This thesis explores how to best choose data when curve fitting using power exponential functions. The power exponential functions used are μ(b; x)=(xe1-x)b and Φ(ρ; x)=((1-x)ex)ρ . We use a number of designs such as the equidistant design, the Chebyshev design and the the D-optimal design to compare which design gives the best fit. A few examples including the logistic and the heidler function are looked at during the comparison. The measurement of the errors were made based on the sum of least squares errors in the first part and the maximum error in the second part. MATLAB was used in this comparison.

In 2011, Oregon was one of many states in the U.S. consolidating their education governance around an early learning, K-12, and postsecondary hub. This study uses legislator-voting data to investigate the relationship between this consolidated model and endogenous policy formulation processes. This study employs a separable temporal exponential random graph model (STERGM) to investigate how an education governance shift toward consolidated authority relates to bipartisan outcomes for education-related bills over time. Oregon legislator voting networks were analyzed for cohesion, centrality, and community detection measures, as well as by legislator attributes (e.g. gender, party, and title) to test the association they had on the likelihood of forming ties with other legislators. Finally, to study the relationship of bipartisanship with legislators’ likelihood to vote commonly, I added the legislators’ political party attributes within dyads to analyze the association that having different political parties had on legislators’ common votes. The results highlight evidence of legislator networks that were very dense at each time point included in the study, with a high likelihood of forming ties. However, when Oregon shifted to centralized education governance model their legislator networks became more distributed and cohesive when compared to other years included in the longitudinal study. It is possible that such a shift prompted collaboration among legislators resulting in mutuality that increased the likelihood for underrepresented groups of legislators (e.g. females and republicans) to vote commonly with their colleagues. Aligned with previous research, this study found that centralized governing bodies reinforced by political legislation provided collaborative initiatives for the legislative community. Attending to bipartisan voting patterns dynamically through a governance shift is a valuable investigation that will provide nuanced inferences about education governance and policymaking for states making similar consolidated governance shifts in the future.

O estudo comparou o desempenho preditivo dos modelos de previsão de redes neurais e de suavização exponencial, empregando dados diários do preço da arroba do boi gordo futuro (BM&FBOVESPA) entre janeiro de 2010 até dezembro de 2015. Os resultados mostram que modelos relativamente mais complexos como redes neurais não necessariamente apresentam melhor desempenho se comparados a modelos mais simples, e também mostram que a classificação relativa muda conforme variam as medidas de ajuste e/ou horizonte de previsão além de vantagens associadas a combinação de diversos modelos. / This study compared the predictive performance between neural network models and exponential smoothing, using daily data of live cattle future price (BM&FBOVESPA) from January 2010 to December 2015. The results show that relatively more complex models like neural networks do not necessarily display better performance compared to simpler ones. Results also shows that relative classification changes with respect to adjust measures and/or forecast horizons changes besides advantages achieved by model combinaion.

Estuda-se o transporte de portadores de carga no interior de um isolante dotado de centros profundos de retenção de carga. Supõe-se que os portadores tenham sido depositados na superfície livre do isolante por meio de uma descarga corona rápida e que ai a densidade superficial de carga decaia exponencialmente. Para obter-se o campo elétrico E = E (x,t) no interior do isolante. Integra-se essa equação pelo método das características e obtêm-se expressões analíticas para as linhas de corrente x = x (t,te) (te, designando o tempo de saída da carga da superfície) e para o campo elétrico E = E (t,te) ao longo de cada uma das linhas. São apresentadas famílias de curvas x = x(t,te) e de E = E(t,te),. Eliminando-se graficamente te entre as duas famílias, obtem-se a família de curvas E = E(x) parametrizada em t. Usou-se planímetro para determinar a área debaixo de cada curva E = E(x), e com isso constrói-se a curva de decaimento de potencial / The transport of charge carriers in presence of bulk traps inside an insulator. It is supposed that the carriers were deposited on the surface by a pulse of charge decaying thereafter exponentially with the time. In order to find the electric fielhd electric field E(x,t), the method of characteristics is employed, taking as parameter the time te when the leaves the surface; and ththeir position X=(t,te) and the electric field E=E(x,te) are obtained. By graphicall eliminatination, curves of E(x) are obtained for various times t. A planimeter was used to find the potential at every time as a function of the time

