Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks. Copyright (C) EPLA, 2009

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.

Global Gene Expression Analysis during Germination in the Chytridiomycete Blastocladiella emersonii

Blastocladiella emersonii is an aquatic fungus of the Chytridiomycete class. During germination, the zoospore, a motile nongrowing cell, goes through a cascade of morphological changes that culminates with its differentiation into the germling cell, capable of coenocytic vegetative growth. Transcriptome analyses of B. emersonii cells were carried out during germination induced under various environmental conditions. Microarray data analyzing 3,563 distinct B. emersonii genes revealed that 26% of them are differentially expressed during germination in nutrient medium at at least one of the time points investigated. Over 500 genes are upregulated during the time course of germination under those conditions, most being related to cell growth, including genes involved in protein biosynthesis, DNA transcription, energetic metabolism, carbohydrate and oligopeptide transport, and cell cycle control. On the other hand, several transcripts stored in the zoospores are downregulated during germination in nutrient medium, such as genes involved in signal transduction, amino acid transport, and chromosome organization. In addition, germination induced in the presence of nutrients was compared with that triggered either by adenine or potassium ions in inorganic salt solution. Several genes involved in cell growth, induced during germination in nutrient medium, do not show increased expression when B. emersonii zoospores germinate in inorganic solution, suggesting that nutrients exert a positive effect on gene transcription. The transcriptome data also revealed that most genes involved in cell signaling show the same expression pattern irrespective of the initial germination stimulus.

Effects of the antimicrobial peptide gomesin on the global gene expression profile, virulence and biofilm formation of Xylella fastidiosa

In the xylem vessels of susceptible hosts, such as citrus trees, Xylella fastidiosa forms biofilm-like colonies that can block water transport, which appears to correlate to disease symptoms. Besides aiding host colonization, bacterial biofilms play an important role in resistance against antimicrobial agents, for instance antimicrobial peptides (AMPs). Here, we show that gomesin, a potent AMP from a tarantula spider, modulates X. fastidiosa gene expression profile upon 60 min of treatment with a sublethal concentration. DNA microarray hybridizations revealed that among the upregulated coding sequences, some are related to biofilm production. In addition, we show that the biofilm formed by gomesin-treated bacteria is thicker than that formed by nontreated cells or cells exposed to streptomycin. We have also observed that the treatment of X. fastidiosa with a sublethal concentration of gomesin before inoculation in tobacco plants correlates with a reduction in foliar symptoms, an effect possibly due to the trapping of bacterial cells to fewer xylem vessels, given the enhancement in biofilm production. These results warrant further investigation of how X. fastidiosa would respond to the AMPs produced by citrus endophytes and by the insect vector, leading to a better understanding of the mechanism of action of these molecules on bacterial virulence.

Global Gene Expression Analysis during Sporulation of the Aquatic Fungus Blastocladiella emersonii

The Blastocladiella emersonii life cycle presents a number of drastic biochemical and morphological changes, mainly during two cell differentiation stages: germination and sporulation. To investigate the transcriptional changes taking place during the sporulation phase, which culminates with the production of the zoospores, motile cells responsible for the dispersal of the fungus, microarray experiments were performed. Among the 3,773 distinct genes investigated, a total of 1,207 were classified as differentially expressed, relative to time zero of sporulation, at at least one of the time points analyzed. These results indicate that accurate transcriptional control takes place during sporulation, as well as indicating the necessity for distinct molecular functions throughout this differentiation process. The main functional categories overrepresented among upregulated genes were those involving the microtubule, the cytoskeleton, signal transduction involving Ca(2+), and chromosome organization. On the other hand, protein biosynthesis, central carbon metabolism, and protein degradation were the most represented functional categories among downregulated genes. Gene expression changes were also analyzed in cells sporulating in the presence of subinhibitory concentrations of glucose or tryptophan. Data obtained revealed overexpression of microtubule and cytoskeleton transcripts in the presence of glucose, probably causing the shape and motility problems observed in the zoospores produced under this condition. In contrast, the presence of tryptophan during sporulation led to upregulation of genes involved in oxidative stress, proteolysis, and protein folding. These results indicate that distinct physiological pathways are involved in the inhibition of sporulation due to these two classes of nutrient sources.