On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

Conformal deformation of equilibrium measures in normal random ensembles

We investigate the eigenvalue statistics of ensembles of normal random matrices when their order N tends to infinite. In the model, the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We study the conformal deformations of equilibrium measures of normal random ensembles to the real line and give sufficient conditions for it to weakly converge to a Wigner measure.

The degree of polydispersity in micellar dispersions: A sum rule approach

Statistical properties of a two-dimensional ideal dispersion of polydisperse micelles are derived by analyzing the convergence properties of a sum rule set by mass conservation. Internal micellar degrees of freedom are accounted for by a microscopic model describing small displacements of the constituting amphiphiles with respect to their equilibrium positions. The transfer matrix (TM) method is employed to compute internal micelle partition function. We show that the conditions under which the sum rule is saturated by the largest eigenvalue of the TM determine the value of amphiphile concentration above which the dispersion becomes highly polydisperse and micelle sizes approach a Schultz distribution. (C) 2011 Elsevier B.V. All rights reserved.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

HQET at order 1/m: II. Spectroscopy in the quenched approximation

Using Heavy Quark Effective Theory with non-perturbatively determined parameters in a quenched lattice calculation, we evaluate the splittings between the ground state and the first two radially excited states of the B(s) system at static order. We also determine the splitting between first excited and ground state, and between the B(s)* and B(s) ground states to order 1/m(b). The Generalized Eigenvalue Problem and the use of all-to-all propagators are important ingredients of our approach.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

We're Chained: an analysis of systemic risk in finance

This dissertation presents two papers on how to deal with simple systemic risk measures to assess portfolio risk characteristics. The first paper deals with the Granger-causation of systemic risk indicators based in correlation matrices in stock returns. Special focus is devoted to the Eigenvalue Entropy as some previous literature indicated strong re- sults, but not considering different macroeconomic scenarios; the Index Cohesion Force and the Absorption Ratio are also considered. Considering the S&P500, there is not ev- idence of Granger-causation from Eigenvalue Entropies and the Index Cohesion Force. The Absorption Ratio Granger-caused both the S&P500 and the VIX index, being the only simple measure that passed this test. The second paper develops this measure to capture the regimes underlying the American stock market. New indicators are built using filtering and random matrix theory. The returns of the S&P500 is modelled as a mixture of normal distributions. The activation of each normal distribution is governed by a Markov chain with the transition probabilities being a function of the indicators. The model shows that using a Herfindahl-Hirschman Index of the normalized eigenval- ues exhibits best fit to the returns from 1998-2013.

Avaliação de características de desempenho e de carcaça de codornas de corte por meio da análise de componentes principais

Foram utilizados dados de 288 codornas de corte (Coturnix coturnix coturnix) para avaliar a possibilidade de resumir a informação contida no complexo de variáveis originais, eliminando-se variáveis inexpressivas por meio da técnica de componentes principais. Foram registrados o peso vivo (PVIVO) e pesos do peito (PPEITO), das coxas (PCOXA), da gordura abdominal (GA), das vísceras comestíveis (fígado, moela e coração) (FIG, MOELA e CORA) e da carcaça eviscerada (PCEVIS). As carcaças foram secas e trituradas para a avaliação do teor matéria seca (MS), gordura (GORD) e proteína bruta (PB). Dos 11 componentes principais, sete (63,6%) apresentaram variância menor que 0,7 (autovalor inferior a 0,7), sendo sugeridas para descarte, respectivamente, em ordem de menor importância, para explicar a variação total das seguintes variáveis: PCEVIS, PPEITO, PCOXA, CORA, FIG MOELA e GORD. Com base nos resultados, recomenda-se manter as seguintes variáveis em experimentos futuros: PVIVO, MS, PB e GA.

Contribuições para a análise de sinais neuronais e biomédicos

Following the new tendency of interdisciplinarity of modern science, a new field called neuroengineering has come to light in the last decades. After 2000, scientific journals and conferences all around the world have been created on this theme. The present work comprises three different subareas related to neuroengineering and electrical engineering: neural stimulation; theoretical and computational neuroscience; and neuronal signal processing; as well as biomedical engineering. The research can be divided in three parts: (i) A new method of neuronal photostimulation was developed based on the use of caged compounds. Using the inhibitory neurotransmitter GABA caged by a ruthenium complex it was possible to block neuronal population activity using a laser pulse. The obtained results were evaluated by Wavelet analysis and tested by non-parametric statistics. (ii) A mathematical method was created to identify neuronal assemblies. Neuronal assemblies were proposed as the basis of learning by Donald Hebb remain the most accepted theory for neuronal representation of external stimuli. Using the Marcenko-Pastur law of eigenvalue distribution it was possible to detect neuronal assemblies and to compute their activity with high temporal resolution. The application of the method in real electrophysiological data revealed that neurons from the neocortex and hippocampus can be part of the same assembly, and that neurons can participate in multiple assemblies. (iii) A new method of automatic classification of heart beats was developed, which does not rely on a data base for training and is not specialized in specific pathologies. The method is based on Wavelet decomposition and normality measures of random variables. Throughout, the results presented in the three fields of knowledge represent qualification in neural and biomedical engineering

Escala de atitudes frente ao HIV/AIDS: análise de fatores

OBJETIVO: Este trabalho apresenta resultados acerca das propriedades psicométricas da Escala de atitudes frente ao HIV/AIDS. Os dados, provenientes de uma amostra de 549 alunos entre universitários, ensinos médio e ensino fundamental. MÉTODOS: Os dados foram tratados pelo método dos componentes principais da análise fatorial. A análise final, postulado um eigenvalue mínimo de 2, resultou cinco fatores. Foram eliminados itens que apresentaram carga fatorial menor que 0,30. Neste estudo, o menor alfa observado foi de 0,79. Portanto, é provável que todos os 47 itens do instrumento final elaborado meçam o mesmo construto: atitude frente ao HIV/AIDS. RESULTADOS: Escores inferiores a 96 foram considerados fraco grau de conhecimento sobre HIV/AIDS; entre 96 e 192 moderado grau de conhecimento e acima de 192 alto grau de conhecimento sobre HIV/AIDS. Foram estabelecidos os fatores: 1, 2 e 3, sendo fator geral de percepção da informação técnico-científica; fator de percepção da informação técnico-científica versus sexualidade e preconceito; fator de percepção da informação técnico-científica no uso de drogas, respectivamente. CONCLUSÕES: O alfa de Cronbach encontrado para a escala como um todo foi de 0,859, sugerindo fortemente a existência da fidedignidade do instrumento que se mostrou útil para avaliar o grau de conhecimento acerca do HIV/AIDS e o risco decorrente do desconhecimento, entre estudantes.

Estudo das propriedades psicométricas do inventário de estilos parentais de young no Brasil

Parenting styles concern overall interaction characteristics between parents and children. To assess them, it is important to build and adapt valid and reliable instruments. The main objectives of this dissertation were to translate, adapt and evaluate the psychometric properties of the Young Parenting Inventory (YPI) for the Brazilian context, as seek associations between the YPI and Familiogram Test (FG). In current study, YPI was adapted to Portuguese by backtranslation method. Content analyses were made by five judges. 920 high school and college students (543 females), whose ages were between 14 and 69 years (M = 21.3, SD = 6.1), filled out the research instruments. Data were collected in Natal, Petrolina and Brasilia cities and Porto Alegre metropolitan region. The results confirmed the existence of five factors. Final version of the YPI was composed by 49 items. Exploratory factorial analysis (principal components) were conducted using oblimin rotation. Five factors extracted explained 45.12% of the maternal scale variance and 47.59% of paternal scale. Each factor explained, at least, 3% of the variance and showed Eigenvalue over than 1.5. All items have factorial loadings values above 0.3. The confirmatory factorial analysis has showed fit statistics reasonably adequate: for maternal scale,  ² [1114] = 4636.38, p < 0.001,  ² / df = 4.16, with GFI = 0.83, AGFI = 0.81 and RMSEA = 0.06; for paternal scale,  ² [1114] = 5133.69 p < 0.001,  ² / df = 4.61, with GFI = 0.81, AGFI = 0.79 and RMSEA = 0,06. Thus, final instrument was composed by the following factors: (I) Disconnection and Rejection ( = 0.89 and 0.90), (II) Affectivity and Emotional Stability ( = 0.85 and 0.88); (III) Overvigilance and Other Directedness ( = 0.83 and 0.85), (IV) Overprotection and Impaired Autonomy ( = 0.78 and 0.79) and (V) Impaired Limits ( = 0.66 and 0.71). Finally, relations between the YPI and FG were assessed. Pearson's correlations between the YPI and FG showed moderated associations, particularly between the factors Affectivity (YPI) and Affection (FG) (r = 0.69 and 0.7 for maternal and paternal scale, respectively); and the factors Disconnection and Rejection (YPI) and Conflict (FG) (r = 0.59 and 0.58). The regression models indicated that over than 40% of variance of factors of FG can be predicted by factors of YPI. Beta coefficients for Affection-Affectivity relation were 0.67 (maternal scale) and 0.53 (paternal scale); for Disconnection-Conflict relation were 0.31 (maternal scale) and 0.44 (paternal scale). We conclude the YPI has adequate psychometric parameters and can be used in future research in this area. However, adjustments in the structure of the YPI were made. Moreover, it is suggested further studies to consider other samples and variables, increasing the knowing of parenting styles and the Young‟s theory in the Brazilian context

Modal transformation applied to double three-phase transmission lines

Double three-phase transmission lines are analyzed in this paper using a modal transformation model. The main attribute of this model is the use of a single real transformation matrix based on line geometrical characteristics and the Clarke matrix. Because of this, for any line point, the electrical values can be accessed for phase domain or mode domain using the considered transformation matrix and without convolution methods. For non-transposed symmetrical lines the errors between the model results and the exact modes are insignificant values. The eigenvector and eigenvalue analyses for transposed lines search the similarities among the three analyzed transposition types and the possible simplifications for a non-transposed case.

Modal transformation analyses for double three-phase transmission lines

Eigenvector and eigenvalue analyses are carried out for double three-phase transmission lines, studying the application of a constant and real phase-mode transformation matrix and the errors of this application to mode line models. Employing some line transposition types, exact results are obtained with a single real transformation matrix based on Clarke's matrix and line geometrical characteristics. It is shown that the proposed technique leads to insignificant errors when a nontransposed case is considered. For both cases, transposed and nontransposed, the access to the electrical values (voltage and current, for example) is provided through a simple matrix multiplication without convolution methods. Using this facility, an interesting model for transmission line analysis is obtained even though the nontransposed case errors are not eliminated. The main advantages of the model are related to the transformation matrix: single, real, frequency independent, and identical for voltage and current.

Estudo das limitações impostas ao amortecimento de oscilações eletromecânicas pelos zeros da FTMA de controladores suplementares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)