Siegel détermina un domaine fondamental à l'aide de la réduction de Minkowski des formes quadratiques. Il donna tous les détails concernant ce domaine pour le genre 1. C'est la détermination du domaine fondamental de Minkowski présentée comme deuxième condition et la condition maximal height présentée comme troisième condition, qui empêchent la précision exacte de ce domaine pour le cas général. Les derniers résultats ont été obtenus par Gottschling pour le genre 2 en 1959. Elle est depuis restée inexplorée et mal comprise notamment les différents domaines de Minkowski. Afin d'identifier ce domaine fondamental pour le genre 3, nous présentons des résultats concernant sa troisième condition. Chaque fonction abélienne peut être écrite en termes de fonctions rationnelles des fonctions thêta et de leurs dérivées. Cela permet l'expression de la solution des systèmes intégrables en fonction des fonctions thêta. Ces solutions sont pertinentes dans la description de surfaces de vagues d'eau, de l'optique non linéaire. Deconinck et Van Hoeij ont éveloppé et mis en oeuvre des algorithmes pour construire la matrice de Riemann et Deconinck et al. ont développé le calcul des fonctions thêta correspondantes. Deconinck et al. ont utilisé l'algorithme de Siegel pour atteindre approximativement le domaine fondamental de Siegel et ont adopté l'algorithme LLL pour trouver le vecteur le plus court. Alors que nous utilisons ici un nouvel algorithme de réduction de Minkowski jusqu'à dimension 5 et une détermination exacte du vecteur le plus court pour des dimensions supérieures. / Siegel determined a fundamental domain using the Minkowski reduction of quadratic forms. He gave all the details concerning this domain for genus 1. It is the determination of the Minkowski fundamental domain presented as the second condition and the maximal height condition, presented as the third condition, which prevents the exact determination of this domain for the general case. The latest results were obtained by Gottschling for the genus 2 in 1959. It has since remained unexplored and poorly understood, in particular the different regions of Minkowski reduction. In order to identify Siegel's fundamental domain for genus 3, we present some results concerning the third condition of this domain. Every abelian function can be written in terms of rational functions of theta functions and their derivatives. This allows the expression of solutions of integrable systems in terms of theta functions. Such solutions are relevant in the description of surface water waves, non linear optics. Because of these applications, Deconinck and Van Hoeij have developed and implemented al-gorithms for computing the Riemann matrix and Deconinck et al. have developed the computation of the corresponding theta functions. Deconinck et al. have used Siegel's algorithm to approximately reach the Siegel fundamental domain and have adopted the LLL reduction algorithm to nd the shortest lattice vector. However, we opt here to use a Minkowski algorithmup to dimension 5 and an exact determination of the shortest lattice vector for greater dimensions.

Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.

