La protection des ressources naturelles marines est un enjeu fort pour les décideurs publics. Le développement récent des aires marines protégées (AMP) contribue à ces enjeux de préservation. Les AMP ont pour objectifs de conserver les écosystèmes marins et côtiers tout en favorisant les activités humaines. La complexité de ces objectifs les rend difficiles à atteindre. L’objectif de cette thèse est de mener une analyse ex ante d’un projet d’une AMP aux îles Kuriat (Tunisie). Cette analyse représente une aide aux décideurs pour une meilleure gouvernance en intégrant les acteurs impliqués (pêcheur, visiteur, plaisancier) dans le processus de gestion. Pour ce faire, nous appliquons la méthode d’évaluation contingente (MEC) à des échantillons des pêcheurs et des visiteurs aux îles Kuriat. Nous nous intéressons au traitement des biais de sélection et d’échantillonnage et à l’incertitude sur la spécification des modèles économétriques lors de la mise en œuvre de la MEC. Nous faisons appel au modèle HeckitBMA,qui est une combinaison du modèle de Heckman (1979) et de l’inférence bayésienne, pour calculer le consentement à recevoir des pêcheurs. Nous utilisons aussi le modèle Zero inflated ordered probit (ZIOP), qui est une combinaison d’un probit binaire avec un probit ordonné, pour calculer le consentement à payer des visiteurs après avoir corrigé l’échantillon par imputation multiple. Nos résultats montrent que les groupes d’acteurs se distinguent par leur activité et leur situation économique ce qui les amène à avoir des perceptions différentes. Cela permet aux décideurs d’élaborer une politique de compensation permettant d’indemniser les acteurs ayant subi un préjudice. / The protection of marine natural resources is a major challenge for policy makers. The recent development of marine protected areas (MPAs) contributes to the preservation issues. MPAs are aimed to preserve the marine and coastal ecosystems while promoting human activities. The complexity of these objectives makes them difficult to reach. The purpose of this work is to conduct an ex-ante analysis of a proposed MPA to Kuriat Islands (Tunisia). This analysis is an aid to decision makers for better governance by integrating the actors involved (fisherman, visitor, boater) in the management process. To do this, we use the contingent valuation method (CVM) to samples of fishermen and visitors to the islands Kuriat. We are interested in the treatment of selection and sampling bias and uncertainty about specifying econometric models during the implementation of the CVM. We use the model HeckitBMA, which is a combination of the Heckman model (1979) and Bayesian inference, to calculate the willingness to accept of fishermen. We also use the model Zero inflated ordered probit (ZIOP), which is a combination of a binary probit with an ordered probit, to calculate the willingness to pay of visitors after correcting the sample by multiple imputation. Our results show that groups of actors are distinguished by their activity and economic conditions that cause them to have different perceptions. This allows policy makers to develop a policy of compensation to compensate the players who have been harmed.

Cryo-electron microscopy (cryo-EM) has been established as the leading imaging technique for structural studies from small proteins to whole cells at a molecular level. The great advances in cryo-EM have led to the ability to provide unique insights into a wide variety of biological processes in a close to native, hydrated state at near-atomic resolutions. The developments of computational approaches have significantly contributed to the exciting achievements of cryo-EM. This dissertation emphasizes new approaches to address image processing problems in cryo-EM, including tilt series alignment evaluation, simultaneous determination of sample thickness, tilt, and electron mean free path based on Beer-Lambert law, Model-Based Iterative Reconstruction (MBIR) on tomographic data, minimization of objective lens astigmatism in instrument alignment and defocus and magnification dependent astigmatism of TEM images. The final goal of these methodological developments is to improve the 3D reconstruction of cryo-EM and visualize more detailed characterization.

Les travaux de cette thèse s'inscrivent dans le domaine des équations aux dérivées partielles et sont liés à la problématique des changements d'échelle dans le contexte de la cinétique des gaz. En effet, sachant qu'il existe plusieurs niveaux de description pour un gaz, on cherche à relier les différentes échelles associées dans un cadre où une part d'aléa intervient. Dans une première partie, on établit la dérivation rigoureuse de l'équation de Boltzmann linéaire sans cut-off en partant d'un système de particules interagissant via un potentiel à portée infinie en partant d'un équilibre perturbé.La deuxième partie traite du passage d'un modèle BGK stochastique avec champ fort à une loi de conservation scalaire avec forçage stochastique. D'abord, on établit l'existence d'une solution au modèle BGK considéré. Sous une hypothèse additionnelle, on prouve alors la convergence vers une formulation cinétique associée à la loi de conservation avec forçage stochastique.Au cours de la troisième partie, on quantifie dans le cas à vitesses discrètes le défaut de régularité dans les lemmes de moyenne et on établit un lemme de moyenne stochastique dans ce même cas. On applique alors le résultat au cadre de l'approximation de Rosseland pour établir la limite diffusive associée à ce modèle.Enfin, on s'intéresse à l'étude numérique du modèle de Uchiyama de particules carrées à quatre vitesses en dimension deux. Après avoir adapté les méthodes de simulation développées dans le cas des sphères dures, on effectue une étude statistique des limites à différentes échelles de ce modèle. On rejette alors l'hypothèse d'un mouvement Brownien fractionnaire comme limite diffusive / The work of this thesis belongs to the field of partial differential equations and is linked to the problematic of scale changes in the context of kinetic of gas. Indeed, knowing that there exists different scales of description for a gas, we want to link these different associated scales in a context where some randomness acts, in initial data and/or distributed on all the time interval. In a first part, we establish the rigorous derivation of the linear Boltzmann equation without cut-off starting from a particle system interacting via a potential of infinite range starting from a perturbed equilibrium. The second part deals with the passage from a stochastic BGK model with high-field scaling to a scalar conservation law with stochastic forcing. First, we establish the existence of a solution to the considered BGK model. Under an additional assumption, we prove then the convergence to a kinetic formulation associated to the conservation law with stochastic forcing. In the third part, first we quantify in the case of discrete velocities the defect of regularity in the averaging lemmas. Then, we establish a stochastic averaging lemma in that same case. We apply then the result to the context of Rosseland approximation to establish the diffusive limit associated to this model.Finally, we are interested into the numerical study of Uchiyama's model of square particles with four velocities in dimension two. After adapting the methods of simulation which were developed in the case of hard spheres, we carry out a statistical study of the limits at different scales of this model. We reject the hypothesis of a fractional Brownian motion as diffusive limit

This thesis addresses the problem where we want to apply machine learning over a small data set of multivariate time series. A challenge when classifying data is when the data set is small and overfitting is at risk. Augmentation of small data sets might avoid overfitting. The multivariate time series used in this project represent motion data of people with reconstructed ACLs and a control group. The approach was pairing motion data from the training set and using Euclidean Barycentric Averaging to create a new set of synthetic motion data so as to increase the size of the training set. The classifiers used were Dynamic Time Warping -One Nearest neighbour and Time Series Forest. In our example we found this way of increasing the training set a less productive strategy. We also found Time Series Forest to generally perform with higher accuracy on the chosen data sets, but there may be more effective augmentation strategies to avoid overfitting.

MSc (Statistics) / Department of Statistics / Wind offers an environmentally sustainable energy resource that has seen increasing global adoption in recent years. However, its intermittent, unstable and stochastic nature hampers its representation among other renewable energy sources. This work addresses the forecasting of wind speed, a primary input needed for wind energy generation, using data obtained from the South African Wind Atlas Project. Forecasting is carried out on a two days ahead time horizon. We investigate the predictive performance of artificial neural networks (ANN) trained with Bayesian regularisation, decision trees based stochastic gradient boosting (SGB) and generalised additive models (GAMs). The results of the comparative analysis suggest that ANN displays superior predictive performance based on root mean square error (RMSE). In contrast, SGB shows outperformance in terms of mean average error (MAE) and the related mean average percentage error (MAPE). A further comparison of two forecast combination methods involving the linear and additive quantile regression averaging show the latter forecast combination method as yielding lower prediction accuracy. The additive quantile regression averaging based prediction intervals also show outperformance in terms of validity, reliability, quality and accuracy. Interval combination methods show the median method as better than its pure average counterpart. Point forecasts combination and interval forecasting methods are found to improve forecast performance. / NRF

La séparation aveugle de sources audio dans le cas sous-déterminé est un problème mathématique complexe dont il est aujourd'hui possible d'obtenir une solution satisfaisante, à condition de sélectionner la méthode la plus adaptée au problème posé et de savoir paramétrer celle-ci soigneusement. Afin d'automatiser cette étape de sélection déterminante, nous proposons dans cette thèse de recourir au principe de fusion. L'idée est simple : il s'agit, pour un problème donné, de sélectionner plusieurs méthodes de résolution plutôt qu'une seule et de les combiner afin d'en améliorer la solution. Pour cela, nous introduisons un cadre général de fusion qui consiste à formuler l'estimée d'une source comme la combinaison de plusieurs estimées de cette même source données par différents algorithmes de séparation, chaque estimée étant pondérée par un coefficient de fusion. Ces coefficients peuvent notamment être appris sur un ensemble d'apprentissage représentatif du problème posé par minimisation d'une fonction de coût liée à l'objectif de séparation. Pour aller plus loin, nous proposons également deux approches permettant d'adapter les coefficients de fusion au signal à séparer. La première formule la fusion dans un cadre bayésien, à la manière du moyennage bayésien de modèles. La deuxième exploite les réseaux de neurones profonds afin de déterminer des coefficients de fusion variant en temps. Toutes ces approches ont été évaluées sur deux corpus distincts : l'un dédié au rehaussement de la parole, l'autre dédié à l'extraction de voix chantée. Quelle que soit l'approche considérée, nos résultats montrent l'intérêt systématique de la fusion par rapport à la simple sélection, la fusion adaptative par réseau de neurones se révélant être la plus performante. / Underdetermined blind source separation is a complex mathematical problem that can be satisfyingly resolved for some practical applications, providing that the right separation method has been selected and carefully tuned. In order to automate this selection process, we propose in this thesis to resort to the principle of fusion which has been widely used in the related field of classification yet is still marginally exploited in source separation. Fusion consists in combining several methods to solve a given problem instead of selecting a unique one. To do so, we introduce a general fusion framework in which a source estimate is expressed as a linear combination of estimates of this same source given by different separation algorithms, each source estimate being weighted by a fusion coefficient. For a given task, fusion coefficients can then be learned on a representative training dataset by minimizing a cost function related to the separation objective. To go further, we also propose two ways to adapt the fusion coefficients to the mixture to be separated. The first one expresses the fusion of several non-negative matrix factorization (NMF) models in a Bayesian fashion similar to Bayesian model averaging. The second one aims at learning time-varying fusion coefficients thanks to deep neural networks. All proposed methods have been evaluated on two distinct corpora. The first one is dedicated to speech enhancement while the other deals with singing voice extraction. Experimental results show that fusion always outperform simple selection in all considered cases, best results being obtained by adaptive time-varying fusion with neural networks.

Dynamische Systeme mit Gedächtnis spielen in verschiedensten Anwendungen und Forschungsgebieten eine wesentliche Rolle. Gedächtnis bedeutet dabei, dass das zukünftige Systemverhalten nicht nur durch den aktuellen Zustand festgelegt wird, sondern im Allgemeinen auch durch vergangenen Zustände. Ein prominenter Vertreter für dieses Verhalten ist die Hysterese. Aufgrund der unterschiedlichen Mechanismen, welche zum Auftreten von Hysterese führen können, haben sich eine Vielzahl an Modellen etabliert, um diese zu beschreiben und zu modellieren. Zwei häufig verwendete Modelle sind dabei das Random Field Ising-Model und das Preisach-Model. Beide Modelle unterscheiden sich grundlegend in der Art, wie es zu Hysterese kommt. Während beim Random Field Ising-Model Hysterese aufgrund der Wechselwirkung benachbarter Spins auftritt, benutzt das Preisach-Model hingegen eine Vielzahl an elementaren bistabilen Relais, um komplexes hysteretisches Verhalten abzubilden. Trotz dieser Unterschiedlichkeit zeigen beide Modelle ähnliche Eigenschaften wie return point memory und wipe-out. Wir wollen in dieser Arbeit das dynamische Verhalten eines einfachen harmonischen Oszillators untersuchen, welcher mithilfe eines Feedback-Loops an ein hysteretisches Spinsystem gekoppelt wird. Es soll das Verhalten dieses Hybrid-Systems, das sowohl aus kontinuierlichen als auch aus diskreten Variablen besteht, für verschieden große Spinsysteme untersucht werden. Wir konzentrieren uns dabei auf drei vereinfachte Spinkonfigurationen. Dies ermöglicht uns, unter Verwendung der Preisach-Theorie, den Limes eines unendlich großen Spinsystems analytisch zu beschreiben. Wir zeigen, dass sich das Verhalten von dynamischen Systemen gekoppelt an ein endliches Spinsystem im Allgemeinen von Systemen gekoppelt an ein unendliches Spinsystem unterscheidet. Im Zuge dessen werden wir eine Methode vorstellen, um Lyapunov Spektren für dynamische Systeme mit preisachartiger Hysterese und glatter Dichte zu bestimmen. Wir zeigen weiterhin, dass bestimmte relevante Größen wie fraktale Dimension und Magnetisierung im Allgemeinen kein selbstmittelndes Verhalten aufweisen. Diese Resultate können erhebliche Auswirkungen auf die Vergleichbarkeit und Interpretation von Theorie und Experiment bei dynamischen Systemen mit Hysterese haben. / Dynamical systems with memory play a huge role in technical applications as well as in different research fields. In general memory means, the systems' behavior is not only determined by its last state, but also by the history of previous states. One prominent example of such behavior is the hysteresis. Caused by the many reasons for hysteretic behavior, multiple models for hysteresis have been developed over the past hundred years. Two commonly used models are the Random Field Ising Model and the Preisach model. Both models differ in the way, how the memory is build into the system. Whereas, the Random Field Ising Model shows hysteresis because of the interaction between nearby spins, the complex hysteresis of the Preisach model is build by a superposition of elementary bi-stable relays. Besides these differences, both models show similar hysteric behavior like return point memory and wipe-out. In this work, we want to investigate the dynamical behavior of a simple harmonic oscillator coupled to Ising spins in a closed loop way, showing hysteresis. The system consists of discrete and continuous degrees of freedom, and therefore it has a hybrid character. Concentrating on three simplified spin interactions, on one hand we investigate the dynamical properties of the system for a varying finite number of spins and on the other hand we use the Preisach model to calculate the limit of an infinite number of spins. We find, that dynamical systems coupled to a finite and infinite number of spins, respectively, in general behave differently. Thereby, we develop a method to determine the whole Lyapunov spectrum for systems with Preisach like hysteresis and a smooth density. Furthermore, we show that some dynamical properties like the fractal dimension and the magnetization in general do not show self-averaging. These findings could have a huge impact on the comparability and interpretation of theoretical and experimental results in the context of dynamical systems with hysteresis.

Structure learning of Bayesian Networks (BNs) is an NP-hard problem, and the use of sub-optimal strategies is essential in domains involving many variables. One of them is to generate multiple approximate structures and then to reduce the ensemble to a representative structure. It is possible to use the occurrence frequency (on the structures ensemble) as the criteria for accepting a dominant directed edge between two nodes and thus obtaining the single structure. In this doctoral research, it was made an analogy with an adapted one-dimensional random-walk for analytically deducing an appropriate decision threshold to such occurrence frequency. The obtained closed-form expression has been validated across benchmark datasets applying the Matthews Correlation Coefficient as the performance metric. In the experiments using a recent medical dataset, the BN resulting from the analytical cutoff-frequency captured the expected associations among nodes and also achieved better prediction performance than the BNs learned with neighbours thresholds to the computed. In literature, the feature accounted along of the perturbed structures has been the edges and not the directed edges (arcs) as in this thesis. That modified strategy still was applied to an elderly dataset to identify potential relationships between variables of medical interest but using an increased threshold instead of the predict by the proposed formula - such prudence is due to the possible social implications of the finding. The motivation behind such an application is that in spite of the proportion of elderly individuals in the population has increased substantially in the last few decades, the risk factors that should be managed in advance to ensure a natural process of mental decline due to ageing remain unknown. In the learned structural model, it was graphically investigated the probabilistic dependence mechanism between two variables of medical interest: the suspected risk factor known as Metabolic Syndrome and the indicator of mental decline referred to as Cognitive Impairment. In this investigation, the concept known in the context of BNs as D-separation has been employed. Results of the carried out study revealed that the dependence between Metabolic Syndrome and Cognitive Variables indeed exists and depends on both Body Mass Index and age. / O aprendizado da estrutura de uma Rede Bayesiana (BN) é um problema NP-difícil, e o uso de estratégias sub-ótimas é essencial em domínios que envolvem muitas variáveis. Uma delas consiste em gerar várias estruturas aproximadas e depois reduzir o conjunto a uma estrutura representativa. É possível usar a frequência de ocorrência (no conjunto de estruturas) como critério para aceitar um arco dominante entre dois nós e assim obter essa estrutura única. Nesta pesquisa de doutorado, foi feita uma analogia com um passeio aleatório unidimensional adaptado para deduzir analiticamente um limiar de decisão apropriado para essa frequência de ocorrência. A expressão de forma fechada obtida foi validada usando bases de dados de referência e aplicando o Coeficiente de Correlação de Matthews como métrica de desempenho. Nos experimentos utilizando dados médicos recentes, a BN resultante da frequência de corte analítica capturou as associações esperadas entre os nós e também obteve melhor desempenho de predição do que as BNs aprendidas com limiares vizinhos ao calculado. Na literatura, a característica contabilizada ao longo das estruturas perturbadas tem sido as arestas e não as arestas direcionadas (arcos) como nesta tese. Essa estratégia modificada ainda foi aplicada a um conjunto de dados de idosos para identificar potenciais relações entre variáveis de interesse médico, mas usando um limiar aumentado em vez do previsto pela fórmula proposta - essa cautela deve-se às possíveis implicações sociais do achado. A motivação por trás dessa aplicação é que, apesar da proporção de idosos na população ter aumentado substancialmente nas últimas décadas, os fatores de risco que devem ser controlados com antecedência para garantir um processo natural de declínio mental devido ao envelhecimento permanecem desconhecidos. No modelo estrutural aprendido, investigou-se graficamente o mecanismo de dependência probabilística entre duas variáveis de interesse médico: o fator de risco suspeito conhecido como Síndrome Metabólica e o indicador de declínio mental denominado Comprometimento Cognitivo. Nessa investigação, empregou-se o conceito conhecido no contexto de BNs como D-separação. Esse estudo revelou que a dependência entre Síndrome Metabólica e Variáveis Cognitivas de fato existe e depende tanto do Índice de Massa Corporal quanto da idade.

Structure learning of Bayesian Networks (BNs) is an NP-hard problem, and the use of sub-optimal strategies is essential in domains involving many variables. One of them is to generate multiple approximate structures and then to reduce the ensemble to a representative structure. It is possible to use the occurrence frequency (on the structures ensemble) as the criteria for accepting a dominant directed edge between two nodes and thus obtaining the single structure. In this doctoral research, it was made an analogy with an adapted one-dimensional random-walk for analytically deducing an appropriate decision threshold to such occurrence frequency. The obtained closed-form expression has been validated across benchmark datasets applying the Matthews Correlation Coefficient as the performance metric. In the experiments using a recent medical dataset, the BN resulting from the analytical cutoff-frequency captured the expected associations among nodes and also achieved better prediction performance than the BNs learned with neighbours thresholds to the computed. In literature, the feature accounted along of the perturbed structures has been the edges and not the directed edges (arcs) as in this thesis. That modified strategy still was applied to an elderly dataset to identify potential relationships between variables of medical interest but using an increased threshold instead of the predict by the proposed formula - such prudence is due to the possible social implications of the finding. The motivation behind such an application is that in spite of the proportion of elderly individuals in the population has increased substantially in the last few decades, the risk factors that should be managed in advance to ensure a natural process of mental decline due to ageing remain unknown. In the learned structural model, it was graphically investigated the probabilistic dependence mechanism between two variables of medical interest: the suspected risk factor known as Metabolic Syndrome and the indicator of mental decline referred to as Cognitive Impairment. In this investigation, the concept known in the context of BNs as D-separation has been employed. Results of the carried out study revealed that the dependence between Metabolic Syndrome and Cognitive Variables indeed exists and depends on both Body Mass Index and age. / O aprendizado da estrutura de uma Rede Bayesiana (BN) é um problema NP-difícil, e o uso de estratégias sub-ótimas é essencial em domínios que envolvem muitas variáveis. Uma delas consiste em gerar várias estruturas aproximadas e depois reduzir o conjunto a uma estrutura representativa. É possível usar a frequência de ocorrência (no conjunto de estruturas) como critério para aceitar um arco dominante entre dois nós e assim obter essa estrutura única. Nesta pesquisa de doutorado, foi feita uma analogia com um passeio aleatório unidimensional adaptado para deduzir analiticamente um limiar de decisão apropriado para essa frequência de ocorrência. A expressão de forma fechada obtida foi validada usando bases de dados de referência e aplicando o Coeficiente de Correlação de Matthews como métrica de desempenho. Nos experimentos utilizando dados médicos recentes, a BN resultante da frequência de corte analítica capturou as associações esperadas entre os nós e também obteve melhor desempenho de predição do que as BNs aprendidas com limiares vizinhos ao calculado. Na literatura, a característica contabilizada ao longo das estruturas perturbadas tem sido as arestas e não as arestas direcionadas (arcos) como nesta tese. Essa estratégia modificada ainda foi aplicada a um conjunto de dados de idosos para identificar potenciais relações entre variáveis de interesse médico, mas usando um limiar aumentado em vez do previsto pela fórmula proposta - essa cautela deve-se às possíveis implicações sociais do achado. A motivação por trás dessa aplicação é que, apesar da proporção de idosos na população ter aumentado substancialmente nas últimas décadas, os fatores de risco que devem ser controlados com antecedência para garantir um processo natural de declínio mental devido ao envelhecimento permanecem desconhecidos. No modelo estrutural aprendido, investigou-se graficamente o mecanismo de dependência probabilística entre duas variáveis de interesse médico: o fator de risco suspeito conhecido como Síndrome Metabólica e o indicador de declínio mental denominado Comprometimento Cognitivo. Nessa investigação, empregou-se o conceito conhecido no contexto de BNs como D-separação. Esse estudo revelou que a dependência entre Síndrome Metabólica e Variáveis Cognitivas de fato existe e depende tanto do Índice de Massa Corporal quanto da idade.

<div> This thesis proposes an artificial neural network (NN) model to predict fuel consumption in heavy vehicles. The model uses predictors derived from vehicle speed, mass, and road grade. These variables are readily available from telematics devices that are becoming an integral part of connected vehicles. The model predictors are aggregated over a fixed distance traveled (i.e., window) instead of fixed time interval. It was found that 1km windows is most appropriate for the vocations studied in this thesis. Two vocations were studied, refuse and delivery trucks.</div><div><br></div><div> The proposed NN model was compared to two traditional models. The first is a parametric model similar to one found in the literature. The second is a linear regression model that uses the same features developed for the NN model.</div><div><br></div><div> The confidence level of the models using these three methods were calculated in order to evaluate the models variances. It was found that the NN models produce lower point-wise error. However, the stability of the models are not as high as regression models. In order to improve the variance of the NN models, an ensemble based on the average of 5-fold models was created. </div><div><br></div><div> Finally, the confidence level of each model is analyzed in order to understand how much error is expected from each model. The mean training error was used to correct the ensemble predictions for five K-Fold models. The ensemble K-fold model predictions are more reliable than the single NN and has lower confidence interval than both the parametric and regression models.</div>