Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Poisson Distribution”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,423 records · Page 79Linked to original sources
PubMed2004

Velocity and hierarchical spread of epidemic outbreaks in scale-free networks.

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.

Disease Outbreaks↗
PubMedDate not supplied

Progress of a half century in the study of the Luria-Delbrück distribution.

The Luria-Delbrück mutation model has been mathematically formulated in a number of ways. This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants. These issues include the probability generating functions, moments (cumulants), computational methods and asymptotics. This review emphasizes basic principles which not only help to unify existing results but also allow for a few useful extensions. In addition, the review offers a historical perspective and some new explanations of divergent moments.

Genetics↗
PubMed2005

Analyzing protein lists with large networks: edge-count probabilities in random graphs with given expected degrees.

We present an analytical framework to analyze lists of proteins with large undirected graphs representing their known functional relationships. We consider edge-count variables such as the number of interactions between a protein and a list, the size of a subgraph induced by a list, and the number of interactions bridging two lists. We derive approximate analytical expressions for the probability distributions of these variables in a model of a random graph with given expected degrees. Probabilities obtained with the analytical expressions are used to mine a protein interaction network for functional modules, characterize the connectedness of protein functional categories, and measure the strength of relations between modules.

Algorithms↗
PubMed2004

TCP isoeffect analysis using a heterogeneous distribution of radiosensitivity.

A formula for the alpha/beta ratio is derived using the heterogeneous (population averaged) tumor control model. This formula is nearly identical to the formula obtained using the homogeneous (individual) tumor control model, but the new formula includes extra terms showing that the alpha/beta ratio, the ratio of the mean value of a divided by the mean value of beta that would be observed in a patient population, explicitly depends on the survival level and heterogeneity. The magnitude of this correction is estimated for prostate cancer, and this appears to raise the mean value of the ratio estimate by about 20%. The method also allows investigation of confidence limits for alpha/beta based on a population distribution of radiosensitivity. For a widely heterogeneous population, the upper 95% confidence interval for the alpha/beta ratio can be as high as 7.3 Gy, even though the population mean is between 2.3 and 2.6 Gy.

Cell Survival↗
PubMed2006

Probing gene expression in live cells, one protein molecule at a time.

We directly observed real-time production of single protein molecules in individual Escherichia coli cells. A fusion protein of a fast-maturing yellow fluorescent protein (YFP) and a membrane-targeting peptide was expressed under a repressed condition. The membrane-localized YFP can be detected with single-molecule sensitivity. We found that the protein molecules are produced in bursts, with each burst originating from a stochastically transcribed single messenger RNA molecule, and that protein copy numbers in the bursts follow a geometric distribution. The quantitative study of low-level gene expression demonstrates the potential of single-molecule experiments in elucidating the workings of fundamental biological processes in living cells.

Bacterial Proteins↗
PubMed2006

Particle size limits to meet USP content uniformity criteria for tablets and capsules.

Content uniformity (CU) of pharmaceutical dosage units can be affected by active pharmaceutical ingredient (API) particle size and size distribution. Previous authors have estimated this impact but use of different particle size descriptors led to confusion and difficulty in applying the theoretical models developed. We show that when the same descriptors for particle size and distribution are used (i.e., median diameter on a weight basis (d(50)) and geometric standard deviation (sigma(g))), previously published models are consistent. The approach of Yalkowsky and Bolton4 [Pharm Res 7:962-966, 1990] is modified to use these descriptors and updated for current USP28/NF23 CU criteria. A nomograph is provided to allow easy estimation of an acceptable d(50) for a given dose and sigma(g). To test the model's validity, tablets were manufactured over a wide range of doses and assayed for CU. As predicted, %relative standard deviation (RSD) increased as dose decreased. However, for APIs that deviate significantly from the assumed log-normal distribution, sigma(g) is more appropriately described by the upper region of the API size distribution, presumably because large particles have greatest influence on CU. At very low doses, CU values deviate significantly from normality, consistent with the presence of single large API particles causing super-potent dosage units.

Algorithms↗
PubMed2005

Prevention of work related eye injuries: long term assessment of the effectiveness of a multicomponent intervention among metal workers.

