Relaxation times of kinetically constrained spin models with glassy dynamics

We analyze the density and size dependence of the relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models for strong or fragile glasses and for systems undergoing jamming transitions. For the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any density $\rho<1$ and for the Knight model below the critical density at which the glass transition occurs, we show that the persistence and the spin-spin time auto-correlation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. For FA2f in $d\geq 2$, we also prove a super-Arrhenius scaling of the form $\exp(1/(1-\rho))\leq \tau\leq\exp(1/(1-\rho)^2)$. For FA1f in $d$=$1,2$ we rigorously prove the power law scalings recently derived in \cite{JMS} while in $d\geq 3$ we obtain upper and lower bounds consistent with findings therein. Our results are based on a novel multi-scale approach which allows to analyze $\tau$ in presence of kinetic constraints and to connect time-scales and dynamical heterogeneities. The techniques are flexible enough to allow a variety of constraints and can also be applied to conservative stochastic lattice gases in presence of kinetic constraints.Comment: 4 page

On the dynamical behavior of the ABC model

We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature

Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size $\ell$ in contact with particle reservoirs at the boundary. We prove that, as for non--degenerate rates, the inverse of the spectral gap and the logarithmic Sobolev constant grow as $\ell^2$. It is also shown how one can obtain, via a scaling limit from the logarithmic Sobolev inequality, the exponential decay of a macroscopic entropy associated to a degenerate parabolic differential equation (porous media equation). We analyze finally the tagged particle displacement for the stationary process in infinite volume. In dimension larger than two we prove that, in the diffusive scaling limit, it converges to a Brownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure

Dog filariosis in the Lazio region (Central Italy): first report on the presence of Dirofilaria repens

BACKGROUND: Epidemiological investigations were carried out in the Lazio Region to assess the status of canine filariosis and to evaluate the actual risk for veterinary and medical public health. METHODS: Since August 2001 to June 2003, a total of 972 canine blood samples, collected in public kennels and from private owners animals of the 5 Provinces of the Region, were tested. The presence of filarial parasites was evaluated by microscopy and bio-molecular techniques; the species identification was performed by means of the same diagnostic tools. RESULTS: A total of 17/972 (1.75%; 95%CI 1.06%–2.85%) blood samples were parasitized by D. repens,13 out them drawn by dogs resident in the Province of Roma, and 4 in the other provinces. Multivariate analysis was performed in order to evaluate the association between filariosis and risk factors. The origin from coastal territories seems to be a significant risk factor to acquire the infection. CONCLUSION: This is the first report of canine filariosis in the Lazio Region, where D. repens was before reported only in foxes. The risk of human zoonotic infection is stressed, and the absence of other filarial species is discusse

Consanguinity and polygenic diseases: a model for antibody deficiencies

Primary immunodeficiencies represent a heterogeneous group of disorders of the immune system, predisposing to various types of infections. Among them, common variable immunodeficiency is the most common symptomatic antibody deficiency. It includes several different forms characterized by defects in the terminal stage of B lymphocyte differentiation, leading to markedly reduced immunoglobulin serum levels and increased susceptibility to bacterial infections. The clinical phenotype is complex, including autoimmunity, granulomatous inflammation, lymphoproliferative disorders and malignancies. Rare autosomal recessive mutations in a number of single genes have recently been reported. However, the underlying genetic defects remain unknown in the majority of cases. In order to seek new genes responsible for the disease, we studied a consanguineous Italian family through exome sequencing combined with homozygosity mapping. Six missense homozygous variants passed our filtering selection and at least two of them were associated with some aspects of the pathological phenotype. Our data remark the complexity of immune system disorders and emphasize the difficulty to understand the significance of genetic results and their correlation with the disease phenotype

Non-equilibrium dynamics of spin facilitated glass models

We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically constrained models, and then present new results for the behaviour of the one-spin facilitated Fredrickson-Andersen and East models in various spatial dimensions. The time evolution of one-time quantities, such as the energy density, and the detailed properties of two-time correlation and response functions are studied using a combination of theoretical approaches, including exact mappings of master operators and reductions to integrable quantum spin chains, field theory and renormalization group, and independent interval and timescale separation methods. The resulting analytical predictions are confirmed by means of detailed numerical simulations. The models we consider are characterized by trivial static properties, with no finite temperature singularities, but they nevertheless display a surprising variety of dynamic behaviour during aging, which can be directly related to the existence and growth in time of dynamic lengthscales. Well-behaved fluctuation-dissipation ratios can be defined for these models, and we study their properties in detail. We confirm in particular the existence of negative fluctuation-dissipation ratios for a large number of observables. Our results suggest that well-defined violations of fluctuation-dissipation relations, of a purely dynamic origin and unrelated to the thermodynamic concept of effective temperatures, could in general be present in non-equilibrium glassy materials.Comment: 72 pages, invited contribution to special issue of JSTAT on "Principles of Dynamics of Nonequilibrium Systems" (Programme at Newton Institute Cambridge). v2: New data added to Figs. 11, 23, 24, new Fig. 26 on East model in d=3, minor improvements to tex

Theophylline as a precision therapy in a young girl with PIK3R1 immunodeficiency

Based on its phosphatidylinositol 3-kinase-delta (PI3Kd) inhibitory properties, theophylline was administered to a young girl with activated PI3Kd syndrome (APDS). We report reduced frequency of infections, decreased lymphoproliferation, and noticeable changes in immunophenotype, encouraging further trials with theophylline in children with APDS