STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Nonlocal growth processes and conformal invariance

Up to now the raise-and-peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one parameter. Depending on its value one has a gapped phase, a critical point where one has conformal invariance, and a gapless phase with changing values of the dynamical critical exponent z. In this model, adsorption is local but desorption is not. The raise-and-strip model presented here, in which desorption is also nonlocal, has the same phase diagram. The critical exponents are different as are some physical properties of the model. Our study suggests the possible existence of a whole class of stochastic models in which one can observe conformal invariance.

QUASI-TOPOLOGICAL QUANTUM FIELD THEORIES AND Z(2) LATTICE GAUGE THEORIES

We consider a two-parameter family of Z(2) gauge theories on a lattice discretization T(M) of a three-manifold M and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space Gamma. We show that there is a region Gamma(0) subset of Gamma where the partition function and the expectation value h < W-R(gamma)> i of the Wilson loop can be exactly computed. Depending on the point of Gamma(0), the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of M. The Wilson loop on the other hand, does not depend on the topology of gamma. However, for a subset of Gamma(0), < W-R(gamma)> depends on the size of gamma and follows a discrete version of an area law. At the zero temperature limit, the spin-gauge model approaches the topological and the quasi-topological regions depending on the sign of the coupling constant.

Behavior of the thermal diffusivity of native and oxidized human low-density lipoprotein solutions studied by the Z-scan technique

Modifications in low-density lipoprotein (LDL) have emerged as a major pathogenic factor of atherosclerosis, which is the main cause of morbidity and mortality in the western world. Measurements of the heat diffusivity of human LDL solutions in their native and in vitro oxidized states are presented by using the Z-Scan (ZS) technique. Other complementary techniques were used to obtain the physical parameters necessary to interpret the optical results, e. g., pycnometry, refractometry, calorimetry, and spectrophotometry, and to understand the oxidation phase of LDL particles. To determine the sample's thermal diffusivity using the thermal lens model, an iterative one-parameter fitting method is proposed which takes into account several characteristic ZS time-dependent and the position-dependent transmittance measurements. Results show that the thermal diffusivity increases as a function of the LDL oxidation degree, which can be explained by the increase of the hydroperoxides production due to the oxidation process. The oxidation products go from one LDL to another, disseminating the oxidation process and caring the heat across the sample. This phenomenon leads to a quick thermal homogenization of the sample, avoiding the formation of the thermal lens in highly oxidized LDL solutions. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.JBO.17.10.105003]

Between the court and the revolution: the role of one ""merchant"" in America, capital of portuguese Empire

The article discusses the trajectory of Manuel Luis da Veiga which, as a merchant in Portugal (where he was born) invested to install a factory in Pernambuco after the arrival of Real Family in the Rio de Janeiro, considering the changes, in these days, in the Portuguese Empire. It focuses the political sociabilities, remarking the role of Veiga in the court and his writings on political economy, understanding both as two linked dimensions of his social practice. It points out that his trajectory shows a deeply changing world in terms of paradigms, impossible to be understood simply in patterns of what was old or new in the beginning of XIX century.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Linker for Activation of T-cell Family Member2 (LAT2) a Lipid Raft Adaptor Protein for AKT Signaling, Is an Early Mediator of Alkylphospholipid Anti-leukemic Activity

Lipid rafts are highly ordered membrane domains rich in cholesterol and sphingolipids that provide a scaffold for signal transduction proteins; altered raft structure has also been implicated in cancer progression. We have shown that 25 mu M 10-(octyloxy) decyl-2-(trimethylammonium) ethyl phosphate (ODPC), an alkylphospholipid, targets high cholesterol domains in model membranes and induces apoptosis in leukemia cells but spares normal hematopoietic and epithelial cells under the same conditions. We performed a quantitative (SILAC) proteomic screening of ODPC targets in a lipid-raft-enriched fraction of leukemic cells to identify early events prior to the initiation of apoptosis. Six proteins, three with demonstrated palmitoylation sites, were reduced in abundance. One, the linker for activation of T-cell family member 2 (LAT2), is an adaptor protein associated with lipid rafts in its palmitoylated form and is specifically expressed in B lymphocytes and myeloid cells. Interestingly, LAT2 is not expressed in K562, a cell line more resistant to ODPC-induced apoptosis. There was an early loss of LAT2 in the lipid-raft-enriched fraction of NB4 cells within 3 h following treatment with 25 mu M ODPC. Subsequent degradation of LAT2 by proteasomes was observed. Twenty-five mu M ODPC inhibited AKT activation via myeloid growth factors, and LAT2 knockdown in NB4 cells by shRNA reproduced this effect. LAT2 knockdown in NB4 cells also decreased cell proliferation and increased cell sensitivity to ODPC (7.5X), perifosine (3X), and arsenic trioxide (8.5X). Taken together, these data indicate that LAT2 is an early mediator of the anti-leukemic activity of alkylphospholipids and arsenic trioxide. Thus, LAT2 may be used as a target for the design of drugs for cancer therapy. Molecular & Cellular Proteomics 11: 10.1074/mcp.M112.019661, 1898-1912, 2012.

