Occupancy of a single site by many random walkers

We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin, which is unoccupied. The random-walk model is taken to be a continuous-time random walk and the pausing-time density at the target site is allowed to differ from the pausing-time density at other sites. We calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time T. We also find the variance for the cumulative time during which the site is unoccupied. The large-T behavior of the variance differs according as the random walk is transient or recurrent. It is shown that the variance is proportional to T at large T in three or more dimensions, it is proportional to T3/2 in one dimension and to TlnT in two dimensions.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Is trauma in Switzerland any different? epidemiology and patterns of injury in major trauma - a 5-year review from a Swiss trauma centre.

Switzerland, the country with the highest health expenditure per capita, is lacking data on trauma care and system planning. Recently, 12 trauma centres were designated to be reassessed through a future national trauma registry by 2015. Lausanne University Hospital launched the first Swiss trauma registry in 2008, which contains the largest database on trauma activity nationwide. METHODS: Prospective analysis of data from consecutively admitted shock room patients from 1 January 2008 to 31 December 2012. Shock room admission is based on physiology and mechanism of injury, assessed by prehospital physicians. Management follows a surgeon-led multidisciplinary approach. Injuries are coded by Association for the Advancement of Automotive Medicine (AAAM) certified coders. RESULTS: Over the 5 years, 1,599 trauma patients were admitted, predominantly males with a median age of 41.4 years and median injury severity score (ISS) of 13. Rate of ISS >15 was 42%. Principal mechanisms of injury were road traffic (40.4%) and falls (34.4%), with 91.5% blunt trauma. Principal patterns were brain (64.4%), chest (59.8%) and extremity/pelvic girdle (52.9%) injuries. Severe (abbreviated injury scale [AIS] score ≥ 3) orthopaedic injuries, defined as extremity and spine injuries together, accounted for 67.1%. Overall, 29.1% underwent immediate intervention, mainly by orthopaedics (27.3%), neurosurgeons (26.3 %) and visceral surgeons (13.9%); 43.8% underwent a surgical intervention within the first 24 hours and 59.1% during their hospitalisation. In-hospital mortality for patients with ISS >15 was 26.2%. CONCLUSION: This is the first 5-year report on trauma in Switzerland. Trauma workload was similar to other European countries. Despite high levels of healthcare, mortality exceeds published rates by >50%. Regardless of the importance of a multidisciplinary approach, trauma remains a surgical disease and needs dedicated surgical resources.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

Class of correlated random networks with hidden variables

We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Proteomic analysis of membrane rafts of melanoma cells identifies protein patterns characteristic of the tumor progression stage.

The molecular mechanisms controlling the progression of melanoma from a localized tumor to an invasive and metastatic disease are poorly understood. In the attempt to start defining a functional protein profile of melanoma progression, we have analyzed by LC-MS/MS the proteins associated with detergent resistant membranes (DRMs), which are enriched in cholesterol/sphingolipids-containing membrane rafts, of melanoma cell lines derived from tumors at different stages of progression. Since membrane rafts are involved in several biological processes, including signal transduction and protein trafficking, we hypothesized that the association of proteins with rafts can be regulated during melanoma development and affect protein function and disease progression. We have identified a total of 177 proteins in the DRMs of the cell lines examined. Among these, we have found groups of proteins preferentially associated with DRMs of either less malignant radial growth phase/vertical growth phase (VGP) cells, or aggressive VGP and metastatic cells suggesting that melanoma cells with different degrees of malignancy have different DRM profiles. Moreover, some proteins were found in DRMs of only some cell lines despite being expressed at similar levels in all the cell lines examined, suggesting the existence of mechanisms controlling their association with DRMs. We expect that understanding the mechanisms regulating DRM targeting and the activity of the proteins differentially associated with DRMs in relation to cell malignancy will help identify new molecular determinants of melanoma progression.

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Quantum relaxation in random magnets

We present a comprehensive study of the low-temperature magnetic relaxation in random magnets. The first part of the paper contains theoretical analysis of the expected features of the relaxation, based upon current theories of quantum tunneling of magnetization. Models of tunneling, dissipation, the crossover from the thermal to the quantum regime, and the effect of barrier distribution on the relaxation rate are discussed. It is argued that relaxation-type experiments are ideally suited for the observation of magnetic tunneling, since they automatically provide the condition of very low barriers. The second part of the paper contains experimental results on transition-metal¿rare-earth amorphous magnets. Structural and magnetic characterization of materials is presented. The temperature and field dependence of the magnetic relaxation is studied. Our key observation is a nonthermal character of the relaxation below a few kelvin. The observed features are in agreement with theoretical suggestions on quantum tunneling of magnetization.