Limit cycles for dynamic crawling locomotors with periodic prescribed shape

We study the asymptotic evolution of a family of dynamic models of crawling locomotion, with the aim to introduce a well-posed characterization of a gait as a limit behaviour. The locomotors, which might have a discrete or continuous body, move on a line with a periodic prescribed shape change, and might possibly be subject to external forcing (e.g. crawling on a slope). We discuss how their behaviour is affected by different types of friction forces, including also set-valued ones such as dry friction. We show that, under mild natural assumptions, the dynamics always converge to a relative periodic solution. The asymptotic average velocity of the crawler yet might still depend on its initial state, so we provide additional assumption for its uniqueness. In particular, we show that the asymptotic average velocity is unique both for strictly monotone friction forces, and also for dry friction, provided in the latter case that the actuation is sufficiently smooth (for discrete models) or that the friction coefficients are always nonzero (for continuous models). We present several examples and counterexamples illustrating the necessity of our assumptions

Heterogeneity in susceptibility to infection can explain high reinfection rates

Heterogeneity in susceptibility and infectivity is inherent to infectious disease transmission in nature. Here we are concerned with the formulation of mathematical models that capture the essence of heterogeneity while keeping a simple structure suitable of analytical treatment. We explore the consequences of host heterogeneity in the susceptibility to infection for epidemiological models for which immunity conferred by infection is partially protective, known as susceptible-infected-recovered-infected (SIRI) models. We analyze the impact of heterogeneity on disease prevalence and contrast the susceptibility profiles of the subpopulations at risk for primary infection and reinfection. We present a systematic study in the case of two frailty groups. We predict that the average rate of reinfection may be higher than the average rate of primary infection, which may seem paradoxical given that primary infection induces life-long partial protection. Infection generates a selection mechanism whereby fit individuals remain in S and frail individuals are transferred to R. If this effect is strong enough we have a scenario where, on average, the rate of reinfection is higher than the rate of primary infection even though each individual has a risk reduction following primary infection. This mechanism may explain high rates of tuberculosis reinfection recently reported. Finally, the enhanced benefits of vaccination strategies that target the high-risk groups are quantified.http://dx.doi.org/10.1016/j.jtbi.2009.03.01

Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence

In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are give

Linguistic abstractions for programming and policing autonomic computing systems

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PBFT vs proof-of-authority: Applying the CAP theorem to permissioned blockchain

Permissioned blockchains are arising as a solution to federate companies prompting accountable interactions. A variety of consensus algorithms for such blockchains have been proposed, each of which has different benefits and drawbacks. Proof-of-Authority (PoA) is a new family of Byzantine fault-tolerant (BFT) consensus algorithms largely used in practice to ensure better performance than traditional Practical Byzantine Fault Tolerance (PBFT). However, the lack of adequate analysis of PoA hinders any cautious evaluation of their effectiveness in real-world permissioned blockchains deployed over the Internet, hence on an eventually synchronous network experimenting Byzantine nodes. In this paper, we analyse two of the main PoA algorithms, named Aura and Clique, both in terms of provided guarantees and performances. First, we derive their functioning including how messages are exchanged, then we weight, by relying on the CAP theorem, consistency, availability and partition tolerance guarantees. We also report a qualitative latency analysis based on message rounds. The analysis advocates that PoA for permissioned blockchains, deployed over the Internet with Byzantine nodes, do not provide adequate consistency guarantees for scenarios where data integrity is essential. We claim that PBFT can fit better such scenarios, despite a limited loss in terms of performance

Glutathione-Induced Release of Zeatin From Functionalized Gold Nanovectors

The paper shows our preliminary results on the different spectroscopic behavior of three types of gold nanoparticles (obtained respectively by chemical synthesis, laser ablation in pure water and laser ablation in a citrate solution) modified with trans-zeatin, a plant growth regulator, in presence of glutathione. The reaction of ligand substitution of the adsorbed zeatin with glutathione is studied through surface enhanced Raman spectroscopy and is revealed to occur only when citrate-laser ablated gold nanoparticles are employed, making these particles potentially good candidates as vehicles of zeatin inside plant cells for future agricultural applications

Glutathione-Induced Release of Zeatin From Functionalized Gold Nanovectors

The paper shows our preliminary results on the different spectroscopic behavior of three types of gold nanoparticles (obtained respectively by chemical synthesis, laser ablation in pure water and laser ablation in a citrate solution) modified with trans-zeatin, a plant growth regulator, in presence of glutathione. The reaction of ligand substitution of the adsorbed zeatin with glutathione is studied through surface enhanced Raman spectroscopy and is revealed to occur only when citrate-laser ablated gold nanoparticles are employed, making these particles potentially good candidates as vehicles of zeatin inside plant cells for future agricultural applications