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PubMed2002

Spectral statistics of the k-body random-interaction model.

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmüller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.

Journal Article↗
PubMed2002

Field statistics of two vectorially superposed wave populations.

Field statistics of observed waves and radiation constrain the physics of the emission process and source region. However, data often contain two or more superposed signals or a signal superposed on a noise background, creating difficulties for interpretation. Here, the combined probability distribution of the field formed by vector superposition of two signals, each with specified statistics, is written as a double integral with integrable singularities. The analytic result and its numerical solutions for combinations of Gaussian and lognormally distributed signals show that these predictions differ from those for field or intensity convolution and from the individual wave distributions. At high fields, the combined distribution takes the qualitative form of the dominant individual distribution (which is localized or otherwise extends to larger fields) but develops a significant tail at low fields due to vector superposition of almost antiparallel fields with similar magnitudes. It is shown that very nearly power-law distributions can develop in significant field domains, despite neither component distribution being power law. This is relevant to alternative interpretations in terms of self-organized criticality and certain modulational wave instabilities. The formalism is then applied to observations of the Vela pulsar, resulting in greatly improved fits to data and different interpretations. Specifically, the results are strong evidence that stochastic growth theory (SGT) is relevant and that the approximate power-law statistics found at some phases are not intrinsic but rather due to vector convolution of a Gaussian background with a lognormal; the latter is interpretable in terms of SGT. The field statistics are consistent with the emission mechanism being a direct linear instability or indirect generation via linear mode conversion of nonescaping waves driven by a linear instability. They are inconsistent with nonlinear self-focusing instabilities generating the observed pulsar radiation. This formalism and its results should also be widely applicable to other types of wave growth in inhomogeneous media.

Journal Article↗
PubMed2003

Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number.

We study the level statistics (second half moment I0 and rigidity Delta(3)) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers g. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like toward Wigner-like behavior with increasing g. On investigating the wave functions, we find many chaotic functions that can be described as a random superposition of regular wave functions. The amplitude distribution P(psi) of these chaotic functions was found to be Gaussian with the typical value of the localization volume V(loc) approximately equal 0.33. For systems with periodic boundaries we find several additional energy regimes, where I0 is relatively close to the Poisson limit. In these regimes, the eigenfunctions are either regular or localized functions, where P(psi) is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. An interesting intermediate case between chaotic and localized eigenfunctions also appears.

Journal Article↗
PubMed2003

Recovering isotropic statistics in turbulence simulations: the Kolmogorov 4/5th law.

One of the main benchmarks in direct numerical simulations of three-dimensional turbulence is the Kolmogorov prediction for third-order structure functions with homogeneous and isotropic statistics in the infinite Reynolds number limit. Previous direct numerical simulations (DNS) techniques to obtain isotropic statistics have relied on time-averaging structure functions in a few directions over many eddy-turnover times, using forcing schemes carefully constructed to generate isotropic data. Motivated by recent theoretical work, which removes isotropy requirements by spherically averaging the structure functions over all directions, we will present results which supplement long-time averaging by angle-averaging over up to 73 directions from a single flow snapshot. The directions are among those natural to a square computational grid, and are weighted to approximate the spherical average. We use this angle-averaging procedure to compare the statistically steady flows generated by two different forcing schemes in a periodic box. Our results show that despite the apparent differences in the two flows, their isotropic components, as measured by the Kolmogorov laws, are essentially identical. This procedure may be used to investigate the isotropic part of the small-scale statistics of any quantity of interest. The averaging process is inexpensive, and for the Kolmogorov 4/5 law, reasonable results can be obtained from a single snapshot of data. This implies consistency with the recently derived local versions of the Kolmogorov laws, which do not require long-time averages.

Journal Article↗
PubMed2004

Statistical methods of parameter estimation for deterministically chaotic time series.

