Dans ce travail nous étudions les propriétés arithmétiques et statistiques d'une nouvelle classe de fonctions de comptage des chiffres appelées fonctions digitales restreintes. Nous présentons tout d'abord les principales propriétés des suites engendrées par une substitution ou un $q$-automate ainsi que la suite célèbre de Thue-Morse et ses généralisations, puis nous comparons ces notions avec celle de fonction digitale restreinte.Nous étudions ensuite les sommes d'exponentielles associées à ces fonctions digitales restreintes ainsi que leur application d'une part à l'étude de la répartition modulo 1 des fonctions digitales restreintes et d'autre part à l'étude des propriétés statistiques des suites arithmétiques définies par des fonctions digitales restreintes.Dans la dernière partie de ce travail on étudie la représentation géométrique de ces sommes d'exponentielle à la lumière des travaux antérieurs de Dekking et Mendès-France ce qui nous conduit à énoncer plusieurs problèmes ouverts. / In this work we study the arithmetic and statistic properties of a new class of digital counting functions called restricted digital functions. We first present the main properties of sequences generated by a substitution or a $q$-automate followed by presenting the famous Thue-Morse sequence and its generalizations, then we compare these notions with the one of the restricted digital function.We then study the exponential sums associated with these restricted digital function and their implementation on the one hand to the study of uniform distribution modulo 1 of these restricted digital functions and on the other, to the study of the statistical properties of the arithmetic sequences defined by restricted digital functions.In the last part of this work we study the geometric representation of these exponential sums in the light of previous works of Dekking and Mendès-France which leads us to announce several open problems.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2015-12-16T12:34:13Z No. of bitstreams: 1 andredinizdeoliveira.pdf: 3666386 bytes, checksum: 0179545867fe6173fdae7f0b67dff2d3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2015-12-16T15:15:19Z (GMT) No. of bitstreams: 1 andredinizdeoliveira.pdf: 3666386 bytes, checksum: 0179545867fe6173fdae7f0b67dff2d3 (MD5) / Made available in DSpace on 2015-12-16T15:15:19Z (GMT). No. of bitstreams: 1 andredinizdeoliveira.pdf: 3666386 bytes, checksum: 0179545867fe6173fdae7f0b67dff2d3 (MD5) Previous issue date: 2015-05-27 / Esta tese propõe dois métodos de estimação fasorial do componente fundamental. O pri-meiro estima o fasor na presença de componentes harmônicos, decaimento CC exponen-cial e ruído. O segundo estima o fasor na presença de componentes harmônicos, inter-harmônicos, inter-harmônicos variantes no tempo, decaimento CC exponencial e ruído. Todos os componentes de sinais utilizados são modelados e, para facilitar o entendimento dos métodos que serão propostos, os componentes são divididos em dois grupos: compo-nentes gerais e componentes extras. Alguns algoritmos de estimação existentes na litera-tura são estudados e dois são escolhidos para compor as proposições: DFT com suas va-riações e métodos de subespaços. O primeiro método sintetiza e implementa uma janela seguida da aplicação de uma DTFT para eliminar os componentes fundamental e harmô-nicos do sinal. O resultado é utilizado para estimar a influência do decaimento CC expo-nencial no componente fundamental. Esta influência é subtraída de uma estimação faso-rial via DFT para obter o componente fundamental correto. O segundo método utiliza esta mesma estrutura, entretanto insere um método de subespaço para calcular a frequência e constante de tempo dos componentes extras. Essa união cria um algoritmo distinto dos encontrados na literatura e nomeado de DTFT ESPRIT. A partir da possibilidade dos novos cálculos, o método consegue estimar o componente fundamental na presença de inter-harmônicos e inter-harmônicos variantes no tempo, além de harmônicos, decai-mento CC exponencial e ruído. / This thesis proposes two methods to estimate the phasor of the fundamental frequency component. The first one estimates the phasor in the presence of harmonic, decaying DC, and noise. The second one estimates the phasor in the presence of harmonics, inter-har-monics, time-varying inter-harmonics, decaying DC, and noise. All the signal compo-nents to be used are modeled and divided in two groups (general components and extra componentes) to better understand the proposed methods. The existing estimation algo-rithms in the literature are studied and described. Two algorithms are chosen as part of the new propositions: DFT and its variations and subspaces methods. The first method synthesizes and implements a DTFT window to eliminate the fundamental frequency and harmonic components of the signal. The result is used to estimate the influence of the decaying DC in the fundamental frequency component. This influence is subtracted from a phasor estimation via DFT in order to get the correct fundamental component. The second method has the same structure, however uses a subspace method for computing the frequency and time constant of the extra components. This combination creates a new algorithm named DTFT ESPRIT. From the new variable computing, the method is able to estimate the fundamental frequency component in the presence of different types of components as well as harmonics, decaying DC, and noise: inter-harmonics and time-varying inter-harmonics.

La ecuación de la difusión neutrónica describe la población de neutrones de un reactor nuclear. Este trabajo trata con este modelo para reactores nucleares con geometría hexagonal. En primer lugar se estudia la ecuación de la difusión neutrónica. Este es un problema diferencial de valores propios, llamado problema de los modos Lambda. Para resolver el problema de los modos Lambda se han comparado diferentes métodos en geometrías unidimensionales, resultando como el mejor el método de elementos espectrales. Usando este método discretizamos los operadores en geometrías bidimensiones y tridimensionales, resolviendo el problema algebraica de valores propios resultante con el método de Arnoldi. La distribución de neutrones estado estacionario se utiliza como condición inicial para la integración de la ecuación de la difusión neutrónica dependiente del tiempo. Se utiliza un método de Euler implícito para integrar en el tiempo. Cuando un nodo está parcialmente insertado aparece un comportamiento no físico de la solución, el efecto ``rod cusping'', que se corrige mediante la ponderación de las secciones eficaces con el flujo del paso de tiempo anterior. Cuando la solución de los sistemas algebraicos que surgen en el método hacia atrás, un método de Krylov se utiliza para resolver los sistemas resultantes, y diferentes estrategias de precondicionamiento se evalúan se. La primera consiste en el uso de la estructura de bloque obtenido por los grupos de energía para resolver el sistema por bloques, y diferentes técnicas de aceleración para el esquema iterativo de bloques y un precondicionador utilizando esta estructura de bloque se proponen. Además se estudia un precondicionador espectral, que hace uso de la información en un subespacio de Krylov para precondicionar el siguiente sistema. También se proponen métodos exponenciales de segundo y cuarto orden integrar la ecuación de difusión neutrónica dependiente del tiempo, donde la exponencial de la matriz del sistema tiene qu / González Pintor, S. (2012). Approximation of the Neutron Diffusion Equation on Hexagonal Geometries [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/17829 / Palancia

Dans les applications modernes des statistiques et de l'apprentissage, il est courant que les données récoltées présentent un certain nombre d'imperfections. En particulier, les données sont souvent hétérogènes, c'est-à-dires qu'elles contiennent à la fois des informations quantitatives et qualitatives, incomplètes, lorsque certaines informations sont inaccessibles ou corrompues, et multi-sources, c'est-à-dire qu'elles résultent de l'agrégation de plusieurs jeux de données indépendant. Dans cette thèse, nous développons plusieurs méthodes pour l'analyse de données hétérogènes, incomplètes et multi-source. Nous nous attachons à étudier tous les aspects de ces méthodes, en fournissant des études théoriques précises, ainsi que des implémentations disponibles au public, et des évaluations empiriques. En particulier, nous considérons en détail deux applications issues de l'écologie pour la première et de la médecine pour la seconde. / In modern applications of statistics and machine learning, one often encounters many data imperfections. In particular, data are often heterogeneous, i.e. combine quantitative and qualitative information, incomplete, with missing values caused by machine failure or nonresponse phenomenons, and multi-source, when the data result from the compounding of diverse sources. In this dissertation, we develop several methods for the analysis of multi-source, heterogeneous and incomplete data. We provide a complete framework, and study all the aspects of the different methods, with thorough theoretical studies, open source implementations, and empirical evaluations. We study in details two particular applications from ecology and medical sciences.

