Sensor networks are an evolving technology that promise numerous applications. The random and dynamic structure of sensor networks has motivated the suggestion of greedy data-routing algorithms. / In this thesis stochastic models are developed to study the advancement of messages under greedy routing in sensor networks. A model framework that is based on homogeneous spatial Poisson processes is formulated and examined to give a better understanding of the stochastic dependencies arising in the system. The effects of the model assumptions and the inherent dependencies are discussed and analyzed. A simple power-saving sleep scheme is included, and its effects on the local node density are addressed to reveal that it reduces one of the dependencies in the model. / Single hop expressions describing the advancement of messages are derived, and asymptotic expressions for the hop length moments are obtained. Expressions for the distribution of the multihop advancement of messages are derived. These expressions involve high-dimensional integrals, which are evaluated with quasi-Monte Carlo integration methods. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The subsequent results agree extremely well with those obtained via routing simulations. A renewal process model is proposed to model multihop advancements, and is justified under certain assumptions. / The model framework is extended by incorporating a spatially dependent density, which is inversely proportional to the sink distance. The aim of this extension is to demonstrate that an inhomogeneous Poisson process can be used to model a sensor network with spatially dependent node density. Elliptic integrals and asymptotic approximations are used to describe the random behaviour of hops. The final model extension entails including random transmission radii, the effects of which are discussed and analyzed. The thesis is concluded by giving future research tasks and directions.

This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken from application areas including finance, physical object tracking and audio restoration. The work in this thesis can be broadly divided into three themes: system and parameter estimation in linear jump-diffusion systems, non-parametric model (system) estimation and batch audio restoration. For linear jump-diffusion systems, efficient state estimation methods based on the variable rate particle filter are presented for the general linear case (chapter 3) and a new method of parameter estimation based on Particle MCMC methods is introduced and tested against an alternative method using reversible-jump MCMC (chapter 4). Non-parametric model estimation is examined in two settings: the estimation of non-parametric environment models in a SLAM-style problem, and the estimation of the network structure and forms of linkage between multiple objects. In the former case, a non-parametric Gaussian process prior model is used to learn a potential field model of the environment in which a target moves. Efficient solution methods based on Rao-Blackwellized particle filters are given (chapter 5). In the latter case, a new way of learning non-linear inter-object relationships in multi-object systems is developed, allowing complicated inter-object dynamics to be learnt and causality between objects to be inferred. Again based on Gaussian process prior assumptions, the method allows the identification of a wide range of relationships between objects with minimal assumptions and admits efficient solution, albeit in batch form at present (chapter 6). Finally, the thesis presents some new results in the restoration of audio signals, in particular the removal of impulse noise (pops and clicks) from audio recordings (chapter 7).

