Cálculos de integrais de Feynman em teorias de campos

Pós-graduação em Física - IFT

Genes de efeito principal e locos de características quantitativas (QTL) em suínos

Pós-graduação em Zootecnia - FMVZ

Aplicações das Cadeias de Markov para o Ensino Médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Caracterización multivariada de los temporales para su aplicación en el dimensionamiento del manto principal

En esta tesis se presenta una metodología para la caracterización del oleaje, dentro del marco de las nuevas Recomendaciones para Obras Marítimas (ROM 0.0.-00 y ROM 1.0-09), por ser una de las principales acciones que afectan a la estabilidad de las estructuras marítimas. Debido al carácter aleatorio intrínsecamente multivariado de la acción considerada, las tormentas, su caracterización paramétrica se realiza en términos de funciones cópula uniparamétricas. Las variables consideradas son altura de ola significante del pico de la tormenta, el periodo medio asociado y la magnitud, o número de olas, de todo el ciclo de solicitación. Para establecer un patrón teórico de evolución de la tormenta que permita extrapolar las muestras fuera de la región con datos se analizan los modelos teóricos existentes, comprobándose que no reproducen adecuadamente las tormentas constituidas por estados de mar con un peso importante de oleaje swell. Para evitar esta limitación se proponen cuatro modelos teóricos de evolución de tormentas con distintas formas geométricas. El análisis de los modelos existentes y los propuestos pone de relieve que el Modelo Magnitud Equivalente de Tormenta (EMS= Equivalent Magnitude Storm) con la forma triangular es el que mejor adapta las tormentas constituidas por estados de mar típicos del viento. Para tormentas con un mayor grado de desarrollo, el modelo teórico de tormenta EMS con la forma trapezoidal es el adecuado. De las aproximaciones propuestas para establecer el periodo medio de los sucesivos estados de mar del ciclo de solicitación. la propuesta por Martín Soldevilla et al., (2009) es la más versátil y , en general , mejor reproduce la evolución de todo tipo de tormentas. La caracterización de las tormentas se complementa con la altura de ola máxima. Debido a la mayor disponibilidad y longitud temporal de los datos sintéticos frente a las registros, la práctica totalidad de los análisis de extremos se realizan con tormentas sintéticas en las que la distribución de olas individuales es desconocida. Para evitar esta limitación se utilizan modelos teóricos de distribución de olas acordes a las características de cada uno de los estados de mar que conforman la tormenta sintética. Para establecer dichas características se utiliza la curtosis y en función de su valor la altura de ola máxima se determina asumiendo una determinada distribución de olas. Para estados de mar lineales la distribución de olas individuales de Rayleigh es la considerada. Para condiciones no lineales de gran ancho de banda el modelo de distribución de olas propuesto por Dawson, (2004) es el utilizado y si es de banda estrecha las predicciones de (Boccotti, (1989), Boccotti et al., (2013)) se compara con las resultantes del modelo de Dawson. La caracterización de la evolución de las tormentas en términos multivariados es aplicada al estudio de la progresión del daño del manto principal de diques en talud, y al rebase de las olas. Ambos aspectos cubren el segundo objetivo de la tesis en el que se propone una nueva formulación para el dimensionamiento de mantos constituidos por bloques cúbicos de hormigón. Para el desarrollo de esta nueva formulación se han utilizado los resultados recogidos en los estudios de estabilidad del manto principal de diques talud realizados en modelo físico a escala reducida en el Centro de Estudios de Puertos y Costas (CEDEX) desde la década de los 80 empleando, en su mayoría, bloques paralelepípedos cúbicos de hormigón. Por este motivo y porque los últimos diques construidos en la costa Española utilizan este tipo de pieza, es por lo que la formulación planteada se centra en este tipo de pieza. Después de un primer análisis de las fórmulas de cálculo y de evolución existentes, se llega a la conclusión de que es necesario realizar un esfuerzo de investigación en este campo, así como ensayos en laboratorio y recogida de datos in-situ con base a desarrollar fórmulas de evolución de daño para mantos constituidos por piezas diferentes a la escollera, que tenga en cuenta las principales variables que condiciona su estabilidad. En esta parte de la tesis se propone un método de análisis de evolución de daño, que incluye el criterio de inicio de avería, adecuada para diques en talud constituidos por bloque cúbicos de hormigón y que considera la incidencia oblicua, el daño acumulado y el rebase. This thesis proposes a methodology to estimate sea waves, one of the main actions affecting the maritime structures stability, complying with (ROM 0.0.-00 & ROM 1.0-09.Due to the multivariate behavior of sea storms, the characterization of the structures of sea storms is done using copula function. The analyzed variables are the significant height wave, mean period and magnitude or number of waves during the storm history. The storm evolution in terms of the significant height wave and the mean period is also studied in other to analyze the progressive failure modes. The existing models of evolution are studied, verifying that these approximations do not adjust accurately for developed waves. To overcome this disadvantage, four evolution models are proposed, with some geometrical shapes associated to fit any development degree. The proposed Equivalent Magnitude Storm model, EMS, generally obtains the best results for any kind of storm (predominant sea, swell or both). The triangle is recommended for typical sea storms whereas the trapezoid shape is much more appropriate for more developed storm conditions.The Martín Soldevilla et al., (2009) approach to estimate the mean period is better than others approaches used.The storm characterization is completed with the maximum wave height of the whole storm history. Due to synthetic historical waves databases are more accessible and longer than recorded database, the extreme analyses are done with synthetic data. For this reason the individual waves’ distribution is not known. For that limitation to be avoided, and depending on the characteristics of every sea states, one theoretical model of waves is choose and used. The kurtosis parameter is used to distinguish between linear and nonlinear sea states. The Rayleigh model is used for the linear sea states. For the nonlinear sea states, Dawson, (2004) approach is used for non-narrow bandwidth storms, comparing the results with the Boccotti, (1989), Boccotti et al., (2013) approach, with is used for narrow bandwidth storms. The multivariate and storm evolution characterization is used to analyze of stone armour damage progression and wave overtopping discharge. Both aspects are included in the second part of the thesis, with a new formula is proposed to design cubes armour layer. The results the stability studies of armour layer, done in the Centre for Harbours and Coastal Studies (CEDEX) laboratory are used for defining a new stability formula. For this reason and because the last biggest breakwater built in Spain using the cube, the damage progression is analyze for this kind of concrete block. Before to analyze the existing formulae, it is concluded that it is necessary more investigation, more tests in laboratory and data gathering in situ to define damage evolution formulae to armour of other kind of pieces and that takes to account the principal variables. This thesis proposed a method to calculate the damage progression including oblique waves, accumulated damage, and overtopping effect. The method also takes account the beginning of the movement of the blocks.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Statistical Numerical Methods for Eigenvalue Problem. Parallel Implementation

