Seemingly stable chemical kinetics can be stable, marginally stable or unstable

We present three examples of chemical reaction networks whose ordinary differential equation scaling limits are almost identical and in all cases stable. Nevertheless, the Markov jump processes associated to these reaction networks display the full range of behaviors: one is stable (positive recurrent), one is unstable (transient) and one is marginally stable (null recurrent). We study these differences and characterize the invariant measures by Lyapunov function techniques. In particular, we design a natural set of such functions which scale homogeneously to infinity, taking advantage of the same scaling behavior of the reaction rates

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 discuss the optimality of our assumptions on the decay of the jump rates. 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

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

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 users. 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 users in a system-optimal fashion, while accounting for their temporal preferences. We instantiate the framework in a parallel-network whereby users 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 users are charged when traveling on the first, fast arc, whilst they are rewarded when traveling on the second, slower arc. We assume the users to be rational and model their choices through a game where each user 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 users’ urgency. We complement our study through numerical simulations. Our results show that it is possible to achieve a system-optimal solution whilst significantly reducing the users’ perceived discomfort when compared to a centralized optimal but urgency-unaware policy

On-chip integrated amplifiers and lasers utilizing rare-earth-ion activation

This contribution reviews our recent results on rare-earth-ion-doped integrated amplifiers and lasers. We have concentrated our efforts on complex-doped polymers, amorphous Al2O3, and crystalline potassium double tungstates

Effects of Fat Supplementation in Dairy Goats on Lipid Metabolism and Health Status

Fat supplementation has long been used in dairy ruminant nutrition to increase the fat content of milk and supply energy during particularly challenging production phases. Throughout the years, advances have been made in the knowledge of metabolic pathways and technological treatments of dietary fatty acids (FAs), resulting in safer and more widely available lipid supplements. There is an awareness of the positive nutraceutical effects of the addition of eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) to fat supplementation, which provides consumers with healthier animal products through manipulation of their characteristics. If it is true that benefits to human health can be derived from the consumption of animal products rich in bioactive fatty acids (FAs), then it is reasonable to think that the same effect can occur in the animals to which the supplements are administered. Therefore, recent advances in fat supplementation of dairy goats with reference to the effect on health status have been summarized. In vivo trials and in vitro analysis on cultured cells, as well as histological and transcriptomic analyses of hepatic and adipose tissue, have been reviewed in order to assess documented relationships between specific FAs, lipid metabolism, and immunity