Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Satellite Rainfall Estimates Over South America - Possible Applicability to the Water Management of Large Watersheds1

This work analyzes high-resolution precipitation data from satellite-derived rainfall estimates over South America, especially over the Amazon Basin. The goal is to examine whether satellite-derived precipitation estimates can be used in hydrology and in the management of larger watersheds of South America. High spatial-temporal resolution precipitation estimates obtained with the CMORPH method serve this purpose while providing an additional hydrometeorological perspective on the convective regime over South America and its predictability. CMORPH rainfall estimates at 8-km spatial resolution for 2003 and 2004 were compared with available rain gauge measurements at daily, monthly, and yearly accumulation time scales. The results show the correlation between satellite-derived and gauge-measured precipitation increases with accumulation period from daily to monthly, especially during the rainy season. Time-longitude diagrams of CMORPH hourly rainfall show the genesis, strength, longevity, and phase speed of convective systems. Hourly rainfall analyses indicate that convection over the Amazon region is often more organized than previously thought, thus inferring that basin scale predictions of rainfall for hydrological and water management purposes have the potential to become more skillful. Flow estimates based on CMORPH and the rain gauge network are compared to long-term observed average flow. The results suggest this satellite-based rainfall estimation technique has considerable utility. Other statistics for monthly accumulations also suggest CMORPH can be an important source of rainfall information at smaller spatial scales where in situ observations are lacking.

Evaluating microfossil content of dental calculus from Brazilian sambaquis

To date, limited numbers of dental calculus samples have been analyzed by researchers in diverse parts of the world. The combined analyses of these have provided some general guidelines for the analysis of calculus that is non-destructive to archaeological teeth. There is still a need for a quantitative study of large numbers of calculus samples to establish protocols, assess the level of contamination, evaluate the quantity of microfossils in dental calculus, and to compare analysis results with the literature concerning the biology of calculus formation. We analyzed dental calculus from 53 teeth from four Brazilian sambaquis. Sambaquis are the shell-mounds that were established prehistorically along the Brazilian coast. The analysis of sambaqui dental calculi shows that there are relatively high concentrations of microfossils (phytoliths and starch), mineral fragments, and charcoal in dental calculus. Mineral fragments and charcoal are possibly contaminants. The largest dental calculi have the lowest concentrations of microfossils. Biologically, this is explained by individual variation in calculus formation between people. Importantly, starch is ubiquitous in dental calculus. The starch and phytoliths show that certainly Dioscorea (yam) and Araucaria angustifolia (Parana pine) were eaten by sambaqui people. Araceae (arum family), Ipomoea batatas (sweet potato) and Zea mays (maize) were probably in their diet. (C) 2009 Elsevier Ltd. All rights reserved.

Population genetic analysis of large sequence polymorphisms in Plasmodium falciparum blood-stage antigens

Plasmodium falciparum, the causative agent of human malaria, invades host erythrocytes using several proteins on the surface of the invasive merozoite, which have been proposed as potential vaccine candidates. Members of the multi-gene PfRh family are surface antigens that have been shown to play a central role in directing merozoites to alternative erythrocyte receptors for invasion. Recently, we identified a large structural polymorphism, a 0.58 Kb deletion, in the C-terminal region of the PfRh2b gene, present at a high frequency in parasite populations from Senegal. We hypothesize that this region is a target of humoral immunity. Here, by analyzing 371 P. falciparum isolates we show that this major allele is present at varying frequencies in different populations within Senegal, Africa, and throughout the world. For allelic dimorphisms in the asexual stage antigens, Msp-2 and EBA-175, we find minimal geographic differentiation among parasite populations from Senegal and other African localities, suggesting extensive gene flow among these populations and/or immune-mediated frequency-dependent balancing selection. In contrast, we observe a higher level of inter-population divergence (as measured by F(st)) for the PfRh2b deletion, similar to that observed for SNPs from the sexual stage Pfs45/48 loci, which is postulated to be under directional selection. We confirm that the region containing the PfRh2b polymorphism is a target of humoral immune responses by demonstrating antibody reactivity of endemic sera. Our analysis of inter-population divergence suggests that in contrast to the large allelic dimorphisms in EBA-175 and Msp-2, the presence or absence of the large PfRh2b deletion may not elicit frequency-dependent immune selection, but may be under positive immune selection, having important implications for the development of these proteins as vaccine candidates. (C) 2009 Elsevier B.V. All rights reserved.

A Precise Formulation of the Third Law of Thermodynamics

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature I""(0) are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or ""by a finite number of operations""), it admits as corollary, under a continuity assumption, that all points of I""(0) are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.

Phantom accretion by black holes and the generalized second law of thermodynamics

The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the generalized second law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by the generalized second law. (C) 2010 Elsevier B.V. All rights reserved.