Counting Integer flows in Networks

This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics \cite{persi}. Our methods clearly surpass traditional exhaustive enumeration and other algorithms and can even yield formulas when the input data contains some parameters. These methods are based on the study of rational functions with poles on arrangements of hyperplanes

Intertwining operators and unitary representations II

AbstractFor a linear semisimple Lie group with a compact Cartan subgroup, the authors obtain formulas for the action of intertwining operators on certain subspaces of standard induced representations. These formulas provide explicit limitations on the pool of candidates for irreducible unitary representations, since the only possible invariant inner product is given by such an intertwining operator

Single and multiple-trait BLUP in genetic selection of parents and hybrids of grain sorghum.

To increase yield, breeding programs must search for innovative and efficient methodologies for the development and selection of superior genotypes. Therefore, this study aimed to compare the single- and multiple-trait best linear unbiased prediction (BLUP) in genetic selection of parents and hybrids of grain sorghum. For this, an experiment conducted in alpha-lattice design with two replications was used. Flowering time (FT), plant height (PH), and grain yield (GY) were evaluated in 502 grain sorghum hybrids obtained by the cross of ten restorer lines and 54 male-sterile lines. Variance components were estimated via restricted maximum likelihood (REML). Significant effects of restorer lines, of male-sterile lines, and of specific combining ability were detected by the likelihood ratio test (LRT). The estimates of variance components, genetic parameters, and correlations were similar when obtained via single- and multiple traitBLUP. Considering hybrids, the multipl

Comportamento de híbridos de sorgo granífero cultivados na segunda safra no município de SINOP-MT.

O sorgo é uma gramínea de clima tropical de dias curtos, metabolismo C4, com eficiente mecanismo morfofisiológico, possuindo características de resistência ao déficit hídrico e habilidade de se manter dormente no período de seca (SANTOS, 2003; MAGALHAES; DURÃES, 2003). Tais características fazem com que esta cultura seja opção para cultivo em segunda safra, principalmente em períodos e regiões cujo cultivo de milho seja de risco pela possibilidade de restrições hídricas para fechamento do ciclo da planta. O levantamento da área plantada com sorgo na Safra 2013/14 é de 731 mil ha com produtividade de grãos de 2.587 kg ha-1 (CONAB, 2015). Maiores produtividades são alcançadas em lavouras que, seguindo planejamento adequado de plantio, utilizam sementes de cultivares recomendados para sua região de plantio. O melhoramento genético de plantas desenvolve variedades adaptadas a diferentes regiões e condições de cultivo, tornando importante que o produtor identifique aquelas que melhor se modele a sua realidade. Para tal, estudos de comportamento produtivo de genótipos no intuito de seleção daqueles com maior potencial produtivo e retorno econômico são recomendados antes do plantio de grandes áreas. Neste intuito, o presente trabalho avaliou o comportamento produtivo de híbridos de sorgo granífero cultivados em segunda safra, no município de Sinop, região norte de Mato Grosso.Editado por Aisy B. Baldoni, Fabiana A. de Rezende, José Ângelo N. de Menezes Júnior, Luciano B. Lopes, Sílvia de C. C. Botelho

Maturity curve of sweet sorghum in function of total soluble solids concentration

Sweet sorghum (Sorghum bicolor (L.) Moench) has been standing out as a source of feedstock for ethanol production in Brazil from January to April (period characterized as off-season of sugarcane). The aim of this study was to construct a maturity curve of two sweet sorghum cultivars, BRS 508 and BRS 511, in order to identify the ideal point of harvest for each material and estimate the maximum of total soluble solids (TSS) reached by the cultivars. For this purpose, an experiment was carried out at Embrapa Agrossilvipastoril, located in Sinop-MT. The seeds of each cultivar were mechanically sown in contiguous lines, spaced 0.7m, aiming to establish a population 140,000 plants ha -1 . Fifteen days after flowering (DAF), plants were harvested weekly during nine weeks (71 DAF), aiming to evaluate TSS of each cultiva r along this period of time. The TSS was measured by digital refractometer ( o Brix scale) using syrup from stems of each cultivar by an electric milling. The maturity curves of each cultivar were constructed by values of TSS measured during nine weeks and the regression equations were obtained for each cultivar. In order to estimate the optimal harvest moment, the maximum point was calculated by derivation of the original equation. By deriving such equations, it was possible to estimate the number of DAF of each cultivar in order to know the highest TSS concentrations, whic h can be considered as the point of maximum maturity. In addition, the maximum TSS concentrations were estimated for each cultivar. The results showed that the cultivar BRS 508 obtained maximum concentration of 20.4 °Brix at 51 DAF. On the other hand, the cultivar BRS 511 presented a TSS peak value of 17.6 °Brix at 50 DAF. It was noted that BRS 508 obtained a higher content of TSS than BRS 511, with a magnitude approximately of 2 °Brix. However, the maturity cycles of both cultivars were similar, 50 and 51 DAF (around 130 days after sowing). After this period, the TSS concentrations tended to decrease for both genotypes, decreasing, consequently, the yield of ethanol per volume of syrup. The next stage of this work will be the evaluation of TSS and the volume of syrup produced, such characteristics are better correlated to the ethanol production and will help in the identification of the cultivar with better performance

Single- and multiple-trait BLUP in genetic selection of parents and hybrids of grain sorghum.

To increase yield, breeding programs must search for innovative and efficient methodologies for the development and selection of superior genotypes. Therefore, this study aimed to compare the single- and multiple-trait best linear unbiased prediction (BLUP) in genetic selection of parents and hybrids of grain sorghum. For this, an experiment conducted in alpha-lattice design with two replications was used. Flowering time (FT), plant height (PH), and grain yield (GY) were evaluated in 502 grain sorghum hybrids obtained by the cross of ten restorer lines and 54 male-sterile lines. Variance components were estimated via restricted maximum likelihood (REML). Significant effects of restorer lines, of male-sterile lines, and of specific combining ability were detected by the likelihood ratio test (LRT). The estimates of variance components, genetic parameters, and correlations were similar when obtained via single- and multiple traitBLUP. Considering hybrids, the multipl