Randomness is an invaluable resource in theoretical computer science. However, pure random bits are hard to obtain. Quasi-randomness is a tool that has been widely used in eliminating/reducing the randomness from randomized algorithms. In this thesis, we study some aspects of quasi-randomness in graphs. Specifically, we provide an algorithm and a lower bound for two different kinds of regularity lemmas. Our algorithm for FK-regularity is derived using a spectral characterization of quasi-randomness. We also use a similar spectral connection to also answer an open question about quasi-random tournaments. We then provide a "Wowzer" type lower bound (for the number of parts required) for the strong regularity lemma. Finally, we study the derandomization of complexity classes using Turing machine simulations. 1. Connections between quasi-randomness and graph spectra. Quasi-random (or pseudo-random) objects are deterministic objects that behave almost like truly random objects. These objects have been widely studied in various settings (graphs, hypergraphs, directed graphs, set systems, etc.). In many cases, quasi-randomness is very closely related to the spectral properties of the combinatorial object that is under study. In this thesis, we discover the spectral characterizations of quasi-randomness in two different cases to solve open problems. A Deterministic Algorithm for Frieze-Kannan Regularity: The Frieze-Kannan regularity lemma asserts that any given graph of large enough size can be partitioned into a number of parts such that, across parts, the graph is quasi-random. . It was unknown if there was a deterministic algorithm that could produce a parition satisfying the conditions of the Frieze-Kannan regularity lemma in deterministic sub-cubic time. In this thesis, we answer this question by designing an O(n[superscript]w) time algorithm for constructing such a partition, where w is the exponent of fast matrix multiplication. Even Cycles and Quasi-Random Tournaments: Chung and Graham in had provided several equivalent characterizations of quasi-randomness in tournaments. One of them is about the number of "even" cycles where even is defined in the following sense. A cycle is said to be even, if when walking along it, an even number of edges point in the wrong direction. Chung and Graham showed that if close to half of the 4-cycles in a tournament T are even, then T is quasi-random. They asked if the same statement is true if instead of 4-cycles, we consider k-cycles, for an even integer k. We resolve this open question by showing that for every fixed even integer k geq 4, if close to half of the k-cycles in a tournament T are even, then T must be quasi-random. 2. A Wowzer type lower bound for the strong regularity lemma. The regularity lemma of Szemeredi asserts that one can partition every graph into a bounded number of quasi-random bipartite graphs. Alon, Fischer, Krivelevich and Szegedy obtained a variant of the regularity lemma that allows one to have an arbitrary control on this measure of quasi-randomness. However, their proof only guaranteed to produce a partition where the number of parts is given by the Wowzer function, which is the iterated version of the Tower function. We show here that a bound of this type is unavoidable by constructing a graph H, with the property that even if one wants a very mild control on the quasi-randomness of a regular partition, then any such partition of H must have a number of parts given by a Wowzer-type function. 3. How fast can we deterministically simulate nondeterminism? We study an approach towards derandomizing complexity classes using Turing machine simulations. We look at the problem of deterministically counting the exact number of accepting computation paths of a given nondeterministic Turing machine. We provide a deterministic algorithm, which runs in time roughly O(sqrt(S)), where S is the size of the configuration graph. The best of the previously known methods required time linear in S. Our result implies a simulation of probabilistic time classes like PP, BPP and BQP in the same running time. This is an improvement over the currently best known simulation by van Melkebeek and Santhanam.

In this thesis we have focused on two topics: Discrete Quantum Walks and Quantum Image Processing. Our work is a contribution within the field of quantum computation from the perspective of a computer scientist. With the purpose of finding new techniques to develop quantum algorithms, there has been an increasing interest in studying Quantum Walks, the quantum counterparts of classical random walks. Our work in quantum walks begins with a critical and comprehensive assessment of those elements of classical random walks and discrete quantum walks on undirected graphs relevant to algorithm development. We propose a model of discrete quantum walks on an infinite line using pairs of quantum coins under different degrees of entanglement, as well as quantum walkers in different initial state configurations, including superpositions of corresponding basis states. We have found that the probability distributions of such quantum walks have particular forms which are different from the probability distributions of classical random walks. Also, our numerical results show that the symmetry properties of quantum walks with entangled coins have a non-trivial relationship with corresponding initial states and evolution operators. In addition, we have studied the properties of the entanglement generated between walkers, in a family of discrete Hadamard quantum walks on an infinite line with one coin and two walkers. We have found that there is indeed a relation between the amount of entanglement available in each step of the quantum walk and the symmetry of the initial coin state. However, as we show with our numerical simulations, such a relation is not straightforward and, in fact, it can be counterintuitive. Quantum Image Processing is a blend of two fields: quantum computation and image processing. Our aim has been to promote cross-fertilisation and to explore how ideas from quantum computation could be used to develop image processing algorithms. Firstly, we propose methods for storing and retrieving images using non-entangled and entangled qubits. Secondly, we study a case in which 4 different values are randomly stored in a single qubit, and show that quantum mechanical properties can, in certain cases, allow better reproduction of original stored values compared with classical methods. Finally, we briefly note that entanglement may be used as a computational resource to perform hardware-based pattern recognition of geometrical shapes that would otherwise require classical hardware and software.