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When a new nodal core simulator is developed, like all other simulators, it must go through an extensive verification and validation effort where, in the first stage, it will be tested against appropriate reference tools in various theoretical benchmark problems. The series of tests consist of comparing several geometries, from the simplest to the most complex, by simulating them with the nodal core simulator developed and with some higher order solver representing the reference solution, in this case on the Serpent2 Monte Carlo transport code. The aim of this master’s thesis is to carry out one part of these tests. It consisted in simulating a three-dimensional (3D) 2x2 mini boiling water reactor (BWR) core with the latest version of the Westinghouse BWR nodal core simulator POLCA8, and in comparing the outcome of these simulations against Serpent2 reference results. Prior to this work, POLCA8 was successfully tested on a 3D single-channel benchmark problem using the same Serpent2/POLCA8 methodology. However, this benchmark problem considered in this work is challenging in several aspects. Indeed, the nodal core simulator should accurately predict the eigenvalues and power distribu- tions against reference results, and this by taking into account axial leakage, resulting from the passage from two-dimensional (2D) infinite lattice physics calculations to 3D simulations, or strong axial flux gradients due to the insertion or withdrawal of the control rods after a certain depletion. This last effect is known as the Control Blade History (CBH) effect and will be the main focus of this study. In addition to the development of a new version of the nodal core simulator, a new version of the Westinghouse deterministic transport code PHOENIX5 is also under development. The accuracy of PHOENIX5 was indirectly tested through this benchmark by providing the cross sections for the POLCA8 simulations. In addition, Serpent2 based nodal cross sections were generated to POLCA8 to provide means of comparing these two sets of nodal cross section data. The results obtained lead to the conclusion that the CBH model gives very good results, especially with regard to all power distributions, and especially those after the removal of the control bars when needed most.keywords: Nodal Core Analysis, Monte Carlo Methods, CBH Effects / När en ny nodal-kärnsimulator utvecklas, som alla andra simulatorer, måste den genomgå en omfattande verifierings och valideringsinsats där den i det första steget kommer att testas mot lämpliga referensverktyg i olika teoretiska riktmärkesproblem. Testserien består av att jämföra flera geometrier, från den enklaste till den mest komplexa, genom att simulera dem med den utvecklade nodkärnsimulatorn och med någon högre ord- ningslösning som representerar referenslösningen, i detta fall på Serpent2 Monte Carlo-transportkoden. Syftet med detta examensarbete är att genomföra en del av dessa tester. Den bestod av att simulera en tredimensionell (3D) 2x2 mini-kokande vattenreaktor (BWR) -kärna med den senaste versionen av Westinghouse BWR- nodalkärnasimulator POLCA8, och att jämföra resultatet av dessa simuleringar mot Serpent2-referensresultat. Före detta arbete testades POLCA8 framgångsrikt på ett 3D-enkanaligt riktmärkesproblem med samma Serpent2 / POLCA8-metodik. Detta riktmärkesproblem som beaktas i detta arbete är dock utmanande i flera aspekter. I själva verket bör nodkärnsimulatorn noggrant förutsäga egenvärdena och kraftfördelningarna mot referensre- sultat, och detta genom att ta hänsyn till axiellt läckage, resulterande från övergången från tvådimensionella (2D) oändliga gitterfysikberäkningar till 3D-simuleringar eller starkt axiellt flöde gradienter på grund av att styrstavarna sätts in eller dras ut efter en viss utarmning. Denna sista effekt är känd som CBH-effekten (Control Blade History) och kommer att vara huvudfokus för denna studie. Förutom utvecklingen av en ny version av nodal core-simulatorn är också en ny version av Westinghouse deterministiska transportkod PHOENIX5 under utveckling. PHOENIX5: s noggrannhet testades indirekt genom detta riktmärke genom att tillhandahålla tvärsnitt för POLCA8-simuleringar. Dessutom genererades Serpent2-baserade nodtvärsnitt till POLCA8 för att tillhandahålla medel för att jämföra dessa två uppsättningar av nodtvärsnittsdata. De erhållna resultaten leder till slutsatsen att CBH-modellen ger mycket bra resultat, särskilt med avseende på alla effektfördelningar, och särskilt de som har tagits bort när man behöver mest.

<p> In analyzing the processes involved in neutron radiography, there is a need for a well-defined mathematical structure which can simultaneously be used in practical situations without great difficulty. In this report, the edge-spread function method of analysis is considered in some detail. The basic theory is developed, and both the general and the specific viewpoint are considered, in terms of the mathematical functions used. The usefulness of ESF theory in predicting optical density patterns is illustrated. Specific applications of the theory are developed; in particular, studies of image resolution and unsharpness are undertaken. </p> <p> To determine whether or not ESF methods are a good representation of the physical situation, some alternate methods which consider radiography from a more basic viewpoint are developed. The first of these is a strictly numerical approach, where experimental data is examined without specifying a model for the image formation process; a matrix formulation suitable for characterizing an image is developed. </p> <p> The second alternate method involves the use of Monte Carlo methods; this allows the incorporation of more realistic parameters into the analysis. For example, screen-film separation and object scattering of neutrons, and their effects on the image, are evaluated. Finally, a two-dimensional analysis of a simple problem is considered, with the end result being a confirmation of the usefulness of ESF theory. </p> / Thesis / Master of Engineering (MEngr)

The spherical sampling of the incident radiance function entails a high computational cost. Therefore the llumination integral must be evaluated using a limited set of samples. Such a restriction raises the question of how to obtain the most accurate approximation possible with such a limited set of samples. In this thesis, we show that existing Monte Carlo-based approaches can be improved by fully exploiting the information available which is later used for careful samples placement and weighting.The first contribution of this thesis is a strategy for producing high quality Quasi-Monte Carlo (QMC) sampling patterns for spherical integration by resorting to spherical Fibonacci point sets. We show that these patterns, when applied to the rendering integral, are very simple to generate and consistently outperform existing approaches. Furthermore, we introduce theoretical aspects on QMC spherical integration that, to our knowledge, have never been used in the graphics community, such as spherical cap discrepancy and point set spherical energy. These metrics allow assessing the quality of a spherical points set for a QMC estimate of a spherical integral.In the next part of the thesis, we propose a new heoretical framework for computing the Bayesian Monte Carlo quadrature rule. Our contribution includes a novel method of quadrature computation based on spherical Gaussian functions that can be generalized to a broad class of BRDFs (any BRDF which can be approximated sum of one or more spherical Gaussian functions) and potentially to other rendering applications. We account for the BRDF sharpness by using a new computation method for the prior mean function. Lastly, we propose a fast hyperparameters evaluation method that avoids the learning step.Our last contribution is the application of BMC with an adaptive approach for evaluating the illumination integral. The idea is to compute a first BMC estimate (using a first sample set) and, if the quality criterion is not met, directly inject the result as prior knowledge on a new estimate (using another sample set). The new estimate refines the previous estimate using a new set of samples, and the process is repeated until a satisfying result is achieved.

