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

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

Comparative measurements of carbon dioxide fluxes from two nearby towers in a central Amazonian rainforest: the Manaus LBA site

Forests around Manaus have staged the oldest and the longest forest-atmosphere CO2 exchange studies made anywhere in the Amazon. Since July 1999 the exchange of CO2, water, and energy, as well as weather variables, have been measured almost continuously over two forests, 11 km apart, in the Cuieiras reserve near Manaus, Brazil. This paper presents the sites and climatology of the region based upon the new data sets. The landscape consists of plateaus dissected by often waterlogged valleys, and the two sites differ in terms of the relative areas of those two landscape components represented in the tower footprints. The radiation and wind climate was similar to both towers. Generally, both the long-wave and short-wave radiation input was less in the wet than in the dry season. The energy balance closure was imperfect (on average 80%) in both towers, with little variation in energy partitioning between the wet and dry seasons; likely a result of anomalously high rainfall in the 1999 dry season. Fluxes of CO2 also showed little seasonal variation except for a slightly shorter daytime uptake duration and somewhat lower respiratory fluxes in the dry season. The net effect is one of lower daily net ecosystem exchange (NEE) in the dry season. The tower, which has less waterlogged valley areas in its footprint, measured a higher overall CO2 uptake rate. We found that on first sight, NEE is underestimated during calm nights, as was observed in many other tower sites before. However, a closer inspection of the diurnal variation of CO2 storage fluxes and NEE suggests that at least part of the nighttime deficits is recovered from either lateral influx of CO2 from valleys or outgassing of soil storage. Therefore there is a high uncertainty in the magnitude of nocturnal NEE, and consequently preliminary estimates of annual carbon uptake reflecting this range from 1 to 8 T ha-1 y-1, with an even higher upper range for the less waterlogged area. The high uptake rates are clearly unsustainable and call for further investigations into the integral carbon balance of Amazon landscapes

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

Variação estacional do preço da melancia comercializada na região do Submédio São Francisco, período 1995-2005.

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Análise do custo de produção e rentabilidade do cultivo do maracujazeiro na região do Submédio São Francisco.

Tendo em vista a importância econômica e social que tem a exploração do maracujá no Submédio São Francisco, procurou-se, nesta pesquisa, analisar os custos de produção e a rentabilidade da exploração de maracujá nesse agropólo. Como trata-se de um cultivo que demanda elevados custos de produção, é importante que o produtor, além de alcançar uma alta produtividade, obtenha também uma rentabilidade significativa