Two behavioural studies were conducted at the University of Saskatchewan beef feedlot. In the first study, the temperament of 400 steers was determined using both objective and subjective measures. The consistency of temperament, over repeated tests and between different measures, was also tested. The objective behavioural tests were conducted during the individual restraint of the steers using strain gauges and an MMD (movement-measuring-device). The time required for the steers to exit the area was also recorded. Subjective assessment of animals responsiveness during restraint was recorded on a scale of 1-5 (calm to wild). The consistency of individual differences in a steers response within the evaluation series and across repetitions, shows that this trait may represent a stable personality of the animal. The significant relationship between objective and subjective measures demonstrates that objective measures of temperament can be used to replace the traditional subjective scale as it has the added advantage of reducing inter- and intra-observer variability. The positive relationship of subjective scores and MMD values with the steers performance (average daily weight gain) shows not only that a calm temperament is conducive to productivity, but also that objective measures can replace subjective techniques for assessing temperament for performance evaluation. In the second study the reactivity of a subset of the original 400 steers (262 animals from 8 pens) to a novel stimulus was assessed. The purpose of this experiment was to determine if a steers behavioural response in the novel test was correlated to its temperament assessment determined in the first study. A remote controlled ball was dropped from the ceiling of a salt feeder while a steer licked the salt. Two overhead cameras connected to a monitor through a VCR and time lapse recorder permitted us to observe and document the response. A lack of correlation between measures of handling and novelty measures show that reactivity of animals in the handling chute and their responsiveness to the novel stimulus do not represent one and the same trait.

Two behavioural studies were conducted at the University of Saskatchewan beef feedlot. In the first study, the temperament of 400 steers was determined using both objective and subjective measures. The consistency of temperament, over repeated tests and between different measures, was also tested. The objective behavioural tests were conducted during the individual restraint of the steers using strain gauges and an MMD (movement-measuring-device). The time required for the steers to exit the area was also recorded. Subjective assessment of animals responsiveness during restraint was recorded on a scale of 1-5 (calm to wild). The consistency of individual differences in a steers response within the evaluation series and across repetitions, shows that this trait may represent a stable personality of the animal. The significant relationship between objective and subjective measures demonstrates that objective measures of temperament can be used to replace the traditional subjective scale as it has the added advantage of reducing inter- and intra-observer variability. The positive relationship of subjective scores and MMD values with the steers performance (average daily weight gain) shows not only that a calm temperament is conducive to productivity, but also that objective measures can replace subjective techniques for assessing temperament for performance evaluation. In the second study the reactivity of a subset of the original 400 steers (262 animals from 8 pens) to a novel stimulus was assessed. The purpose of this experiment was to determine if a steers behavioural response in the novel test was correlated to its temperament assessment determined in the first study. A remote controlled ball was dropped from the ceiling of a salt feeder while a steer licked the salt. Two overhead cameras connected to a monitor through a VCR and time lapse recorder permitted us to observe and document the response. A lack of correlation between measures of handling and novelty measures show that reactivity of animals in the handling chute and their responsiveness to the novel stimulus do not represent one and the same trait.

This thesis introduces a novel mobility model based on so called &ldquo / 2D correlated diffusion process&rdquo / . In this model, motion components over x and y axes are dependent. Joint density function of the process is derived. The expected exit time from an arbitrary domain is characterized by a boundary value problem. Analytical solution of this problem is given for a specific case. Numerical solution of the problem is presented by several examples. The results obtained in these examples are verified by simulations. The expected exit time computed by this method holds for any given 2D domain and any given starting position inside.

La théorie des processus de branchement multi-type en environnement i.i.d. est considérablement moins développée que dans le cas univarié, et les questions fondamentales ne sont pas résolues en totalité à ce jour. Les réponses exigent une compréhension profonde du comportement des produits des matrices i.i.d. à coefficients positifs. Sous des hypothèses assez générales et lorsque les fonctions génératrices de probabilité des lois de reproduction sont “linéaire fractionnaires”, nous montrons que la probabilité de survie à l’instant n du processus de branchement multi-type en environnement aléatoire est proportionnelle à 1/√n lorsque n → ∞. La démonstration de ce résultat suit l’approche développée pour étudier les processus de branchement uni-variés en environnement aléatoire i. i. d. Il utilise de façon cruciale des résultats récents portant sur les fluctuations des normes de produits de matrices aléatoires i.i.d. / The theory of multi-type branching process in i.i.d. environment is considerably less developed than for the univariate case, and fundamental questions are up to date unsolved. Answers demand a solid understanding of the behavior of products of i.i.d. matrices with non-negative entries. Under mild assumptions, when the probability generating functions of the reproduction laws are fractional-linear, the survival probability of the multi-type branching process in random environment up to moment n is proportional to 1/√n as n → ∞. Techniques for univariate branching process in random environment and methods from the theory of products of i.i.d. random matrices are required.

Les systèmes hybrides sont des systèmes dynamiques, caractérisés par un comportementdual, une interaction entre une partie discrète et une partie continue de fonctionnement.Dans le centre de notre travail se trouve une classe particulière de systèmeshybrides, plus spécifiquement les systèmes stochastiques à commutation que nous modélisonsà l’aide des Chaînes de Markov en temps continu et des équations différentielles.Le comportement aléatoire de ce type de système nécessite une commande spécialequi s’adapte aux événements arbitraires qui peuvent changer complètement l’évolutiondu système. Nous avons choisi une politique de contrôle basée sur les événements quiest déclenchée seulement quand il est nécessaire (sur un événement incontrôlable - parexemple un seuil qui est atteint), et jusqu’à ce que certaines conditions de fonctionnementsont remplies (le système revient dans l’état normal).Notre approche vise le développement d’un modèle probabiliste qui permet de calculerun critère de performance (en occurrence l’énergie du système) pour la politiquede contrôle choisie. Nous proposons d’abord une méthode de simulation à événementsdiscrets pour le système stochastique à commutation commandé, qui nous donne la possibilitéde réaliser une optimisation directe de la commande appliquée sur le système etaussi de valider les modèles analytiques que nous avons construit pour l’application ducontrôle.Un modèle analytique pour déterminer l’énergie consommée par le système a étéconçu en utilisant les probabilités de sortie de la région de contrôle, respectivement lestemps de séjour dans la chaîne de Markov avant et après avoir atteint les limites decontrôle. La dernière partie du travail présente la comparaison des résultats obtenusentre la méthode analytique et la simulation. / Hybrid systems are dynamical systems, characterized by a dual behaviour, a continuousinteraction between a discrete and a continuous functioning part. The center ofour work is represented by a particular class of hybrid systems, more specific by thestochastic switching systems which we model using continuous time Markov chains anddifferential equations.The random behaviour of such systems requires a special command which adapts tothe arbitrary events that can completely change the evolution of the system. We chose anevent-based control policy which is triggered only when it’s necessary (on an unforeseenevent - for example when a threshold that is reached), and until certain functioningconditions are met (the system returns in the normal state).Our approach aims to develop a probabilistic model that calculates a performancecriterion (in this case the energy of the system) for the proposed control policy. We startby proposing a discrete event simulation for the controlled stochastic switching system,which gives us the opportunity of applying a direct optimisation of the control command.It also allows us to compare the results with the ones obtained by the analytical modelswe have built when the event-based control is applied.An analytical model for computing the energy consumed by the system to apply thecontrol is designed by using the exit probabilities of the control region, respectively, thesojourn times of the Markov chain before and after reaching the control limits. The lastpart of this work presents the results we have obtained when comparing the analyticaland the simulation method.

Comment les protéïnes trouvent-elles leur chemin vers les rares endroits des molécules d’ADN où elles peuvent perpétuer le processus de vie ? De nombreuses études récentes tendent à prouver que seule une dynamique intermittente, c’est à dire à (au moins) deux régimes permet ce processus. L’objet principal de cette thèse est une étude rigoureuse d’un modèle simplifié de dynamique intermittente. Dans ce modèle la molécule alterne des dynamiques browniennes dans le "bulk" et sur la "surface" (i.e. la molécule d’ADN dans l’exemple plus haut) jusqu’à ce qu’elle atteigne sa cible, une petite fenêtre sur la surface: le temps passé par la molécule à la surface est naturellement modélisé comme une variable exponentielle de paramètre λ. Le principal résultat de la thèse est que quels que soient les paramètres, la recherche purement "par le bulk" n’est jamais optimale, ce qui légitime la thèse de la dynamique intermittente. On y caractérise aussi le cas où le temps optimal est atteint pour λ > 0. L’outil mathématique nouveau est l’introduction d’un opérateur autoadjoint et de sa base orthonormée de vecteurs propres. Cette étude permet d’obtenir un développement asymptotique à λ grand du temps moyen d’atteinte de la cible. Par ailleurs, un modèle nouveau est introduit: c’est celui du tore qui porte un paramètre supplémentaire, à savoir son module. Il est montre dans cette thèse que certaines valeurs du module conduisent à prouver que la stratégie intermittente est considérablement meilleure que celle de la pure diffusion dans le bulk. / How do proteins find their way towards the rare places on DNA molecules where they need to go in order to perpetuate the life process ? Many recent works tend to show that only an intermittent dynamics, that is a dynamics with two or more regimes, allows this process. The main goal of this PhD is a rigorous study of a simplified model of intermittent dynamics. In this model the molecule alternates diffusion in the bulk with a different kind of diffusion on the surface until it reaches its target consisting in a small window on the surface. The time spent by the molecule on the surface is naturally modeled as following an exponential law with parameter λ. The main result of this thesis is to show that, whatever the parameters are, a pure bulk strategy is never optimal, thus reinforcing the hypothesis of intermittent dynamics. One also characterizes the case where the optimal timed is attained for λ > 0. The new mathematical tool is the introduction of a self-adjoint operator and the use of its orthonormal basis of eigenvectors. This tool allows to obtain a precise asymptotic behavior of the mean exit time for λ large. Besides that a new geometrical model is developed, called the torus model. This new model carries a new parameter, namely its modulus. It is shown in this thesis that for some values of the modulus the optimized exit time is significantly (allowing experimental checking for instance) shorter than the pure bulk search.

Les processus auto-stabilisants sont définis comme des solutions d'équations différentielles stochastiques dont le terme de dérive contient à la fois le gradient d'un potentiel ainsi qu'un terme non-linéaire au sens de McKean qui attire le processus vers sa propre loi de distribution. On dispose de nombreux résultats lorsque l'environnement est convexe. L'objet de ce travail est de les étendre autant que possible au cas général notamment lorsque le paysage contient plusieurs puits. Des différences fondamentales sont constatées.Le premier chapitre prouve l'existence d'une solution forte. Le second s'intéresse aux lois de probabilités d'une telle solution. En particulier, l'existence et la non-unicité des mesures stationnaires sont mises en évidence sous des hypothèses faibles. Les chapitres trois et quatre sont affectés au comportement de ces mesures lorsque le coefficient de diffusion tend vers 0.Le chapitre cinq met en relation le processus auto-stabilisant avec des systèmes particulaires via une « propagation du chaos ». Il est ainsi possible de transposer certains résultats du système de particules sur le processus non-markovien et réciproquement. Le chapitre six est dédié au dénombrement exact des mesures stationnaires.Le chapitre sept est employé pour l'étude du comportement en temps long. D'une part, un résultat de convergence dans un cas simple est fourni. D'autre part, un principe de grandes déviations est mis en évidence par l'utilisation des résultats de Freidlin et Wentzell / Self-stabilizing processes are defined as the solutions of stochastic differential equations which drift term contains the gradient of a potential and a term nonlinear in the sense of McKean which attracts the process to its own law distribution. There are many results if the landscape is convex. The purpose of this work is to extend these in the general case especially when the landscape contains contains several wells. Essential differences are found.The first chapter proves the strong existence of a solution. The second one deals with the probability measure of the solution. Particularly, the existence and the non-uniqueness of the stationary measures are highlighted under weak assumptions. Chapter three and four are assigned to the asymptotic analysis in the small noise limit of these measures.Chapter five connects the self-stabilizing process and some particle systems via a « propagation of chaos ». It is thus possible to translate some results from the particle systems to the non-markovian process and reciprocally.Chapter seven is used to study the long time behavior. In one hand, a convergence's result is provided in a simple case. In the other hand, a large deviations principle is highlighted by using the results of Freidlin and Wentzell