Aberrant transcript produced by a splice donor site deletion in the TECTA gene is associated with autosomal dominant deafness in a Brazilian family

We ascertained a Brazilian family with nine individuals affected by autosomal dominant nonsyndromic sensorineural hearing loss. The bilateral hearing loss affected mainly mid-high frequencies, was apparently stable with an early onset. Microsatellites close to the DFNA8/DFNA12 locus, which harbors the TECTA gene, showed significant multipoint lod scores (32) close to marker D11S4107. Sequencing of the exons and exon-intron boundaries of the TECTA gene in one affected subject revealed the deletion c.5383 + 5delGTGA in the 5' end of intron 16, that includes the last two bases of the donor splice site consensus sequence. This mutation segregates with deafness within the family. To date, 33 different TECTA mutations associated with autossomal dominant hearing loss have been described. Among them is the mutation reported herein, first described by Hildebrand et al. (2011) in a UK family. The audioprofiles from the UK and Brazilian families were similar. In order to investigate the transcripts produced by the mutated allele, we performed cDNA analysis of a lymphoblastoid cell line from an affected heterozygote with the c.5383 + 5delGTGA and a noncarrier from the same family. The analysis allowed us to identify an aberrant transcript with skipping of exon 16, without affecting the reading frame. One of the dominant TECTA mutations already described, a synonymous substitution in exon 16 (c.5331 G<A), was also shown to affect splicing resulting in an aberrant transcript lacking exon 16. Despite the difference in the DNA level, both the synonymous substitution in exon 16 (c.5331 G<A) and the mutation described herein affect splicing of exon 16, leading to its skipping. At the protein level they would have the same effect, an in-frame deletion of 37 amino-acids (p.S1758Y/G1759_N1795del) probably leading to an impaired function of the ZP domain. Thus, like the TECTA missense mutations associated with dominant hearing loss, the c5383 + 5delGTGA mutation does not have an inactivating effect on the protein. (C) 2012 Elsevier B.V. All rights reserved.

A TRAINING COURSE ON BIOETHICS FOR FAMILY HEALTH STRATEGY PROFESSIONALS IN SANTO ANDRE, SP

This case report presents the experience of a training course on bioethics for nurses and physicians of the Family Health Strategy in Santo Andre, SP. This study is based on problem-based learning and deliberative bioethics, and aimed at presenting the deliberation procedure as a means of handling ethical issues. Contents were addressed in a cross-section manner through five sequential activity sessions at two different moments of concentration with one dispersion interval. In the first moment of concentration, key concepts and deliberative bioethics contents were developed. The second involved deliberation sessions on moral conflicts, which were selected and prepared during the dispersion interval. Participants evaluated the deliberation as an appropriate instrument to deal with the ethical issues they are faced with. Problem-based learning was an effective educational strategy for continuing education in deliberative bioethics.

Variable expressivity of osteogenesis imperfecta in a Brazilian family due to p.G1079S mutation in the COL1A1 gene

Osteogenesis imperfecta (OI) is a Mendelian disease with genetic heterogeneity characterized by bone fragility, recurrent fractures, blue sclerae, and short stature, caused mostly by mutations in COL1A1 or COL1A2 genes, which encode the pro-alpha 1(I) and pro-alpha 2(I) chains of type I collagen, respectively. A Brazilian family that showed variable expression of autosomal dominant OI was identified and characterized. Scanning for mutations was carried out using SSCP and DNA sequence analysis. The missense mutation c.3235G>A was identified within exon 45 of the COL1A1 gene in a 16-year-old girl diagnosed as having OI type I; it resulted in substitution of a glycine residue (G) by a serine (S) at codon 1079 (p.G1079S). The proband's mother had the disease signs, but without bone fractures, as did five of nine uncles and aunts of the patient. All of them carried the mutation, which was excluded in four healthy brothers of the patient's mother. This is the first description in a Brazilian family with OI showing variable expression; only one among seven carriers for the c.3235G>A mutation developed bone fractures, the most striking clinical feature of this disease. This finding has a significant implication for prenatal diagnosis in OI disease.