Orientador: Manoel Ferreira Borges Neto / Banca: José Márcio Machado / Banca: Siovani Cintra Felipussi / Resumo: Com o intuido de bem fundamentar bases teóricas para futuras aplicações dos octônios à Mecânica Quântica, Computação Quântica e Criptografia, um dos objetivos maiores deste trabalho é o de determinar e estudar a analiticidade e hiperperiodicidade de funções octoniônicas, de acordo com o Teorema (3.1), enunciado e demonstrado apropriadamente no texto. Além disso, determina-se para as Funções Trigonométricas Octoniônicas a sua periodicidade, enunciada e demonstrada nos Teoremas (3.2) e (3.3). Outro aspecto relevante abordado diz respeito a uma extensão octoniônica da Função Logarítmica, que pode ser importante para aplicações à Física Teórica de Várias dimensões. / Abstract: With the main purpose of setting up a sound theoretical basis in order to apply octonionic algebra to both Quantum Mechanics and Quantum Computation and Criptography, I have studied and determined the regularity of the exponential octonionic function, through the Theorem (3.1). Moreover the determination of the Trigonometrical Octonionic Function is also made and it is obtained its regularity, stated in Theorem (3.2) and (3.3). An octonionic extension of the Logaritimic Function is also well explored, which opens the possibility of a large number of applications in Theoretical Physics of higher dimensions. / Mestre

by Wai Ho Mow. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 116-124). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Spread Spectrum Technique --- p.2 / Chapter 1.1.1 --- Pulse Compression Radars --- p.3 / Chapter 1.1.2 --- Spread Spectrum Multiple Access Systems --- p.6 / Chapter 1.2 --- Definitions and Notations --- p.8 / Chapter 1.3 --- Organization of this Thesis --- p.12 / Chapter 2 --- Lower Bounds on Correlation of Sequences --- p.15 / Chapter 2.1 --- Welch's Lower Bounds and Sarwate's Generalization --- p.16 / Chapter 2.2 --- A New Construction and Bounds on Odd Correlation --- p.23 / Chapter 2.3 --- Known Sequence Sets Touching the Correlation Bounds --- p.26 / Chapter 2.4 --- Remarks on Other Bounds --- p.27 / Chapter 3 --- Perfect Polyphase Sequences: A Unified Approach --- p.29 / Chapter 3.1 --- Generalized Bent Functions and Perfect Polyphase Sequences --- p.30 / Chapter 3.2 --- The General Construction of Chung and Kumar --- p.32 / Chapter 3.3 --- Classification of Known Constructions ...........； --- p.34 / Chapter 3.4 --- A Unified Construction --- p.39 / Chapter 3.5 --- Desired Properties of Sequences --- p.41 / Chapter 3.6 --- Proof of the Main Theorem --- p.45 / Chapter 3.7 --- Counting the Number of Perfect Polyphase Sequences --- p.49 / Chapter 3.8 --- Results of Exhaustive Searches --- p.53 / Chapter 3.9 --- A New Conjecture and Its Implications --- p.55 / Chapter 3.10 --- Sets of Perfect Polyphase Sequences --- p.58 / Chapter 4 --- Aperiodic Autocorrelation of Generalized P3/P4 Codes --- p.61 / Chapter 4.1 --- Some Famous Polyphase Pulse Compression Codes --- p.62 / Chapter 4.2 --- Generalized P3/P4 Codes --- p.65 / Chapter 4.3 --- Asymptotic Peak-to-Side-Peak Ratio --- p.66 / Chapter 4.4 --- Lower Bounds on Peak-to-Side-Peak Ratio --- p.67 / Chapter 4.5 --- Even-Odd Transformation and Phase Alphabet --- p.70 / Chapter 5 --- Upper Bounds on Partial Exponential Sums --- p.77 / Chapter 5.1 --- Gauss-like Exponential Sums --- p.77 / Chapter 5.1.1 --- Background --- p.79 / Chapter 5.1.2 --- Symmetry of gL(m) and hL(m) --- p.80 / Chapter 5.1.3 --- Characterization on the First Quarter of gL(m) --- p.83 / Chapter 5.1.4 --- Characterization on the First Quarter of hL(m) --- p.90 / Chapter 5.1.5 --- Bounds on the Diameters of GL(m) and HL(m) --- p.94 / Chapter 5.2 --- More General Exponential Sums --- p.98 / Chapter 5.2.1 --- A Result of van der Corput --- p.99 / Chapter 6 --- McEliece's Open Problem on Minimax Aperiodic Correlation --- p.102 / Chapter 6.1 --- Statement of the Problem --- p.102 / Chapter 6.2 --- A Set of Two Sequences --- p.105 / Chapter 6.3 --- A Set of K Sequences --- p.110 / Chapter 7 --- Conclusion --- p.113 / Bibliography --- p.124

