The music of Alejandro Viñao is driven primarily by rhythm rather than traditional classical music components such as melody, harmony, and formal structures. As such, this focus on rhythm showcases the innovation of multiple time, defined as the musical simulation of various meters and tempi. Pioneered by Conlon Nancarrow, this rhythmic innovation is identified within Water (2013). The purpose of this dissertation is to provide insight and analysis of the specific musical characteristics of Viñao’s compositional style. These characteristics include the use of rhythmic grooves, attractors, echo effect, tenuto markings, Euclidean rhythms, and water imagery. Once this analysis has been completed, this dissertation then highlights the necessary practicalities of performance by discussing aspects such as conducting, rehearsal preparation, setup configuration, mallet considerations, and the technical aspects of performing bongos and congas.

When forecasting time series variables, it is usual to use only the information provided by past observations to foresee potential future developments. However, if available, additional information should be taken into account to get the forecast. For example, let us consider a case where the Government announces an economic target for next year. Since the Government has the empowerment to implement the economic or social policies to approach the target, an analyst that does not consider this information to get the forecast and makes use only of the historical record of the variables, will not anticipate the change on the economic system. In fact, if predictions based on historical data would be invalid when a policy change affects the economy, the economic agents are forward rather than backward-looking and adapt their expectations and behavior to the new policy stance. Thus, given some targets for the variables under study it is important to know the simultaneous future path that will lead to achieving those targets. Here it is considered the case in which a system of variables are to be forecasted with the aid of a VAR model with a cointegration relationship. The paths projected forward into the future as a combination of the model-based forecasts and the additional information provides what is known as a restricted forecast.This work is an attempt to contribute to the literature on Restricted Forecasting Theory for Multiple Time Series within the VAR framework. Specifically, Chapter 2 decomposes the JCT into single tests by a variance-covariance matrix associated with the restrictions and derives the formulas of a feasible JCT that accounts for estimated parameters. Chapter 3 develops, by Lagrangian optimization, the restricted forecasts of the multiple time series process with structural change, as well as its mean squared error. In addition, the univariate time series types of changes are considered here in a multivariate setting. Finally, Chapter 4 derives a methodology for forecasting multivariate time series that satisfy a contemporaneous binding constraint for which there exists a future target. A Monte Carlo study of a VEC model with one unit root shows that, for a forecast horizon large enough, the forecasts obtained with the proposed methodology are more efficient. A more detailed account of these contributions is provided below.

In this dissertation, the robust stability of uncertain continuous and discrete singularly perturbed systems with multiple time delays is investigated. Firstly, the asymptotic stability for a class of linear continuous singularly perturbed systems with multiple time delays is investigated. A simple estimate of an upper bound of singular perturbation parameter is proposed such that the original system is asymptotically stable for any . Moreover, a delay-dependent criterion, but -independent, is proposed to guarantee the asymptotic stability of the original system. Secondly, we consider the robust stability problem of uncertain continuous singularly perturbed systems with multiple time delays. Two delay-dependent criteria are proposed to guarantee the robust stability of a class of uncertain continuous multiple time-delay singularly perturbed systems subject to unstructured perturbations. Thirdly, the robust D-stability of nominally stable discrete uncertain systems with multiple time delays is considered. Finally, the robust stability of nominally stable uncertain discrete singularly perturbed systems with multiple time delays subject to unstructured and structured perturbations is investigated. Some criteria, delay-dependent or delay-independent, will be proposed to guarantee the robust stability of the uncertain discrete multiple time-delay singularly perturbed systems. The improvements of our results over those in recent literature are also illustrated if the comparisons are possible. Some numerical examples will also be provided to illustrate our main results.