Thesis (M.S.)--University of North Carolina Wilmington, 2008. / Title from PDF title page (viewed May 27, 2009) Includes bibliographical references (p. 31-34)

Made available in DSpace on 2015-03-03T11:52:41Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-24Bitstream added on 2015-03-03T12:06:08Z : No. of bitstreams: 1 000804349.pdf: 687208 bytes, checksum: 513575bcf70cbc15996bc5c0fdb99657 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Técnicas para seleção de características tem sido amplamente estudadas pela comunidade científica de reconhecimento de padrões e areas afins, dado que o problema de encontrar o subconjunto das características que maximiza a taxa de acerto de uma técnica de classificação de padrões pode ser modelado como um problema de otimização. Metodologias baseadas em inteligência evolucionista, tais como aquelas que simulam dinâmicas sociais e de interação entre morcegos, algumas espécies de aves e outros insetos, tem sido recentemente aplicadas nesse contexto. Assim sendo, o presente trabalho visou o estudo e desenvolvimento de técnicas de seleção de características utilizando abordagens de otimização evolucionistas, sendo elas: BBA - Binary Bat Algorithm, BCSS - Binary Charged System Search, BCS - Binary Cuckoo Search, BKH - Binary Krill Herd e BSSO - Binary Social-Spider Optimization. Experimentos realizados em seis bases de dados utilizando as técnicas propostas em conjunto com outras cinco técnicas (BGA - Binary Genetic Algorithm, BPSO - Binary Particle Swarm Optimization, BFA - Binary Fire y Algorithm, BGSA - Binary Gravitational Search Algorithm, BHS - Binary Harmony Search) mostraram a eficácia das técnicas evolucionistas propostas quando utilizadas em conjunto com o classificador OPF. O BSSO - Binary Social-Spider Optimization apresentou a melhor acurácia em 3 bases, chegando a aumentar a taxa de acerto do classificador OPF em até 19%, bem como, selecionou o menor número de características em cinco das seis bases. Em relação ao tempo de execuçãao, o BKH - Binary Krill Herd obteve o segundo melhor tempo em cinco bases, ficando atrás somente do BHS - Binary Harmony Search / Techniques for feature selection have been widely studied by the pattern recognition scientific community and related fields, as the problem of finding the subset of features that maximizes the classifier rate can be modeled as a optimization problem. Methodologies based on evolutionary intelligence, such as those that simulate social dynamics and interaction between bats, some species of birds and other insects, have recently been applied in this context. Therefore, this work aimed to the study and development of feature selection techniques using evolutionary optimization approaches: BBA - Binary Bat Algorithm, BCSS - Binary Charged System Search, BCS - Binary Cuckoo Search, BKH - Binary Krill Herd e BSSO - Binary Social-Spider Optimization. Experiments conducted in six databases using the proposed techniques together with ve other techniques (BGA - Binary Genetic Algorithm, BPSO - Binary Particle Swarm Optimization, BFA - Binary Fire y Algorithm, BGSA - Binary Gravitational Search Algorithm, BHS - Binary Harmony Search) have shown the efiectiveness of proposed evolutionary techniques when used with the OPF classifier. The BSSO - Binary Social-Spider Optimization showed the best accuracy on 3 datasets coming to increase the OPF classification rate in up to 19%. Also, SSO has selected the smallest number features in ve of the six datasets. Regarding the runtime, BKH - Binary Krill Herd was the second fastest technique in ve datasets, being only slower then BHS - Binary Harmony Search technique

