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.

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.

Neonatal anthropometry: a tool to evaluate the nutritional status and predict early and late risks

Neonatal anthropometry is an inexpensive, noninvasive and convenient tool for bedside evaluation, especially in sick and fragile neonates. Anthropometry can be used in neonates as a tool for several purposes: diagnosis of foetal malnutrition and prediction of early postnatal complications; postnatal assessment of growth, body composition and nutritional status; prediction of long-term complications including metabolic syndrome; assessment of dysmorphology; and estimation of body surface. However, in this age group anthropometry has been notorious for its inaccuracy and the main concern is to make validated indices available. Direct measurements, such as body weight, length and body circumferences are the most commonly used measurements for nutritional assessment in clinical practice and in field studies. Body weight is the most reliable anthropometric measurement and therefore is often used alone in the assessment of the nutritional status, despite not reflecting body composition. Derived indices from direct measurements have been proposed to improve the accuracy of anthropometry. Equations based on body weight and length, mid-arm circumference/head circumference ratio, and upper-arm cross-sectional areas are among the most used derived indices to assess nutritional status and body proportionality, even though these indices require further validation for the estimation of body composition in neonates.

Early literacy development in Catalan: characteristics and instructional influence

Resumo: Este artigo analisa a relação entre o nível de consciência fonológica, conhecimento das letra e as estratégias utilizadas para ler e escrever, em crianças de cinco anos, ensinadas em catalão. Participaram 69 crianças de três classes diferentes. Cada um dos seus professores utilizava um método diferente de ensino: analítico, sintético ou analítico-sintético. As crianças foram avaliadas no início e no final do ano letivo em: Reconhecimento de letras, segmentação palavra oral, leitura de palavras, leitura de um texto curto e um ditado. Foram realizadas análises de granulação fina em nas respostas das crianças, para identificar estratégias e padrões específicos. A análise qualitativa indica que a capacidade de segmentar uma palavra em sílabas por via oral parece ser suficiente para as crianças começarem a ler de uma forma convencional. Além disso, a consciência fonológica e o conhecimento das letras são usados em formas relativamente diferentes, dependendo do tipo de texto a ser lido. As abordagens de ensino dos professores parecem ter uma influência nos resultados das crianças.

A construção de uma parentalidade confiante: influência do Modelo Touchpoints na relação educadorfamília

Dissertação apresentada na Escola Superior de Educação de Lisboa, para obtenção do grau de Mestre em Ciências da Educação - Especialidade Intervenção Precoce

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.

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.

Estudo prévio para a realização de manual de iniciação ao cravo: relatório de estágio:

Mestrado em Ensino da Música.

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.