Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can replace the state matrix in a state-space model with the sparse matrix of the shift encoder.

This work describes a framework for simultaneous estimation and modeling (SEAM) of dynamic systems using non-Gaussian belief fusion by first presenting the relevant fundamental formulations, then building upon these formulations incrementally towards a more general and ubiquitous framework. Multi-Gaussian belief fusion (MBF) is introduced as a natural and effective method of fusing non-Gaussian probability distribution functions (PDFs) in arbitrary dimensions efficiently and with no loss of accuracy. Construction of some multi-Gaussian structures for potential use in MBF is addressed. Furthermore, recursive Bayesian estimation (RBE) is developed for linearized systems with uncertainty in model parameters, and a rudimentary motion model correction stage is introduced. A subsequent improvement to motion model correction for arbitrarily non-Gaussian belief is developed, followed by application to observation models. Finally, SEAM is generalized to fully nonlinear and non-Gaussian systems. Several parametric studies were performed on simulated experiments in order to assess the various dependencies of the SEAM framework and validate its effectiveness in both estimation and modeling. The results of these studies show that SEAM is capable of improving estimation when uncertainty is present in motion and observation models as compared to existing methods. Furthermore, uncertainty in model parameters is consistently reduced as these parameters are updated throughout the estimation process. SEAM and its constituents have potential uses in robotics, target tracking and localization, state estimation, and more. / Doctor of Philosophy / The simultaneous estimation and modeling (SEAM) framework and its constituents described in this dissertation aim to improve estimation of signals where significant uncertainty would normally introduce error. Such signals could be electrical (e.g. voltages, currents, etc.), mechanical (e.g. accelerations, forces, etc.), or the like. Estimation is accomplished by addressing the problem probabilistically through information fusion. The proposed techniques not only improve state estimation, but also effectively "learn" about the system of interest in order to further refine estimation. Potential uses of such methods could be found in search-and-rescue robotics, robust control algorithms, and the like. The proposed framework is well-suited for any context where traditional estimation methods have difficulty handling heightened uncertainty.

The power requirements imposed on an active vibration isolation system are quite important to the overall system design. In order to improve the efficiency of an active isolation system we analyze different feedback control strategies which will provide electrical energy regeneration. The active isolation system is modeled in a state-space form for two different types of actuators: a piezoelectric stack actuator and a linear electromagnetic (EM) actuator. During regenerative operation, the power is flowing from the mechanical disturbance through the electromechanical actuator and its switching drive into the electrical storage device (batteries or capacitors). We demonstrate that regeneration occurs when controlling one or both of the flow states (velocity and/or current). This regenerative control strategy affects the closed loop dynamics of the isolator which sees its damping reduced. / Master of Science

Distributed generation for consumer applications is a relatively new field and it is difficult to satisfy both cost and performance targets. High expectations coupled with extreme cost cutting to compete with traditional technologies make converter design difficult. As power electronics mature more opportunities arise for entry into this lucrative area. An excellent understanding of converter dynamics is crucial in producing a well performing and cost competitive system. The six-switch single-phase inverter proposed in this thesis is a prime candidate for use in single households and small businesses. Its compact size and compatibility with existing electrical standards make its integration easy. However, little work is available on characterizing the system from a controls point of view. In particular balancing the two outputs with an uneven load is a concern. This thesis uses nodal and loop analysis to formulate a mathematical model of the six-switch single-phase inverter. A non-linear time invariant model is constructed for circuit simulation; details found in real circuits are added. A hardware-in-the-loop (HIL) configuration is used for more accurate simulation. In fact, its use makes for an almost seamless transition between simulation and hardware experimentation. A detailed explanation of the HIL system developed is presented. The system is simulated under various load conditions. Uneven loads and lightly loaded conditions are thoroughly examined. Controllers are verified in simulation and then are tested on real hardware using the HIL system. DC bus disturbance rejection and non-linear loads are also investigated. Acceptable inverter performance is demonstrated without expensive current sensors or high sampling frequency. / Master of Science

State-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides new ecological insights. I extend the state-space framework to create multi-species models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures and models with many parameters to limited data; often the case in ecological studies. I have taken a Bayesian model fitting approach in this thesis. The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s capabilities. The harrier data are believed to be known without error, while missing data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including one species as a covariate in the other’s model. Finally, models are included for the harriers’ alternate prey. The single- and multi-species state-space models for the predator-prey interactions provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.

