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 1,045 records · Page 58Linked to original sources
PubMed2005

Alternative approaches for the estimation of the band broadening parameters in single-detection size exclusion chromatography.

New approaches for the determination of the extent of symmetric and asymmetric band broadening (BB) in size exclusion chromatography (SEC) are presented. For this purpose raw data was simulated by starting with either a theoretical Poisson number chain length distribution (NCLD), or a log-normal weight chain length distribution (WCLD). Each distribution was first converted to a BB-free mass chromatogram, as typically obtained from a standard differential refractive index detector. Then, the broadened (or "measured") chromatograms were simulated by convoluting the BB-free chromatograms with a BB function, which was assumed to follow symmetrical (Gauss) as well as unsymmetrical (exponentially modified Gauss) function. A broad range of BB parameters (standard deviation, sigma(BB), and exponential decay, tau(BB)) was used for the simulations. The approaches are based on the determination of the points of inflection belonging to the peak of the broadened chromatogram, and closed as well as empirically derived equations connecting the peak width, its variance, and the parameters sigma(BB) and tau(BB). The developed methods are applicable for Poisson distributions well above a peak chain length of 100.

Chromatography, Gel↗
PubMed2004

N-mixture models for estimating population size from spatially replicated counts.

Spatial replication is a common theme in count surveys of animals. Such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability. In this article, I describe a class of models (N-mixture models) which allow for estimation of population size from such data. The key idea is to view site-specific population sizes, N, as independent random variables distributed according to some mixing distribution (e.g., Poisson). Prior parameters are estimated from the marginal likelihood of the data, having integrated over the prior distribution for N. Carroll and Lombard (1985, Journal of American Statistical Association 80, 423-426) proposed a class of estimators based on mixing over a prior distribution for detection probability. Their estimator can be applied in limited settings, but is sensitive to prior parameter values that are fixed a priori. Spatial replication provides additional information regarding the parameters of the prior distribution on N that is exploited by the N-mixture models and which leads to reasonable estimates of abundance from sparse data. A simulation study demonstrates superior operating characteristics (bias, confidence interval coverage) of the N-mixture estimator compared to the Caroll and Lombard estimator. Both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence.

Animals↗
PubMed1986

Partition structures, Polya urns, the Ewens sampling formula, and the ages of alleles.

It has recently been shown that the Ewens sampling formula may be generated by a Polya-like urn model. A genealogical proof of this result equates the labelling of balls in the urn to the partition by age of alleles in the sample. This urn construction is shown to be equivalent to the construction of Kingman (Proc. Roy. Soc. London Ser. A 361 (1978), 1-20) using a Poisson-Dirichlet "paintbox" and as a consequence, the partition by ages is seen to be equivalent to the size biased permutation of the Poisson-Dirichlet distribution. This approach unifies and extends many results on ages of alleles, the Polya urn, and the Poisson-Dirichlet distribution. Furthermore the Ewens sampling formula is characterized as being the only partition structure which may be generated by an urn-like mechanism.

Age Factors↗
PubMed1994

Poisson-like fluctuation patterns of revertants of leucine auxotrophy (leu-500) in Salmonella typhimurium caused by delay in mutant cell division.

Leu+ mutants from Salmonella typhimurium leu-500 strain MA412 arise at high frequencies and mutant colonies appear over a broad range of time on selective plates. This observation suggested that these Leu+ mutants might be induced or "directed."= If such a mechanism was responsible, mutants should originate on selective plates rather than in the preceding culture in nonselective conditions and should give rise to Poisson-like fluctuation curves upon plating of sister cultures on selective medium. Poisson-like distribution profiles were indeed observed for Leu+ mutants of S. typhimurium MA412. However, an explanation for the observed Poisson-like fluctuation patterns without a need for selection-induced mutations was found. Microscopical analysis and cell mass/viable count measurements showed that the size of Leu+ mutant cells was often much larger than those of nonmutants. This size difference was a stable characteristic of a large proportion of Leu+ mutants, was observed both in stationary and growing culture and did not measurably affect the division rates of the cells in nutrient broth. As the transition from normal-sized nonmutant to oversized mutant cells during the nonselective culture phase of the fluctuation experiment may have been accompanied by a period with no or few completed cell division cycles, the number of mutant offspring may have been smaller than that of sibling nonmutants. Such underrepresentation of mutants in the final culture is expected to give rise to Poisson-like fluctuation patterns without invoking "directed" mutations.

Cell Division↗
PubMed1998

Detection of total- and partial-body irradiation in a monkey model: a comparative study of chromosomal aberration, micronucleus and premature chromosome condensation assays.

