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.

Magma flow, exsolution processes and rock metasomatism in the Great Messejana-Plasencia dyke (Iberian Peninsula)

Magma flow in dykes is still not well understood; some reported magnetic fabrics are contradictory and the potential effects of exsolution and metasomatism processes on the magnetic properties are issues open to debate. Therefore, a long dyke made of segments with different thickness, which record distinct degrees of metasomatism, the Messejana-Plasencia dyke (MPD), was studied. Oriented dolerite samples were collected along several cross-sections and characterized by means of microscopy and magnetic analyses. The results obtained show that the effects of metasomatism on rock mineralogy are important, and that the metasomatic processes can greatly influence anisotropy degree and mean susceptibility only when rocks are strongly affected by metasomatism. Petrography, scanning electron microscopy (SEM) and bulk magnetic analyses show a high-temperature oxidation-exsolution event, experienced by the very early Ti-spinels, during the early stages of magma cooling, which was mostly observed in central domains of the thick dyke segments. Exsolution reduced the grain size of the magnetic carrier (multidomain to single domain transformation), thus producing composite fabrics involving inverse fabrics. These are likely responsible for a significant number of the 'abnormal' fabrics, which make the interpretation of magma flow much more complex. By choosing to use only the 'normal' fabric for magma flow determination, we have reduced by 50 per cent the number of relevant sites. In these sites, the imbrication angle of the magnetic foliation relative to dyke wall strongly suggests flow with end-members indicating vertical-dominated flow (seven sites) and horizontal-dominated flow (three sites).

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.

Seismic imaging of the western Iberian crust using ambient noise: Boundaries and internal structure of the Iberian Massif

We present new Rayleigh-wave dispersion maps of the western Iberian Peninsula for periods between 8 and 30 s, obtained from correlations of seismic ambient noise, following the recent increase in seismic broadband network density in Portugal and Spain. Group velocities have been computed for each station pair using the empirical Green's functions generated by cross-correlating one-day-length seismic ambient-noise records. The resulting high-path density allows us to obtain lateral variations of the group velocities as a function of period in cells of 0.5 degrees x 0.5 degrees with an unprecedented resolution. As a result we were able to address some of the unknowns regarding the lithospheric structure beneath SW Iberia. The dispersion maps allow the imaging of the major structural units, namely the Iberian Massif, and the Lusitanian and Algarve Meso-Cenozoic basins. The Cadiz Gulf/Gibraltar Strait area corresponds to a strong low-velocity anomaly, which can be followed to the largest period inverted, although slightly shifted to the east at longer periods. Within the Iberian Massif, second-order perturbations in the group velocities are consistent with the transitions between tectonic units composing the massif. (C) 2013 Elsevier B.V. All rights reserved.

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.

Modelação de um sistema de alarme sísmico para a Peninsula Ibérica

Modelou-se um Sistema de Alarme Sísmico para a Península Ibérica que, em função da situação sísmica dada, permite determinar o Grau de Alarme Sísmico, para uma região, durante um determinado horizonte temporal.Utilizaram-se dois precursores sísmicos: • as condições iniciais do modelo de simulação utilizado para gerar o processo de ocorrências sísmicas na Península Ibérica, que corresponde ao passado sísmico recente; • a Sismicidade Local, ou seja o número de ocorrências sísmicas de qualquermagnitude, registadas na região em estudo, durante um período de tempo. Com base na Teoria dos Conjuntos Vagos, determinou-se o grau de alarme relativo a cada um dos precursores utilizados. A média pesada dos valores de grau de alarme origina o Grau deAlarme Sísmico. Os ‘pesos’ envolvidos nessa média foram obtidos com recurso à metodologia AHP, tomando como critérios, as percentagens de sismos previstos (ou de falhas), falsos alarmes e tempo de alarme.O Sistema desenvolvido foi calibrado com base em 12 situações sísmicas reais ocorridas naPenínsula Ibérica.

Moisture recycling in the Iberian Peninsula from a regional climate simulation: spatiotemporal analysis and impact on the precipitation regime

The contribution of the evapotranspiration from a certain region to the precipitation over the same area is referred to as water recycling. In this paper, we explore the spatiotemporal links between the recycling mechanism and the Iberian rainfall regime. We use a 9 km resolution Weather Research and Forecasting simulation of 18 years (1990-2007) to compute local and regional recycling ratios over Iberia, at the monthly scale, through both an analytical and a numerical recycling model. In contrast to coastal areas, the interior of Iberia experiences a relative maximum of precipitation in spring, suggesting a prominent role of land-atmosphere interactions on the inland precipitation regime during this period of the year. Local recycling ratios are the highest in spring and early summer, coinciding with those areas where this spring peak of rainfall represents the absolute maximum in the annual cycle. This confirms that recycling processes are crucial to explain the Iberian spring precipitation, particularly over the eastern and northeastern sectors. Average monthly recycling values range from 0.04 in December to 0.14 in June according to the numerical model and from 0.03 in December to 0.07 in May according to the analytical procedure. Our analysis shows that the highest values of recycling are limited by the coexistence of two necessary mechanisms: (1) the availability of sufficient soil moisture and (2) the occurrence of appropriate synoptic configurations favoring the development of convective regimes. The analyzed surplus of rainfall in spring has a critical impact on agriculture over large semiarid regions of the interior of Iberia.

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