A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Mapping of a Myosin-binding Domain and a Regulatory Phosphorylation Site in M-Protein, a Structural Protein of the Sarcomeric M Band

The myofibrils of cross-striated muscle fibers contain in their M bands cytoskeletal proteins whose main function seems to be the stabilization of the three-dimensional arrangement of thick filaments. We identified two immunoglobin domains (Mp2–Mp3) of M-protein as a site binding to the central region of light meromyosin. This binding is regulated in vitro by phosphorylation of a single serine residue (Ser76) in the immediately adjacent amino-terminal domain Mp1. M-protein phosphorylation by cAMP-dependent kinase A inhibits binding to myosin LMM. Transient transfection studies of cultured cells revealed that the myosin-binding site seems involved in the targeting of M-protein to its location in the myofibril. Using the same method, a second myofibril-binding site was uncovered in domains Mp9–Mp13. These results support the view that specific phosphorylation events could be also important for the control of sarcomeric M band formation and remodeling.

Functional and structural mapping of human cerebral cortex: Solutions are in the surfaces

The human cerebral cortex is notorious for the depth and irregularity of its convolutions and for its variability from one individual to the next. These complexities of cortical geography have been a chronic impediment to studies of functional specialization in the cortex. In this report, we discuss ways to compensate for the convolutions by using a combination of strategies whose common denominator involves explicit reconstructions of the cortical surface. Surface-based visualization involves reconstructing cortical surfaces and displaying them, along with associated experimental data, in various complementary formats (including three-dimensional native configurations, two-dimensional slices, extensively smoothed surfaces, ellipsoidal representations, and cortical flat maps). Generating these representations for the cortex of the Visible Man leads to a surface-based atlas that has important advantages over conventional stereotaxic atlases as a substrate for displaying and analyzing large amounts of experimental data. We illustrate this by showing the relationship between functionally specialized regions and topographically organized areas in human visual cortex. Surface-based warping allows data to be mapped from individual hemispheres to a surface-based atlas while respecting surface topology, improving registration of identifiable landmarks, and minimizing unwanted distortions. Surface-based warping also can aid in comparisons between species, which we illustrate by warping a macaque flat map to match the shape of a human flat map. Collectively, these approaches will allow more refined analyses of commonalities as well as individual differences in the functional organization of primate cerebral cortex.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Global properties of the mapping between local amino acid sequence and local structure in proteins.

Local protein structure prediction efforts have consistently failed to exceed approximately 70% accuracy. We characterize the degeneracy of the mapping from local sequence to local structure responsible for this failure by investigating the extent to which similar sequence segments found in different proteins adopt similar three-dimensional structures. Sequence segments 3-15 residues in length from 154 different protein families are partitioned into neighborhoods containing segments with similar sequences using cluster analysis. The consistency of the sequence-to-structure mapping is assessed by comparing the local structures adopted by sequence segments in the same neighborhood in proteins of known structure. In the 154 families, 45% and 28% of the positions occur in neighborhoods in which one and two local structures predominate, respectively. The sequence patterns that characterize the neighborhoods in the first class probably include virtually all of the short sequence motifs in proteins that consistently occur in a particular local structure. These patterns, many of which occur in transitions between secondary structural elements, are an interesting combination of previously studied and novel motifs. The identification of sequence patterns that consistently occur in one or a small number of local structures in proteins should contribute to the prediction of protein structure from sequence.

Mapping leaf surface landscapes.

Leaf surfaces provide the ecologically relevant landscapes to those organisms that encounter or colonize the leaf surface. Leaf surface topography directly affects microhabitat availability for colonizing microbes, microhabitat quality and acceptability for insects, and the efficacy of agricultural spray applications. Prior detailed mechanistic studies that examined particular fungi-plant and pollinator-plant interactions have demonstrated the importance of plant surface topography or roughness in determining the outcome of the interactions. Until now, however, it has not been possible to measure accurately the topography--i.e., the three-dimensional structure--of such leaf surfaces or to record precise changes in patterns of leaf surface elevation over time. Using contact mode atomic force microscopy, we measured three-dimensional coordinates of upper leaf surfaces of Vaccinium macrocarpon (cranberry), a perennial plant, on leaves of two age classes. We then produced topographic maps of these leaf surfaces, which revealed striking differences between age classes of leaves: old leaves have much rougher surfaces than those of young leaves. Atomic force microscope measurements were analyzed by lag (1) autocorrelation estimates of leaf surfaces by age class. We suggest that the changes in topography result from removal of epicuticular lipids and that the changes in leaf surface topography influence phylloplane ecology. Visualizing and mapping leaf surfaces permit detailed investigations into leaf surface-mediated phenomena, improving our understanding of phylloplane interactions.

