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At least 685 records · Page 38Linked to original sources
PubMed2006

A theory and model to explain the skin melanoma epidemic.

Before 1955, the incidence of malignant melanoma in Nordic countries increased from birth to approximately 30 years of age, when it levelled off to around five cases per 100,000 person-years. From 1957 onwards, the incidence no longer stabilized at the age of 30 years, but continued to increase with age to at least 100 cases per 100,000 person-years. The aims of this study were to examine this sudden change in melanoma trends and to develop an explanatory model. The Nordic Cancer Registries and the American Cancer Society provided age-specific incidence data. Birth cohorts of melanoma incidence for men were plotted against calendar year and age. A theory and a corresponding mathematical model were developed to explain the time trends in all cohorts, as well as the reported age-specific incidence and age-standardized incidence over time. A statistical distribution of time to sickness fitted all the post-1957 data. Earlier studies have indicated that body-resonant frequency modulation broadcasting radiation from 1955 onwards may affect melanoma incidence. The proposed model may shed light on the melanoma epidemic and may be useful in predicting future melanoma trends based on known birth cohort data and possible effects from policy changes with regard to population exposure to electromagnetic radiation.

Adult↗
PubMed2003

Length of stay data as a guide to hospital economic performance for ICU patients.

CONTEXT: Length of stay data are increasingly used to monitor ICU economic performance. How such material is presented greatly affects its utility. OBJECTIVE: To develop a weighted length of stay index and to estimate expected length of stay. To assess alternative ways to summarize weighted length of stay to evaluate ICU economic performance. DESIGN: Retrospective database study. SUBJECTS: Data for 751 ICU patients in 1998 at two hospitals used to develop weighted length of stay index. Data on 42,237 patients from 72 ICUs used as the basis of economic performance evaluation. MAIN OUTCOME MEASURES: Difference between actual and expected weighted length of stay, where expected weighted length of stay is based on patient clinical characteristics. RESULTS: Length of stay statistically explains approximately 85 to 90% of interpatient variation in hospital costs. The first ICU day is approximately four times as expensive, and other ICU days approximately 2.5 times as expensive, as non-ICU hospital days. In a regression model for weighted length of stay, patient clinical characteristics explain 26% of variation. ICU economic performance can be measured by excess weighted length of stay of a "typical" patient or by occurrence of long excess weighted lengths of stay. Although different summary measures of performance are highly correlated, choice of measure affects relative ranking of some ICUs' performance. CONCLUSION: Providers of statistical data on ICU economic performance should adjust length of stay for patient characteristics and provide multiple summary measures of the statistical distribution, including measures that address both the typical patient and outliers.

Accounting↗
PubMed2001

The small world inside large metabolic networks.

The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics efforts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and find that this network is a small-world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The small-world architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.

Escherichia coli↗
PubMed1999

Some properties of multifractality at solid-on-solid growth processes.

It is shown that multifractality of large deposition probabilities observed in a simple model of crystal growth (the Das Sarma model with neglected surface diffusion, desorption, and hop) corresponds to another type of statistical distribution: multifractal Bernoulli distribution. Lognormal distribution is also discussed in this context.

Journal Article↗
PubMed2000

Microscopic dynamics underlying anomalous diffusion

The time-dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a nonlinear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A 222, 347 (1995)]. The scope of the present paper is twofold. First, we show that this distribution can be obtained also as a solution of the nonlinear porous media equation. Second, we prove that the time-dependent Tsallis distribution can be obtained also as a solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A 237, 229 (1997)] with coefficients depending on the velocity, which describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in the presence of multiplicative noise.

Journal Article↗
PubMed2000

Unstable dimension variability and synchronization of chaotic systems

The nonhyperbolic structure of synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits an unstable dimension variability, which is an extreme form of nonhyperbolicity. We analyze the dynamics in the synchronization manifold and in its transversal direction, where a tonguelike structure is formed, through a system of two coupled chaotic maps. The unstable dimension variability is revealed in the statistical distribution of the finite-time transversal Lyapunov exponent, having both negative and positive values. We also point out that unstable dimension variability is a cause of severe modeling difficulty.

Journal Article↗
PubMed2001

Basins of attraction on random topography.

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes.

Journal Article↗
PubMed2001

Singular statistics.

We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically, and explicit calculations are performed for the two-point correlation function. This problem naturally appears in, e.g., rank-1 perturbation of an integrable Hamiltonian and, in particular, when a delta-function potential is added to an integrable billiard.

Journal Article↗
PubMed2002

Large-scale topological and dynamical properties of the Internet.

We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a 3-yr time interval. We find that the connectivity structure of the Internet presents statistical distributions settled in a well-defined stationary state. The large-scale properties are characterized by a scale-free topology consistent with previous observations. Correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the Internet. The study of the Internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models. We compare the properties of growing network models with the present real Internet data analysis.

Journal Article↗
PubMed2002

Localization in band random matrix models with and without increasing diagonal elements.

It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dimensions can be introduced for nonperturbative parts of eigenfunctions, and by employing intermediate basis states, which can improve the method of the reduced Hamiltonian matrix. The latter model deviates from the standard band random matrix model mainly in two aspects: (i) the root mean square of diagonal elements is larger than that of off-diagonal elements within the band, and (ii) statistical distributions of the matrix elements are close to the Lévy distribution in their central parts, except in the high top regions.