La présente thèse couvre deux principaux thèmes de recherche qui seront présentés dans deux parties et précédés par un prolegomenon commun. Dans ce dernier nous introduisons les concepts essentiels et nous exploitons aussi le lien entre les deux parties.<p><p>Dans la première partie, le principal objet d’intérêt est la soi-disant fonctionnelle exponentielle de processus de Lévy. La loi de cette variable aléatoire joue un rôle primordial dans de nombreux domaines divers tant sur le plan théorique que dans des domaines appliqués. Doney dérive une factorisation de la loi arc-sinus en termes de suprema de processus stables indépendants et de même index. Une factorisation similaire de la loi arc-sinus en termes de derniers temps de passage au niveau 1 de processus de Bessel peut aussi être établie en utilisant un résultat dû à Getoor. Des factorisations semblables d’une variable de Pareto en termes des mêmes objets peut également être obtenue. Le but de cette partie est de donner une preuve unifiée et une généralisation de ces factorisations qui semblent n’avoir aucun lien à première vue. Même s’il semble n’y avoir aucune connexion entre le supremum d’un processus stable et le dernier temps de passage d’un processus de Bessel, il peut être montré que ces variables aleatoires sont liées à des fonctionnelles exponentielles de processus de Lévy spécifiques. Notre contribution principale dans cette partie et aussi au niveau de caractérisations de la loi de la fonctionnelle exponentielle sont des factorisations de la loi arc-sinus et de variables de Pareto généralisées. Notre preuve s’appuie sur une factorisation de Wiener-Hopf récente de Patie et Savov.<p>Dans la deuxième partie, motivée par le fait que la dérivée fractionnaire de Caputo et d’autres opérateurs fractionnaires classiques coïncident avec le générateur de processus de Markov auto-similaires positifs particuliers, nous introduisons des opérateurs généralisés de Caputo et nous étudions certaines propriétés. Nous nous intéressons particulièrement aux conditions sous lesquelles ces opérateurs coïncident avec les générateurs infinitésimaux de processus de Markov auto-similaires positifs généraux. Dans ce cas, nous étudions les fonctions invariantes de ces opérateurs qui admettent une représentation en termes de séries entières. Nous précisons que cette classe de fonctions contient les fonctions de Bessel modifiées, les fonctions de Mittag-Leffler ainsi que plusieurs fonctions hypergéométriques. Nous proposons une étude unifiant et en profondeur de cette classe de fonctions. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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People use shortcuts to make decisions to efficiently deal with a large volume of information. Linear thinking is one shortcut and it contributes to exponential growth bias which means underestimation of exponential growth values. This study examined differences in exponential growth bias in the context of the stock market and COVID-19 cases. Moreover, this research analyzed correlation between exponential growth bias and worry for health and for the economy in the contexts of COVID-19 and stock market. A total of 120 participants completed an online survey in which they were randomly assigned to the COVID-19 or stock market group. A 2 x 3 repeated measures ANOVA showed no significant differences depending on the group. Moreover, ANOVA showed that bias increased in line with the increase in the percentages analyzed for both groups. Exploratory Pearson analysis showed that there was a significant negative correlation between worry for the economy and exponential growth bias of 15% and 40% growth scenarios in COVID-19 group. There were no significant correlations between worry for the economy or health in the stock market group. The conclusion is that people use shortcuts which leads them to biased decision- making. For example, when calculating exponential values, people think linearly and it leads them to exponential growth bias, what in practice results in estimating values lower than they are. Interventions, as education with aim to reduce exponential growth bias are proposed for the future research.

