<p>A systematic approach to retrieve individual parts in a monaural music recording with its score is introduced. We are interested in isolating the accompaniment part by removing the solo part from a recording of concerto music in which a solo instrument is accompanied by an orchestra. We require the music audio, the score, and optionally a sample library of individual notes played in isolation. Our approach is based on explicit knowledge of the musical audio at the semantic level (notes or chords) from an audio-score alignment. Such knowledge allows the spectrogram energy to be decomposed into note-based models that could be trained with the sample library. Our approach can be divided into: (1) "masking" to estimate a solo mask to remove the solo and (2) "reconstruction" to impute the missing harmonics of the orchestra notes that have been inevitably damaged in masking. </p><p> In "masking," we estimate a 2-dimensional binary mask to classify each time-frequency cell of the short-time Fourier Transform (STFT) spectrogram as either solo or accompaniment in STFT domain. We mainly employ an Expectation Maximization (EM) algorithm to decompose spectrogram magnitude into note-based models. In this process of "erasing" the soloist&rsquo;s contribution to the mixture by applying the mask, the remaining orchestra is degraded. In "reconstruction," we propose a novel technique to repair such degradation. We use a state-space model for each note partial which is represented by a slowing-changing amplitude envelope and an "unwrapped" phase sequence. Such amplitude-phase representation can be computed by Kalman smoothing. It allows us to "transpose" intact partials of the orchestra part onto the degraded time-frequency region. Objective metrics and subjective listening are used on real and synthesized musical audio data for evaluation and parameter optimization. </p>

<p> The timely adoption of technology for organizations in making the right investment or divestment can be achieved by using multicriteria decision making approach with integrated views of established innovation theories, industry best practices in technology acquisition lifecycle, statistical analysis of available technology profiles, expert opinion and trend analysis. This research aimed to develop an analytical approach to assess the correlation among objective data (such as innovation maturity rating and market penetration) and subjective data (such as benefit rating and &ldquo;time to plateau&rdquo;) to provide organizations insights in technology adoption decisions. The objective of this study is not to study the Gartner&rsquo;s Hype Cycles but to utilize the longitudinal technology innovation profile data as factors for informed technology adoption decision. We combined mapping with Department of Defense Technology Readiness Level, statistical analysis, correlations, multiple regression analysis and trend analysis to provides an objective and quantifiable methodology to provide insight into the characteristics of innovations. The goal is to derive a logical and balanced approach for organizations&rsquo; decision-making base on objective (as in the technology maturity rating and market survey) and subjective (as in the expert opinion in benefit rating and time to plateau predictions) data analysis. We used Rogers&rsquo; concept of &ldquo;Diffusion of Innovation&rdquo; as a notional reference for Organizational Technology Adoption to conduct a statistical analysis of a selected set of 345 Gartner&rsquo;s technology profile data from 2009 to 2015. We used market penetration data as a proxy for technology acceptance. To ensure the fit for purpose, we compared Gartner&rsquo;s definition of technology maturity with that of the Department of Defense Technology Readiness Level (TRL). The trending data on market penetration, maturity rating, benefit rating and time to technology plateau determined that the 2^nd Order Polynomial Model provided the best statistical goodness of fit in all cases. We discuss the non-linear nature of the data and the for more predictive association of technological maturity with organizational adoption. Further empirical approaches with traditional analysis, machine learning or artificial intelligence would allow researchers to test, to explore and to better understand the diffusion of innovation first pioneered by Rogers, Moore and Bass.</p><p>

Verifica como as Instituições oficiais de informação estatística lidam com a disseminação numa nova mídia, observando de que maneira disponibilizam suas informações na Web, investigando o tratamento, a disponibilização e o acesso dado às informações nos sites estatísticos, estabelecendo relações entre a forma de estruturação dessas informações, a navegação dos sites e o uso das ferramentas da linguagem da Web para criar os contextos de entendimento da informação estatística. Observa em que medida as interfaces criadas nos sites estatísticos garantem a circulação da informação pelos diversos segmentos do público usuário, a partir do conceito de Espiral da Cultura Científica proposto por Vogt (2003) e tem como objetivo verificar, supondo a cultura para a ciência, como as informações veiculadas alcançam os atores envolvidos no processo de circulação da informação. Foram considerados os sites de instituições oficiais governamentais, nacionais e internacionais, responsáveis ou participantes de sistemas nacionais de estatísticas demográficas e socioeconômicas, dentre os quais, três foram selecionados: IBGE Instituto Brasileiro de Geografia e Estatística (Brasil), INE Instituto Nacional de Estatística (Portugal) e INEGI Instituto Nacional de Estadística, Geografia e Informática (México). Pela observação, pudemos perceber que a Web dispõe de recursos únicos para a difusão e divulgação do conhecimento científico, sendo instrumento de grande valia na sua disseminação. Exemplos interessantes foram encontrados nos sites observados, destancando-se os recursos de contextualização dos dados, o uso da linguagem e de ícones significativos e a associação das informações por meio de links. / It verifies how the official Institutions of statistics information deal with the dissemination in a new media, observing how they show the information on the WEB. The treatment, the dissemination form / way and the access to the information to statistical sites are analyzed to establish relations between the information structures form, the language form, the site navigation and the use of Web tools to create the contexts of agreement of the information. Remark how the new interfaces created on the statistical sites guarantee the information dissemination for the diverse segments of the public use, from the Vogts concept (2003) in Spiral of the Scientific Culture, and has as objective to verify, assuming the culture for science, how the propagated information reach the involved actors on the statistical information dissemination process The governmental official institutions Web sites, nationals or internationals, responsible or participant of national systems of demographic and social-economics statisticians had been considered which we select: the (IBGE) Brazilian Institute of Geography and Statistics site ( Brazil), the (INE) National Statistics Institute site (Portugal) and the (INEGI) National Institute of Statistics, Geography and Computer Science (Mexico). For the comment, we even could notice that Web makes use of only resources for the diffusion and spreading of the scientific knowledge, however much of the diffusion and the spreading mainly demands the comment of the language questions. Interesting examples had been found in the observed sites, detaching the resources of the data context, the use of the language and significant icons and the association of the information by links.