MSC subject classification: 65C05, 65U05.

Análise do crescimento econômico no Rio Grande do Sul através da aplicação de cadeias de Markov

O estudo do crescimento econômico é de suma importância para que possamos averiguar a trajetória de uma economia ao longo do tempo, a proposta desse trabalho é analisar o crescimento econômico no estado do Rio Grande do Sul, através do instrumental das cadeias de Markov, a ideia principal do estudo está na hipótese de convergência de renda. Primeiramente será testado a hipótese de convergência de renda do estado por meio das microrregiões, para isso serão utilizados dados de produto per capita dos anos de 1990, 2000 e 2010. Também será testado a hipótese de convergência para os municípios do Conselho Regional de Desenvolvimento Sul, situado no Rio Grande do Sul, utilizando dados de renda per capita dos anos de 1991, 2000 e 2010. Os resultados obtidos para as microrregiões do Rio Grande do Sul mostram que as economias não estão convergindo em sua totalidade para uma classe de renda especifica, porém é percebido que no longo prazo haverá uma maior concentração das microrregiões nos extratos de renda próximos a média, o tempo esperado para que as economias cheguem ao seu estado estacionário é de seis períodos. Por meio dos resultados obtidos para a região do Corede Sul, temos que as economias convergirão em sua maioria para a classe de renda médio pobre, seguido pela classe dos médios ricos. Ambas as classes estão situadas próximas a média regional, sendo que as classes de renda pobre e rico situadas aos extremos serão extintas no longo prazo. O tempo esperado para que as economias cheguem ao estado estacionário é de onze períodos.