Several recent empirical studies, particularly in the regional economic growth literature, emphasize the importance of explicitly accounting for uncertainty surrounding model specification. Standard approaches to deal with the problem of model uncertainty involve the use of Bayesian model-averaging techniques. However, Bayesian model-averaging for spatial autoregressive models suffers from severe drawbacks both in terms of computational time and possible extensions to more flexible econometric frameworks. To alleviate these problems, this paper presents two global-local shrinkage priors in the context of high-dimensional matrix exponential spatial specifications. A simulation study is conducted to evaluate the performance of the shrinkage priors. Results suggest that they perform particularly well in high-dimensional environments, especially when the number of parameters to estimate exceeds the number of observations. Moreover, we use pan-European regional economic growth data to illustrate the performance of the proposed shrinkage priors.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2016-11-29T11:25:22Z No. of bitstreams: 1 Carlos Willians Paschoal.pdf: 3019426 bytes, checksum: e3288d4fbd7054a639ed1029f451317e (MD5) / Made available in DSpace on 2016-11-29T11:25:22Z (GMT). No. of bitstreams: 1 Carlos Willians Paschoal.pdf: 3019426 bytes, checksum: e3288d4fbd7054a639ed1029f451317e (MD5) Previous issue date: 2016-08-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research had as aim investigates how and if the Mathematical Model can be a facilitator of teaching Probability of Exponential Distribution to engineering. We had as an aim answer the follow question: Will Mathematical Model be a favorable teaching methodology to learn Probability of Exponential Distribution in an engineering course? We Used the methodology, Mathematical Model, as described by Bassanezi (2004), Biembengut and Hein (2008), Almeida, Silva and Vertuan (2012), and others who showed the steps to create activities sequence. The theoretical framework was based on the Theory of Didactic Situations from Brousseau (2008), Silva (2008), Freitas (2008), and Teixeira and Passos (2013), which was organized in parallel with the Mathematical Model and the Theory of Didactic Situations based on the work of Dias and Santo (2014), the intention was built an analysis grid to analyze the activities sequence. This sequence was applied to 2º year students from Chemistry Production Engineering from a private institution at São Paulo state. It was realized two meetings, one to organize the experiment and other to obtain the mathematical model from Exponential Distribution. From the data collected we realized its validation in the source problem and in questions from the didactic book proposed in the amendment. This sequence was divided in four activities, which steps of mathematical model, typology of didactics situations and the means structures were identified and analyzed in each of them. This analysis found that the steps foreseen were met, but the students did not achieve a general model, therefore it was needed a step of institutionalization on the validation step. The use of the model was assimilated by the participants’ students who understood the methodology as helpful and motivating. They were able to apply the Exponential Distribution in other problems from didactic books. This research was limited to analyze how the Exponential Distribution can be taught by the Mathematical Model methodology, presenting as future perspective the possibility of reproduction the activity in several topics that include teaching random variable beyond the surveys from types of state of art or metaanalysis about what was researched on the topic / Essa pesquisa teve como objetivo investigar se a Modelagem Matemática pode ser um facilitador do ensino da Distribuição de Probabilidade Exponencial para Engenharias. Tivemos como objetivo responder à seguinte questão de pesquisa: Será a Modelagem Matemática, uma metodologia de ensino favorável à aprendizagem da Distribuição de Probabilidade Exponencial, em um curso de Engenharia? Utilizamos a metodologia Modelagem Matemática, conforme descrita por Bassanezi (2004), Biembengut e Hein (2008), Almeida, Silva e Vertuan (2012) entre outros, que nos inspiraram nos passos para criação de uma sequência de atividades. O referencial teórico está fundamentado na Teoria das Situações Didáticas de Brousseau (2008), Silva (2008), Freitas (2008) e Teixeira e Passos (2013). Foi organizado uma comparação entre a Modelagem Matemática e a Teoria das Situações didáticas com base no trabalho de Dias e Santo (2014), com o intuito de criar uma grade de análise da sequência de atividades. Esta foi aplicada para alunos do 2º ano de Engenharia de Produção Química de uma instituição de ensino particular do Estado de São Paulo, em dois encontros, um para a organização da experimentação, e outro para obtenção do modelo matemático da Distribuição Exponencial. A partir dos dados coletados efetuamos sua validação no problema de origem e em questões retiradas de um livro didático proposto na ementa do referido curso. Esta sequência, foi dividida em quatro atividades, sendo que as etapas da Modelagem Matemática, a Tipologia das Situações Didáticas e as estruturas do meio foram identificadas e analisadas em cada uma. Nesta análise constatou-se que as etapas previstas foram cumpridas, mas que os alunos não chegaram a um modelo geral, sendo necessária uma etapa de institucionalização no meio da etapa de validação. O uso do modelo foi assimilado pelos alunos participantes que entenderam a metodologia como útil e motivadora, sendo capazes de aplicar a Distribuição Exponencial em outros problemas, retirados de livros didáticos. Esta pesquisa se limitou à análise de como a Distribuição Exponencial pode ser ensinada por meio da metodologia da Modelagem Matemática, apresentando como perspectiva futura a possibilidade de reprodução da atividade em diversos tópicos que englobam o ensino de variáveis aleatórias, além de levantamentos de estados da arte ou metanálises sobre o que já foi pesquisado no tema

Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. Exponential family embeddings extend the idea of word embeddings to other types of high-dimensional data. Exponential family embeddings have three ingredients; embeddings as latent variables, a predefined conditioning set for each observation called the context and a conditional likelihood from the exponential family. The embeddings are inferred with a scalable algorithm. This thesis highlights three advantages of the exponential family embeddings model class: (A) The approximations used for existing methods such as word2vec can be understood as a biased stochastic gradients procedure on a specific type of exponential family embedding model --- the Bernoulli embedding. (B) By choosing different likelihoods from the exponential family we can generalize the task of learning distributed representations to different application domains. For example, we can learn embeddings of grocery items from shopping data, embeddings of movies from click data, or embeddings of neurons from recordings of zebrafish brains. On all three applications, we find exponential family embedding models to be more effective than other types of dimensionality reduction. They better reconstruct held-out data and find interesting qualitative structure. (C) Finally, the probabilistic modeling perspective allows us to incorporate structure and domain knowledge in the embedding space. We develop models for studying how language varies over time, differs between related groups of data, and how word usage differs between languages. Key to the success of these methods is that the embeddings share statistical information through hierarchical priors or neural networks. We demonstrate the benefits of this approach in empirical studies of Senate speeches, scientific abstracts, and shopping baskets.

The main contribution of this thesis is to derive the properties and present a closed from solution of the exotic options under some specific types of Levy processes, such as American put options, American call options, British put options, British call options and American knock-out put options under either double exponential jump-diffusion processes or one-sided exponential jump-diffusion processes. Compared to the geometric Brownian motion, exponential jump-diffusion processes can better incorporate the asymmetric leptokurtic features and the volatility smile observed from the market. Pricing the option with early exercise feature is the optimal stopping problem to determine the optimal stopping time to maximize the expected options payoff. Due to the Markovian structure of the underlying process, the optimal stopping problem is related to the free-boundary problem consisting of an integral differential equation and suitable boundary conditions. By the local time-space formula for semi-martingales, the closed form solution for the options value can be derived from the free-boundary problem and we characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation arising from the early exercise premium (EEP) representation. Chapter 2 and Chapter 3 discuss American put options and American call options respectively. When pricing options with early exercise feature under the double exponential jump-diffusion processes, a non-local integral term will be found in the infinitesimal generator of the underlying process. By the local time-space formula for semi-martingales, we show that the value function and the optimal stopping boundary are the unique solution pair to the system of two integral equations. The significant contributions of these two chapters are to prove the uniqueness of the value function and the optimal stopping boundary under less restrictive assumptions compared to previous literatures. In the degenerate case with only one-sided jumps, we find that the results are in line with the geometric Brownian motion models, which extends the analytical tractability of the Black-Scholes analysis to alternative models with jumps. In Chapter 4 and Chapter 5, we examine the British payoff mechanism under one-sided exponential jump-diffusion processes, which is the first analysis of British options for process with jumps. We show that the optimal stopping boundaries of British put options with only negative jumps or British call options with only positive jumps can also be characterized as the unique solution to a nonlinear integral equation arising from the early exercise premium representation. Chapter 6 provides the study of American knock-out put options under negative exponential jump-diffusion processes. The conditional memoryless property of the exponential distribution enables us to obtain an analytical form of the arbitrage-free price for American knock-out put options, which is usually more difficult for many other jump-diffusion models.