Modeling discrete time stochastic processes with block frames

Abstract. This paper develops the concept of block frames which was introduced in an earlier article to provide a geometric and yet computationally efficient approach to some problems of time series analysis. The concept is extended to deal with a greater range of issues, related in particular to weak stationarity and to causality relationships between stochastic flows. It is also shown how to use information generating function systems to force an essentially linear theory to account for non-linear phenomena

Sistemas granulares evolutivos

Orientador: Fernando Antonio Campos GomideTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente tem-se observado um crescente interesse em abordagens de modelagem computacional para lidar com fluxos de dados do mundo real. Métodos e algoritmos têm sido propostos para obtenção de conhecimento a partir de conjuntos de dados muito grandes e, a princípio, sem valor aparente. Este trabalho apresenta uma plataforma computacional para modelagem granular evolutiva de fluxos de dados incertos. Sistemas granulares evolutivos abrangem uma variedade de abordagens para modelagem on-line inspiradas na forma com que os humanos lidam com a complexidade. Esses sistemas exploram o fluxo de informação em ambiente dinâmico e extrai disso modelos que podem ser linguisticamente entendidos. Particularmente, a granulação da informação é uma técnica natural para dispensar atenção a detalhes desnecessários e enfatizar transparência, interpretabilidade e escalabilidade de sistemas de informação. Dados incertos (granulares) surgem a partir de percepções ou descrições imprecisas do valor de uma variável. De maneira geral, vários fatores podem afetar a escolha da representação dos dados tal que o objeto representativo reflita o significado do conceito que ele está sendo usado para representar. Neste trabalho são considerados dados numéricos, intervalares e fuzzy; e modelos intervalares, fuzzy e neuro-fuzzy. A aprendizagem de sistemas granulares é baseada em algoritmos incrementais que constroem a estrutura do modelo sem conhecimento anterior sobre o processo e adapta os parâmetros do modelo sempre que necessário. Este paradigma de aprendizagem é particularmente importante uma vez que ele evita a reconstrução e o retreinamento do modelo quando o ambiente muda. Exemplos de aplicação em classificação, aproximação de função, predição de séries temporais e controle usando dados sintéticos e reais ilustram a utilidade das abordagens de modelagem granular propostas. O comportamento de fluxos de dados não-estacionários com mudanças graduais e abruptas de regime é também analisado dentro do paradigma de computação granular evolutiva. Realçamos o papel da computação intervalar, fuzzy e neuro-fuzzy em processar dados incertos e prover soluções aproximadas de alta qualidade e sumário de regras de conjuntos de dados de entrada e saída. As abordagens e o paradigma introduzidos constituem uma extensão natural de sistemas inteligentes evolutivos para processamento de dados numéricos a sistemas granulares evolutivos para processamento de dados granularesAbstract: In recent years there has been increasing interest in computational modeling approaches to deal with real-world data streams. Methods and algorithms have been proposed to uncover meaningful knowledge from very large (often unbounded) data sets in principle with no apparent value. This thesis introduces a framework for evolving granular modeling of uncertain data streams. Evolving granular systems comprise an array of online modeling approaches inspired by the way in which humans deal with complexity. These systems explore the information flow in dynamic environments and derive from it models that can be linguistically understood. Particularly, information granulation is a natural technique to dispense unnecessary details and emphasize transparency, interpretability and scalability of information systems. Uncertain (granular) data arise from imprecise perception or description of the value of a variable. Broadly stated, various factors can affect one's choice of data representation such that the representing object conveys the meaning of the concept it is being used to represent. Of particular concern to this work are numerical, interval, and fuzzy types of granular data; and interval, fuzzy, and neurofuzzy modeling frameworks. Learning in evolving granular systems is based on incremental algorithms that build model structure from scratch on a per-sample basis and adapt model parameters whenever necessary. This learning paradigm is meaningful once it avoids redesigning and retraining models all along if the system changes. Application examples in classification, function approximation, time-series prediction and control using real and synthetic data illustrate the usefulness of the granular approaches and framework proposed. The behavior of nonstationary data streams with gradual and abrupt regime shifts is also analyzed in the realm of evolving granular computing. We shed light upon the role of interval, fuzzy, and neurofuzzy computing in processing uncertain data and providing high-quality approximate solutions and rule summary of input-output data sets. The approaches and framework introduced constitute a natural extension of evolving intelligent systems over numeric data streams to evolving granular systems over granular data streamsDoutoradoAutomaçãoDoutor em Engenharia Elétric