Journal Article↗
PubMed2002

Irreversibility resulting from contact with a heat bath caused by the finiteness of the system.

When a small dynamical system that is initially in contact with a heat bath is detached from this heat bath and then caused to undergo a quasi-static adiabatic process, the resulting statistical distribution of the system's energy differs from that of an equilibrium ensemble. Subsequent contact of the system with another heat bath is inevitably irreversible, hence the entire process cannot be reversed without a net energy transfer to the heat baths.

Journal Article↗
PubMed2002

From gene families and genera to incomes and internet file sizes: why power laws are so common in nature.

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes of incomes, cities, internet files, biological taxa, and in gene family and protein family frequencies.

Journal Article↗
PubMed2003

Random walk through fractal environments.

We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D(F) of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D(F)< or =2 can thus be considered as defective Levy walks. The distribution of jump increments for D(F)>2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D(F)<2, the diffusion is dominated by the finite escape rate. Diffusion for D(F)>2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations.

Journal Article↗
PubMed2003

Thermostatistic properties of a q-generalized Bose system trapped in an n-dimensional harmonic oscillator potential.

The thermostatistic properties of a q-generalized boson system trapped in an n-dimensional harmonic oscillator potential are studied, based on the generalized statistic distribution derived from Tsallis' entropy. The density of states, total number of particles, critical temperature at which Bose-Einstein condensation occurs, internal energy, and heat capacity at constant volume are derived. The characteristics of Bose-Einstein condensation of the system are discussed in detail. It is found from the results obtained here that the thermostatistic properties of such a system depend closely on parameter q, dimensional number of the space, and frequency of the harmonic oscillator; and the external potential has a great influence on the thermostatistic properties of the system.

Journal Article↗
PubMed2004

Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback.

We have investigated the transient characteristics of two types of chaos synchronization in a semiconductor laser subject to optical feedback: complete synchronization and strong injection locking-type synchronization. We have calculated the statistical distribution of the transient response time of synchronization when the initial position in the starting attractor is varied. For complete synchronization, the distribution of the transient response time has much larger average and variance than the average period of the chaotic oscillations. Conversely, a short transient response time is obtained for strong injection locking-type synchronization. We found that the transient response time is dependent upon the maximum Lyapunov exponent of the chaotic temporal waveform for complete synchronization, whereas it is almost constant for strong injection locking-type synchronization.

Journal Article↗
PubMed2004

Fluctuations of doublet splittings using the annular billiard.

We study the statistical distribution of quantum energy splittings due to a dynamical tunneling. The system, the annular billiard, has whispering quasimodes due to a discrete symmetry that exists even when chaos is present in the underlying classical dynamics. Symmetric and antisymmetric combinations of these quasimodes correspond to quantum doublet states whose degeneracies decrease as the circles become more eccentric. We construct numerical ensembles composed of splittings for two distinct regimes, one which we call semiclassical for high quantum numbers and high energies where the whispering regions are connected by chaos, and other which we call quantal for low quantum numbers, low energies, and near integrable where dynamical tunneling is not a dominant mechanism. In both cases we observe a variation on the fluctuation amplitudes, but their mean behaviors follow the formula of Leyvraz and Ullmo [J. Phys. A 29, 2529 (1996)]. A description of a three-level collision involving a doublet and a singlet is also provided through a numerical example.

Journal Article↗
PubMed2005

Loops structure of the Internet at the autonomous system level.

We present here a study of the clustering and loops in a graph of the Internet at the autonomous systems level. We show that, even if the whole structure is changing with time, the statistical distributions of loops of order 3, 4, and 5 remain stable during the evolution. Moreover, we will bring evidence that the Internet graphs show characteristic Markovian signatures, since the structure is very well described by two-point correlations between the degrees of the vertices. This indeed proves that the Internet belongs to a class of network in which the two-point correlation is sufficient to describe their whole local (and thus global) structure. Data are also compared to present Internet models.

Journal Article↗
PubMed2005

Statistical wave scattering through classically chaotic cavities in the presence of surface absorption.

We propose a model to describe the statistical properties of wave scattering through a classically chaotic cavity in the presence of surface absorption. Experimentally, surface absorption could be realized by attaching an "absorbing patch" to the inner wall of the cavity. In our model, the cavity is connected to the outside by a waveguide with N open modes (or channels), while an experimental patch is simulated by an "absorbing mirror" attached to the inside wall of the cavity; the mirror, consisting of a waveguide that supports N(a) channels, with absorption inside and a perfectly reflecting wall at its end, is described by a subunitary scattering matrix S(a). The number of channels N(a) , as a measure of the geometric cross section of the mirror, and the lack of unitarity P(a) = [symbol: see text]N(a) - S(a)(+)S(a) , as a measure of absorption, are under our control: these parameters have an important physical significance for real experiments. The absorption strength in the cavity is quantified by gamma(a) = tr P(a). The statistical distribution of the resulting S matrix for N = 1 open channel and only one absorbing channel, N(a) = 1, is solved analytically for the orthogonal and unitary universality classes, beta = 1 and beta = 2, respectively, and the results are compared with those arising from numerical simulations. The relation with other models existing in the literature, in some of which absorption has a volumetric character, is also studied.

Journal Article↗