This thesis studies bubbles in the U.S. stock market and how they are influenced by monetary policy pursued by the FED. Using Kalman filtering, the log-real price of S&P 500 is decomposed into a market-fundamentals component and a bubble component. The market-fundamentals component depends on the expected future dividends and the required rate of return, while the bubble component is treated as an unobserved state vector in the state-space model. The results suggest that, mainly in recent decades, the bubble has accounted for a substantial portion of S&P 500 price dynamics and might have played a significant role during major bull and bear markets. The innovation of this thesis is that it goes one step further and investigates the effects of monetary policy on both estimated components of S&P 500. For this purpose, the block- restriction VAR model is employed. The findings indicate that the decreasing interest rates have a significant short-term positive effect on the market-fundamentals component but not on the bubble. On the other hand, quantitative easing seems to have a positive effect on the bubble but not on the market-fundamentals component. Finally, the results suggest that the FED has not been successful at distinguishing between stock price movements due to fundamentals or the price misalignment.

Regression testing of an evolving software system may involve significant challenges. While, there would be a requirement of maximising the probability of finding out if the latest changes to the system has broken some existing feature, it needs to be done as economically as possible. A particularly important class of software systems are API libraries. Such libraries would typically constitute a very important component of many software systems. High quality requirements make it imperative to continually optimise the internal implementation of such libraries without affecting the external interface. Therefore, it is preferred to guide the regression testing by some kind of formal specification of the library. The testing problem comprises of three parts: computation of test data, execution of test, and analysis of test results. Current research mostly focuses on the first part. The objective of test data computation is to maximise the probability of uncovering bugs, and to do it with as few test cases as possible. The problem of test data computation for regression testing is to select a subset of the original test suite running which would suffice to test for bugs probably inserted in the modifications done after the last round of testing. A variant of this problem is that of regression testing of API libraries. The regression testing of an API is usually done by making function calls in such a way that the sequence of function calls thus made suffices a test specification. The test specification in turn embodies some concept of completeness. In this thesis, we focus on the problem of test sequence computation for the regression testing of API libraries. At the heart of this method lies the creation of a state space model of the API library by reverse engineering it by executing the system, with guidance from an formal API specification. Once the state space graph is obtained, it is used to compute test sequences for satisfying some test specification. We analyse the theoretical complexity of the problem of test sequence computation and provide various heuristic algorithms for the same. State space explosion is a classical problem encountered whenever there is an attempt of creating a finite state model of a program. Our method also faces this limitation. We explore a simple and intuitive method of ameliorating this problem – by simply reducing the size of the state vector. We develop the theoretical insights into this method. Also, we present experimental results indicating the practical effectiveness of this method. Finally, we bring all this together into the design and implementation of a tool called Modest.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-23T11:16:42Z No. of bitstreams: 1 arquivototal.pdf: 1343904 bytes, checksum: dfca90c2164204a1513fc4a55eca4527 (MD5) / Made available in DSpace on 2016-03-23T11:16:43Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1343904 bytes, checksum: dfca90c2164204a1513fc4a55eca4527 (MD5) Previous issue date: 2015-05-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Our purpose is to study the geometry of Riemannian immersions in certain semi- Riemannian manifolds. Initially, considering linearWeingarten hypersurfaces immersed in locally symmetric manifolds and, imposing suitable constraints on the scalar curvature, we guarantee that such a hypersurface is either totally umbilical or isometric to a isoparametric hypersurface with two distinct principal curvatures, one of them being simple. In higher codimension, we use a Simons type formula to obtain new characterizations of hyperbolic cylinders through the study of submanifolds having parallel normalized mean curvature vector field in a semi-Riemannian space form. Finally, we investigate the rigidity of complete spacelike hypersurfaces immersed in the steady state space via applications of some maximum principles. / Nos propomos estudar a geometria de imersões Riemannianas em certas variedades semi-Riemannianas. Inicialmente, consideramos hipersuperfícies Weingarten lineares imersas em variedades localmente simétricas e, impondo restrições apropriadas à curvatura escalar, garantimos que uma tal hipersuperfície é totalmente umbílica ou isométrica a uma hipersuperfície isoparamétrica com duas curvaturas principais distintas, sendo uma destas simples. Em codimensão alta, usamos uma fórmula do tipo Simons para obter novas caracterizações de cilindros hiperbólicos a partir do estudo de subvariedades com vetor curvatura média normalizado paralelo em uma forma espacial semi-Riemanniana. Finalmente, investigamos a rigidez de hipersuperfícies tipo-espaço completas imersas no steady state space via aplicações de alguns princípios do máximo.