PURPOSE: To investigate the efficacy of three cytogenetic methods (dicentrics, micronuclei (MN) and premature chromosome condensation (PCC) analysis) for assessment of the unirradiated fraction and the persistence of damage after total-body (TB) and partial-body (PB) irradiation of rhesus monkeys (Macaca mulatta). MATERIALS AND METHODS: Animals were exposed to X-rays (5 Gy), either TB or PB, with about 6% of marrow cells shielded. Blood samples were collected at different times after exposure, i.e. 1, 3 and 7 days, and cultures were set up for the different cytogenetic endpoints. In addition, blood count analysis was performed before and after irradiation. RESULTS: Blood count analysis was not suitable for discriminating between TB and PB exposure. By using Poisson or overdispersion distribution as the basis, it was not possible to distinguish TB from PB irradiation when dicentric chromosomes and MN were analysed. PCC analysis, in contrast, showed a Poisson distribution after TB exposure and overdispersion after PB exposure. Using the PCC assay, reliable dose estimates could be obtained up to 7 days after irradiation. CONCLUSIONS: For dicentrics and MN, shielding of 6% of bone marrow cells was found to be too small to estimate the unirradiated fraction accurately. The PCC technique was useful for dose assessment and the inhomogeneous exposure of 6% was detected within a short period of time after exposure.

Animals↗
PubMed1982

Local regulation of transmitter release from rodent sympathetic nerve terminals?

1. Electrophysiological techniques were used to observe the release of transmitter from single release sites in the sympathetic neuro-effector junction of the rodent vas deferens. Transmitter release produces transient peaks in the rate of depolarization of the smooth muscle cells, known as 'discrete events'. 2. The amplitude distributions of stimulus-evoked discrete events in both mouse and guinea-pig vas are multi-modal. In the mouse, the distribution fits a Poisson with a 'quantal content' of about two. There are too many zeros in the amplitude distributions of guinea-pig discrete events to fit a Poisson distribution, and it is likely that in this species there is a mechanism preceding the transmitter release process which may occasionally prevent it operating. 3. alpha-adrenoreceptor agonists and antagonists produce, respectively, left and right shifts in the amplitude distributions of discrete events at a single latency, with no change in the amplitudes at the modes. 4. There is, however, no evidence of any inhibitory relationship between either discrete events evoked by successive stimuli, or early and late discrete events following a given stimulus. 5. Transmitter release at this junction is therefore packeted, with few quanta released by each stimulus. Release from single sites is affected in ways compatible with the 'alpha-feed-back' hypothesis by alpha-adrenoreceptor agonists and antagonists, but in the absence of drugs we can find no evidence of any local feed-back inhibition of transmitter release.

Animals↗
PubMed1995

Exact inbreeding coefficient and effective size of finite populations under partial sib mating.

An exact recurrence equation for inbreeding coefficient is derived for a partially sib-mated population of N individuals mated in N/2 pairs. From the equation, a formula for effective size (Ne) taking second order terms of 1/N into consideration is derived. When the family sizes are Poisson or equally distributed, the formula reduces to Ne = [(4 - 3 beta) N/(4 - 2 beta)] + 1 or Ne = [(4 - 3 beta) N/(2 - 2 beta)] - 8/(4 - 3 beta), approximately. For the special case of sib-mating exclusion and Poisson distribution of family size, the formula simplifies to Ne = N + 1, which differs from the previous results derived by many authors by a value of one. Stochastic simulations are run to check our results where disagreements with others are involved.

Animals↗
PubMed1996

Formulae and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the two-sample design: a review.

This paper is a compendium of exact and asymptotic formulae and tables for estimating the sample size in a clinical trial with two treatment groups and a dichotomous outcome. The paper provides separate formulae for equal and unequal treatment group sizes, formulae for the calculation of power given the sample size, and complete references for all formulae and tables cited.

Binomial Distribution↗
PubMed2006

A search model and figure of merit for observer data acquired according to the free-response paradigm.

Search is a basic activity that is performed routinely in many different tasks. In the context of medical imaging it involves locating lesions in images under conditions of uncertainty regarding the number and locations of lesions that may be present. A search model is presented that applies to situations, as in the free-response paradigm, where on each image the number of normal regions that could be mistaken for lesions is unknown, and the number of observer generated localizations of suspicious regions (marks) is unpredictable. The search model is based on a two-stage model that has been proposed in the literature, according to which, at the first stage (the preattentive stage) the observer uses mainly peripheral vision to identify likely lesion candidates, and at the second stage the observer decides (i.e., cognitively evaluates) whether or not to report the candidates. The search model regards the unpredictable numbers of lesion and non-lesion localizations as random variables and models them via appropriate statistical distributions. The model has three parameters quantifying the lesion signal-to-noise ratio, the observer's expertise at rejecting non-lesion locations, and the observer's expertise at finding lesions. A figure-of-merit quantifying the observer's search performance is described. The search model bears a close resemblance to the initial detection and candidate analysis (IDCA) model that has been recently proposed for analysing computer aided detection (CAD) algorithms. The ability to analytically model and quantify the search process would enable more powerful assessment and optimization of performance in these activities, which could be highly significant.

