There has been an enormous growth in the generation of time series data in the past decade. This trend is caused by widespread adoption of IoT technologies, the data generated by monitoring of cloud computing resources, and cyber physical systems. Although time series data have been a topic of discussion in the domain of data management for several decades, this recent growth has brought the topic to the forefront. Many of the time series management systems available today lack the necessary features to successfully manage and process the sheer amount of time series being generated today. In this today we stive to examine the field and study the prior work in time series management. We then propose a large system capable of handling time series management end to end, from generation to consumption by the end user. Our system is composed of open-source data processing frameworks. Our system has the capability to collect time series data, perform stream processing over it, store it for immediate and future processing and create necessary visualizations. We present the implementation of the system and perform experimentations to show its scalability to handle growing pipelines of incoming data from various sources.

En el presente trabajo de investigación se analiza y explora la presencia de los diferentes estereotipos y arquetipos con los que los guionistas, en su mayoría, trabajan y lo representan en los diferentes personajes hombres y mujeres de nivel principal y/o secundario de los diferentes programas de la televisión peruana, ya sea de ficción o de programas de entretenimiento. Es así que, mediante la pregunta y objetivos delimitados se podrá analizar si existe alguna estereotipación en los diferentes programas audiovisuales que se encuentran en la parrilla nacional. / This paper analyzes and explores the presence of the different stereotypes and archetypes with which the writers, for the most part, work and represent it in the different main and / or secondary level male and female characters of the different programs. of Peruvian television, either fiction or entertainment programs. Thus, by means of the question and delimited objectives, it will be possible to analyze if there is any stereotyping in the different audiovisual programs that are on the national grid. / Trabajo de investigación

The purpose of this paper was to determine the economic, sociopolitical, and other related factors which account for the variation in state expenditures across time. Utah was selected as the test state and data were collected from school records, political rosters, employment statistics, and a variety of federal government documents. Particular emphasis was placed on three areas: the cause-effect relationships between variables, relating the model to a body of economic theory, and demonstrating how the model may be applied in forecasting state expenditure needs. Supply-and-demand analysis was the underlying economic theory. A simultaneous-equation model consisting of four equations--demand for state expenditures, supply of state expenditures, federal grants to states, and an equilibrium condition--was constructed and tested . The paper also discusses the problems of serial correlation and mulli-collinearity.

We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's Eigenvalue Conjecture to the study of the nonvanishing of the Eisenstein Series $E(z,s)$ for Hecke congruence subgroups $Gamma_0(N)$ at $s=frac {1+i}{2}$.

In this thesis, the main objective is to study the presence of Gibbs phenomenon and the Gibbs constant in Fourier-Legendre series. The occurrence of The Gibbs phenomenon is a well known consequence when approximating functions with Fourier series that have points of discontinuity. Consequently, the initial focus was to examine Fourier seriesand the occurrence of Gibbs phenomenon in this context. Next, we delve into Legendrepolynomials, showing their applicability to be expressed as a Fourier series due to theirorthogonality in [−1, 1]. We then continue to explore Gibbs phenomenon for Fourier-Legendre series. The findings proceeds to confirm the existence of the Gibbs phenomenon for Fourier-Legendre series, but most notebly, the values of the error seem to convergeto the same number as for Fourier series which is the Gibbs constant.

