Queuing for an infinite bus line and aging branching process

We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for a bus if this latter is less than d\_i stations before, where d\_i is non-decreasing. We determine the asymptotic behavior of a single bus and when two buses eventually coalesce almost surely by coupling arguments. Three regimes appear, two of which leading to a.s. coalescing of the buses.The approach relies on a connection with aged structured branching processes with immigration and varying environment. We need to prove a Kesten Stigum type theorem, i.e. the a.s. convergence of the successive size of the branching process normalized by its mean. The technics developed combines a spine approach for multitype branching process in varying environment and geometric ergodicity along the spine to control the increments of the normalized process

Heat Conduction Networks: Disposition of Heat Baths and Invariant Measure

We consider a model of heat conduction networks consisting of oscillators in contact with heat baths at different temperatures. Our aim is to generalize the results concerning the existence and uniqueness of the stationnary state already obtained when the network is reduced to a chain of particles. Using Lasalle's principle, we establish a condition on the disposition of the heat baths among the network that ensures the uniqueness of the invariant measure. We will show that this condition is sharp when the oscillators are linear. Moreover, when the interaction between the particles is stronger than the pinning, we prove that this condition implies the existence of the invariant measure

Polymères Dirigés et Réseaux Conducteurs de Chaleur - Systèmes de mécanique statistique à l'équilibre et hors équilibre

This PhD thesis presents two examples arising in statistical mechanics. Directed polymers in random environment are a model of an equilibrium system. We give a criterium based on the comparison between network and environment entropies to provide an improved lower bound on the critical temperature. We also use some well-known results about Anderson Parabolic Equation to obtain an asymptotic on the free energy. We also use directed polymers to give a simple proof of the independance on the initial condition of the Lyapunov function in the Anderson Parabolic Equation.Heat conduction networks are studied out of equilibrium. When the interacting potentials are harmonic, we give a geometric interpretation of the existence and uniqueness of the invariant measure using a completeness theorem. When this geometric condition fails to occur, we give an explicit invariant of the Hamiltonian flow. We generalize the uniqueness results to analytic potentials. We also show that the Hörmander condition is sufficient to obtain uniqueness of the invariant measure via weak controlability. Lasalle's principle is used to avoid Hörmander's condition. We will also bring up the problem of existence.Dans cette thèse, nous étudions deux exemples issus de la mécanique statistique. Les polymères dirigés en environnement aléatoire sont un modèle de système se trouvant à l'état d'équilibre. Nous donnons un critère de comparaison entre les entropies du réseau et de l'environnement permettant d'améliorer la borne inférieure sur la température critique. Nous utilisons également certains résultats connus dans le cadre de l'équation d'Anderson parabolique pour obtenir le comportement asymptotique de l'énergie libre. Par ailleurs, nous utilisons les polymères dirigés pour donner une preuve simple de l'indépendance de la fonction de Lyapunov de l'équation d'Anderson parabolique par rapport à la condition initiale.Les réseaux conducteurs de chaleur sont étudiés hors équilibre. Lorsque les potentiels d'interaction sont harmoniques, nous donnons une interprétation géométrique de la condition d'existence et d'unicité de la mesure invariante via un théorème de complétude. Dans le cas où cette condition fait défaut, nous explicitons une quantité invariante par le flot hamiltonien. Nous généralisons ensuite les résultats d'unicité à des potentiels analytiques. Nous montrons que la condition de Hörmander est suffisante pour avoir l'unicité de la mesure invariante via la contrôlabilité. Le principe de Lasalle est ensuite utilisé pour montrer l'unicité sans la condition d'Hörmander. Nous évoquons également le problème de l'existence de telles mesures

Polymères dirigés et réseaux conducteurs de chaleur (systèmes de mécanique statistique à l'équilibre et hors équilibre)

NANTES-BU Sciences (441092104) / SudocSudocFranceF

Control measures to prevent the increase of paratuberculosis prevalence in dairy cattle herds: an individual-based modelling approach

Paratuberculosis, a gastrointestinal disease caused by Mycobacterium avium subsp. paratuberculosis (Map), can lead to severe economic losses in dairy cattle farms. Current measures are aimed at controlling prevalence in infected herds, but are not fully effective. Our objective was to determine the most effective control measures to prevent an increase in adult prevalence in infected herds. We developed a new individual-based model coupling population and infection dynamics. Animals are characterized by their age (6 groups) and health state (6 states). The model accounted for all transmission routes and two control measures used in the field, namely reduced calf exposure to adult faeces and test-and-cull. We defined three herd statuses (low, moderate, and high) based on realistic prevalence ranges observed in French dairy cattle herds. We showed that the most relevant control measures depend on prevalence. Calf management and test-and-cull both were required to maximize the probability of stabilizing herd status. A reduced calf exposure was confirmed to be the most influential measure, followed by test frequency and the proportion of infected animals that were detected and culled. Culling of detected high shedders could be delayed for up to 3 months without impacting prevalence. Management of low prevalence herds is a priority since the probability of status stabilization is high after implementing prioritized measures. On the contrary, an increase in prevalence was particularly difficult to prevent in moderate prevalence herds, and was only feasible in high prevalence herds if the level of control was high

MOESM4 of Control measures to prevent the increase of paratuberculosis prevalence in dairy cattle herds: an individual-based modelling approach

Additional file 4. Influence of control measure modalities on the probability of non-degrading herd status over a 10-year period. (Panel A) Relative importance of each test-and-cull parameter linked to the predictive statistical model built with the Random Forest Classifier method, and (panel B) associated probability of non-degrading herd status over a 10-year period and according to initial herd status (A2, B, and C, in lines) and reduction of calf exposure (expo = 0.65, 0.5, and 0.35, in columns)

MOESM3 of Control measures to prevent the increase of paratuberculosis prevalence in dairy cattle herds: an individual-based modelling approach

Additional file 3. Precision of predictive statistical models built with the Random Forest Classifier method. All combinations of initial herd status (early low adult prevalence: A1; low adult prevalence: A2; moderate adult prevalence: B; high adult prevalence: C), year (5, 10, and 15 years), and calf exposure (no reduction: expo = 1; and 3 levels of reduction: expo = 0.65, 0.5, and 0.35) are shown. Accuracies are considered as good enough when above 70%