Made available in DSpace on 2015-03-03T11:52:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-08-27Bitstream added on 2015-03-03T12:06:57Z : No. of bitstreams: 1 000807064.pdf: 1315518 bytes, checksum: a9d0bfb3006b4cedb3d545508e96efc4 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O estudo da cintilação ionosférica, causada por flutuações na amplitude e na fase de um sinal eletromagnético quando este passa por irregularidades na densidade de elétrons da ionosfera, tem assumido um papel muito importante na pesquisa ionosférica e também no posicionamento por satélite. Isso se deve à crescente influência do GNSS na navegação e no sensoriamento remoto e também pelo fato da cintilação degradar severamente o desempenho desses sistemas. Ainda existem muitas lacunas a serem preenchidas para que possa ser proposto algum método efetivo para correção dos efeitos causados nos sinais GNSS ou mesmo previsão da cintilação, principalmente para a região equatorial, em que está situado o Brasil. Portanto, nessa dissertação objetiva-se investigar a cintilação sob uma perspectiva multiescala, abordando para tanto, a análise multirresolução a partir de wavelets não decimadas. Como consequência, os resultados desta investigação das séries temporais obtidas dos índices S4 de cintilação mostram a presença de um padrão que se repete na série em dias consecutivos em que há presença de dados. Tal comportamento periódico, que apresenta formato de U mostra estar relacionado com o efeito do multicaminho e pode influenciar na análise do índice S4 de cintilação ionosférica, fazendo-se necessário eliminá-lo. Através da decomposição em multiescala do período com baixos índices de cintilação é possível estimar o efeito do multicaminho, cuja repetibilidade é evidenciada nas escalas mais suaves. Uma vez estimado, esse efeito pode ser removido da série dos índices S4 no período de forte cintilação... / The study of the ionospheric scintillation, which is caused by fluctuations in the amplitude and phase of an electromagnetic signal when it passes through irregularities in the density of electrons in the ionosphere, has become very important in ionospheric research and also in satellite positioning. This is due to the increasing influence of GNSS navigation and remote sensing, and also because the scintillation severely degrade the performance of these systems. There are still many gaps to be fulfilled before the propositon of some effective method for correcting of the effects of the scintillation on GNSS signals or even its prediction, especially for equatorial region, which includes Brazil. This dissertation aims to investigate the ionospheric scintillation under a multiscale aspects using a multiresolution analysis from non-decimated wavelets. The investigation of the time series obtained of the S4 scintillation index showed the presence of a pattern that is repeated in the series on consecutive days in which there are data. This periodic behavior, which has U format and can be related to the effect of the multipath, influences the analysis of S4 ionospheric scintillation index, and should be eliminated. Through multiscale decomposition of the period with low scintillation index it is possible to estimate the multipath effect, which is evident in the smoother scales. Once identified and estimated, this effect can be removed from the S4 index series in the strong scintillation period...

The aim of the study was to investigate what influence the use of computers using MS Excel and RJS Graph software has on grade 11 Eritrean students' understanding of functions in the learning of mathematics. An empirical investigation using quantitative and qualitative research methods was carried out. A pre-test (task 1) and a post-test (task 2), a questionnaire and an interview schedule were used to collect data. Two randomly selected sample groups (i.e. experimental and control groups) of students were involved in the study. The experimental group learned the concepts of functions, particularly quadratic functions using computers. The control group learned the same concepts through the traditional paper-pencil method. The results indicated that the use of computers has a positive impact on students' understanding of functions as reflected in their achievement, problem-solving skills, motivation, attitude and the classroom environment. / Educational Studies / M. Ed. (Math Education)

Orientador: João Paulo Papa / Banca: Alexandre Levada / Banca: Antônio Carlos Sementille / Resumo: Técnicas de aprendizado de máquina, usualmente, objetivam aprender alguma superfície que separe amostras de classes diferentes por meio de sua representação vetorial. Entretanto, existem muitas aplicações que podem, eventualmente, perder informações essenciais e inerentes da estrutura dos dados em tal representação e, com o crescimento de base de dados com alta dimensionalidade, essas informações se tornam cada vez mais importantes. Os espaços de representação de dados com curvatura, baseados em trabalhos na area da Matemática e Física, têm despertado interesse por parte da comunidade de aprendizado de máquina com o intuito de resolver tal situação. Esses espaços de representação são baseados em tensores, os quais mantém a estrutura original dos dados, bem como permitem a utilização de variedades em superfícies com curvatura não nula. Esta dissertação de mestrado apresenta uma revisão bibliográfica sobre abordagens de aprendizado de máquina baseadas em tensores, bem como um referencial teórico sobre algebra multilinear. Também e apresentado um estudo da aplicabilidade do classificador Floresta de Caminhos Otimos, do inglês Optimum-Path Forest - OPF, em espaços tensoriais através da técnica Análise de Componentes Principais Multilineares, bem como a comparação dos resultados obtidos com outras técnicas conhecidas na literatura em contexto de reconhecimento em fotos e vídeos. Também foi demonstrado que o OPF pode obter maior acurácia em algumas situações quando se trabalha com características no espaço tensorial / Abstract: Machine learning techniques usually learn some decision surface that separates samples from di erent classes by means of their vectorial representation. However, there exist many applications that might lose important information that are strongly related to the data itself. Additionally, such information has gained importance with the popularity of high-dimensional datasets. As such, works based on Mathematics and Physics, where curvature-based space representations have been used in several application, have gained attention by the machine learning community. Such representations are based on tensors, which keep the original structure of the data, as well as they allow us to use manifolds in curvature-based spaces. This master's dissertation presents a review of the literature with respect to tensor-based machine learning techniques, as well as a brief review about multilinear algebra. We also evaluate the performance of the Optimum-Path Forest classi er (OPF) in tensor-oriented spaces by means of the Multilinear Principal Component Analysis, as well as its comparison against with other related techniques is also performed. It is shown OPF can bene t from such feature space representation in some situations / Mestre