Dans une première partie, on s'intéresse à un système d'EDP stochastiques variant selon deux échelles de temps, et plus particulièrement à l'approximation de la composante lente à l'aide d'un schéma numérique efficace. On commence par montrer un principe de moyennisation, à savoir la convergence de la composante lente du système vers la solution d'une équation dite moyennée. Ensuite on prouve qu'un schéma numérique de type Euler fournit une bonne approximation d'un coefficient inconnu apparaissant dans cette équation moyennée. Finalement, on construit et on analyse un schéma de discrétisation du système à partir des résultats précédents, selon la méthodologie dite HMM (Heterogeneous Multiscale Method). On met en évidence l'ordre de convergence par rapport au paramètre d'échelle temporelle et aux différents paramètres du schéma numérique- on étudie les convergences au sens fort (approximation des trajectoires) et au sens faible (approximation des lois). Dans une seconde partie, on étudie une méthode d'approximation de solutions d'EDP paraboliques, en combinant une approche semi-lagrangienne et une discrétisation de type Monte-Carlo. On montre d'abord dans un cas simplifié que la variance dépend des pas de discrétisation- enfin on fournit des simulations numériques de solutions, afin de mettre en avant les applications possibles d'une telle méthode. / In a first part, we are interested in the behavior of a system of Stochastic PDEs with two time-scales- more precisely, we focus on the approximation of the slow component thanks to an efficient numerical scheme. We first prove an averaging principle, which states that the slow component converges to the solution of the so-called averaged equation. We then show that a numerical scheme of Euler type provides a good approximation of an unknown coefficient appearing in the averaged equation. Finally, we build and we analyze a discretization scheme based on the previous results, according to the HMM methodology (Heterogeneous Multiscale Method). We precise the orders of convergence with respect to the time-scale parameter and to the parameters of the numerical discretization- we study the convergence in a strong sense - approximation of the trajectories - and in a weak sense - approximation of the laws. In a second part, we study a method for approximating solutions of parabolic PDEs, which combines a semi-lagrangian approach and a Monte-Carlo discretization. We first show in a simplified situation that the variance depends on the discretization steps. We then provide numerical simulations of solutions, in order to show some possible applications of such a method.

The Global Initiative for Chronic Obstructive Lung Disease (GOLD) guidelinesare used to guide clinical practices for treating Chronic Obstructive Pulmonary Disease (COPD). GOLD focuses heavily on stable COPD patients, limiting its use fornon-stable COPD patients such as those with severe, acute exacerbations of COPD (AECOPD) that require hospitalization. Although AECOPD can be heterogeneous, it can lead to deterioration of health and early death. Electronic health records (EHRs) can be used to analyze patient data for understanding disease progression and generating guideline evidence for AECOPD patients. However, because of its structure and representation, retrieving, analyzing, and properly interpreting EHR data can be challenging, and existing tools do not provide granular analytic capabil-ities for this data.<div><br></div><div>This dissertation presents, develops, and implements a novel approach that systematically captures the effect of interventions during patient medical encounters, and hence may support evidence generation for clinical guidelines in a systematic and principled way. A conceptual framework that structures components, such as data storage, aggregation, extraction, and visualization, to support EHR data analytics for granular analysis is introduced. We develop a software framework in Python based on these components to create longitudinal representations of raw medical data extracted from the Medical Information Mart for Intensive Care (MIMIC-III) clinical database. The software framework consists of two tools: Patient Aggregated Care Events (PACE), a novel tool for constructing and visualizing entire medical histories of both individual patients and patient cohorts, and Mark SIM, a Markov Chain Monte Carlo modeling and simulation tool for predicting clinical outcomes through probabilistic analysis that captures granular temporal aspects of aggregated, clinicaldata.<br></div><div><br></div><div>We assess the efficacy of antibiotic treatment and the optimal time of initiationfor in-hospitalized AECOPD patients as an application to probabilistic modeling. We identify 697 AECOPD patients of which 26.0% were administered antibiotics. Our model simulations show a 50% decrease in mortality rate as the number of patients administered antibiotics increase, and an estimated 5.5% mortality rate when antibiotics are initially administrated after 48 hours vs 1.8% when antibiotics are initially administrated between 24 and 48 hours. Our findings suggest that there may be amortality benefit in initiation of antibiotics early in patients with acute respiratory failure in ICU patients with severe AECOPD.<br></div><div><br></div><div>Thus, we show that it is feasible to enhance representation of EHRs to aggregate patients’ entire medical histories with temporal trends and support complex clinical questions to drive clinical guidelines for COPD.<br></div>