Made available in DSpace on 2015-03-03T15:22:32Z (GMT). No. of bitstreams: 1 FranciscoMCM.pdf: 1391370 bytes, checksum: 2bdc2511202e3397ea85e69a321f5847 (MD5) Previous issue date: 2010-02-10 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process / Neste trabalho estudamos os modelos de Markov ocultos tanto em espa?o de estados finito quanto em espa?o de estados geral. No caso discreto, estudamos os algoritmos para frente e para tr?s para determinar a probabilidade da sequ?ncia observada e, em seguida, estimamos os par?metros do modelo via algoritmo EM. No caso geral, estudamos os estimadores do tipo n?cleo e os utilizamos para conseguir uma sequ?ncia de estimadores que converge na norma L1 para a fun??o densidade do processo observado

<p>Transcriptional regulation has been studied intensively in recent decades. One important aspect of this regulation is the interaction between regulatory proteins, such as transcription factors (TF) and nucleosomes, and the genome. Different high-throughput techniques have been invented to map these interactions genome-wide, including ChIP-based methods (ChIP-chip, ChIP-seq, etc.), nuclease digestion methods (DNase-seq, MNase-seq, etc.), and others. However, a single experimental technique often only provides partial and noisy information about the whole picture of protein-DNA interactions. Therefore, the overarching goal of this dissertation is to provide computational developments for jointly modeling different experimental datasets to achieve a holistic inference on the protein-DNA interaction landscape. </p><p>We first present a computational framework that can incorporate the protein binding information in MNase-seq data into a thermodynamic model of protein-DNA interaction. We use a correlation-based objective function to model the MNase-seq data and a Markov chain Monte Carlo method to maximize the function. Our results show that the inferred protein-DNA interaction landscape is concordant with the MNase-seq data and provides a mechanistic explanation for the experimentally collected MNase-seq fragments. Our framework is flexible and can easily incorporate other data sources. To demonstrate this flexibility, we use prior distributions to integrate experimentally measured protein concentrations. </p><p>We also study the ability of DNase-seq data to position nucleosomes. Traditionally, DNase-seq has only been widely used to identify DNase hypersensitive sites, which tend to be open chromatin regulatory regions devoid of nucleosomes. We reveal for the first time that DNase-seq datasets also contain substantial information about nucleosome translational positioning, and that existing DNase-seq data can be used to infer nucleosome positions with high accuracy. We develop a Bayes-factor-based nucleosome scoring method to position nucleosomes using DNase-seq data. Our approach utilizes several effective strategies to extract nucleosome positioning signals from the noisy DNase-seq data, including jointly modeling data points across the nucleosome body and explicitly modeling the quadratic and oscillatory DNase I digestion pattern on nucleosomes. We show that our DNase-seq-based nucleosome map is highly consistent with previous high-resolution maps. We also show that the oscillatory DNase I digestion pattern is useful in revealing the nucleosome rotational context around TF binding sites. </p><p>Finally, we present a state-space model (SSM) for jointly modeling different kinds of genomic data to provide an accurate view of the protein-DNA interaction landscape. We also provide an efficient expectation-maximization algorithm to learn model parameters from data. We first show in simulation studies that the SSM can effectively recover underlying true protein binding configurations. We then apply the SSM to model real genomic data (both DNase-seq and MNase-seq data). Through incrementally increasing the types of genomic data in the SSM, we show that different data types can contribute complementary information for the inference of protein binding landscape and that the most accurate inference comes from modeling all available datasets. </p><p>This dissertation provides a foundation for future research by taking a step toward the genome-wide inference of protein-DNA interaction landscape through data integration.</p> / Dissertation