Problems in formal verification are often stated in terms of finite automata and extensions thereof. In this thesis we investigate several such algorithmic problems. In the first part of the thesis we develop a theory of completeness thresholds in Bounded Model Checking. A completeness threshold for a given model M and a specification φ is a bound k such that, if no counterexample to φ of length k or less can be found in M, then M in fact satisfies φ. We settle a problem of Kroening et al. [KOS⁺11] in the affirmative, by showing that the linearity problem for both regular and ω-regular specifications (provided as finite automata and Buchi automata respectively) is PSPACE-complete. Moreover, we establish the following dichotomies: for regular specifications, completeness thresholds are either linear or exponential, whereas for ω-regular specifications, completeness thresholds are either linear or at least quadratic in the recurrence diameter of the model under consideration. Given a formula in a temporal logic such as LTL or MTL, a fundamental problem underpinning automata-based model checking is the complexity of evaluating the formula on a given finite word. For LTL, the complexity of this task was recently shown to be in NC [KF09]. In the second part of the thesis we present an NC algorithm for MTL, a quantitative (or metric) extension of LTL, and give an AC¹ algorithm for UTL, the unary fragment of LTL. We then establish a connection between LTL path checking and planar circuits which, among others, implies that the complexity of LTL path checking depends on the Boolean connectives allowed: adding Boolean exclusive or yields a temporal logic with P-complete path-checking problem. In the third part of the thesis we study the decidability of the reachability problem for parametric timed automata. The problem was introduced over 20 years ago by Alur, Henzinger, and Vardi [AHV93]. It is known that for three or more parametric clocks the problem is undecidable. We translate the problem to reachability questions in certain extensions of parametric one-counter machines. By further reducing to satisfiability in Presburger arithmetic with divisibility, we obtain decidability results for several classes of parametric one-counter machines. As a corollary, we show that, in the case of a single parametric clock (with arbitrarily many nonparametric clocks) the reachability problem is NEXP-complete, improving the nonelementary decision procedure of Alur et al. The case of two parametric clocks is open. Here, we show that the reachability is decidable in this case of automata with a single parameter.

Made available in DSpace on 2016-04-01T17:54:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-08-21. Added 1 bitstream(s) on 2016-04-01T18:00:15Z : No. of bitstreams: 1 000859943.pdf: 1070364 bytes, checksum: 04d8c74205b7c2df31f68a75600abada (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Técnicas de aprendizado de máquina, usualmente, objetivam aprender alguma superfície que separe amostras de classes diferentes por meio de sua representação vetorial. Entretanto, existem muitas aplicações que podem, eventualmente, perder informações essenciais e inerentes da estrutura dos dados em tal representação e, com o crescimento de base de dados com alta dimensionalidade, essas informações se tornam cada vez mais importantes. Os espaços de representação de dados com curvatura, baseados em trabalhos na area da Matemática e Física, têm despertado interesse por parte da comunidade de aprendizado de máquina com o intuito de resolver tal situação. Esses espaços de representação são baseados em tensores, os quais mantém a estrutura original dos dados, bem como permitem a utilização de variedades em superfícies com curvatura não nula. Esta dissertação de mestrado apresenta uma revisão bibliográfica sobre abordagens de aprendizado de máquina baseadas em tensores, bem como um referencial teórico sobre algebra multilinear. Também e apresentado um estudo da aplicabilidade do classificador Floresta de Caminhos Otimos, do inglês Optimum-Path Forest - OPF, em espaços tensoriais através da técnica Análise de Componentes Principais Multilineares, bem como a comparação dos resultados obtidos com outras técnicas conhecidas na literatura em contexto de reconhecimento em fotos e vídeos. Também foi demonstrado que o OPF pode obter maior acurácia em algumas situações quando se trabalha com características no espaço tensorial / Machine learning techniques usually learn some decision surface that separates samples from di erent classes by means of their vectorial representation. However, there exist many applications that might lose important information that are strongly related to the data itself. Additionally, such information has gained importance with the popularity of high-dimensional datasets. As such, works based on Mathematics and Physics, where curvature-based space representations have been used in several application, have gained attention by the machine learning community. Such representations are based on tensors, which keep the original structure of the data, as well as they allow us to use manifolds in curvature-based spaces. This master's dissertation presents a review of the literature with respect to tensor-based machine learning techniques, as well as a brief review about multilinear algebra. We also evaluate the performance of the Optimum-Path Forest classi er (OPF) in tensor-oriented spaces by means of the Multilinear Principal Component Analysis, as well as its comparison against with other related techniques is also performed. It is shown OPF can bene t from such feature space representation in some situations