In this work, we focus on enhancing the efficacy of predictive modeling in operational management decision making in two different settings: Essay 1 focuses on demand forecasting for the companies and the second study utilizes longitudinal data to analyze the illicit drug seizure and overdose deaths in the United States. In Essay 1, we utilize an operational system (newsvendor model) to evaluate the forecast method outcome and provide guidelines for forecast method (the exponential smoothing model) performance assessment and judgmental adjustments. To assess the forecast outcome, we consider not only the common forecast error minimization approach but also the profit maximization at the end of the forecast horizon. Including profit in our assessment enables us to determine if error minimization always results in maximum profit. We also look at the different levels of profit margin to analyze their impact on the forecasting method performance. Our study also investigates how different demand patterns influence maximizing the forecasting method performance. Our study shows that the exponential smoothing model family has a better performance in high-profit products, and the rate of decrease in performance versus demand uncertainty is higher in a stationary demand environment.In the second essay, we focus on illicit drug overdose death rate. Illicit drug overdose deaths are the leading cause of injury death in the United States. In 2017, overdose death reached the highest ever recorded level (70,237), and statistics show that it is a growing problem. The age adjusted rate of drug overdose deaths in 2017 (21.7 per 100,000) is 9.6% higher than the rate in 2016 (19.8 per 100,000) (U. S. Drug Enforcement Administration, 2018, p. V). Also, Marijuana consumption among youth has increased since 2009. The magnitude of the illegal drug trade and its resulting problems have led the government to produce large and comprehensive datasets on a variety of phenomena relating to illicit drugs. In this study, we utilize these datasets to examine how marijuana usage among youth influence excessive drug usage. We measure excessive drug usage in terms of drug overdose death rate per state. Our study shows that illegal marijuana consumption increases excessive drug use. Also, we analyze the pattern of most frequently seized illicit drugs and compare it with drugs that are most frequently involved in a drug overdose death. We further our analysis to study seizure patterns across layers of heroin and cocaine supply chain across states. This analysis reveals that most active layers of the heroin supply chain in the American market are retailers and wholesalers, while multi-kilo traffickers are the most active players in the cocaine supply chain. In summary, the studies in this dissertation explore the use of analytical, descriptive, and predictive models to detect patterns to improve efficacy and initiate better operational management decision making.

[pt] O objetivo deste trabalho é inserir variáveis exógenas no modelo Holt-Winters com múltiplos ciclos, genuinamente univariado. Serão usados dados horários de demanda de energia elétrica provenientes de uma cidade da região sudeste do Brasil e dados de temperatura, tanto em sua forma primitiva quanto derivada, por exemplo, indicadores de dias quentes, o chamado cooling degree days (CDD). Com isso, pretende-se melhorar o poder preditivo do modelo, gerando previsões com maior acurácia. / [en] The aim of this thesis is to insert exogenous variables in the model Holt-Winters with multiple cycles, genuinely univariate. Hourly data will be used for electricity demand from a city in southeastern Brazil and temperature data, both in its original form as derived, for example, indicators of hot days, cooling degree days called (CDD). With this, we intend to improve the predictive power of the model, generating predictions with greater accuracy.

The thesis analyzes the network traffic on a router with open source firmware. First is chosen a software platform, based on compatibility with available equipment. Then are assessed properties necessary for the development of custom applications. Support for various programming languages provided by the SDK, development environment and the available modules and libraries, for working with network interface. Based on these factors is then chose method to realize the program. He is implemented on the OpenWRT firmware in C / C + + using network library pcap. These funds are used to capture and analyze network traffic. Obtained data are processed using methods of technical analysis, namely on the basis of moving averages, Stochastic oscillator and Bollinger bands. Based on results of these methods are generated and verified estimates of traffic. They are based on linear extrapolation, simplified for fixed intervals. The validity of each method is verified on base of the estimated value. Method is verified if estimated value of the traffic volume is in the Bollinger band, which is given by the standard deviation. Each method is tested several times in real traffic with different input parameters. Then is evaluated the influence of parameters on the error rate of methods. Individual methods are compared and evaluated based on the behavior in different scenarios and based on the average relative error.