Record statistics in random vectors and quantum chaos

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records that is non-universal but tends to the Gumbel distribution asymptotically. The quantum standard map is used to study these statistics for the effect of correlations apart from normalization. It is seen that in the mixed phase space regime the number of intensity records is a power law in the dimensionality of the state as opposed to the logarithmic growth for random states.Comment: figures redrawn, discussion adde

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include

Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomena is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.Comment: 8 pages; 2 figures; paper presented in APFA 6 conferenc

Asian pollution climatically modulates mid-latitude cyclones following hierarchical modelling and observational analysis

Increasing levels of anthropogenic aerosols in Asia have raised considerable concern regarding its potential impact on the global atmosphere, but the magnitude of the associated climate forcing remains to be quantified. Here, using a novel hierarchical modelling approach and observational analysis, we demonstrate modulated mid-latitude cyclones by Asian pollution over the past three decades. Regional and seasonal simulations using a cloud-resolving model show that Asian pollution invigorates winter cyclones over the northwest Pacific, increasing precipitation by 7% and net cloud radiative forcing by 1.0 W m(-2) at the top of the atmosphere and by 1.7 W m(-2) at the Earth's surface. A global climate model incorporating the diabatic heating anomalies from Asian pollution produces a 9% enhanced transient eddy meridional heat flux and reconciles a decadal variation of mid-latitude cyclones derived from the Reanalysis data. Our results unambiguously reveal a large impact of the Asian pollutant outflows on the global general circulation and climate.Multidisciplinary SciencesSCI(E)[email protected]; [email protected]

Cosmic Rays Accelerated at Cosmological Shock Waves

Based on hydrodynamic numerical simulations and diffusive shock acceleration model, we calculated the ratio of cosmic ray (CR) to thermal energy. We found that the CR fraction can be less than similar to 0.1 in the intracluster medium, while it would be of order unity in the warm-hot intergalactic mediumopen2

Random sequential adsorption on a dashed line

We study analytically and numerically a model of random sequential adsorption (RSA) of segments on a line, subject to some constraints suggested by two kinds of physical situations: - deposition of dimers on a lattice where the sites have a spatial extension; - deposition of extended particles which must overlap one (or several) adsorbing sites on the substrate. Both systems involve discrete and continuous degrees of freedom, and, in one dimension, are equivalent to our model, which depends on one length parameter. When this parameter is varied, the model interpolates between a variety of known situations : monomers on a lattice, "car-parking" problem, dimers on a lattice. An analysis of the long-time behaviour of the coverage as a function of the parameter exhibits an anomalous 1/t^2 approach to the jamming limit at the transition point between the fast exponential kinetics, characteristic of the lattice model, and the 1/t law of the continuous one.Comment: 14 pages (Latex) + 4 Postscript figure

Parking and the visual perception of space

Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data

A relational database within the Leg Club Network – an audit

The growing prevalence of venous leg ulcers in an ageing population presents challenges for wound care and management. The Lindsay Leg Club model is an alternative approach to the management of leg health that can improve patient outcomes. This paper reports on an audit of a relational database held within the Leg Club Network, containing records of more than 17,000 patients (known as members) who attended a Leg Club in a 5-year period (2014-2019). In total, over 266,000 member leg assessments and treatments were entered into the database. The average nursemember attendance time was 28 minutes, with a skill-mix of 23% senior nurses, 70% qualified and associate nurses and 7% nurses in supervisory roles. Healing rates averaged 62% after 12 weeks. Recurrence rates were 20% after 12 weeks. Annual clinical and volunteer hours averaged 821 hours and 800 hours respectively. Staffing costs were £28 per wound treatment or leg assessment with a typical duration of 27 minutes. 71% of members were aged 70-94, which indicates the need for a service that caters for the specific requirements of this age group. However, no data on psychosocial and well-being outcomes were recorded. Their inclusion in further developments of this database is recommended

A record-driven growth process

We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node possessing a quality. The new incoming node connects to the preexisting node with best quality, that is, with record value for the quality. The emergent structure is that of a growing network, where groups are formed around record nodes (nodes endowed with the best intrinsic qualities). Special emphasis is put on the statistics of leaders (nodes whose degrees are the largest). The asymptotic probability for a node to be a leader is equal to the Golomb-Dickman constant omega=0.624329... which arises in problems of combinatorical nature. This outcome solves the problem of the determination of the record breaking rate for the sequence of correlated inter-record intervals. The process exhibits temporal self-similarity in the late-time regime. Connections with the statistics of the cycles of random permutations, the statistical properties of randomly broken intervals, and the Kesten variable are given.Comment: 30 pages,5 figures. Minor update