We discuss the possibility of applying some standard statistical methods (the least-square method, the maximum likelihood method, and the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional dynamic system (the logistic map) containing an observational noise. A "segmentation fitting" maximum likelihood (ML) method is suggested to estimate the structural parameter of the logistic map along with the initial value x(1) considered as an additional unknown parameter. The segmentation fitting method, called "piece-wise" ML, is similar in spirit but simpler and has smaller bias than the "multiple shooting" previously proposed. Comparisons with different previously proposed techniques on simulated numerical examples give favorable results (at least, for the investigated combinations of sample size N and noise level). Besides, unlike some suggested techniques, our method does not require the a priori knowledge of the noise variance. We also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed Bayesian approaches. We note the trade off between the need of using a large number of data points in the ML analysis to decrease the bias (to guarantee consistency of the estimation) and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition. The method of statistical moments for the estimation of the parameter of the logistic map is discussed. This method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically (not only numerically).

Journal Article↗
PubMed2004

Statistics of wave functions and currents induced by spin-orbit interaction in chaotic billiards.

We show that the wave function and current statistics in chaotic Robnik billiards crucially depend on the constant of the spin-orbit interaction (SOI). For small constant the current statistics is described by universal current distributions derived for slightly opened chaotic billiards [Saichev et al., J. Phys. A 35, L87 (2002)] although one of the components of the spinor eigenfunctions is not universal. For strong SOI both components of the spinor eigenstate are complex random Gaussian fields. This observation allows us to derive the distributions of spin-orbit persistent currents which well describe numerical statistics. For intermediate values of the statistics of the eigenstates and currents, both are deeply nonuniversal.

Journal Article↗
PubMed2001

Inverse statistics of smooth signals: the case of two dimensional turbulence.

The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, E(k) approximately k(-alpha), 3< or =alpha<5, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bifractal distribution. We also investigate two dimensional turbulent flows in the direct cascade regime, which display a more complex behavior. We give numerical evidences that the inverse statistics of 2D turbulent flows is described by a multifractal probability distribution; i.e., the statistics of laminar events is not simply captured by the exponent alpha characterizing the spectrum.

Journal Article↗
PubMed2001

Statistical conservation laws in turbulent transport.

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. With very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

Journal Article↗
PubMed2003

Fractional statistics in the fractional quantum Hall effect.

A microscopic confirmation of the fractional statistics of the quasiparticles in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at nu=1/3 and nu=2/5 by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.

Journal Article↗
PubMed2006

One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics.

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.

Journal Article↗
PubMed1984

Trends in ischemic heart disease mortality and morbidity in Perth Statistical Division.

Trends in mortality from Ischemic Heart Disease (IHD) and other principal causes of death, and in hospital admission rates for Acute Myocardial Infarction (AMI) have been studied in residents aged 35-64 years of the Perth Statistical Division for the period 1968-1982. Death rates were based on data abstracted from official statistics or computer tapes of unit death records. Hospital admission rates were derived from the computer tapes of the Western Australian Hospital Inpatient Survey, 1968-1982. Since 1968, mortality from IHD has fallen in the Perth Statistical Division in both males and females by 30% and 33%, respectively. This fall has occurred principally in deaths occurring out-of-hospital and has been accompanied by similar falls in mortality from other vascular diseases and in total mortality. Hospital admission rates for Acute Myocardial Infarction (AMI) in the Perth Statistical Division have fallen since 1971 by 17% in males and 27% in females. These findings taken together suggest that the improvement in IHD mortality in Western Australia has been due mainly to a fall in the incidence of acute manifestations of IHD (sudden death and AMI), rather than improvements in case fatality. The possible underlying mechanisms responsible for this are discussed.

Adult↗
PubMed2000

Mortality variation across Australia: descriptive data for states and territories, and statistical divisions.