Verifica como as Instituições oficiais de informação estatística lidam com a disseminação numa nova mídia, observando de que maneira disponibilizam suas informações na Web, investigando o tratamento, a disponibilização e o acesso dado às informações nos sites estatísticos, estabelecendo relações entre a forma de estruturação dessas informações, a navegação dos sites e o uso das ferramentas da linguagem da Web para criar os contextos de entendimento da informação estatística. Observa em que medida as interfaces criadas nos sites estatísticos garantem a circulação da informação pelos diversos segmentos do público usuário, a partir do conceito de Espiral da Cultura Científica proposto por Vogt (2003) e tem como objetivo verificar, supondo a cultura para a ciência, como as informações veiculadas alcançam os atores envolvidos no processo de circulação da informação. Foram considerados os sites de instituições oficiais governamentais, nacionais e internacionais, responsáveis ou participantes de sistemas nacionais de estatísticas demográficas e socioeconômicas, dentre os quais, três foram selecionados: IBGE Instituto Brasileiro de Geografia e Estatística (Brasil), INE Instituto Nacional de Estatística (Portugal) e INEGI Instituto Nacional de Estadística, Geografia e Informática (México). Pela observação, pudemos perceber que a Web dispõe de recursos únicos para a difusão e divulgação do conhecimento científico, sendo instrumento de grande valia na sua disseminação. Exemplos interessantes foram encontrados nos sites observados, destancando-se os recursos de contextualização dos dados, o uso da linguagem e de ícones significativos e a associação das informações por meio de links. / It verifies how the official Institutions of statistics information deal with the dissemination in a new media, observing how they show the information on the WEB. The treatment, the dissemination form / way and the access to the information to statistical sites are analyzed to establish relations between the information structures form, the language form, the site navigation and the use of Web tools to create the contexts of agreement of the information. Remark how the new interfaces created on the statistical sites guarantee the information dissemination for the diverse segments of the public use, from the Vogts concept (2003) in Spiral of the Scientific Culture, and has as objective to verify, assuming the culture for science, how the propagated information reach the involved actors on the statistical information dissemination process The governmental official institutions Web sites, nationals or internationals, responsible or participant of national systems of demographic and social-economics statisticians had been considered which we select: the (IBGE) Brazilian Institute of Geography and Statistics site ( Brazil), the (INE) National Statistics Institute site (Portugal) and the (INEGI) National Institute of Statistics, Geography and Computer Science (Mexico). For the comment, we even could notice that Web makes use of only resources for the diffusion and spreading of the scientific knowledge, however much of the diffusion and the spreading mainly demands the comment of the language questions. Interesting examples had been found in the observed sites, detaching the resources of the data context, the use of the language and significant icons and the association of the information by links.

