Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented with a numerical study.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Estrutura a partir do Movimento em Sistemas Autónomos

Mestrado em Engenharia Electrotécnica e de Computadores - Ramo de Sistemas Autónomos

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.

Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Hausdorff dimension versus smoothness

There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.

Low genetic diversity in Wolbachia-Infected Culex quinquefasciatus (Diptera: Culicidae) from Brazil and Argentina

Culex quinquefasciatus is a vector of human pathogens, including filarial nematodes and several viruses. Although its epidemiological relevance is known to vary across geographical regions, an understanding of its population genetic structure is still incipient. In light of this, we evaluated the genetic diversity of Cx. quinquefasciatus and Cx. pipiens x Cx. quinquefasciatus hybrids collected from nine localities in Brazil and one site in Argentina. We used mitochondrial genes cox1 and nd4, along with the coxA and wsp genes of the maternally-inherited Wolbachia endosymbiont. The nd4 fragment was invariant between samples, whilst cox1 exhibited four haplotypes that separated two types of Cx. quinquefasciatus, one clustered in southern Brazil. Low sequence diversity was generally observed, being discussed. Both Brazilian and Argentinian mosquitoes were infected with a single Wolbachia strain. As reported in previous studies with these populations, cox1 and nd4 diversity is not congruent with the population structure revealed by nuclear markers or alar morphology. Future Cx. quinquefasciatus research should, if possible, evaluate mtDNA diversity in light of other markers.

Credit cycle identification: A Markov-switching application

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

The brushstroke and materials of Amadeo de Souza-Cardoso combined in an authentication tool

Nowadays, authentication studies for paintings require a multidisciplinary approach, based on the contribution of visual features analysis but also on characterizations of materials and techniques. Moreover, it is important that the assessment of the authorship of a painting is supported by technical studies of a selected number of original artworks that cover the entire career of an artist. This dissertation is concerned about the work of modernist painter Amadeo de Souza-Cardoso. It is divided in three parts. In the first part, we propose a tool based on image processing that combines information obtained by brushstroke and materials analysis. The resulting tool provides qualitative and quantitative evaluation of the authorship of the paintings; the quantitative element is particularly relevant, as it could be crucial in solving authorship controversies, such as judicial disputes. The brushstroke analysis was performed by combining two algorithms for feature detection, namely Gabor filter and Scale Invariant Feature Transform. Thanks to this combination (and to the use of the Bag-of-Features model), the proposed method shows an accuracy higher than 90% in distinguishing between images of Amadeo’s paintings and images of artworks by other contemporary artists. For the molecular analysis, we implemented a semi-automatic system that uses hyperspectral imaging and elemental analysis. The system provides as output an image that depicts the mapping of the pigments present, together with the areas made using materials not coherent with Amadeo’s palette, if any. This visual output is a simple and effective way of assessing the results of the system. The tool proposed based on the combination of brushstroke and molecular information was tested in twelve paintings obtaining promising results. The second part of the thesis presents a systematic study of four selected paintings made by Amadeo in 1917. Although untitled, three of these paintings are commonly known as BRUT, Entrada and Coty; they are considered as his most successful and genuine works. The materials and techniques of these artworks have never been studied before. The paintings were studied with a multi-analytical approach using micro-Energy Dispersive X-ray Fluorescence spectroscopy, micro-Infrared and Raman Spectroscopy, micro-Spectrofluorimetry and Scanning Electron Microscopy. The characterization of Amadeo’s materials and techniques used on his last paintings, as well as the investigation of some of the conservation problems that affect these paintings, is essential to enrich the knowledge on this artist. Moreover, the study of the materials in the four paintings reveals commonalities between the paintings BRUT and Entrada. This observation is supported also by the analysis of the elements present in a photograph of a collage (conserved at the Art Library of the Calouste Gulbenkian Foundation), the only remaining evidence of a supposed maquete of these paintings. The final part of the thesis describes the application of the image processing tools developed in the first part of the thesis on a set of case studies; this experience demonstrates the potential of the tool to support painting analysis and authentication studies. The brushstroke analysis was used as additional analysis on the evaluation process of four paintings attributed to Amadeo, and the system based on hyperspectral analysis was applied on the painting dated 1917. The case studies therefore serve as a bridge between the first two parts of the dissertation.

Online consumer behavior: The tablet shopper – A new kind of customer?

Tablet computers are on the rise and are increasingly superseding stationary computers in terms of modern online shopping. This paper therefore aims on understanding how tablet and website characteristics might impact online consumer behavior. The collected data resulted from focus groups and in-depth interviews conducted with a technology affine audience. It has shown that tablets indeed may have shifted shopping behavior from utilitarian towards rather recreational attributes. Discussions also revealed high customer expectations towards visited shopping websites and prevailing deficits. Thus, harnessing the concept of experiential flow is crucial. Compelling experiences are required to increase the duration of stay and consequently the likelihood of increased purchases.

Inventário de Medos III : Avaliação das qualidades psicométricas em uma amostra portuguesa

Este estudo teve como objetivo avaliar as qualidades psicométricas do Fear Survey Schedule-III, em uma amostra portuguesa. Participaram 1.980 sujeitos selecionados por conveniência a partir de uma população adulta normativa. As idades dos participantes estavam compreendidas entre os 18 e os 80 anos (M = 39,5, DP = 8,5), sendo 59% do sexo feminino. As qualidades psicométricas da escala foram avaliadas em suas facetas de sensibilidade psicométrica, validade de construto e confi abilidade. A validade externa de construto foi avaliada com análise multigrupos em amostra aleatória e independente da amostra de validação inicial. O modelo fatorial original proposto apresentou um ajustamento inaceitável à amostra de validação. Procedeu-se ao refi namento do modelo de medida em uma parte da amostra, selecionada aleatoriamente. Em conclusão, o modelo de medida simplifi cado apresentou uma boa qualidade de ajustamento fatorial e foi invariante em uma segunda amostra independente da primeira. Propôs-se uma nova estrutura hierárquica, com fator de 2ª ordem designado por “Medos”, que revelou boas qualidades psicométricas (sensibilidade, validade de construto e confi abilidade).