OBJECTIVE: To describe variation in all cause and selected cause-specific mortality rates across Australia. METHODS: Mortality and population data for 1997 were obtained from the Australian Bureau of Statistics. All cause and selected cause-specific mortality rates were calculated and directly standardised to the 1997 Australian population in 5-year age groups. Selected major causes of death included cancer, coronary artery disease, cerebrovascular disease, diabetes, accidents and suicide. Rates are reported by statistical division, and State and Territory. RESULTS: All cause age-standardised mortality was 6.98 per 1000 in 1997 and this varied 2-fold from a low in the statistical division of Pilbara, Western Australia (5.78, 95% confidence interval 5.06-6.56), to a high in Northern Territory--excluding Darwin (11.30, 10.67-11.98). Similar mortality variation (all p < 0.0001) exists for cancer (1.01-2.23 per 1000) and coronary artery disease (0.99-2.23 per 1000), the two biggest killers. Larger variation (all p < 0.0001) exists for cerebrovascular disease (0.7-11.8 per 10,000), diabetes (0.7-6.9 per 10,000), accidents (1.7-7.2 per 10,000) and suicide (0.6-3.8 per 10,000). Less marked variation was observed when analysed by State and Territory, but Northern Territory consistently has the highest age-standardised mortality rates. CONCLUSIONS: Analysed by statistical division, substantial mortality gradients exist across Australia, suggesting an inequitable distribution of the determinants of health. Further research is required to better understand this heterogeneity.

Age Factors↗
PubMed1992

Delayed increases in liver cirrhosis mortality and frequency of alcoholic liver cirrhosis following an increment and redistribution of alcohol consumption in Finland: evidence from mortality statistics and autopsy survey covering 8533 cases in 1968-1988.

Changes in the legal restrictions for alcohol consumption in 1969 liberated purchasing and marketing of low-alcohol beer. Subsequently, within the space of 5 years, the per capita consumption of absolute alcohol increased from 4.2 to 6.5 liters. To evaluate the possible effects of this change upon liver cirrhosis mortality as well as prevalence of liver cirrhosis in autopsy series, we surveyed mortality statistics and data from 8,533 medicolegal autopsies in 1968 through 1988. Liver cirrhosis mortality statistics revealed a highly significant (p less than 0.001) increase from 6.4 to 13.7 per 100,000 during the period, and similarly, the prevalence of liver cirrhosis in the autopsy series showed a highly significant (p less than 0.001) increase from 3.0% to 6.1%. More specifically, this increase was attributable to a highly significantly (Chi-square 15.4, p less than 0.001) increased proportion of alcoholic liver cirrhosis occurring at a younger age and almost exclusively in males. The stepwise mode of increase as well as the changes in sex and age distribution of cirrhosis since 1969 could be interpreted as an effect of distribution of consumption to a new generation of consumers. The forensic autopsy series seemed to reflect changes in per capita consumption with a shorter time lag than with mortality statistics. Additionally, only 7% of the 448 cirrhotics singled out from this material exhibited liver cirrhosis as a cause of death and were thus also included in the official mortality statistics, suggesting the greater accuracy of our forensic autopsy series.

Adult↗
PubMed2005

The ALS/MND prevalence in Sweden estimated by riluzole sales statistics.

OBJECTIVES: To determine whether sales statistics for riluzole can be used as a marker for the prevalence of amyotrophic lateral sclerosis (ALS)/motor neuron disease (MND) in Sweden. MATERIALS AND METHODS: A questionnaire was sent to all neurological units in Sweden asking about the numbers of patients with ALS/MND and whether these patients were treated with riluzole. Sales statistics for riluzole were obtained from the 906 public pharmacies and 89 hospital pharmacies in Sweden. RESULTS: Eighty percent of the neurological units answered the questionnaire. The estimated prevalence in September 2003 from the questionnaire was 5.4/100,000 inhabitants. The sales expressed in defined daily dose/100,000 inhabitants/day was 3.8. For the counties the correlation between these two parameters was 0.83. CONCLUSION: Estimated prevalence is highly correlated with sales statistics for riluzole. Riluzole sales statistics could be used as a crude marker for the prevalence of ALS/MND in Sweden.

Adolescent↗
PubMedDate not supplied

Can't miss: conquer any number task by making important statistics simple. Part 5. Comparing two confidence intervals, standard error of the difference between two means and between two proportions.

