Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

In permanent transit: discourses and maps of the intercultural experience

Instituto Politécnico do Porto. Instituto Superior de Contabilidade e Administração do Porto

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

China e Japão - uma análise intercultural contemporânea

Ao longo dos séculos, a China e o Japão foram criando histórias, representações, discursos e identidades que certas vezes se cruzaram e outras vezes se afastaram. Este trabalho é uma reflexão sobre cultura e interculturalidade, porque está relacionado com a produção e a circulação de significados (Hall, 1997:2), numa análise da identidade e da representação da China e do Japão e também das representações que estes dois países têm um do outro. Esta análise integra factos que vão desde a 1ª Guerra Mundial até à actualidade, tornando este estudo contemporâneo. Ao longo do meu trabalho, quando falo em representação, refiro-me à forma como o mundo é socialmente construído e representado por nós e para nós (Chris Barker 2000:8).

Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.

Arrow plot and CA maps on microarray preprocessing methods

Microarray allow to monitoring simultaneously thousands of genes, where the abundance of the transcripts under a same experimental condition at the same time can be quantified. Among various available array technologies, double channel cDNA microarray experiments have arisen in numerous technical protocols associated to genomic studies, which is the focus of this work. Microarray experiments involve many steps and each one can affect the quality of raw data. Background correction and normalization are preprocessing techniques to clean and correct the raw data when undesirable fluctuations arise from technical factors. Several recent studies showed that there is no preprocessing strategy that outperforms others in all circumstances and thus it seems difficult to provide general recommendations. In this work, it is proposed to use exploratory techniques to visualize the effects of preprocessing methods on statistical analysis of cancer two-channel microarray data sets, where the cancer types (classes) are known. For selecting differential expressed genes the arrow plot was used and the graph of profiles resultant from the correspondence analysis for visualizing the results. It was used 6 background methods and 6 normalization methods, performing 36 pre-processing methods and it was analyzed in a published cDNA microarray database (Liver) available at http://genome-www5.stanford.edu/ which microarrays were already classified by cancer type. All statistical analyses were performed using the R statistical software.

Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

The Cornerstones of Modern Government Maps, Weights and Measures and Census in Liberal Portugal (19th century)

Thesis submitted for assessment with a view to obtaining the degree of Doctor in History and Civilisation from the European University Institute

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Visualization of clusters in geo-referenced data using three-dimensional self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

CARTO-SOM - Cartogram creation using self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Exploratory geospatial data analysis using self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Enhanced PCA-based localization using depth maps with missing data

In this paper a new method for self-localization of mobile robots, based on a PCA positioning sensor to operate in unstructured environments, is proposed and experimentally validated. The proposed PCA extension is able to perform the eigenvectors computation from a set of signals corrupted by missing data. The sensor package considered in this work contains a 2D depth sensor pointed upwards to the ceiling, providing depth images with missing data. The positioning sensor obtained is then integrated in a Linear Parameter Varying mobile robot model to obtain a self-localization system, based on linear Kalman filters, with globally stable position error estimates. A study consisting in adding synthetic random corrupted data to the captured depth images revealed that this extended PCA technique is able to reconstruct the signals, with improved accuracy. The self-localization system obtained is assessed in unstructured environments and the methodologies are validated even in the case of varying illumination conditions.

A Exploração Aeroespacial no Âmbito da Segurança e da Defesa. O Caso da China

Dissertação de Mestrado em Ciência Política e Relações Internacionais Área de Especialização: Relações Internacionais

A multivariate analysis of the relationship between work ability and S. japonicum infection in Dongting Lake Region, in China

A cross-sectional case-control study on the association between the reduced work ability and S. japonicum infection was carried out in a moderate endemic area for schistosomiasis japonica in the southern part of Dongting lake in China. A total of 120 cases with reduced work ability and 240 controls paired to the case by age, sex, occupation and without reduced work ability, participated in the study. The mean age for individuals was 37.6 years old (21-60), the ratio of male: female was 60:40, the prevalence of S. japonicum in the individuals was 28.3%. The results obtained in this study showed that the infection of S. japonicum in case and control groups was 49.2% (59/120) and 17.9% (43/240), respectively. Odds ratio for reduced work ability among those who had schistosomiasis was 4.34 (95%), confidence interval was 2.58-7.34, and among those who had S. japonicum infection (egg per gram > 100) was up to 12.67 (95%), confidence interval was 3.64-46.39. After odds ratio was adjusted by multiple logistic regression, it was confirmed that heavier intensity of S. japonicum infection and splenomegaly due to S. japonicum infection were the main risk factors for reduced work ability in the population studied.