Made available in DSpace on 2015-04-09T12:28:25Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-02-25Bitstream added on 2015-04-09T12:47:36Z : No. of bitstreams: 1 000811257.pdf: 6065923 bytes, checksum: 2f62e4d931cb75542832b3627b24b710 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Em problemas convencionais de reconhecimento de padrões, dado um conjunto de classes, cada instância do problema e associada a uma e somente uma classe. No entanto, alguns problemas reais de classificaço apresentam instâncias que podem ser associadas a mais de uma classe simultaneamente, esses problemas são denotados como classificação com múltiplos rótulos. Entre problemas dessa natureza, podemos destacar categorização de filmes e músicas, classificação de documentos, análise funcional de genes etc. Contudo, os problemas de classificação com múltiplos rótulos não são diretamente tratáveis por técnicas convencionais, o que justifica o interesse da comunidade de reconhecimento de padrões nesses tipos de problemas. Embora muitos métodos tenham sido propostos na literatura, há ainda muito a ser explorado, principalmente no uso de novos algoritmos convencionais de aprendizado de máquinas adaptados ou não aos problemas com múltiplos rótulos. O classificador supervisionado Floresta de Caminhos Otimos (Optimum- Path Forest - OPF) e um algoritmo determinístico aplicado a problemas convencionais de classificação, no entanto, ainda não foi investigado em problemas com múltiplos rótulos. Nesse contexto, investigamos neste trabalho a aplicação de classificadores baseados em OPF em problemas de múltiplos rótulos. Analisamos duas versões do classificador OPF: (i) a tradicional baseada em grafo completo e (ii) a versão baseada no grafo k-vizinhos mais próximos (OPFkNN). Para manipulação das bases com múltiplos rótulos, utilizamos dois métodos de transformação de problemas, o Binary Relevance e Label Powerset. Propusemos também algumas modificações nas fases de treinamento e classificação do OPFkNN com o objetivo de melhor os resultados desse classificador combinado a métodos de transformação de problemas. Os experimentos realizados em sete bases de dados públicas mostraram que as modifica ções ... / In conventional problems of pattern recognition, given a set of classes, each instance of the problem is associated with one and only one class. However, some real classification problems have instances that can be associated with more than one class at the same time, these problems are denoted as classification with multilabel. Among such problems, we highlight movies and music categorization, document classification, functional gene analysis etc. Nevertheless, the classification problems with multilabel are not directly treatable by conventional techniques, which explains the interest of pattern recognition community in these types of problems. Although many methods have been proposed in the literature, there is still much to be explored, especially in the use of novel conventional machine learning algorithms adapted or not to problems with multlabels. The Optimum-Path Forest (OPF) classifier is a supervised and deterministic algorithm applied to conventional classification problems, however, it has been not investigated in problems with multilabel. In this context, we investigated in this work the application of OPF-based classifiers on multilabel problems. We analyzed two versions of OPF-based classi ers: (i) the traditional one based on complete graph and (ii) the one based on k-nearest neighbors graph (OPFkNN). For manipulation of multilabel datasets, we used two transformation methods, the Binary Relevance and Label Powerset. We also proposed some changes in the training and classification phases of OPFkNN aiming to achieve better results when combined it with transformation methods. Experiments performed in seven public datasets showed that changes in OPFkNN improve outcomes. Comparison with the J48 classifier, ... / FAPESP: 2011/14094-1