This thesis is divided into two parts dealing with the optimization problems in Markov decision processes (MDPs) and different neural network-based numerical solvers for partial differential equations (PDEs). In Part I we analyze the optimization problem arising in (partially observable) Markov decision processes using tools from algebraic statistics and information geometry, which can be viewed as neighboring fields of applied algebra and differential geometry, respectively. Here, we focus on infinite horizon problems and memoryless stochastic policies. Markov decision processes provide a mathematical framework for sequential decision-making on which most current reinforcement learning algorithms are built. They formalize the task of optimally controlling the state of a system through appropriate actions. For fully observable problems, the action can be selected knowing the current state of the system. This case has been studied extensively and optimizing the action selection is known to be equivalent to solving a linear program over the (generalized) stationary distributions of the Markov decision process, which are also referred to as state-action frequencies. In Chapter 3, we study partially observable problems where an action must be chosen based solely on an observation of the current state, which might not fully reveal the underlying state. We characterize the feasible state-action frequencies of partially observable Markov decision processes by polynomial inequalities. In particular, the optimization problem in partially observable MDPs is described as a polynomially constrained linear objective program that generalizes the (dual) linear programming formulation of fully observable problems. We use this to study the combinatorial and algebraic complexity of this optimization problem and to upper bound the number of critical points over the individual boundary components of the feasible set. Furthermore, we show that our polynomial programming formulation can be used to effectively solve partially observable MDPs using interior point methods, numerical algebraic techniques, and convex relaxations. Gradient-based methods, including variants of natural gradient methods, have gained tremendous attention in the theoretical reinforcement learning community, where they are commonly referred to as (natural) policy gradient methods. In Chapter 4, we provide a unified treatment of a variety of natural policy gradient methods for fully observable problems by studying their state-action frequencies from the standpoint of information geometry. For a variety of NPGs and reward functions, we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Morimura and co-authors and Kakade by observing that these arise from the Hessian geometries of the entropy and conditional entropy, respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. We provide experimental evidence indicating that our predicted rates are essentially tight. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the inverse penalization strength, which recovers existing results as special cases. Part II addresses neural network-based PDE solvers that have recently experienced tremendous growth in popularity and attention in the scientific machine learning community. We focus on two approaches that represent the approximation of a solution of a PDE as the minimization over the parameters of a neural network: the deep Ritz method and physically informed neural networks. In Chapter 5, we study the theoretical properties of the boundary penalty for these methods and obtain a uniform convergence result for the deep Ritz method for a large class of potentially nonlinear problems. For linear PDEs, we estimate the error of the deep Ritz method in terms of the optimization error, the approximation capabilities of the neural network, and the strength of the penalty. This reveals a trade-off in the choice of the penalization strength, where too little penalization allows large boundary values, and too strong penalization leads to a poor solution of the PDE inside the domain. For physics-informed networks, we show that when working with neural networks that have zero boundary values also the second derivatives of the solution are approximated whereas otherwise only lower-order derivatives are approximated. In Chapter 6, we propose energy natural gradient descent, a natural gradient method with respect to second-order information in the function space, as an optimization algorithm for physics-informed neural networks and the deep Ritz method. We show that this method, which can be interpreted as a generalized Gauss-Newton method, mimics Newton’s method in function space except for an orthogonal projection onto the tangent space of the model. We show that for a variety of PDEs, natural energy gradients converge rapidly and approximations to the solution of the PDE are several orders of magnitude more accurate than gradient descent, Adam and Newton’s methods, even when these methods are given more computational time.:Chapter 1. Introduction 1 1.1 Notation and conventions 7 Part I. Geometry of Markov decision processes 11 Chapter 2. Background on Markov decision processes 12 2.1 State-action frequencies 19 2.2 The advantage function and Bellman optimality 23 2.3 Rational structure of the reward and an explicit line theorem 26 2.4 Solution methods for Markov decision processes 35 Chapter 3. State-action geometry of partially observable MDPs 44 3.1 The state-action polytope of fully observables systems 45 3.2 State-action geometry of partially observable systems 54 3.3 Number and location of critical points 69 3.4 Reward optimization in state-action space (ROSA) 83 Chapter 4. Geometry and convergence of natural policy gradient methods 94 4.1 Natural gradients 96 4.2 Natural policy gradient methods 101 4.3 Convergence of natural policy gradient flows 107 4.4 Locally quadratic convergence for regularized problems 128 4.5 Discussion and outlook 131 Part II. Neural network-based PDE solvers 133 Chapter 5. Theoretical analysis of the boundary penalty method for neural network-based PDE solvers 134 5.1 Presentation and discussion of the main results 137 5.2 Preliminaries regarding Sobolev spaces and neural networks 146 5.3 Proofs regarding uniform convergence for the deep Ritz method 150 5.4 Proofs of error estimates for the deep Ritz method 156 5.5 Proofs of implications of exact boundary values in residual minimization 167 Chapter 6. Energy natural gradients for neural network-based PDE solvers 174 6.1 Energy natural gradients 176 6.2 Experiments 183 6.3 Conclusion and outlook 192 Bibliography 193

This thesis proposes a collection of analytical and computational methods for inferring an underlying social structure of a given population, observed only via timestamped occurrences of its members across a range of locations. It shows that such data streams have a modular and temporally-focused structure, neither fully ordered nor completely random, with individuals appearing in "gathering events". By exploiting such structure, the thesis proposes an appropriate mapping of those spatio-temporal data streams to a social network, based on the co-occurrences of agents across gathering events, while capturing the uncertainty over social ties via the use of probability distributions. Given the extracted graphs mentioned above, an approach is proposed for studying their community organisation. The method considers communities as explanatory variables for the observed interactions, producing overlapping partitions and node membership scores to groups. The aforementioned models are motivated by a large ongoing experiment at Wytham woods, Oxford, where a population of Parus major wild birds is tagged with RFID devices and a grid of feeding locations generates thousands of spatio-temporal records each year. The methods proposed are applied on such data set to demonstrate how they can be used to explore wild bird sociality, reveal its internal organisation across a variety of different scales and provide insights into important biological processes relating to mating pair formation.