Análise do crescimento econômico no Rio Grande do Sul através da aplicação de cadeias de markov

O estudo do crescimento econômico é de suma importância para que possamos averiguar a trajetória de uma economia ao longo do tempo, a proposta desse trabalho é analisar o crescimento econômico no estado do Rio Grande do Sul, através do instrumental das cadeias de Markov, a ideia principal do estudo está na hipótese de convergência de renda. Primeiramente será testado a hipótese de convergência de renda do estado por meio das microrregiões, para isso serão utilizados dados de produto per capita dos anos de 1990, 2000 e 2010. Também será testado a hipótese de convergência para os municípios do Conselho Regional de Desenvolvimento Sul, situado no Rio Grande do Sul, utilizando dados de renda per capita dos anos de 1991, 2000 e 2010. Os resultados obtidos para as microrregiões do Rio Grande do Sul mostram que as economias não estão convergindo em sua totalidade para uma classe de renda especifica, porém é percebido que no longo prazo haverá uma maior concentração das microrregiões nos extratos de renda próximos a média, o tempo esperado para que as economias cheguem ao seu estado estacionário é de seis períodos. Por meio dos resultados obtidos para a região do Corede Sul, temos que as economias convergirão em sua maioria para a classe de renda médio pobre, seguido pela classe dos médio ricos. Ambas as classes estão situadas próximas a média regional, sendo que as classes de renda pobre e rico situadas aos extremos serão extintas no longo prazo. O tempo esperado para que as economias cheguem ao estado estacionário é de onze períodos.

A risk model with an observer in a Markov environment

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Fluorescence and reflectance spectroscopy for identification of atherosclerosis in human carotid arteries using principal components analysis

Objectives: The aim of this work was to verify the differentiation between normal and pathological human carotid artery tissues by using fluorescence and reflectance spectroscopy in the 400- to 700-nm range and the spectral characterization by means of principal components analysis. Background Data: Atherosclerosis is the most common and serious pathology of the cardiovascular system. Principal components represent the main spectral characteristics that occur within the spectral data and could be used for tissue classification. Materials and Methods: Sixty postmortem carotid artery fragments (26 non-atherosclerotic and 34 atherosclerotic with non-calcified plaques) were studied. The excitation radiation consisted of a 488-nm argon laser. Two 600-mu m core optical fibers were used, one for excitation and one to collect the fluorescence radiation from the samples. The reflectance system was composed of a halogen lamp coupled to an excitation fiber positioned in one of the ports of an integrating sphere that delivered 5 mW to the sample. The photo-reflectance signal was coupled to a 1/4-m spectrograph via an optical fiber. Euclidean distance was then used to classify each principal component score into one of two classes, normal and atherosclerotic tissue, for both fluorescence and reflectance. Results: The principal components analysis allowed classification of the samples with 81% sensitivity and 88% specificity for fluorescence, and 81% sensitivity and 91% specificity for reflectance. Conclusions: Our results showed that principal components analysis could be applied to differentiate between normal and atherosclerotic tissue with high sensitivity and specificity.

NGC 7097: THE ACTIVE GALACTIC NUCLEUS AND ITS MIRROR, REVEALED BY PRINCIPAL COMPONENT ANALYSIS TOMOGRAPHY

Three-dimensional spectroscopy techniques are becoming more and more popular, producing an increasing number of large data cubes. The challenge of extracting information from these cubes requires the development of new techniques for data processing and analysis. We apply the recently developed technique of principal component analysis (PCA) tomography to a data cube from the center of the elliptical galaxy NGC 7097 and show that this technique is effective in decomposing the data into physically interpretable information. We find that the first five principal components of our data are associated with distinct physical characteristics. In particular, we detect a low-ionization nuclear-emitting region (LINER) with a weak broad component in the Balmer lines. Two images of the LINER are present in our data, one seen through a disk of gas and dust, and the other after scattering by free electrons and/or dust particles in the ionization cone. Furthermore, we extract the spectrum of the LINER, decontaminated from stellar and extended nebular emission, using only the technique of PCA tomography. We anticipate that the scattered image has polarized light due to its scattered nature.

Hubble parameter reconstruction from a principal component analysis: minimizing the bias

Aims. A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Methods. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. Results. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.