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Time-series forecasting has long been studied and remains an important research task. In scenarios where multiple time series need to be forecast, approaches that exploit the mutual impact between time series results in more accurate forecasts. This has been demonstrated in various applications, including demand forecasting and traffic forecasting, among others. Hence, this dissertation focuses on graph-based models, which leverage the internode relations to forecast more efficiently and effectively by associating time series with nodes. This dissertation begins by introducing the notion of graph time-series models in a comprehensive survey of related models. The main contributions of this survey are: (1) A novel categorization is proposed to thoroughly analyze over 20 representative graph time-series models from various perspectives, including temporal components, propagation procedures, and graph construction methods, among others. (2) Similarities and differences among models are discussed to provide a fundamental understanding of decisive factors in graph time-series models. Model challenges and future directions are also discussed. Following the survey, this dissertation develops graph time-series models that utilize complex time-series interactions to yield context-aware, real-time, and probabilistic forecasting. The first method, Context Integrated Graph Neural Network (CIGNN), targets resource forecasting with contextual data. Previous solutions either neglect contextual data or only leverage static features, which fail to exploit contextual information. Its main contributions include: (1) Integrating multiple contextual graphs; and (2) Introducing and incorporating temporal, spatial, relational, and contextual dependencies; The second method, Evolving Super Graph Neural Network (ESGNN), targets large-scale time-series datasets through training on super graphs. Most graph time-series models let each node associate with a time series, potentially resulting in a high time cost. Its main contributions include: (1) Generating multiple super graphs to reflect node dynamics at different periods; and (2) Proposing an efficient super graph construction method based on K-Means and LSH; The third method, Probabilistic Hypergraph Recurrent Neural Network (PHRNN), targets datasets under the assumption that nodes interact in a simultaneous broadcasting manner. Previous hypergraph approaches leverage a static weight hypergraph, which fails to capture the interaction dynamics among nodes. Its main contributions include: (1) Learning a probabilistic hypergraph structure from the time series; and (2) Proposing the use of a KNN hypergraph for hypergraph initialization and regularization. The last method, Graph Deep Factors (GraphDF), aims at efficient and effective probabilistic forecasting. Previous probabilistic approaches neglect the interrelations between time series. Its main contributions include: (1) Proposing a framework that consists of a relational global component and a relational local component; (2) Conducting analysis in terms of accuracy, efficiency, scalability, and simulation with opportunistic scheduling. (3) Designing an algorithm for incremental online learning. / Doctor of Philosophy / Time-series forecasting has long been studied due to its usefulness in numerous applications, including demand forecasting, traffic forecasting, and workload forecasting, among others. In scenarios where multiple time series need to be forecast, approaches that exploit the mutual impact between time series results in more accurate forecasts. Hence, this dissertation focuses on a specific area of deep learning: graph time-series models. These models associate time series with a graph structure for more efficient and effective forecasting. This dissertation introduces the notion of graph time series through a comprehensive survey and analyzes representative graph time-series models to help readers gain a fundamental understanding of graph time series. Following the survey, this dissertation develops graph time-series models that utilize complex time-series interactions to yield context-aware, real-time, and probabilistic forecasting. The first method, Context Integrated Graph Neural Network (CIGNN), incorporates multiple contextual graph time series for resource time-series forecasting. The second method, Evolving Super Graph Neural Network (ESGNN), constructs dynamic super graphs for large-scale time-series forecasting. The third method, Probabilistic Hypergraph Recurrent Neural Network (PHRNN), designs a probabilistic hypergraph model that learns the interactions between nodes as distributions in a hypergraph structure. The last method, Graph Deep Factors (GraphDF), targets probabilistic time-series forecasting with a relational global component and a relational local model. These methods collectively covers various data characteristics and model structures, including graphs, super graph, and hypergraphs; a single graph, dual graphs, and multiple graphs; point forecasting and probabilistic forecasting; offline learning and online learning; and both small and large-scale datasets. This dissertation also highlights the similarities and differences between these methods. In the end, future directions in the area of graph time series are also provided.

The effects of variations in composition on the decomposition process in Al-Zn-Mg-Cu alloys (i.e. – 7xxx-series aluminum alloy) were studied emphasizing their effect on mechanical properties. Several experimental quaternary alloys were studied to compare their behavior with commercial 7xxx-series alloys. The investigation included studies on the effects of natural aging, artificial aging, quench sensitivity, precipitate free zone formation, and homogenization. Additionally, “true aging” curves (i.e. – hardness/strength vs. conductivity) were presented in order to visualize and quantify the entire precipitation process. It is obvious that fluctuations in the main alloying elements/processing parameters can alter the precipitation process, but the purpose of this work was to quantify those changes using standard industrial techniques. It was found that natural aging was detrimental for strength in the T6 temper for alloys containing more than 1.0 wt.% Cu, and was shown to alter the coarsening kinetics in the over-aged condition (T7). Conversely, for alloys with Cu contents less than 0.5% natural aging was shown to be beneficial for strength. Altering the Zn:Mg ratio was also shown to effect natural aging response of an alloy in addition to introducing additional precipitation processes (T-phase). Therefore, this work is a blueprint for advanced alloy manufacturing that allows for the rapid production of new alloys and tempers by narrowing the research focus depending on an alloy’s composition.

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy