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This thesis addresses the sampling problem in a high-dimensional space, i.e., the computation of averages with respect to a defined probability density that is a function of many variables. Such sampling problems arise in many application areas, including molecular dynamics, multiscale models, and Bayesian sampling techniques used in emerging machine learning applications. Of particular interest are thermostat techniques, in the setting of a stochastic-dynamical system, that preserve the canonical Gibbs ensemble defined by an exponentiated energy function. In this thesis we explore theory, algorithms, and numerous applications in this setting. We begin by comparing numerical methods for particle-based models. The class of methods considered includes dissipative particle dynamics (DPD) as well as a newly proposed stochastic pairwise Nosé-Hoover-Langevin (PNHL) method. Splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. When computational efficiency is measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the PNHL method compared to popular alternative schemes in the low-friction regime, without degradation of convergence rate. We propose a pairwise adaptive Langevin (PAdL) thermostat that fully captures the dynamics of DPD and thus can be directly applied in the setting of momentum-conserving simulation. These methods are potentially valuable for nonequilibrium simulation of physical systems. We again report substantial improvements in both equilibrium and nonequilibrium simulations compared to popular schemes in the literature. We also discuss the proper treatment of the Lees-Edwards boundary conditions, an essential part of modelling shear flow. We also study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. These methods are important in multiscale modelling and in the design of new machine learning algorithms for inference and parameterization for large datasets, challenges which are increasingly important in "big data" applications. In addition to providing a more comprehensive discussion of the foundations of these methods, we propose a new numerical method for the adaptive Langevin/stochastic gradient Nosé-Hoover thermostat that achieves a dramatic improvement in numerical efficiency over the most popular stochastic gradient methods reported in the literature. We demonstrate that the newly established method inherits a superconvergence property (fourth order convergence to the invariant measure for configurational quantities) recently demonstrated in the setting of Langevin dynamics. Furthermore, we propose a covariance-controlled adaptive Langevin (CCAdL) thermostat that can effectively dissipate parameter-dependent noise while maintaining a desired target distribution. The proposed method achieves a substantial speedup over popular alternative schemes for large-scale machine learning applications.

Les difficultés à interagir dans le monde social et à s’y adapter sont une plainte centrale des personnes souffrant de troubles psychiatriques et notamment de schizophrénie ou de troubles apparentés. Ces difficultés, qui constituent un frein au processus de réhabilitation psychosociale, pourraient en partie être expliquées par un dysfonctionnement des processus regroupés sous le terme de cognition sociale. La cognition sociale est définie comme la capacité à construire des représentations sur soi-même et autrui, et sur les relations entre soi et les autres, ainsi qu’à utiliser ces représentations de manière flexible, afin de guider le comportement social ; et inclut des processus tels que le traitement des émotions, la théorie de l’esprit, le style attributionnel, la perception et les connaissances sociales. Des déficits concernant les différentes composantes de la cognition sociale ont été largement mis en évidence dans la schizophrénie et les troubles apparentés, et semblent par ailleurs avoir un lien fort avec les difficultés observées dans les domaines du fonctionnement social, mais également des relations privilégiées avec les processus neurocognitifs, même si ces deux composantes semblent relativement indépendantes. Afin de compenser ces troubles, de nombreuses prises en charge de remédiation cognitive ont été proposées ces dernières années. L’objectif de ce travail de thèse a été d’évaluer la possibilité d’améliorer les déficits touchant la sphère de la cognition sociale des personnes souffrant de troubles psychotiques à l’aide d’un outil de remédiation spécifiquement développé à cet effet, le programme RC2S. Etant donnée l’hétérogénéité des déficits touchant la sphère de la cognition sociale dans la schizophrénie, et l’importance fondamentale portée au transfert des compétences dans la vie quotidienne, RC2S a été développé comme une thérapie individualisée et flexible, qui permet aux patients de s’entraîner aux interactions sociales dans un environnement réaliste, et d’adapter la prise en charge aux difficultés spécifiques de la personne. Nous présenterons ici trois études basées sur la méthodologie du cas unique, mettant en évidence l’impact de cette thérapie sur les troubles de la cognition sociale de deux patients souffrant de schizophrénie et d’un patient présentant un trouble de la personnalité schizoïde. / In people with psychiatric disorders, particularly those suffering from schizophrenia and related illnesses, pronounced difficulties in social interactions and adaptation are a key manifestation. These disabilities, which are a serious impediment to psychosocial rehabilitation process, could be partly explained by impairments in processes grouped under the generic term of social cognition. Social cognition is defined as the ability to construct mental representations about others and oneself, and about one’s relationships to others, and to use these representations in a flexible way to guide social behavior. It includes abilities such as emotion processes, theory of mind (ToM), attributional style, and social perception and knowledge. In schizophrenia and related disorders, several components of social cognition are usually altered, and are strongly associated with functional outcome and independent but partly related to neurocognitive processes. The impact of several kinds of interventions and particularly of social cognitive remediation programs has been studied recently, and new strategies and programs in this line are currently being developed. The main objective of this doctoral thesis was to assess the feasibility of improving social cognition in people with psychotic disorders, using a cognitive remediation program specifically designed for this purpose, the RC2S program. Considering that the social cognitive deficits experienced by patients with schizophrenia are very diverse, and that the main objective of social cognitive remediation is to improve patient’s functioning in their social daily life, RC2S was developed as an individualized and flexible program, which allows patients to practice social interactions in a realistic environment, and to adapt therapy to the specificity of every patient’s profile. This manuscript present three single case studies, using specific methodology, to highlight the impact of this new therapy on social cognitive impairments of two people with schizophrenia and one patient with schizoid personality disorder.

This thesis examines techniques that provide a method of computer visualisation of bushfire spread. Existing techniques studied include, Kourtz & O???Regan, Green???s Contact, Heat Accumulation, Percolation modelling and Huygens??? Principle by Anderson et.al., French, Roberts, Richards. Many of these techniques are extended as part of a comprehensive study into how they perform in a two dimensional reference frame (ie over flat terrain only). New techniques are defined for Percolation Modelling and Huygens??? Principle. Each technique is examined in a series of test cases which include computer simulations with no wind, constant wind, variable wind, variable vegetation (including patchy fuel and two fuels) and where fuel burns out. These test cases provide: (a) an incremental approach to understanding the operation of each technique; (b) a basis for comparison; and (c) verification of correctness of the technique in two dimensions. Several of the techniques are shown, by these test cases, to be equivalent. For instance, the Kourtz & O???Regan technique using a square template is equivalent to the Contact Technique, Site percolation is similar to the Heat Accumulation technique and Template percolation is similar to the Contact Technique. Overall the Huygens??? Principle techniques provide the most accurate simulations of bushfire spread.

This thesis examines techniques that provide a method of computer visualisation of bushfire spread. Existing techniques studied include, Kourtz & O???Regan, Green???s Contact, Heat Accumulation, Percolation modelling and Huygens??? Principle by Anderson et.al., French, Roberts, Richards. Many of these techniques are extended as part of a comprehensive study into how they perform in a two dimensional reference frame (ie over flat terrain only). New techniques are defined for Percolation Modelling and Huygens??? Principle. Each technique is examined in a series of test cases which include computer simulations with no wind, constant wind, variable wind, variable vegetation (including patchy fuel and two fuels) and where fuel burns out. These test cases provide: (a) an incremental approach to understanding the operation of each technique; (b) a basis for comparison; and (c) verification of correctness of the technique in two dimensions. Several of the techniques are shown, by these test cases, to be equivalent. For instance, the Kourtz & O???Regan technique using a square template is equivalent to the Contact Technique, Site percolation is similar to the Heat Accumulation technique and Template percolation is similar to the Contact Technique. Overall the Huygens??? Principle techniques provide the most accurate simulations of bushfire spread.

By exploiting the concept of emergent network properties and the hierarchical nature of networks, we have constructed several levels of models facilitating the investigations of issues in the area of respiratory neural control. The first of such models is an intracellular second messenger pathway model, which has been shown to be an important contributor to intracellular calcium metabolism and mediate responses to neuromodulators such as serotonin. At the next level, we have constructed new single neuron models of respiratory-related neurons (e.g. the pre-Btzinger complex neuron and the Hypoglossal motoneuron), where the electrical activities of the neurons are linked to intracellular mechanisms responsible for chemical homeostasis. Beyond the level of individual neurons, we have constructed models of neuron populations where the effects of different component neurons, varying strengths and types of inter-neuron couplings, as well as network topology are investigated. Our results from these simulation studies at different structural levels are in line with experiment observations. The small-world topology, as observed in previous anatomical studies, has been shown here to support rhythm generation along with a variety of other network-level phenomena. The interactions between different inter-neuron coupling types simultaneously manifesting at time-scales orders of magnitude apart suggest possible explanations for variations in the outputs measured from the XII rootlet in experiments. In addition, we have demonstrated the significance of pacemakers, along with the importance of considering neuromodulations and second-messenger pathways in an attempt to understand important physiological functions such as breathing activities.

In dieser Arbeit wird eine neue Methode für den skalenunabhängigen Vergleich von LD-Strukturen in unterschiedlichen genomischen Regionen vorgeschlagen. Verschiedene Aspekte durch Skalen verursachter Probleme – von der Präzision der Schätzung der Marke-reffekte bis zur Genauigkeit der Vorhersage für neue Individuen - wurden untersucht. Darüber hinaus, basierend auf den Leistungsvergleichen von unterschiedlichen statistischen Methoden, wurden Empfehlungen für die Verwendungen der untersuchten Methoden gege-ben. / In dieser Arbeit wird eine neue Methode für den skalenunabhängigen Vergleich von LD-Strukturen in unterschiedlichen genomischen Regionen vorgeschlagen. Verschiedene Aspekte durch Skalen verursachter Probleme – von der Präzision der Schätzung der Marke-reffekte bis zur Genauigkeit der Vorhersage für neue Individuen - wurden untersucht. Darüber hinaus, basierend auf den Leistungsvergleichen von unterschiedlichen statistischen Methoden, wurden Empfehlungen für die Verwendungen der untersuchten Methoden gegeben

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