BACKGROUND: Systematic assessments of the effectiveness of interventions to prevent work related eye injuries are needed. AIM: To investigate the long term effectiveness of a multicomponent prevention campaign. METHODS: The campaign (conducted in collaboration with the local Employers' Association and Trade Unions) targeted all 237 metal-ware factories in the district of Imola, Italy. Based on preliminary inspections, the main intervention included distribution to all factories of specific educational brochures and broadcasting/publication of television/radio programmes and local newspaper articles containing expert advice on the subject. This was followed by a four year "post-intervention reinforcement" period of unannounced official inspections. Main outcome measures analysed were eye injury rates (versus non-eye injury rates) among metal workers during "pre-intervention" (1988-90), "peri-intervention" (1991-92), "post-intervention reinforcement" (1993-96), "late post-intervention" (1997-2000), and "very late post-intervention" (2001-03) periods with respect to two comparison sectors (construction and wood/ceramics). RESULTS: A Poisson regression in which the eye injury rates were modelled for each sector, period, and interaction, adjusting for non-eye injury rates, was chosen. The periods did not by themselves determine an overall reduction in eye injuries. The period/sector interaction terms were related to significant reductions for the metal sector when crossed with the "post-intervention reinforcement" (IRR = 0.77, 95% CI 0.61 to 0.97; % decline = 23.4), the "late post-intervention" (IRR = 0.63, 95% CI 0.50 to 0.79; % decline = 37.4), and the "very late post-intervention" (IRR = 0.58, 95% CI 0.43 to 0.77; % decline = 42.4) periods, suggesting a sustained reduction in eye injury risk following the main intervention. CONCLUSION: Results suggest that a carefully coordinated, extensive, multicomponent intervention can lead to lasting reductions in the burden of eye injuries.

Accidents, Occupational↗
PubMed1996

Marker processes in survival analysis.

In the development of many diseases there are often associated variables which continuously measure the progress of an individual towards the final expression of the disease (failure). Such variables are stochastic processes, here called marker processes, and, at a given point in time, they may provide information about the current hazard and subsequently on the remaining time to failure. Here we consider a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. We develop some basic calculations based on this model. Interest is focused on statistical applications for markers related to estimation of the survival distribution of time to failure, including (i) the use of markers as surrogate responses for failure with censored data, and (ii) the use of markers as predictors of the time elapsed since onset of a survival process in prevalent individuals. Particular attention is directed to potential gains in efficiency incurred by using marker process information.

Biomarkers↗
PubMed2001

Cluster and regional influences on suicide in a Southwestern American Indian tribe.

Suicide is the second leading cause of death among American Indian youth. Elevated rates of suicide in Indian communities have been attributed both to outbreaks and to regional trends. We assessed the contribution of these two factors for a single tribe, and attempted to define a profile of individuals at risk. Data came from the tribe's registry of suicide attempts and completions for 1990-1993 and analysis of death certificates for the period 1985-1996. Using combined tribal and death certificate data, the average annual (age-adjusted) rate of completed suicide among tribal members was 44.7/100,000 for 1990-1993. Within the 45 suicide deaths and serious attempts in this time period, we identified one grouping of seven cases taking place in a 40-day period. All seven involved hanging and youth (13-28 years old). Using death certificate data alone, the average annual rate of suicide death for non-natives in the surrounding county in the period 1985-1996 was 22.7/100,000. Age-adjusted to the county population, the tribal rate for the same period was not significantly different (24.6/100,000). Tribal and county suicide patterns differed by age distribution and method but not by gender. We concluded that both regional trends and clustering contribute to suicide in this community. Further prevention efforts may need to focus on both unique tribal characteristics and shared factors among non-native neighbors.

Adolescent↗
PubMed2002

The formation of ionisation clusters by alpha particles in 'nanometric' volumes of nitrogen: experiment and calculation.

Probability distributions of the size of ion clusters created in 'nanometric' cylindrical volumes of nitrogen by single 4.6 MeV alpha particles were measured and compared with those calculated by Monte Carlo simulation. The diameter of the sensitive volume had a mass per area of between 0.015 and 1.3 micrograms.cm-2 which, for a material at unit density, corresponds to a diameter of between 0.15 nm and 13 nm. These nanometre sizes were simulated experimentally in a device called Jet Counter. The measured or calculated cluster size probabilities confirmed that the formation of ionisation clusters along a 'nanometre' track can be characterised by Poisson's distribution only for very small targets. The present ionisation cluster probabilities produced in 'nanometric' volumes, 2 to 10 nm in diameter, are the first ever determined experimentally and confirmed by Monte Carlo simulation.

Alpha Particles↗
PubMed2000

Pulmonary blood flow remains fractal down to the level of gas exchange.