Mapping striate and extrastriate visual areas in human cerebral cortex.

Functional magnetic resonance imaging (fMRI) was used to identify and map the representation of the visual field in seven areas of human cerebral cortex and to identify at least two additional visually responsive regions. The cortical locations of neurons responding to stimulation along the vertical or horizontal visual field meridia were charted on three-dimensional models of the cortex and on unfolded maps of the cortical surface. These maps were used to identify the borders among areas that would be topographically homologous to areas V1, V2, V3, VP, and parts of V3A and V4 of the macaque monkey. Visually responsive areas homologous to the middle temporal/medial superior temporal area complex and unidentified parietal visual areas were also observed. The topography of the visual areas identified thus far is consistent with the organization in macaque monkeys. However, these and other findings suggest that human and simian cortical organization may begin to differ in extrastriate cortex at, or beyond, V3A and V4.

Structural interpretation of the mutations in the beta-cardiac myosin that have been implicated in familial hypertrophic cardiomyopathy.

In 10-30% of hypertrophic cardiomyopathy kindreds, the disease is caused by > 29 missense mutations in the cardiac beta-myosin heavy chain (MYH7) gene. The amino acid sequence similarity between chicken skeletal muscle and human beta-cardiac myosin and the three-dimensional structure of the chicken skeletal muscle myosin head have provided the opportunity to examine the structural consequences of these naturally occurring mutations in human beta-cardiac myosin. This study demonstrates that the mutations are related to distinct structural and functional domains. Twenty-four are clustered around four specific locations in the myosin head that are (i) associated with the actin binding interface, (ii) around the nucleotide binding site, (iii) adjacent to the region that connects the two reactive cysteine residues, and (iv) in close proximity to the interface of the heavy chain with the essential light chain. The remaining five mutations are in the myosin rod. The locations of these mutations provide insight into the way they impair the functioning of this molecular motor and also into the mechanism of energy transduction.

Papel do ecocardiograma transesofágico tridimensional na ótima seleção do dispositivo para o tratamento percutâneo da comunicação interatrial tipo ostium secundum

