecnológicas que visam maior eficiência na utilização de insumos, serviços e recursos naturais, permitindo elevar a sustentabilidade da produção. Este estudo objetivou mapear as variações espaciais do solo de área com produção integrada de frutas no nordeste do Brasil por meio de técnicas de geoestatística. A área de estudo possui 35,98 ha com coqueiro irrigado por micro-aspersão. Realizou-se a coleta de dados de atributos físico-químicos do solo (teor de argila, granulometria, C orgânico, pH água, P, Ca+Mg, K, Na, Al , SB e CTC) em 93 pontos amostrais. Os dados obtidos foram associados às coordenadas geográficas locadas por GPS. Após efetuou-se o ajuste matemático pelos semivariogramas no aplicativo Surfer 8.0, definindo-se os parâmetros: efeito pepita (C0); alcance da dependência espacial (A0); patamar (C0+C1) e o grau de dependência espacial (C0)/(C0+C1). Por fim, elaborou-se mapas de isolinhas dos atributos a partir do interpolador geoestatístico de krigagem. Os resultados obtidos indicam o predomínio de atributos com elevado grau de heterogeneidade. Os valores médios de P, K e Ca+Mg estão influenciados por correções e adubações sistemáticas realizadas na área. A análise da relação C0/(C0 + C1) revelou grau de dependência espacial de moderado a forte dos atributos analisados. Dessa forma, estabeleceram-se duas unidades de manejo para a área, as quais exigem práticas de irrigação e adubação diferenciadas. A análise da variabilidade espacial dos atributos do solo permitiu tomar decisões gerenciais na produção integrada de frutas

Geoestadística en la producción integrada de frutas en el nordeste de Brasil.

El objetivo de este estudio es mapear las variaciones espaciales del suelo de área con producción integrada de frutas en el nordeste de Brasil por medio de técnicas geoestadísticas. El área de estudio posee 35,98 ha con cocotero irrigado por microaspersión. Se realizó la recolección de datos por medio de atributos físicoquímicos del suelo (tenor de arcilla, granulometría, C orgánico, pH agua, P, Ca+Mg, K, Na, Al, SB y CTC) en 93 puntos muestrales. Los datos fueron asociados a las coordenadas geográficas locales por GPS. Después se efectuó el ajuste matemático por semivariogramas en el aplicativo Surfer 8.0, se definieron los parámetros: efecto pepita (C0); alcance de la dependencia espacial (A0); nivel (C0+C1) y el grado de dependencia espacial (C0)/(C0+C1). Del mismo modo, se elaboraron mapas de isolíneas de atributos a partir del interpolador geoestadístico de kriging. Los resultados obtenidos indican el predominio de atributos con elevado grado de heterogeneidad. El análisis de la relación C0/(C0 + C1) reveló grado de dependencia espacial de moderado a fuerte en los atributos analizados. De esa forma, se establecieron dos unidades de manejo para el área, las cuales exigen prácticas de irrigación y de abono diferenciadas

Exceptional Times for the Dynamical Discrete Web

The dynamical discrete web (DyDW),introduced in 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 exceptional such \tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by H\"{a}ggstrom, 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, H\"{a}ggstrom, Peres and Steif. For example, we prove that the walk from the origin S^\tau_0 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 extend to the dynamical Brownian web, the natural scaling limit of the DyDW

Majority Dynamics and Aggregation of Information in Social Networks

Consider n individuals who, by popular vote, choose among q >= 2 alternatives, one of which is "better" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n tends to infinity. Our interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is "majority dynamics", in which each voter adopts the most popular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of "efficient aggregation of information": in which cases is the better alternative chosen with probability approaching one as n tends to infinity? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the limit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.Comment: 22 page

First report of groundnut ringspot orthotospovirus infecting field pea (Pisum sativum L.) crop in Brazil.

Field pea (Pisum sativum L.) cultivar Axé with symptoms of orthotospovirus infection (~5% incidence) were collected under open field conditions in Brasília-DF, Central Brazil. Ten leaf samples displaying apical chlorosis, necrosis, and deformation were evaluated via serology (ELISA) using antisera (produced at Embrapa Vegetable Crops) specific to the nucleocapsid (N) protein of three Orthotospovirus species: Tomato chlorotic spot orthotospovirus (TCSV), Tomato spotted wilt orthotospovirus (TSWV), and Groundnut ringspot orthotospovirus (GRSV)