The average shape of a fluctuation: universality in excursions of stochastic processes

We study the average shape of a fluctuation of a time series x(t), that is the average value _T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form _T = T^\alpha f(t/T) is obeyed. The scaling function f(s) is to a large extent independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. Let

Average trajectory of returning walks

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For uncorrelated random walks the average shape is semicircular, independently from the single increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations induces non trivial asymmetric shapes, which are studied numerically.Comment: 16 pages, 16 figures; accepted for publication in Phys. Rev.

Analytical results for generalized persistence properties of smooth processes

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.Comment: 21 pages, 4 figures, to appear in Journal of Physics

On the out of equilibrium order parameters in long-range spin-glases

We show that the dynamical order parameters can be reexpressed in terms of the distribution of the staggered auto-correlation and response functions. We calculate these distributions for the out of equilibrium dynamics of the Sherrington-Kirpatrick model at long times. The results suggest that the landscape this model visits at different long times in an out of equilibrium relaxation process is, in a sense, self-similar. Furthermore, there is a similarity between the landscape seen out of equilibrium at long times and the equilibrium landscape. The calculation is greatly simplified by making use of the superspace notation in the dynamical approach. This notation also highlights the rather mysterious formal connection between the dynamical and replica approaches.Comment: 25 pages, Univ. di Roma I preprint #1049 (we replaced the file by the RevTex file, figures available upon request

Brownian forces in sheared granular matter

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilised, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.Comment: 4 pages, 5 figures and 1 tabl

Characteristics of neonatal GBS disease during a multicentre study (2007-2010) and in the year 2012

iNTRODUCTION: The characteristics of Group B Streptococcal (GBS) early onset (EOD) and late onset (LOD) neonatal infections in Italy were analyzed. Two periods were considered, a first 3-years period (2007-2010), when notification of GBS infections was enforced under the auspices of the Italian Ministry of Health, and a second 1 year period (2012) when reporting on neonatal GBS disease continued on voluntary basis. METHODS: A standardized form was used to collect data on cases of neonatal GBS disease. They included both maternal and neonatal data. RESULTS AND DISCUSSION: The two surveys underlined that preterm deliveries, precipitous labor and negatively GBS screened mothers are common causes of EOD occurrence, possibly explained by inadequate, or lack of, intrapartum antibiotic prophylaxis. Nevertheless, measures for reducing prevention failures and EOD incidence by an higher adherence to prevention strategies, as the Centre for Disease Control recommendations, are still possible and should be encouraged

Spontaneous Polarisation Build up in a Room Temperature Polariton Laser

We observe the build up of strong (~50%) spontaneous vector polarisation in emission from a GaN-based polariton laser excited by short optical pulses at room temperature. The Stokes vector of emitted light changes its orientation randomly from one excitation pulse to another, so that the time-integrated polarisation remains zero. This behaviour is completely different to any previous laser. We interpret this observation in terms of the spontaneous symmetry breaking in a Bose-Einstein condensate of exciton-polaritons

Sign-time distribution for a random walker with a drifting boundary

We present a derivation of the exact sign-time distribution for a random walker in the presence of a boundary moving with constant velocity.Comment: 5 page

Coarsening and Slow-Dynamics in Granular Compaction

We address the problem of the microscopic reorganization of a granular medium under a compaction process in the framework of Tetris-like models. We point out the existence of regions of spatial organization which we call domains, and study their time evolution. It turns out that after an initial transient, most of the activity of the system is concentrated on the boundaries between domains. One can then describe the compaction phenomenon as a coarsening process for the domains, and a progressive reduction of domain boundaries. We discuss the link between the coarsening process and the slow dynamics in the framework of a model of active walkers on active substrates.Comment: Revtex 4 pages, 4 figures, in press in PRL. More info http://axtnt3.phys.uniroma1.it/Tetri

Steady state properties of a mean field model of driven inelastic mixtures

We investigate a Maxwell model of inelastic granular mixture under the influence of a stochastic driving and obtain its steady state properties in the context of classical kinetic theory. The model is studied analytically by computing the moments up to the eighth order and approximating the distributions by means of a Sonine polynomial expansion method. The main findings concern the existence of two different granular temperatures, one for each species, and the characterization of the distribution functions, whose tails are in general more populated than those of an elastic system. These analytical results are tested against Monte Carlo numerical simulations of the model and are in general in good agreement. The simulations, however, reveal the presence of pronounced non-gaussian tails in the case of an infinite temperature bath, which are not well reproduced by the Sonine method.Comment: 23 pages, 10 figures, submitted for publicatio