INTRODUCAO: A comunicação interatrial tipo \"ostium secundum\" é um defeito cardíaco congênito caracterizado pela deficiência parcial ou total da lâmina da fossa oval, também chamada de septo primo. Corresponde a 10 a 12% do total de cardiopatias congênitas, sendo a mais frequente na idade adulta. Atualmente a oclusão percutânea é o método terapêutico de escolha em defeitos com características anatômicas favoráveis para o implante de próteses na maioria dos grandes centros mundiais. A ecocardiografia transesofágica bidimensional com mapeamento de fluxo em cores é considerada a ferramenta padrão-ouro para a avaliação anatômica e monitoração durante do procedimento, sendo crucial para a ótima seleção do dispositivo. Neste sentido, um balão medidor é introduzido e insuflado através do defeito de forma a ocluí-lo temporariamente. A medida da cintura que se visualiza no balão (diâmetro estirado) é utilizada como referência para a escolha do tamanho da prótese. Recentemente a ecocardiografia tridimensional transesofágica em tempo real tem sido utilizada neste tipo de intervenção percutânea. Neste estudo avaliamos o papel da mesma na ótima seleção do dispositivo levando-se em consideração as dimensões e a geometria do defeito e a espessura das bordas do septo interatrial. METODO: Estudo observacional, prospectivo, não randomizado, de único braço, de uma coorte de 33 pacientes adultos portadores de comunicação interatrial submetidos a fechamento percutâneo utilizando dispositivo de nitinol autocentrável (Cera ®, Lifetech Scientific, Shenzhen, China). Foram analisadas as medidas do maior e menor diâmetro do defeito, sua área e as medidas do diâmetro estirado com balão medidor obtidas por meio das duas modalidades ecocardiográficas. Os defeitos foram considerados como elípticos ou circulares segundo a sua geometria; as bordas ao redor da comunicação foram consideradas espessas (>2 mm) ou finas. O dispositivo selecionado foi igual ou ate 2 mm maior que o diâmetro estirado na ecocardiografia transesofágica bidimensional (padrão-ouro). Na tentativa de identificar uma variável que pudesse substituir o diâmetro estirado do balão para a ótima escolha do dispositivo uma série de correlações lineares foram realizadas. RESULTADOS: A idade e peso médio foram de 42,1 ± 14,9 anos e 66,0 ± 9,4kg, respectivamente; sendo 22 de sexo feminino. Não houve diferenças estatísticas entre os diâmetros maior e menor ou no diâmetro estirado dos defeitos determinados por ambas as modalidades ecocardiográficas. A correlação entre as medidas obtidas com ambos os métodos foi ótima (r > 0,90). O maior diâmetro do defeito, obtido à ecoardiografia transesofágica tridimensional, foi a variável com melhor correlação com o tamanho do dispositivo selecionado no grupo como um todo (r= 0,89) e, especialmente, nos subgrupos com geometria elíptica (r= 0,96) e com bordas espessas ao redor do defeito (r= 0,96). CONCLUSÃO: Neste estudo em adultos com comunicações interatriais tipo ostium secundum submetidos à oclusão percutânea com a prótese Cera ®, a ótima seleção do dispositivo pôde ser realizada utilizando-se apenas a maior medida do defeito obtida na ecocardiografia transesofágica tridimensional em tempo real, especialmente nos pacientes com defeitos elípticos e com bordas espessas.

A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings. especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging. (C) 2004 Elsevier Inc. All rights reserved.

UMA NOVA CARTOGRAFIA COGNITIVA PARA O ENSINO DA COMUNICAÇÃO

O trabalho proposto é a montar um projeto exploratório funcional que parta da cartografia cognitiva, que é definida como a arte, teoria e técnica de construir mapas do conhecimento, visando com esta cartografia a sua aplicabilidade na estruturação de um conjunto de cursos/saberes da área da Comunicação. Assemelhado ao conceito de mapas conceituais, ou cognitivos, representam o conhecimento organizado e são compostos por conceitos. Este mapas foram desenvolvido a partir da década de setenta por vários pesquisadores. A tese experimento foi montada tendo como base os softwares de relacionamento por temas e interesses dentro de um ambiente de interatividade tridimensional , montado no conceito de arvore do conhecimento relacional. Esta experiência é construída em ambiente tridimensional com uso de softwares 3D que rodam como aplicativos de engines de vídeo games, que são motores gráficos. A base de dados e a interatividade de textos e tarefas é realizada sob a plataforma do MediaWiki, que é o software aberto que roda a Wikipédia. A plataforma de mapas roda dentro de um software MindJet MindManager e do CMAPS. As vídeo conferências são administradas pelo FlashMeeting, de Web conferência. A maioria deles são softwares abertos. Todos operando em sistemas presenciais ou de modulação EAD. A base conceitual está estruturada dentro de uma visão de educação disruptiva, que lança um novo modelo educacional baseado em mapas, visto dentro de uma abordagem de um mundo de múltiplas telas, um mundo da era hiper, um mundo hipermoderno, que tem como base uma cultura da era tecnológica, numa renovação dos conceitos de Cultura, agora revigorados à luz das novas tecnologias e da nova sociedade interligada em rede.