Healthcare quality professionals need to understand and use inferential statistics to interpret sample data from their organizations. Since in quality improvement and healthcare research studies all the data from a population often are not available, investigators take samples and make inferences about that population using inferential statistics. This series of six articles will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals and tests of statistical significance for samples of data. This article, Part 5, demonstrates the comparison of two confidence intervals as a method for estimating the difference between two population means. The concept of the standard error of the difference between two sample means is presented along with the confidence interval for estimating the difference between two population means. The article concludes with the standard error and confidence interval for estimating the difference between two population proportions from a binomial variable.

Confidence Intervals↗
PubMed2006

Synthetic statistical approach reveals a high degree of richness of microbial eukaryotes in an anoxic water column.

Molecular surveys suggest that communities of microbial eukaryotes are remarkably rich, because even large clone libraries seem to capture only a minority of species. This provides a qualitative picture of protistan richness but does not measure its real extent either locally or globally. Statistical analysis can estimate a community's richness, but the specific methods used to date are not always well grounded in statistical theory. Here we study a large protistan molecular survey from an anoxic water column in the Cariaco Basin (Caribbean Sea). We group individual 18S rRNA gene sequences into operational taxonomic units (OTUs) using different cutoff values for sequence similarity (99 to 50%) and systematically apply parametric models and nonparametric estimators to the OTU frequency data to estimate the total protistan diversity. The parametric models provided statistically sound estimates of protistan richness, with biologically meaningful standard errors, maximal data usage, and extensive model diagnostics and were preferable to the available nonparametric tools. Our clone library exceeded 700 clones but still covered only a minority of species and less than half of the larger protistan clades. Our estimates of total protistan richness portray the target community as very rich at all OTU levels, with hundreds of different populations apparently co-occurring in the small (3-liter) volume of our sample, as well as dozens of clades of the highest taxonomic order. These estimates are among the first for microbial eukaryotes that are obtained using state-of-the-art statistical methods and can serve as benchmark numbers for the local diversity of protists.

Anaerobiosis↗
PubMed2002

Underestimates of unintentional firearm fatalities: comparing Supplementary Homicide Report data with the National Vital Statistics System.

OBJECTIVE: A growing body of evidence suggests that the nation's vital statistics system undercounts unintentional firearm deaths that are not self inflicted. This issue was examined by comparing how unintentional firearm injuries identified in police Supplementary Homicide Report (SHR) data were coded in the National Vital Statistics System. METHODS: National Vital Statistics System data are based on death certificates and divide firearm fatalities into six subcategories: homicide, suicide, accident, legal intervention, war operations, and undetermined. SHRs are completed by local police departments as part of the FBI's Uniform Crime Reports program. The SHR divides homicides into two categories: "murder and non-negligent manslaughter" (type A) and "negligent manslaughter" (type B). Type B shooting deaths are those that are inflicted by another person and that a police investigation determined were inflicted unintentionally, as in a child killing a playmate after mistaking a gun for a toy. In 1997, the SHR classified 168 shooting victims this way. Using probabilistic matching, 140 of these victims were linked to their death certificate records. RESULTS: Among the 140 linked cases, 75% were recorded on the death certificate as homicides and only 23% as accidents. CONCLUSION: Official data from the National Vital Statistics System almost certainly undercount firearm accidents when the victim is shot by another person.

Adolescent↗
PubMed2001

Natural image statistics and neural representation.

It has long been assumed that sensory neurons are adapted, through both evolutionary and developmental processes, to the statistical properties of the signals to which they are exposed. Attneave (1954)Barlow (1961) proposed that information theory could provide a link between environmental statistics and neural responses through the concept of coding efficiency. Recent developments in statistical modeling, along with powerful computational tools, have enabled researchers to study more sophisticated statistical models for visual images, to validate these models empirically against large sets of data, and to begin experimentally testing the efficient coding hypothesis for both individual neurons and populations of neurons.

Animals↗