The spatial distribution of pulmonary blood flow is increasingly heterogeneous as progressively smaller lung regions are examined. To determine the extent of perfusion heterogeneity at the level of gas exchange, we studied blood flow distributions in rat lungs by using an imaging cryomicrotome. Approximately 150,000 fluorescent 15-microm-diameter microspheres were injected into tail veins of five awake rats. The rats were heavily anesthetized; the lungs were removed, filled with an optimal cutting tissue compound, and frozen; and the spatial location of every microsphere was determined. The data were mathematically dissected with the use of an unbiased random sampling method. The coefficients of variation of microsphere distributions were determined at varying sampling volumes. Perfusion heterogeneity increased linearly on a log-log plot of coefficient of variation vs. volume, down to the smallest sampling size of 0.53 mm(3). The average fractal dimension, a scale-independent measure of perfusion distribution, was 1.2. This value is similar to that of other larger species such as dogs, pigs, and horses. Pulmonary perfusion heterogeneity increases continuously and remains fractal down to the acinar level. Despite the large degree of perfusion heterogeneity at the acinar level, gases are efficiently exchanged.

Algorithms↗
PubMed2004

Estimating the temporal interval entropy of neuronal discharge.

To better understand the role of timing in the function of the nervous system, we have developed a methodology that allows the entropy of neuronal discharge activity to be estimated from a spike train record when it may be assumed that successive interspike intervals are temporally uncorrelated. The so-called interval entropy obtained by this methodology is based on an implicit enumeration of all possible spike trains that are statistically indistinguishable from a given spike train. The interval entropy is calculated from an analytic distribution whose parameters are obtained by maximum likelihood estimation from the interval probability distribution associated with a given spike train. We show that this approach reveals features of neuronal discharge not seen with two alternative methods of entropy estimation. The methodology allows for validation of the obtained data models by calculation of confidence intervals for the parameters of the analytic distribution and the testing of the significance of the fit between the observed and analytic interval distributions by means of Kolmogorov-Smirnov and Anderson-Darling statistics. The method is demonstrated by analysis of two different data sets: simulated spike trains evoked by either Poissonian or near-synchronous pulsed activation of a model cerebellar Purkinje neuron and spike trains obtained by extracellular recording from spontaneously discharging cultured rat hippocampal neurons.

Action Potentials↗
PubMed1992

Interval estimation for mark-recapture studies of closed populations.

Textbooks continue to recommend the use of an asymptotic normal distribution to provide an interval estimate for the unknown size, N, of a closed population studied by a mark-recapture experiment or multiple-record system. A likelihood interval approach is proposed and its implementation demonstrated for a range of models for such studies, including all main effect and interaction models for incomplete contingency tables.

Animals↗
PubMed1997

Epidemiologic study of occupational injuries among foreign and native workers in Taiwan.

This study was designed to compare the risk of occupational injuries in foreign workers compared to native workers in Taiwan. The cohort of foreign workers under study was constructed by records of legally registered workers migrated from foreign countries to Taiwan from July 1, 1991 to December 31, 1993. The native Taiwanese workers for comparison were labor-insured workers working in the same industries as foreign workers in 1992. The number of occupational injuries in the first year of employment were obtained by matching the cohort of foreign workers with the labor insurance payment records by name, birth date and passport number. The 1-year incidence rate of occupational injuries in the first year of employment was calculated and a standardized morbidity ratio (SMR) was used for comparison with adjustment for age distribution and to accommodate the small sample size of foreign workers. The risk to occupational injuries among total (SMR = 0.86) and male (SMR = 0.58) foreign workers was not higher; indeed, it was even lower, than that among native workers in Taiwan. However, the risk to female migrant workers, especially in the construction industry, was significantly higher than that of female Taiwanese workers (SMR = 1.60). Stratified by industry, the incidence was high in the fabricated metal products manufacturing industry and in machinery and equipment manufacturing industry for male foreign workers, while a high incidence for the female foreign workers occurred in construction industry and rubber products manufacturing industry. The risk of occupational injuries was greater for foreign workers who had been in Taiwan for only a short time. Most of the injuries occurred within the first 6 months of employment. Eighty-four out of the 394 occupational injuries among foreign workers resulted in disabilities. None of the accidents was fatal, but most of the disabilities were severe. The most common disabling injuries were cut or crushed fingers. The finding of a similar distribution of occupational injuries among foreign and native workers indicates that control measures are needed to reduce occupational injuries for all foreign and native workers in Taiwan.