Investigation of chaotic mixing in laminar fluid systems by the use of computational fluid dynamics

This work presents significant development into chaotic mixing induced through periodic boundaries and twisting flows. Three-dimensional closed and throughput domains are shown to exhibit chaotic motion under both time periodic and time independent boundary motions, A property is developed originating from a signature of chaos, sensitive dependence to initial conditions, which successfully quantifies the degree of disorder withjn the mixing systems presented and enables comparisons of the disorder throughout ranges of operating parameters, This work omits physical experimental results but presents significant computational investigation into chaotic systems using commercial computational fluid dynamics techniques. Physical experiments with chaotic mixing systems are, by their very nature, difficult to extract information beyond the recognition that disorder does, does not of partially occurs. The initial aim of this work is to observe whether it is possible to accurately simulate previously published physical experimental results through using commercial CFD techniques. This is shown to be possible for simple two-dimensional systems with time periodic wall movements. From this, and subsequent macro and microscopic observations of flow regimes, a simple explanation is developed for how boundary operating parameters affect the system disorder. Consider the classic two-dimensional rectangular cavity with time periodic velocity of the upper and lower walls, causing two opposing streamline motions. The degree of disorder within the system is related to the magnitude of displacement of individual particles within these opposing streamlines. The rationale is then employed in this work to develop and investigate more complex three-dimensional mixing systems that exhibit throughputs and time independence and are therefore more realistic and a significant advance towards designing chaotic mixers for process industries. Domains inducing chaotic motion through twisting flows are also briefly considered. This work concludes by offering possible advancements to the property developed to quantify disorder and suggestions of domains and associated boundary conditions that are expected to produce chaotic mixing.

An Exploration of parametric software cost estimating models for Jackson Systems Development

Most parametric software cost estimation models used today evolved in the late 70's and early 80's. At that time, the dominant software development techniques being used were the early 'structured methods'. Since then, several new systems development paradigms and methods have emerged, one being Jackson Systems Development (JSD). As current cost estimating methods do not take account of these developments, their non-universality means they cannot provide adequate estimates of effort and hence cost. In order to address these shortcomings two new estimation methods have been developed for JSD projects. One of these methods JSD-FPA, is a top-down estimating method, based on the existing MKII function point method. The other method, JSD-COCOMO, is a sizing technique which sizes a project, in terms of lines of code, from the process structure diagrams and thus provides an input to the traditional COCOMO method.The JSD-FPA method allows JSD projects in both the real-time and scientific application areas to be costed, as well as the commercial information systems applications to which FPA is usually applied. The method is based upon a three-dimensional view of a system specification as opposed to the largely data-oriented view traditionally used by FPA. The method uses counts of various attributes of a JSD specification to develop a metric which provides an indication of the size of the system to be developed. This size metric is then transformed into an estimate of effort by calculating past project productivity and utilising this figure to predict the effort and hence cost of a future project. The effort estimates produced were validated by comparing them against the effort figures for six actual projects.The JSD-COCOMO method uses counts of the levels in a process structure chart as the input to an empirically derived model which transforms them into an estimate of delivered source code instructions.

Spatially structured cognitve models of semantic information:the implications for computerised databases

Existing theories of semantic cognition propose models of cognitive processing occurring in a conceptual space, where ‘meaning’ is derived from the spatial relationships between concepts’ mapped locations within the space. Information visualisation is a growing area of research within the field of information retrieval, and methods for presenting database contents visually in the form of spatial data management systems (SDMSs) are being developed. This thesis combined these two areas of research to investigate the benefits associated with employing spatial-semantic mapping (documents represented as objects in two- and three-dimensional virtual environments are proximally mapped dependent on the semantic similarity of their content) as a tool for improving retrieval performance and navigational efficiency when browsing for information within such systems. Positive effects associated with the quality of document mapping were observed; improved retrieval performance and browsing behaviour were witnessed when mapping was optimal. It was also shown using a third dimension for virtual environment (VE) presentation provides sufficient additional information regarding the semantic structure of the environment that performance is increased in comparison to using two-dimensions for mapping. A model that describes the relationship between retrieval performance and browsing behaviour was proposed on the basis of findings. Individual differences were not found to have any observable influence on retrieval performance or browsing behaviour when mapping quality was good. The findings from this work have implications for both cognitive modelling of semantic information, and for designing and testing information visualisation systems. These implications are discussed in the conclusions of this work.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006