This dissertation addresses the control problem for the general class of control non-affine, non-standard singularly perturbed continuous-time systems. The problem of control for nonlinear multiple time scale systems is addressed here for the first time in a systematic manner. Toward this end, this dissertation develops the theory of feedback passivation for non-affine systems. This is done by generalizing the Kalman-Yakubovich-Popov lemma for non-affine systems. This generalization is used to identify conditions under which non-affine systems can be rendered passive. Asymptotic stabilization for non-affine systems is guaranteed by using these conditions along with well-known passivity-based control methods. Unlike previous non-affine control approaches, the constructive static compensation technique derived here does not make any assumptions regarding the control influence on the nonlinear dynamical model. Along with these control laws, this dissertation presents novel hierarchical control design procedures to address the two major difficulties in control of multiple time scale systems: lack of an explicit small parameter that models the time scale separation and the complexity of constructing the slow manifold. These research issues are addressed by using insights from geometric singular perturbation theory and control laws are designed without making any assumptions regarding the construction of the slow manifold. The control schemes synthesized accomplish asymptotic slow state tracking for multiple time scale systems and simultaneous slow and fast state trajectory tracking for two time scale systems. The control laws are independent of the scalar perturbation parameter and an upper bound for it is determined such that closed-loop system stability is guaranteed. Performance of these methods is validated in simulation for several problems from science and engineering including the continuously stirred tank reactor, magnetic levitation, six degrees-of-freedom F-18/A Hornet model, non-minimum phase helicopter and conventional take-off and landing aircraft models. Results show that the proposed technique applies both to standard and non-standard forms of singularly perturbed systems and provides asymptotic tracking irrespective of the reference trajectory. This dissertation also shows that some benchmark non-minimum phase aerospace control problems can be posed as slow state tracking for multiple time scale systems and techniques developed here provide an alternate method for exact output tracking.

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We consider the problem of capacity expansion in telecommunication networks under uncertain economic conditions with various market structures. We assume that the demands for network capacity have constant price-elasticity, and demand functions are parameterized by an economic condition that is modeled by a discrete time Markov process. We apply dynamic programming to obtain a state-dependent capacity expansion strategy that maximizes expected total discounted cash flow. We incorporate partial reversibility of investment by differentiating the purchasing cost and the salvage value of the capacity. This partial reversibility makes the value function non-differentiable and divides the solution space into BUY, KEEP, and SELL regions. By identifying certain structural properties of the optimal solution, we perform sensitivity analyses on the optimal investment decisions with respect to market parameters. Under the condition that the level of cost depreciation is larger than that of the downside movement of the economic condition in each time period, we are able to obtain an analytical expression for the optimal capacity level and reduce the multi-period investment decision problem into a single-period myopic problem. As a result, optimal capacity increment depends only on the current economic condition. We study this problem under both monopolistic and oligopolistic market structures. In particular, we investigate investment decisions by two firms in a duopoly setting with Cournot competition. We prove the existence and the uniqueness of the Cournot equilibrium strategies in the duopolistic capacity investment problem. In addition, we show how competition between firms affects total available capacity in the market, capacity price, consumer surplus, expected time to a certain level of price reduction, and expected time to the first investment. We perform an empirical analysis to test a theoretical prediction obtained from our model through linear regression utilizing historical market data. By examining several alternative indices as a proxy to the economic condition considered in our model, we show that the Civilian Employment is the best proxy to use in validating the linear relationship between telecommunications capacity expansion and the economic indicator.

