A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.

Adaptive modeling and high quality spectral estimation for speech enhancement

In this work an adaptive modeling and spectral estimation scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for speech enhancement. Both speech and noise signals are modeled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. The model parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The speech enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. This approach is particularly useful as a pre-processing module for parametric based speech recognition systems that rely on spectral time dependent models. The system performance has been evaluated by a set of human listeners and by spectral distances. In both cases the use of this pre-processing module has led to improved results.

Spectral and homogenization problems

Dissertation for the Degree of Doctor of Philosophy in Mathematics

Clustering aplicado à Bolsa de Valores de Lisboa

O objetivo desta dissertação foi estudar um conjunto de empresas cotadas na bolsa de valores de Lisboa, para identificar aquelas que têm um comportamento semelhante ao longo do tempo. Para isso utilizamos algoritmos de Clustering tais como K-Means, PAM, Modelos hierárquicos, Funny e C-Means tanto com a distância euclidiana como com a distância de Manhattan. Para selecionar o melhor número de clusters identificado por cada um dos algoritmos testados, recorremos a alguns índices de avaliação/validação de clusters como o Davies Bouldin e Calinski-Harabasz entre outros.

Algorithms for information extraction and signal annotation on long-term biosignals using clustering techniques

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Unsupervised classification of remote sensing images combining Self Organizing Maps and segmentation techniques

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Clustering medical tourism in Algarve: setting the first steps for the the health authority

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

Development of a fuzzy qualitative risk assessment model applied to construction industry

Dissertação para obtenção do Grau de Doutor em Engenharia Industrial

Recursive neuro fuzzy techniques for online identification and control

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Spectral and coherence estimates on electroencephalogram recordings during arithmetical tasks

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do Grau de Mestre em Engenharia Biomédica

The additive effects in matrix dispersed liquid crystals

Dissertation presented at Faculdade de Ciências e Tecnologia from Universidade Nova de Lisboa to obtain the degree of Master in Chemical and Biochemical Engineering

Data fusion with computational intelligence techniques: a case study of fuzzy inference for terrain assessment

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

A clustering approach for vehicle routing problems with hard time windows

Dissertação para obtenção do Grau de Mestre em Logica Computicional

Automatic extraction of concepts from texts and applications

The extraction of relevant terms from texts is an extensively researched task in Text- Mining. Relevant terms have been applied in areas such as Information Retrieval or document clustering and classification. However, relevance has a rather fuzzy nature since the classification of some terms as relevant or not relevant is not consensual. For instance, while words such as "president" and "republic" are generally considered relevant by human evaluators, and words like "the" and "or" are not, terms such as "read" and "finish" gather no consensus about their semantic and informativeness. Concepts, on the other hand, have a less fuzzy nature. Therefore, instead of deciding on the relevance of a term during the extraction phase, as most extractors do, I propose to first extract, from texts, what I have called generic concepts (all concepts) and postpone the decision about relevance for downstream applications, accordingly to their needs. For instance, a keyword extractor may assume that the most relevant keywords are the most frequent concepts on the documents. Moreover, most statistical extractors are incapable of extracting single-word and multi-word expressions using the same methodology. These factors led to the development of the ConceptExtractor, a statistical and language-independent methodology which is explained in Part I of this thesis. In Part II, I will show that the automatic extraction of concepts has great applicability. For instance, for the extraction of keywords from documents, using the Tf-Idf metric only on concepts yields better results than using Tf-Idf without concepts, specially for multi-words. In addition, since concepts can be semantically related to other concepts, this allows us to build implicit document descriptors. These applications led to published work. Finally, I will present some work that, although not published yet, is briefly discussed in this document.