Random Splitting of Fluid Models: Ergodicity and Convergence

We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector fields preserving some fundamental aspects of the original dynamics. Randomness is injected by sequentially following each vector field for a random amount of time. We show under general assumptions that these random dynamics possess a unique invariant measure and converge almost surely to the original, deterministic model in the small noise limit. We apply our construction to the Lorenz-96 equations, often used in studies of chaos and data assimilation, and Galerkin approximations of the 2D Euler and Navier-Stokes equations. An interesting feature of the models developed is that they apply directly to the conservative dynamics and not just those with excitation and dissipation

Large deviations theory for Markov jump models of chemical reaction networks

We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it, we further establish the corresponding Wentzell–Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicability of our LDP and W-F results. This then justifies the computation of nonequilibrium potential and exponential transition time estimates between different attractors in the large volume limit, for systems that are beyond the reach of standard chemical reaction network theor

Large deviations theory for Markov jump models of chemical reaction networks

We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it, we further establish the corresponding Wentzell–Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicability of our LDP and W-F results. This then justifies the computation of nonequilibrium potential and exponential transition time estimates between different attractors in the large volume limit, for systems that are beyond the reach of standard chemical reaction network theor

Effect of live yeast (Saccharomyces cerevisiae) administration on apparent digestibility of horses

Six mares were divided into two groups of three subjects each in a crossover design on the basis of body weight and age: Control(C)fedabasaldiet,Treatment(T)fedabasaldietand2 Control (C) fed a basal diet, Treatment (T) fed a basal diet and 2 2 g/head/d of live yeast ((S. cerevisiae 4.6x1010 CFU/day).Theexperimentaldesignwasdividedintotwo ).Theexperimentaldesignwasdividedintotwo . The experimental design was divided into two periods named period 1 and period 2 respectively of 35d each, and consisting of 3 different phases. Dur- ing each period all animals were subject to an adaptation phase of 14d (phase1); during phase 2 (18d) and phase 3 live yeast was administered (T) or not (C). Phase 3 consisted in a three days individual fecal collection period all the groups, in order to determine dry matter, organic matter, crude protein, crude fat, NDF and ADF apparent digestion rates using acid insoluble ash (AIA) as internal marker (Bergero et al., 2005). Results obtained evidenced as the administration of S. cerevisiae to mature horses resulted in increased digestibility of dry matter, organic matter, NDF, and ADF

Urgency-aware Optimal Routing in Repeated Games through Artificial Currencies

When people choose routes minimizing their individual delay, the aggregate congestion can be much higher compared to that experienced by a centrally-imposed routing. Yet centralized routing is incompatible with the presence of self-interested agents. How can we reconcile the two? In this paper we address this question within a repeated game framework and propose a fair incentive mechanism based on artificial currencies that routes selfish agents in a system-optimal fashion, while accounting for their temporal preferences. We instantiate the framework in a parallel-network whereby agents commute repeatedly (e.g., daily) from a common start node to the end node. Thereafter, we focus on the specific two-arcs case whereby, based on an artificial currency, the agents are charged when traveling on the first, fast arc, whilst they are rewarded when traveling on the second, slower arc. We assume the agents to be rational and model their choices through a game where each agent aims at minimizing a combination of today's discomfort, weighted by their urgency, and the average discomfort encountered for the rest of the period (e.g., a week). We show that, if prices of artificial currencies are judiciously chosen, the routing pattern converges to a system-optimal solution, while accommodating the agents' urgency. We complement our study through numerical simulations. Our results show that it is possible to achieve a system-optimal solution whilst reducing the agents' perceived discomfort by 14-20% when compared to a centralized optimal but urgency-unaware policy.Comment: Accepted for presentation at the European Control Conference 202

Large deviations for Markov jump processes with uniformly diminishing rates

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further show that our assumptions on the decay of the jump rates are optimal. As a direct application of this work we relax the assumptions needed for the application of LDPs to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise naturally particularly the context of Mass action kinetics

Ethical Criteria for the Admission and Management of Patients in the ICU Under Conditions of Limited Medical Resources: A Shared International Proposal in View of the COVID-19 Pandemic

Introduction The present pandemic has exposed us to unprecedented challenges that need to be addressed not just for the current state, but also for possible future similar occurrences. It is worth pointing out that discussions on the allocation of medical resources may not necessarily refer to an exception, but, unfortunately, to a regular condition for a large part of humanity (1). The criteria for admission to an Intensive Care Unit (ICU) setting generally take into account multiple factors. There must be a diagnostic and prognostic basis for the decisions made, considering both biological factors and patient values and wishes. Furthermore, the decision-making process should, whenever possible, respect the patient's advance directives as well as the relationship with the patient's family or attorney. Therapeutic neglect should be avoided. Having applied standard clinical evaluation criteria for the appropriate treatment of patients with COVID-19, including consideration of prognosis, if a hospital then finds itself unable to provide optimal treatment (e.g., due to a disproportion between the number of patients and the availability of beds, healthcare providers, ventilators, and drugs in the ICU), it becomes necessary to evaluate, case by case, how to achieve justice and the best possible good for the greatest number of patients. It is therefore mandatory to explore alternative solutions; these include increasing available beds and healthcare providers, implementing alternative, though suboptimal, approaches (where appropriate), transferring patients to other clinical units, etc. Making these decisions properly also involves the recovery of the political role of medicine and science (2). If the imbalance between needs and resources reaches a critical level, an emergency triage protocol, following the operational and ethical indications of “disaster medicine,” should be activated. These have been deployed in major and serious natural (earthquakes or tsunamis for example) and technological (factory explosions, public transport accidents for example) disasters, as well as following terrorist attacks (3, 4). The question of the feasibility of developing a clinical evaluation algorithm to support the decision-making of the triage team remains open, though many such protocols have been written. According to the above, we propose the following five ethical criteria for the triage of patients in conditions of limited resources, such as the COVID pandemic. They are the result of an interdisciplinary and intercultural dialogue between specialists from different disciplines. Several of the authors are working in the main epicenters of the crisis and currently are playing a central role in the bioethical, clinical, social and legal aspects of the management of the COVID-19 pandemic

Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime

We study the problem of policy optimization for infinite-horizon discounted Markov Decision Processes with softmax policy and nonlinear function approximation trained with policy gradient algorithms. We concentrate on the training dynamics in the mean-field regime, modeling e.g., the behavior of wide single hidden layer neural networks, when exploration is encouraged through entropy regularization. The dynamics of these models is established as a Wasserstein gradient flow of distributions in parameter space. We further prove global optimality of the fixed points of this dynamics under mild conditions on their initialization