Submitted by Caroline Periotto (carol@ufscar.br) on 2016-09-21T14:53:55Z No. of bitstreams: 1 TeseJAF.pdf: 1812104 bytes, checksum: 817ececd9c05df0ddae3a91de3c8bb14 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-23T18:27:05Z (GMT) No. of bitstreams: 1 TeseJAF.pdf: 1812104 bytes, checksum: 817ececd9c05df0ddae3a91de3c8bb14 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-23T18:27:11Z (GMT) No. of bitstreams: 1 TeseJAF.pdf: 1812104 bytes, checksum: 817ececd9c05df0ddae3a91de3c8bb14 (MD5) / Made available in DSpace on 2016-09-23T18:27:17Z (GMT). No. of bitstreams: 1 TeseJAF.pdf: 1812104 bytes, checksum: 817ececd9c05df0ddae3a91de3c8bb14 (MD5) Previous issue date: 2016-05-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Accurate and robust forecasting methods for univariate time series are critical as the historical data can be used in the strategic planning of such future operations as buying and selling to ensure product inventory and meet market demands. In this context, several competitions for time series forecasting have been organized, with the M3-Competition as the largest. As the winner of M3-Competition, the Theta method has attracted attention from researchers for its predictive performance and simplicity. The Theta method is a combination of other methods, which proposes the decomposition of the deseasonalized time series into two other time series called "theta lines". The first completely removes the curvatures of the data, thus accurately estimating the long-term trend. The second doubles the curvatures to better approximate short-term behavior. Several issues have been raised about the Theta method, even by its originators. They include the number of theta lines, their parameters, weights to combine them, and construction of prediction intervals, among others. This doctorate thesis resolves part of these issues. We derive optimal weights for combine the theta lines, this result is used to derive statistical models which generalizes /approximate the standard Theta method. The statistical methodology is considering for parameter estimation and for compute the prediction intervals. The optimal weights are also used to propose new methods that hold two or more theta lines. Part of proposed methodology is implemented in a package for R-programming language. In an empirical investigation using the M3-Competition data set with more than 3000 time series, the proposed methods/models demonstrated significant accuracy. The study’s primary approach, the Dynamic Optimised Theta Model, outperformed all benchmarks methods, constituting, in all likelihood, the highest-performing method for this data set available in the literature. / Métodos precisos e robustos para prever séries temporais são muito importantes em diversas áreas. Uma vez que os dados históricos são utilizados para o planejamento estratégico de operações futuras, como compra ou venda de determinados produtos para controle de estoque e demanda. Neste contexto, várias competições para métodos de previsão de séries temporais univariadas foram realizadas, sendo a Competição M3 a maior. Ao vencer a Competição M3, o método Theta intrigou pesquisadores por sua capacidade preditiva e simplicidade. O método Theta é uma combinação de outros métodos, o qual propõe decompor a série temporal (desazonalizada) em outras duas séries temporais chamadas de "linhas thetas". A primeira linha theta remove completamente a curvatura dos dados, sendo assim um estimador para a tendência a longo prazo. A segunda linha theta dobra a curvatura da série sendo assim um estimador para a componente de curto prazo. Várias questões relacionadas ao método Theta foram levantadas, algumas pelos próprios autores, como parâmetros ideais para as linhas thetas, pesos para combinar as linhas thetas, construção de intervalos de predição, número ideal de linhas thetas, entre outras. Nesta tese algumas dessas questões são solucionadas. Pesos ótimos para a combinação de linhas thetas são derivados, esses resultados são utilizados para a construção de modelos estatísticos que generalizam/aproximam o método Theta padrão. A metodologia estatística é empregada para estimação dos parâmetros e construção de intervalos de predição. Os pesos ótimos também são utilizados para propor métodos que consideram duas ou mais linhas thetas. Parte da metodologia proposta é implementada em um pacote para a linguagem de programação R. Em um estudo empírico com mais de 3000 séries temporais do conjunto de dados da competição M3, os métodos/modelos propostos mostraram-se acurados. A nossa principal abordagem, o modelo DOTM ("Dynamic Optimised Theta Model") superou todos os concorrentes, sendo possivelmente o método com o melhor desempenho nesse conjunto de dados já disponibilizado na literatura.

No description available.

Master of Science / Department of Computing and Information Sciences / David A. Gustafson / The calculation of reliability based on running test cases refers to the probability of the software not generating faulty output consequent to the testing process. The metric used to measure this reliability is referred in terms of E(Θ) value. The concept of E(Θ) gives precise formulae to calculate the probability of failure of software after testing, debug or operational. This report aims at extending the functionalities of E(Θ) into the realm of multiple faults spread across multiple sub-domains. This generalization involves introduction of a new set of formulae for E(Θ) calculation which can account for faults spread over both single as well as multiple sub-domains in a code. The validity of the formulae is verified by matching the obtained theoretical results against the empirical data generated from running a test case simulator. The report further examines the possibility of an upper bound calculation on the derived formulae and its possible ramifications.

