Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Impact of palm date consumption on microbiota growth and large intestinal health: a randomised, controlled, cross-over, human intervention study

The reported inverse association between the intake of plant-based foods and a reduction in the prevalence of colorectal cancer may be partly mediated by interactions between insoluble fibre and (poly)phenols and the intestinal microbiota. In the present study, we assessed the impact of palm date consumption, rich in both polyphenols and fibre, on the growth of colonic microbiota and markers of colon cancer risk in a randomised, controlled, cross-over human intervention study. A total of twenty-two healthy human volunteers were randomly assigned to either a control group (maltodextrin-dextrose, 37·1 g) or an intervention group (seven dates, approximately 50 g). Each arm was of 21 d duration and was separated by a 14-d washout period in a cross-over manner. Changes in the growth of microbiota were assessed by fluorescence in situ hybridisation analysis, whereas SCFA levels were assessed using HPLC. Further, ammonia concentrations, faecal water genotoxicity and anti-proliferation ability were also assessed using different assays, which included cell work and the Comet assay. Accordingly, dietary intakes, anthropometric measurements and bowel movement assessment were also carried out. Although the consumption of dates did not induce significant changes in the growth of select bacterial groups or SCFA, there were significant increases in bowel movements and stool frequency (P<0·01; n 21) and significant reductions in stool ammonia concentration (P<0·05; n 21) after consumption of dates, relative to baseline. Furthermore, date fruit intake significantly reduced genotoxicity in human faecal water relative to control (P<0·01; n 21). Our data indicate that consumption of date fruit may reduce colon cancer risk without inducing changes in the microbiota.

HiPP: A Novel Hierarchical Point Placement Strategy and its Application to the Exploration of Document Collections

Point placement strategies aim at mapping data points represented in higher dimensions to bi-dimensional spaces and are frequently used to visualize relationships amongst data instances. They have been valuable tools for analysis and exploration of data sets of various kinds. Many conventional techniques, however, do not behave well when the number of dimensions is high, such as in the case of documents collections. Later approaches handle that shortcoming, but may cause too much clutter to allow flexible exploration to take place. In this work we present a novel hierarchical point placement technique that is capable of dealing with these problems. While good grouping and separation of data with high similarity is maintained without increasing computation cost, its hierarchical structure lends itself both to exploration in various levels of detail and to handling data in subsets, improving analysis capability and also allowing manipulation of larger data sets.

On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

Distribution of ABCB1 polymorphisms among Brazilians: impact of population admixture

Introduction: Interethnic admixture is a source of cryptic population structure that may lead to spurious genotype-phenotype associations in pharmacogenomic studies. We studied the impact of population stratification on the distribution of ABCB1 polymorphisms (1236C > T, 2677G > T/A and 3435C > T) among Brazilians, a highly admixed population with Amerindian, European and African ancestral roots. Methods: Individual DNA from 320 healthy adults was genotyped with a panel of ancestry informative markers, and the proportions of African component of ancestry (ACA) were estimated. ABCB1 genotypes were determined by the single base extension/termination method. We describe the association between ABCB1 polymorphisms and ACA by fitting a linear proportional odds logistic regression model to the data. Results: The distribution of the ABCB1 2677G > T/A and 3435C > T, but not the 1236C > T, SNPs displayed a significant trend for decreasing frequency of the T alleles and TT genotypes from White to Intermediate to Black individuals. The same trend was observed in the frequency of the T/nonG/T haplotype at the 1236, 2677 and 3435 loci. When the population sample was proportioned in quartiles, according to the individual ACA estimates, the frequency of the T allele and TT genotype at each locus declined progressively from the lowest (< 0.25 ACA) to the highest (> 0.75 ACA) quartile. Linear proportional odds logistic regression analysis confirmed that the odds of having the T allele at each locus decreases in a continuous manner with the increase of the ACA, throughout the ACA range (0.13-0.94) observed in the overall population sample. A significant association was also detected between the individual ACA estimates and the presence of the T/nonG/T haplotype in the overall population. Conclusion: Self-identification according to the racial/color categories proposed by the Brazilian Census is insufficient to properly control for population stratification in pharmacogenomic studies of ABCB1.

Avaliação da suplementação com vitamina E, na forma natural ou sintética, em mulheres no pós-parto imediato e sua concentração no colostro

The Vitamin E consists of eight chemically homologous forms, designated alpha, beta, gamma and delta tocopherols and tocotrienols. Biologically, the alpha-tocopherol (α-TOH) is the most important. Commercially, are found two types of α-TOH a natural (RRR-alpha-tocopherol) and another synthetic (all-rac-alpha-tocopherol). Both forms are absorbed in the intestine, the liver is a preference in favor of forms 2R, due to transfer protein α-TOH. It has higher affinity to these stereoisomers. Newborns are considered high risk for vitamin E deficiency, mainly premature, these have breast milk as a food source for maintenance of serum α-TOH. Clinical signs such as thrombocytosis, hemolytic anemia, retrolental fibroplasia, intraventricular hemorrhage, bronchopulmonary dysplasia and spinocerebellar degeneration can be found in case of a low intake of α-TOH. Thus, maternal supplementation on postpartum with α-TOH can be an efficient way to increase levels of vitamin E in breast milk and thus the consequently increase the supply of micronutrient for the newborn. However, most studies with vitamin E supplementation have been conducted in animals and little is known about the effect of maternal supplementation in humans, as well as on its efficiency to increase levels of α-TOH in human milk, depending on the shape natural or synthetic. The study included 109 women, divided into three groups: control without supplementation (GC) (n=36), supplemented with natural capsule (GNAT) (n=40) and the synthetic capsule (GSINT) (n=33). Blood samples were collected for determination of maternal nutritional status, and colostrums at initial contact and after 24 hours post-supplementation. Analyses were performed by High Performance Liquid Chromatography. Values of α-TOH in serum below 499.6mg/dL were considered deficient. We used the Kruskal-Wallis test and Tukey test to confirm the increase of alpha-tocopherol in milk and efficiency of administered capsules. Daily consumption of α-TOH was based on daily intake of 500 mL of colostrum by the newborn and compared with the nutritional requirement for children from 0 to 6 months of age, 4 mg / day. The mothers had mean concentration of serum α-TOH in 1016 ± 52, 1236 ± 51 and 1083 ± 61 mg / dL, in CG, GNAT and GSINT respectively. There were no women with deficiiency. The GC did not change the concentrations of α-TOH in colostrum. While women supplemented with natural and synthetic forms increased concentrations of α-TOH colostrum in 57.6% and 39%, respectively. By comparing supplemented groups, it was observed a significant difference (p=0.04), the natural capsule more efficient than the synthetic, approximately 49.6%. Individually, 21.1% of the women provided below 4mg/day of α-TOH, after supplementation for this index declined4.1%. Thus, maternal supplementation postpartum raised the levels of alpha-tocopherol in colostrum, and increased efficiency was observed with the natural form

Efeito de concentrações de herbicidas sobre aspectos biológicos de Fusarium sp. (isolado FCAV#940)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)