An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

Studies of cases in power systems by Sensitivity Analysis oriented by OPF

This paper presents studies of cases in power systems by Sensitivity Analysis (SA) oriented by Optimal Power Flow (OPF) problems in different operation scenarios. The studies of cases start from a known optimal solution obtained by OPF. This optimal solution is called base case, and from this solution new operation points may be evaluated by SA when perturbations occur in the system. The SA is based on Fiacco`s Theorem and has the advantage of not be an iterative process. In order to show the good performance of the proposed technique tests were carried out on the IEEE 14, 118 and 300 buses systems. (C) 2010 Elsevier Ltd. All rights reserved.

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems Of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

Alternative positional FEM applied to thermomechanical impact of truss structures

This paper presents a formulation to deal with dynamic thermomechanical problems by the finite element method. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions, not displacements, to solve the mechanical problem. The thermal problem is solved by a regular finite element method. Such formulation has the advantage of being simple and accurate. As a solution strategy, it has been used as a natural split of the thermomechanical problem, usually called isothermal split or isothermal staggered algorithm. Usual internal variables and the additive decomposition of the strain tensor have been adopted to model the plastic behavior. Four examples are presented to show the applicability of the technique. The results are compared with other authors` numerical solutions and experimental results. (C) 2010 Elsevier B.V. All rights reserved.

SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

Endomyocardial fibrosis: pathological and molecular findings of surgically resected ventricular endomyocardium

Endomyocardial fibrosis (EMF) is a restrictive cardiomyopathy of unknown etiology prevalent in tropical regions affecting the inflow tract and apex of one or both ventricles, which show fibrous thickening of the endocardium and adjacent myocardium. Surgical treatment is recommended for patients in functional classes III or IV (New York Heart Association). The gross and histological features of the heart have been comprehensively studied in autopsies, but studies in surgical samples are still lacking. Histological and immunohistochemical features of EMF in surgical samples collected from 32 patients were described and correlated with clinical data. Polymerase chain reaction (PCR) and reverse transcription-PCR, performed on formalin fixed endomyocardial samples, were used retrospectively to detect genomes of certain cardiotropic viruses and Toxoplasma gondii. Ventricular endocardium was thickened by superficial acellular hyaline collagen fibers type I and III, with predominance of the former type. Besides fibrosis, a chronic inflammatory process and an anomalous lymphatic rich vascular pattern were observed in the deep endocardium, connected to the terminal coronary circulation of the myocardium, which might be an important pathological finding concerning EMF pathogenesis. Molecular analysis of the endomyocardium revealed high incidence of cardiotropic infective agents (6/12, 50%); however, their role in the disease pathogenesis is still controversial.

Characterization of leptospiral proteins that afford partial protection in hamsters against lethal challenge with Leptospira interrogans

Leptospirosis is a worldwide zoonosis caused by pathogenic Leptospira. The whole-genome sequence of Leptospira interrogans serovar Copenhageni together with bioinformatic tools allow us to search for novel antigen candidates suitable for improved vaccines against leptospirosis. This study focused on three genes encoding conserved hypothetical proteins predicted to be exported to the outer membrane. The genes were amplified by PCR from six predominant pathogenic serovars in Brazil. The genes were cloned and expressed in Escherichia coli strain BL21-SI using the expression vector pDEST17. The recombinant proteins tagged with N-terminal 6xHis were purified by metal-charged chromatography. The proteins were recognized by antibodies present in sera from hamsters that were experimentally infected. Immunization of hamsters followed by challenge with a lethal dose of a virulent strain of Leptospira showed that the recombinant protein rLIC12730 afforded statistically significant protection to animals (44 %), followed by rLIC10494 (40 %) and rLIC12922 (30 %). Immunization with these proteins produced an increase in antibody titres during subsequent boosters, suggesting the involvement of a T-helper 2 response. Although more studies are needed, these data suggest that rLIC12730 and rLIC10494 are promising candidates for a multivalent vaccine for the prevention of leptospirosis.

Cerebrospinal fluid levels of chemokines in HIV infected patients with and without opportunistic infection of the central nervous system

Chemokines are chemoattractant cytokines involved in the immune response of a wide variety of diseases. There are few studies assessing their role in opportunistic infections in HIV-infected patients. In this study, we measured CC and CXC chemokines in cerebrospinal fluid (CSF) samples obtained from 40 HIV-infected patients with or without opportunistic infections of the central nervous system (CNS). CSF samples were also analyzed for quantification of total protein, cell count and HIV-1 RNA. HIV+ patients with cryptococcal meningitis had higher levels of CCL2, CCL3, CCL5, CXCL9 and CXCL10 when compared to patients without opportunistic neurological infections. Furthermore, HIV+ patients with associated cryptococcal meningitis had higher levels of CCL3, CXCL9 and CXCL10 when compared to HIV+ patients with associated toxoplasmic encephalitis. CCL3 and CXCL9 levels were positively correlated with CSF HIV-1 RNA levels, CSF protein concentration, and CSF cell count. CXCL10 level was correlated with the CSF viral load and the CSF cell count and CCL5 level was correlated with the CSF cell count. In conclusion, the profile of chemokines in CSF of HIV patients may differ according to the modality of the presented opportunistic infection and according to other biological markers, such as viral load in CSF. These differences are probably related to different patterns of neuroinflammatory responses displayed by patients with different opportunistic neurological infections. (C) 2009 Elsevier B.V. All rights reserved.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

The analytic torsion of a cone over an odd dimensional manifold

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem [3, 2] for a manifold with boundary, according to Bruning and Ma (2006) [5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved.