Complete characterization of convergence to equilibrium for an inelastic Kac model

Pulvirenti and Toscani introduced an equation which extends the Kac caricature of a Maxwellian gas to inelastic particles. We show that the probability distribution, solution of the relative Cauchy problem, converges weakly to a probability distribution if and only if the symmetrized initial distribution belongs to the standard domain of attraction of a symmetric stable law, whose index $\alpha$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $\alpha=\frac{2}{1+p}$. This result is then used: (1) To state that the class of all stationary solutions coincides with that of all symmetric stable laws with index $\alpha$. (2) To determine the solution of a well-known stochastic functional equation in the absence of extra-conditions usually adopted

Kinetic models with randomly perturbed binary collisions

We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases

Erythromycin resistance in Streptococcus pyogenes in Italy.

In a prospective study of acute pharyngitis in Italian children, 69 (38.3%) of 180 isolates of Streptococcus pyogenes were resistant to macrolides. S. pyogenes was eradicated in 12 (63.1%) of 19 patients with erythromycin-resistant S. pyogenes treated with clarithromycin and in 22 (88%) of 25 patients with erythromycin-susceptible strains. The constitutive-resistant phenotype was correlated with failure of macrolide treatment

Statistical Mechanics of the Chinese Restaurant Process: lack of self-averaging, anomalous finite-size effects and condensation

The Pitman-Yor, or Chinese Restaurant Process, is a stochastic process that generates distributions following a power-law with exponents lower than two, as found in a numerous physical, biological, technological and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e. a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.Comment: (5pages, 1 figure

Management of vertebral osteomyelitis over an eight-year period: The UDIPROVE (UDIne PROtocol on VErtebral osteomyelitis)

Objectives: Vertebral osteomyelitis (VO) is a compelling clinical entity for clinicians because of its insidious and indolent course, which makes diagnosis difficult. Methods: All patients with a suspected diagnosis of VO were analyzed over an 8-year period (January 2009 to January 2017). The UDIPROVE protocol (UDIne PROtocol on VErtebral osteomyelitis) was applied in all cases. The primary endpoint was the performance of the UDIPROVE protocol to obtain the causal bacteria of infection. Results: During the study period, 133 episodes of confirmed VO were observed. The etiology of infection was obtained in 73.6% of cases: 70.5% were gram-positive, 16.3% were gram-negative, and 13.2% were mycobacteria. 18F-Fluorodeoxyglucose positron emission tomography/computed tomography (FDG-PET/CT) showed that for tubercular VO, the median standard uptake value (SUV) was higher when compared with VO caused by other bacteria. Clinical cure at the end of therapy was reported in 85.7% of patients. Previous antimicrobial therapy and a delay of more than 5 days in performing biopsy were associated with an undiagnosed etiology of VO. Targeted antibacterial therapy and follow-up with FDG-PET/CT were associated with clinical cure at the end of therapy, while the involvement of more than two vertebrae and inadequate drainage were associated with failure. Conclusions: Rigorous application of the UDIPROVE protocol allowed the causative pathogens of VO to be obtained \u2013 at about twice the rate reported in the literature. The use of FDG-PET/CT for the follow-up of infection was more reliable when compared to magnetic resonance imaging (MRI)