Introduction: The present study aims to understand how the absence of food security and breastfeeding in children at one year of age, which can be considered as adverse childhood experiences, may be associated with brain function as measured by the relative and absolute power spectral density of four frequency bands of brain waves (theta, alpha, beta, and gamma) among a sample of infants from low-socioeconomic (SES) backgrounds at age 12 months old. Methods: A cross-sectional survey was used by the parent study, Baby’s First Years (BFY), to collect quantitative data to understand the associations between breastfeeding, food insecurity, and brain function in a sample of 243 low-SES mothers and their infants at age 12 months old. Breastfeeding was measured as ever breastfed, to understand if a mother had ever initiated breastfeeding of their infant, and breastfeeding duration, measured in months. Household food insecurity (HFI) was measured using the U.S. Household Food Security Survey Module Short Form devised by the USDA. Electroencephalography (EEG) data was collected to assess brain function. Data Analysis: Data was analyzed to determine associations between being ever breastfed, breastfeeding duration, and the presence of HFI and EEG measured relative and absolute theta, alpha, beta, and gamma power in infants at 12 months of age using multiple linear regression (MLR) models based on ordinary least squares (OLS). Results: 77% (n=187) of mothers reported breastfeeding their child at least one time. The mean breastfeeding duration (including the mothers that never breastfed) was 3.6 months (SD=4.12). 27.6% (n=67) of mothers were found to be food insecure. Ever breastfeeding an infant during the first year of life was found to be associated with higher absolute theta power (p<0.05), and higher relative and absolute alpha power (p<0.01). Breastfeeding duration was not found to be associated with relative and absolute theta, alpha, beta or gamma power. Finally, the presence of food insecurity was not found to be associated with relative and absolute theta, alpha, beta or gamma power. Discussion: Differences in brain function may be adaptive for children experiencing adversity because of their lower SES, amongst other factors (Ellis et al., 2020). Ever breastfeeding an infant was associated with higher absolute theta power, which was an unexpected finding. However, relative theta power was not associated with ever breastfeeding, and therefore this finding must cautiously be interpreted. Ever breastfeeding an infant was associated with higher relative and absolute alpha power. It is possible that the increases in relative and absolute alpha power within the sample of infants who were ever breastfed are in part due to the emotional connection that breastfeeding elicits and the characteristics of mothers that decide to initiate breastfeeding as compared to those that do not initiate breastfeeding. This research demonstrates significant associations between ever breastfeeding an infant with brain function in a population of infants from diverse, low SES backgrounds. In contextualizing these changes in brain function as plausible adaptations that infants are developing due to their experiences, an opportunity exists to further explore these associations with brain function to understand the skills that low SES infants are developing during the first year of life.

No description available.

The prevalence of obesity, which is considered as a disease, has been increasing uncontrollably over the last two decades. Obesity is a state of disregulated energy homeostasis characterized by hypothalamic resistance to adiposity signals (insulin and leptin). While many factors are involved in the development of obesity, excess dietary fat has been proposed as one of the main causal factors. This causes disrupted energy homeostasis by inducing both leptin and insulin resistance in the central nervous system. Although brain tissue was considered to be insulin independent for a long time, insulin is now recognized to have important functions in the brain in the regulation of feeding behavior, energy expenditure and peripheral metabolism to maintain energy homeostasis. Recently, our lab discovered that insulin has an anorectic effect when it is applied into the central nucleus of the amygdala (CeA), a response that is similar to its effect when it is intracerebroventricularly (icv) administered into the hypothalamus. Our lab also demonstrated that rats fed a high fat diet lost the anorectic response to CeA insulin and became insulin resistant. These data suggested that insulin signaling in the amygdala had an important role in controlling food intake and energy expenditure in similar ways to the hypothalamus. It also suggests that a high fat diet inhibits amygdala insulin signaling in the CeA. Both in vitro cell culture and in vivo animal studies have been used to investigate the effects of dietary fats on insulin signaling in neuronal cells and in the amygdala. Using both hypothalamic GT1-7 cells and primary amygdala cells in culture, the saturated fatty acid palmitic acid was shown to inhibit insulin signaling (Akt phosphorylation). This response appears to be related to the activation of PKC-θ since the inhibitory effect of palmitic acid on Akt phosphorylation was greater in GT1-7 cells transfected with PKC-θ compared to wild type cells and was abolished in GT1-7 cells transfected with PKC-θ siRNA. Further investigations in vivo confirmed that insulin stimulated Akt and mTOR signaling in the CeA of rats and that the insulin stimulation of Akt phosphorylation, but not mTOR phosphorylation, was inhibited in rats fed a high fat diet for 3 days or by infusing palmitic acid into the CeA for 3 days. These experiments also identified that fatty acid and insulin signaling in the CeA differentially affected Akt and mTOR signaling in the hypothalamus and suggest that these neural connections might be important components of the neural pathways through which insulin in the amygdala affects food intake and peripheral metabolism. This research has provided novel insight into the effects of dietary fats on insulin signaling in an area of the brain, the CeA, that is now recognized to have effects on energy balance and peripheral metabolism.