Accidents, Occupational↗
PubMed1994

Bone remodeling and structural optimization.

Bone remodeling has been viewed both as a process which adapts bone tissue to the mechanical environment at each point in the structure, and as a process which optimally adjusts the tissue distribution within bones to bear the loads placed on them. We have developed a connection between these two views of bone remodeling, in a restricted sense. We start with a remodeling rate equation based on strain energy density. We then define an indicator function which is a weighted sum of total strain energy and a measure of bone mass, and we show that finding bone density distributions in which the remodeling rate equation predicts no changes with time is the same as finding density distributions in which the indicator function is insensitive to small changes in density. The set point in the remodeling rate equation corresponds to a parameter in the indicator function which determines the relative importance of bone mass and strain energy in the optimization indicator function. We have not assessed whether the density distributions which make the density rate of change zero are actually local or global minima for the indicator function in this study, but a related study shows that there is a single unique minimum for the indicator function developed here, implying that a unique solution exists for the bone remodeling rate equations considered in this study.

Biomechanical Phenomena↗
PubMed2000

On variability in the density of corticocortical and thalamocortical connections.

Variability is an important but neglected aspect of connectional neuroanatomy. The quantitative density of the 'same' corticocortical or thalamocortical connection may vary by over two orders of magnitude between different injections of the same tracer. At present, however, the frequency distribution of connection densities is unknown. Therefore, it is unclear what kind of sampling strategies or statistical methods are appropriate for quantitative studies of connectivity. Nor is it clear if the measured variability represents differences between subjects, or if it is simply a consequence of intra-individual differences resulting from experimental technique and the exact placement of tracers relative to local spatial and laminar variation in connectivity. We used quantitative measurements of the density of a large number of corticocortical and thalamocortical connections from our own laboratories and from the literature. Variability in the density of given corticocortical and thalamocortical connections is high, with the standard deviation of density proportional to the mean. The frequency distribution is close to exponential. Therefore, analysis methods relying on the normal distribution are not appropriate. We provide an appendix that gives simple statistical guidance for samples drawn from exponentially distributed data. For a given corticocortical or thalamocortical connection density, between-individual standard deviation is 0.85 to 1.25 times the within-individual standard deviation. Therefore, much of the variability reported in conventional neuroanatomical studies (with one tracer deposited per animal) is due to within-individual factors. We also find that strong, but not weak, corticocortical connections are substantially more variable than thalamocortical connections. We propose that the near exponential distribution of connection densities is a simple consequence of 'patchy' connectivity. We anticipate that connection data will be well described by the negative binomial, a class of distribution that applies to events occurring in clumped or patchy substrates. Local patchiness may be a feature of all corticocortical connections and could explain why strong corticocortical connections are more variable than strong thalamocortical connections. This idea is supported by the columnar patterns of many corticocortical but few thalamocortical connections in the literature.

Animals↗
PubMed1992

Auditory-nerve action potentials form a nonrenewal point process over short as well as long time scales.

The firing patterns of auditory-nerve action potentials exhibit long-term fractal fluctuations that do not arise from the distribution of the interevent intervals, but rather from the ordering of these intervals. Using the serial interevent-interval correlation coefficient, the Fano-factor time curve, and shuffling of interevent intervals, it is shown that adjacent intervals for spontaneous firings exhibit significant correlation. The events are therefore nonrenewal over short as well as long time scales.

Evoked Potentials, Auditory↗
PubMed1995

Human lymphocyte cDNA ordered library analyzed by 2D gel electrophoresis. 2. Frequency distribution of mRNA populations.

Cell-free transcription and translation products from an ordered library of cDNA clones from the CEM human leukemic cell line were submitted to analysis using two-dimensional gel electrophoresis as a read out system. The matrix array of 24 x 16 x 12 wells contained in each of the positions lambda jacII phages from one plaque. Pools of clones along the three axes (24 x-pools, 16 y-pools and 12 z-pools) were established. Results obtained upon matching of 12 x-pools were scrutinized for estimating the frequency of cDNA molecular species in the library. The results obtained are interpreted in such a way that there are no discrete distributions of mRNA molecular species, but rather there is a continuous distribution of mRNA's covering a wide range of frequencies. The lowest frequency found was about 4.5 x 10(-4) and the highest 1.6 x 10(-2). About half of all clones can be found among these low frequency ones (each occurring 0.45 times among 1,000 clones).

Cell-Free System↗