abstract: The technology expansion seen in the last decade for genomics research has permitted the generation of large-scale data sources pertaining to molecular biological assays, genomics, proteomics, transcriptomics and other modern omics catalogs. New methods to analyze, integrate and visualize these data types are essential to unveil relevant disease mechanisms. Towards these objectives, this research focuses on data integration within two scenarios: (1) transcriptomic, proteomic and functional information and (2) real-time sensor-based measurements motivated by single-cell technology. To assess relationships between protein abundance, transcriptomic and functional data, a nonlinear model was explored at static and temporal levels. The successful integration of these heterogeneous data sources through the stochastic gradient boosted tree approach and its improved predictability are some highlights of this work. Through the development of an innovative validation subroutine based on a permutation approach and the use of external information (i.e., operons), lack of a priori knowledge for undetected proteins was overcome. The integrative methodologies allowed for the identification of undetected proteins for Desulfovibrio vulgaris and Shewanella oneidensis for further biological exploration in laboratories towards finding functional relationships. In an effort to better understand diseases such as cancer at different developmental stages, the Microscale Life Science Center headquartered at the Arizona State University is pursuing single-cell studies by developing novel technologies. This research arranged and applied a statistical framework that tackled the following challenges: random noise, heterogeneous dynamic systems with multiple states, and understanding cell behavior within and across different Barrett's esophageal epithelial cell lines using oxygen consumption curves. These curves were characterized with good empirical fit using nonlinear models with simple structures which allowed extraction of a large number of features. Application of a supervised classification model to these features and the integration of experimental factors allowed for identification of subtle patterns among different cell types visualized through multidimensional scaling. Motivated by the challenges of analyzing real-time measurements, we further explored a unique two-dimensional representation of multiple time series using a wavelet approach which showcased promising results towards less complex approximations. Also, the benefits of external information were explored to improve the image representation. / Dissertation/Thesis / Ph.D. Industrial Engineering 2011

L'intégration des sources d'énergies renouvelables sur le réseau électrique est complexe en raison de leur nature intermittente et décentralisée. Le micro-réseau est une approche prometteuse pour interconnecter des générateurs distribués (DGs) locaux, alimenter des charges locales et également échanger de l'énergie avec le réseau électrique de manière contrôlée. Ce mode de production/consommation locales permet d'éviter la transmission d'électricité sur de longues distances, et implique donc une plus grande efficacité. Ces travaux se concentrent sur l'analyse et le contrôle du micro-réseau continu afin que les DGs se répartissent l'alimentation des charges et qu'ils maintiennent également la tension du bus continu. À l'équilibre, les contraintesde la commande du statisme classique (droop control) pour un système comportant de multiples DGs sont analysés, et une méthode de compensation mixte est proposée pour améliorer simultanément le maintien en tension et le partage du courant de charge. En dynamique, le modèle global du système est construit en introduisant une inductance virtuelle dans le circuit équivalent du DG, puis plusieurs modèles d'ordre réduit sont examinés pour vérifier leur efficacité dans l'analyse de la stabilité du système. Un modèle multi-échelle d'ordre réduit (RMM) est proposé afin de conserver les contraintes temporelles ainsi que de réduire la complexité du système. Enfin, une méthode basée sur le contrôle de rejet de perturbation active (ADRC) est présentée afin de mettre en oeuvre le contrôle local de la tension des DG en prenant en compte l'échelle de temps. Cette méthode permet d'améliorer la dynamique du système de contrôle en ajustant la largeur de bande passante de la commande et de l'observateur. Les analyses et les méthodes de contrôle proposées sont vérifiées par des essais expérimentaux dans notre plateforme au laboratoire. / The direct integration of renewable energy resources to the utility grid is pretty tough due to their intermittent feature and dispersed nature. Microgrid is one promising approach to gather the local distributed generators (DGs), supply local loads as well as exchange power with the utility grid as a controllable unit. This local-generation-localconsumption mode is able to avoid the long distance power transmission, thus can benefit a higher efficiency. The control aim of DC microgrids is to make the multiple DGs share the load properly as well as maintain the DCbus voltage stable. In steady state, the constrains of the classic droop control in multiple DGs environment are analyzed, and a mixed compensation method using common current is proposed to improve the voltage and load sharing performance simultaneously. In dynamic state, the system comprehensive model is constructed by the introduction of virtual inductor in the equivalent circuit of the DG, then several reduced-order models are examined to check their effectiveness for the system stability analysis. A reduced-order multi-scale model (RMM) is proposedto keep major time scale information as well as reduce the system complexity. Finally, an active disturbance rejection control (ADRC) based control method is proposed to realize the time scale droop control. It can effectively adjust the dynamic of the local control by adjusting the bandwidth of the Linear Extend State Observer or/and the controller. The proposed analysis and control methods are verified by experimental tests in our laboratory platform.