Intersecções homoclínicas

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

Parallel Computation of 2D Morse-Smale Complexes

The Morse-Smale complex is a useful topological data structure for the analysis and visualization of scalar data. This paper describes an algorithm that processes all mesh elements of the domain in parallel to compute the Morse-Smale complex of large two-dimensional data sets at interactive speeds. We employ a reformulation of the Morse-Smale complex using Forman's Discrete Morse Theory and achieve scalability by computing the discrete gradient using local accesses only. We also introduce a novel approach to merge gradient paths that ensures accurate geometry of the computed complex. We demonstrate that our algorithm performs well on both multicore environments and on massively parallel architectures such as the GPU.

Parallel Computation of 3D Morse-Smale Complexes

The Morse-Smale complex is a topological structure that captures the behavior of the gradient of a scalar function on a manifold. This paper discusses scalable techniques to compute the Morse-Smale complex of scalar functions defined on large three-dimensional structured grids. Computing the Morse-Smale complex of three-dimensional domains is challenging as compared to two-dimensional domains because of the non-trivial structure introduced by the two types of saddle criticalities. We present a parallel shared-memory algorithm to compute the Morse-Smale complex based on Forman's discrete Morse theory. The algorithm achieves scalability via synergistic use of the CPU and the GPU. We first prove that the discrete gradient on the domain can be computed independently for each cell and hence can be implemented on the GPU. Second, we describe a two-step graph traversal algorithm to compute the 1-saddle-2-saddle connections efficiently and in parallel on the CPU. Simultaneously, the extremasaddle connections are computed using a tree traversal algorithm on the GPU.

A review of diseases associated with cage culture systems: diagnosis and control in smale scale fish farming

Fish cage culture is a rapid aquacultural practice of producing fish with more yield compared to traditional pond culture. Several species cultured by this method include Cyprinus carpio, Orechromis niloticus, Sarotherodon galilaeus, Tilapia zilli, Clarias lazera, C. gariepinus, Heterobranchus bidorsalis, Citharinus citharus, Distochodus rostratus and Alestes dentes. However, the culture of fish in cages has some problems that are due to mechanical defects of the cage or diseases due to infection. The mechanical problems which may lead to clogged net, toxicity and easy access by predators depend on defects associated with various types of nets which include fold sieve cloth net, wire net, polypropylene net, nylon, galvanized and welded net. The diseases problems are of two types namely introduced diseases due to parasites. The introduced parasites include Crustaseans, Ergasilus sp. Argulus africana, and Lamprolegna sp, Helminth, Diplostomulum tregnna: Protozoan, Trichodina sp, Myxosoma sp, Myxobolus sp. the second disease problems are inherent diseases aggravated by the very rich nutrient environment in cages for rapid bacterial, saprophytic fungi, and phytoplanktonic bloom resulting in clogging of net, stagnation of water and low biological oxygen demand (BOD). The consequence is fish kill, prevalence of gill rot and dropsy conditions. Recommendations on routine cage hygiene, diagnosis and control procedures to reduce fish mortality are highlighted

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Análise experimental do sistema "vórtice ferradura" no escoamento ao redor de um cilindro circular

Este trabalho apresenta o estudo de um sistema hidrodinâmico encontrada em muitas situações dentro da mecânica dos fluidos: o Vórtice Ferradura. Esta estrutura possui características bastante complexas e seu comportamento ainda é pouco compreendido e explicado. Assim, o escoamento ao redor do cilindro circular, em leito fixo, foi investigado experimentalmente, com o propósito de tentar caracterizar o comportamento hidrodinâmico do Vórtice Ferradura através da visualização de escoamento e medições de pressão. Para o trabalho, um cilindro foi montado. As visualizações do Vórtice foram feitas através de uma janela de visualização na seção de testes do canal. A filmagem foi feita através de uma câmera de vídeo VHS, de uso doméstico, e injeção de corante. As medições de pressão foram feitas através do emprego de transdutores de pressão, e divididas em dois grupos: (i) medições de pressão feitas no leito do canal, na linha de simetria, na região de escoamento próxima ao Vórtice; (ii) medições de pressão do escoamento na superfície do cilindro. As imagens, assim como os dados de transdutor, foram transportados para o meio digital para posterior manipulação e análise. Os resultados confirmam algumas descrições fornecidas pela literatura, bem como, também levantam algumas considerações sobre o assunto: as imagens permitiram a visualização das etapas de formação do Vórtice, descrever modificações em seu diâmetro ao longo dos ensaios, reconhecer a variabilidade espacial de sua posição e detectar a presença de um vórtice secundário. Os dados de transdutor descreveram o campo de pressões no leito do canal, modificado pela presença do cilindro e, ao redor da superfície do mesmo, bem como, o comportamento das flutuações de pressão, correlações, autocorrelações e espectros das flutuações de pressão dos transdutores, para estas situações.

Interpretação eletrostática e a conjectura se Smale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efeito do tipo de ferradura e angulação do casco sobre o movimento do membro torácico em equinos ao trote

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

MS3ALIGN: an efficient molecular surface aligner using the topology of surface curvature

Background: Aligning similar molecular structures is an important step in the process of bio-molecular structure and function analysis. Molecular surfaces are simple representations of molecular structure that are easily constructed from various forms of molecular data such as 3D atomic coordinates (PDB) and Electron Microscopy (EM) data. Methods: We present a Multi-Scale Morse-Smale Molecular-Surface Alignment tool, MS3ALIGN, which aligns molecular surfaces based on significant protrusions on the molecular surface. The input is a pair of molecular surfaces represented as triangle meshes. A key advantage of MS3ALIGN is computational efficiency that is achieved because it processes only a few carefully chosen protrusions on the molecular surface. Furthermore, the alignments are partial in nature and therefore allows for inexact surfaces to be aligned. Results: The method is evaluated in four settings. First, we establish performance using known alignments with varying overlap and noise values. Second, we compare the method with SurfComp, an existing surface alignment method. We show that we are able to determine alignments reported by SurfComp, as well as report relevant alignments not found by SurfComp. Third, we validate the ability of MS3ALIGN to determine alignments in the case of structurally dissimilar binding sites. Fourth, we demonstrate the ability of MS3ALIGN to align iso-surfaces derived from cryo-electron microscopy scans. Conclusions: We have presented an algorithm that aligns Molecular Surfaces based on the topology of surface curvature. Awebserver and standalone software implementation of the algorithm available at http://vgl.serc.iisc.ernet. in/ms3align.

Age validation, growth, mortality, and demographic modeling of spotted gully shark (Triakis megalopterus) from the southeast coast of South Africa

This study documents validation of vertebral band-pair formation in spotted gully shark (Triakis megalopterus) with the use of fluorochrome injection and tagging of captive and wild sharks over a 21-year period. Growth and mortality rates of T. megalopterus were also estimated and a demographic analysis of the species was conducted. Of the 23 OTC (oxytetracycline) -marked vertebrae examined (12 from captive and 11 from wild sharks), seven vertebrae (three from captive and four from wild sharks) exhibited chelation of the OTC and fluoresced under ultraviolet light. It was concluded that a single opaque and translucent band pair was deposited annually up to at least 25 years of age, the maximum age recorded. Reader precision was assessed by using an index of average percent error calculated at 5%. No significant differences were found between male and female growth patterns (P>0.05), and von Bertalanffy growth model parameters for combined sexes were estimated to be L∞=1711.07 mm TL, k=0.11/yr and t0=–2.43 yr (n=86). Natural mortality was estimated at 0.17/yr. Age at maturity was estimated at 11 years for males and 15 years for females. Results of the demographic analysis showed that the population, in the absence of fishing mortality, was stable and not significantly different from zero and particularly sensitive to overfishing. At the current age at first capture and natural mortality rate, the fishing mortality rate required to result in negative population growth was low at F>0.004/ yr. Elasticity analysis revealed that juvenile survival was the principal factor in explaining variability in population growth rate.

Reconstruction of original body size and estimation of allometric relationships for the longfin inshore squid (Loligo pealeii) and northern shortfin squid (Illex illecebrosus)

Quantification of predator-prey body size relationships is essential to understanding trophic dynamics in marine ecosystems. Prey lengths recovered from predator stomachs help determine the sizes of prey most influential in supporting predator growth and to ascertain size-specific effects of natural mortality on prey populations (Bax, 1998; Claessen et al., 2002). Estimating prey size from stomach content analyses is often hindered because of the degradation of tissue and bone by digestion. Furthermore, reconstruction of original prey size from digested remains requires species-specific reference materials and techniques. A number of diagnostic guides for freshwater (Hansel et al., 1988) and marine (Watt et al., 1997; Granadeiro and Silva, 2000) prey species exist; however they are limited to specific geographic regions (Smale et al., 1995; Gosztonyi et al., 2007). Predictive equations for reconstructing original prey size from diagnostic bones in marine fishes have been developed in several studies of piscivorous fishes of the Northwest Atlantic Ocean (Scharf et al., 1998; Wood, 2005). Conversely, morphometric relationships for cephalopods in this region are scarce despite their importance to a wide range of predators, such as finfish (Bowman et al., 2000 ; Staudinger, 2006), elasmobranchs (Kohler, 1987), and marine mammals (Gannon et al., 1997; Williams, 1999).

MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.