Thesis advisor: Solomon Friedberg / We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic representations and make a conjecture that gives an upper bound of the first non-zero occurrence of the liftings, depending only on the unipotent orbit. We prove both global and local results that support the conjecture. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Indiana University-Purdue University Indianapolis (IUPUI) / Early life trauma is a risk factor for a number of neuropsychiatric disorders, including schizophrenia (SZ) and depression. Animal models have played a critical role in understanding how early-life trauma may evoke changes in behavior and biomarkers of altered brain function that resemble these neuropsychiatric disorders. However, since SZ is a complex condition with multifactorial etiology, it is difficult to model the breadth of this condition in a single animal model. Considering this, it is necessary to develop rodent models with clearly defined subsets of pathologies observed in the human condition and their developmental trajectory. Episodic memory is among the cognitive deficits observed in SZ. Theta (6-10 Hz), low gamma (30-50 Hz), and high gamma (50-100 Hz) frequencies in the hippocampus (HC) are critical for encoding and retrieval of memory. Also, theta-gamma comodulation, defined as correlated fluctuations in power between these frequencies, may provide a mechanism for coding episodic sequences by coordinating neuronal activity at timescales required for memory encoding and retrieval. Given that patients with SZ have impaired recognition memory, the overall objectives of these experiments were to assess local field potential (LFP) recordings in the theta and gamma range from the dorsal HC during a recognition memory task in an animal model that exhibits a subclass of symptoms that resemble SZ. In Aim 1, LFPs were recorded from the HC to assess theta and gamma power to determine whether rats that were maternally deprived (MD) for 24-hrs on postnatal day (PND 9), had altered theta and high/low gamma power compared to sham rats during novel object recognition (NOR). Brain activity was recorded while animals underwent NOR on PND 70, 74, and 78. In Aim 2, the effects of theta-low gamma comodulation and theta-high gamma comodulation in the HC were assessed during NOR between sham and MD animals. Furthermore, measures of maternal care were taken to assess if high or low licking/grooming behaviors influenced recognition memory. It was hypothesized that MD animals would have impaired recognition memory and lower theta and low/high gamma power during interaction with both objects compared to sham animals. Furthermore, it was hypothesized that sham animals would have higher theta-gamma comodulation during novel object exploration compared to the familiar object, which would be higher than the MD group. Measures of weight, locomotor activity, and thigmotaxis were also assessed. MD animals were impaired on the NOR task and had no change in theta or low/high gamma power or theta-gamma comodulation when interacting with the novel or familiar object during trials where they performed unsuccessfully or successfully. However, higher theta and gamma power and theta-gamma comodulation was observed in sham animals depending on the object they were exploring or whether it was a successful or unsuccessful trial. These data indicate altered functioning of the HC following MD and a dissociation between brain activity and behavior in this group, providing support that early life trauma can induce cognitive and physiological impairments that are long-lasting. In conclusion, these data identify a model of early life stress with a translational potential, given that there are points of contact between human studies and the MD model. Furthermore, these data provide a set of tools that could be used to further explore how these altered neural mechanisms may influence cognition and behavior.