ADVANCED REFLECTION SEISMIC STUDIES OF PHASE I WEYBURN CO2 SEQUESTRATION MONITORING

Three-dimensional, time-lapse (TL) reflection seismic datasets and well logs collected for Phase I CO2 sequestration project in Weyburn oilfield (southern Saskatchewan, Canada) are utilized for developing new approaches in three research areas: 1) estimation of seismic source waveforms, 2) evaluation of TL acoustic impedance (AI) variations for monitoring CO2 propagation, and 3) rigorous modeling of seismic waves propagating through finely layered rock. All three study areas are interconnected and important for accurate analysis of seismic data and TL monitoring of this and other oil reservoirs undergoing fluid injection. The first approach focuses on estimating the source waveforms from reflection seismic data, which is critical for evaluating accurate well-to-seismic ties as well as in other applications. A simple and effective method is proposed, based on iterative identification of the strongest and sparse reflections in seismic records, which allows estimation of source waveforms through an optimization approach, without well-log control and statistical hypotheses. The method allows correcting for coherent noise which seems to occur in stacked Weyburn data, consisting in (de)amplification and time shifts of the low-frequency components of the records. The method is tested on real and self-similar synthetic well-log models and applied to the Weyburn seismic data. For the second topic, a post-stack waveform-calibration processing procedure is developed in order to achieve accurate consistency of TL datasets. Time shifts between the monitor and baseline records are also measured during this procedure, and an improved method for calculating the TL reflectivity differences is proposed. Further, instead of subtraction of the baseline and monitor AIs, TL AI variations are evaluated directly from the reflectivity differences and baseline AI. AI inversion is performed by an accurate and stable method using the stacked reflection and well-log data, and also seismic velocities measured during data processing. The inverted time shifts and TL AI variations correlate with CO2 distributions within the reservoir and allow estimating parameters of the reservoir. In the third research area, a completely new approach to seismic wave modeling is proposed. Rigorous first-principle continuum mechanics is used instead of the conventional viscoelastic approximation. This modeling considers the existence of internal variables, body-force internal friction, and boundary conditions for internal variables. These factors are disregarded in the viscoelastic model, but they should cause dominant effects on seismic-wave attenuation and velocity dispersion in layered media. Numerical modeling of seismic wave propagation is performed in a model of the Weyburn Field. The resulting wavefield and seismic attenuation parameters are found to strongly depend on the internal boundary conditions between layers. Several types of quality (Q) factors are measured in the modeled synthetic waveforms

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem

Dynamical System Methods in Fluid Dynamics

The workshop was organized around the infusion of new techniques from dynamical systems, geometric methods, multiscale analysis, scientific computation, and control theory into traditional methods in fluid mechanics. It was well attended with about 45 participants with broad geographic representation from all continents. There was an excellent blend of senior researchers, students, postdocs and junior faculty

Simulation of the evolution of large scale structure elements with adaptive multigrid method

http://www.ester.ee/record=b1053241~S1*es

Nonclassical stochastic flows and continuous products

Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noise combined with Poisson point processes, and product systems are much more diverse than Fock spaces. This text is a survey of recent progress in constructing and investigating nonclassical stochastic flows and continuous products of probability spaces and Hilbert spaces.Comment: A survey, 126 pages. Version 3 (final): former Question 9d4 is solved; 8a1 reformulated. Ref [41] added. For readability, sections are reordered (123456..->142536..). Cosmetic changes, mostly in 1b, 2a, 3d, (4a7) (v3 numbers) and Introductio