Estudamos as propriedades estruturais e eletrônicas da molécula emodina (EM), em diferentes condições, do ponto de vista experimental e teórico. Numa primeira parte, realizamos medidas do espectro eletrônico de absorção da EM, em meio solvente (água, clorofórmio e metanol). Nessa parte, obtivemos que o solvente provoca pouco efeito nos deslocamentos das bandas. Numa segunda parte, estudamos a EM, isoladamente e nos três solventes, através de cálculos quânticos com funcional de densidade (B3LYP), conjunto de função base de Pople (6-31G*) e modelo contínuo polariz ável (PCM). Como principais resultados obtivemos que a EM é rígida a menos da orientação relativa das 3 hidroxilas. A mudança orientacional nessas hidroxilas pode provocar formação de até 2 ligações de hidrogênio intramolecular (o que estabiliza sua geometria) e conseqüente uma diminuição no momento dipolo de 5.5 a 1.7D (o que desestabiliza sua interação com a água). Numa terceira parte, realizamos simulações com método Monte Carlo e Dinâmica Molecular em solução. Nessa parte, obtivemos que as ligações de hidrogênio intramoleculares são raramente quebradas devido as interações com o solvente e isso atribui a EM um caráter hidrofóbico. Adicionalmente, utilizando Teoria de Perturbação Termodinâmica nas simulações, calculamos a variação de energia livre de solvatação da EM em partição água/clorofórmio e água/- metanol e obtivemos -2.6 e -4.9 kcal/mol, respectivamente. Esse resultado está em boa concordância com o resultado experimental de -5.6 kcal/mol para partição de água/octanol. Por último, realizamos cálculos do espectro eletrônico de absorção da EM, isoladamente e nos três solventes, considerando as moléculas através do modelo, contínuo de solvente (SCRF) e explícito de solvente, com o método INDO/CIS. Nessa parte, obtivemos que o efeito do solvente é bem descrito teoricamente. / We study the structural and electronic properties of the emodin (EM) in different solvents of experimental and theoretical the point of view. We started performing measurements of the UV-Vis absorption spectrum of the EM in solution (water, chloroform and methanol). Our main result is that the solvent causes little effect on shifts the bands. In the second part of this work, we performing quantum calculations of isolated EM and in the three solutions using density functional (B3LYP), a set of Pople basis function (6-31G*) and the polarizable continuum model (PCM). In this part, our result is that EM presents a rigid conformation unless the orientation of its 3 hydroxyls. The change in these hydroxyls orientation can form up to 2 intramolecular H-bonds (which stabilizes its geometry) and causes a decrease in the dipole moment from 5.5 to 1.7D (which destabilizes its interaction with water). In the third part of this work, we performing Monte Carlo and Molecular Dynamics simulations in solution. Our main result is that the intramolecular H-bonds are rarely broken, even in aqueous solution, and these give to EM a hydrophobic character. Additionally, using Thermodynamics Perturbation Theory in the simulations, we calculate variations of free energy of solvation of EM in partition of water/chloroform and water/methanol and obtained -2.6 and -4.9kcal/mol, respectively. This last result is in good agreement with the experimental result[3] of -5.6kcal/mol for partition of water/octanol. Finally, we performing calculations of UV-Vis absorption spectrum of isolated EM and in the three solutions. In this calculations, we considering the molecules through the continuum solvent (SCRF) and explicit solvent model with the method INDO/CIS. In this part, we obtaining that effect of solvent is well described theoretically.

Quantum Monte Carlo (QMC) methods are a class of stochastic techniques that can be used to compute the properties of electronic systems accurately from first principles. This thesis is mainly concerned with the development of trial wave functions for QMC. An extension of the backflow transformation to inhomogeneous electronic systems is presented and applied to atoms, molecules and extended systems. The backflow transformation I have developed typically retrieves an additional 50% of the remaining correlation energy at the variational Monte Carlo level, and 30% at the diffusion Monte Carlo level; the number of parameters required to achieve a given fraction of the correlation energy does not appear to increase with system size. The expense incurred by the use of backflow transformations is investigated, and it is found to scale favourably with system size. Additionally, I propose a single wave function form for studying the electron-hole system which includes pairing effects and is capable of describing all of the relevant phases of this system. The effectiveness of this general wave function is demonstrated by applying it to a particular transition between two phases of the symmetric electron-hole bilayer, and it is found that using a single wave function form gives a more accurate physical description of the system than using a different wave function to describe each phase. Both of these developments are new, and they provide a powerful set of tools for designing accurate wave functions. Backflow transformations are particularly important for systems with repulsive interactions, while pairing wave functions are important for attractive interactions. It is possible to combine backflow and pairing to further increase the accuracy of the wave function. The wave function technology that I have developed should therefore be useful across a very wide range of problems.