Algorithms↗
PubMedDate not supplied

Checking homogeneity of motifs' distribution in heterogenous sequences.

Studying the distribution of a motif along sequences may help in the understanding of its biological function, or to detect regions of interest. A statistical model is needed to assess the significance of the observed distribution. We propose a heterogenous compound Poisson process to model the possibility of overlap between occurrences and some heterogeneity of the sequence known a priori. The estimation procedure of the parameters is described and tests of homogenous sub-models are proposed. We also consider the detection of rich regions using either cumulated distances or moving intervals, via a homogenization technique. Illustrations of the method are given with applications to bacterial genomes.

Algorithms↗
PubMed2004

Discerning aggregation in homogeneous ensembles: a general description of photon counting spectroscopy in diffusing systems.

In order to discern aggregation in solution, we present a quantum mechanical analog of the photon statistics from fluorescent molecules diffusing through a focused beam. A generating functional is developed to fully describe the experimental physical system as well as the statistics. Histograms of the measured time delay between photon counts are fit by an analytical solution describing the static as well as diffusing regimes. To determine empirical fitting parameters, fluorescence correlation spectroscopy is used in parallel to the photon counting. For expedient analysis, we find that the distribution's deviation from a single Poisson shows a difference between two single fluor monomers or a double fluor aggregate of the same total intensities. Initial studies were performed on fixed-state aggregates limited to dimerization. However preliminary results on reactive species suggest that the method can be used to characterize any aggregating system.

Biophysics↗
PubMed1998

List-mode likelihood: EM algorithm and image quality estimation demonstrated on 2-D PET.

Using a theory of list-mode maximum-likelihood (ML) source reconstruction presented recently by Barrett et al., this paper formulates a corresponding expectation-maximization (EM) algorithm, as well as a method for estimating noise properties at the ML estimate. List-mode ML is of interest in cases where the dimensionality of the measurement space impedes a binning of the measurement data. It can be advantageous in cases where a better forward model can be obtained by including more measurement coordinates provided by a given detector. Different figures of merit for the detector performance can be computed from the Fisher information matrix (FIM). This paper uses the observed FIM, which requires a single data set, thus, avoiding costly ensemble statistics. The proposed techniques are demonstrated for an idealized two-dimensional (2-D) positron emission tomography (PET) [2-D PET] detector. We compute from simulation data the improved image quality obtained by including the time of flight of the coincident quanta.

Algorithms↗
PubMed2000

Reconstruction of two- and three-dimensional images from synthetic-collimator data.

A novel SPECT collimation method, termed the synthetic collimator, is proposed. The synthetic collimator employs a multiple-pinhole aperture and a high-resolution detector. The problem of multiplexing, normally associated with multiple pinholes, is reduced by obtaining projections at a number of pinhole-detector distances. Projections with little multiplexing are collected at small pinhole-detector distances and high-resolution projections are collected at greater pinhole-detector distances. These projections are then reconstructed using the ML-EM algorithm. It is demonstrated through computer simulations that the synthetic collimator has superior resolution properties to a high-resolution parallel-beam (HRPB) collimator and a specially built ultra-high-resolution parallel-beam (UHRPB) collimator designed for our 0.38-mm pixel CdZnTe detectors. It is also shown that reconstructing images in three dimensions is superior to reconstructing them in two dimensions. The advantages of a high-resolution synthetic collimator over the parallel-hole collimators are apparently reduced in the presence of statistical noise. However, a high-sensitivity synthetic collimator was designed which again shows superior properties to the parallel-hole collimators. Finally, it is demonstrated that, for the cases studied, high-resolution detectors are necessary for the proper functionality of the synthetic collimator.

Algorithms↗
PubMed2000

Resolution and noise properties of MAP reconstruction for fully 3-D PET.

We derive approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three-dimensional (3-D) positron emission tomography (PET) data using maximum a posteriori (MAP) estimation. These expressions explicitly account for the spatially variant detector response and sensitivity of a 3-D tomograph. The resulting spatially variant impulse response and covariance are computed using 3-D Fourier transforms. A truncated Gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in MAP reconstruction. Using Monte Carlo simulations and phantom data from the microPET small animal scanner, we show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions. We also describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.

Algorithms↗
PubMed2001

Synchronization of the neural response to noisy periodic synaptic input.

The timing information contained in the response of a neuron to noisy periodic synaptic input is analyzed for the leaky integrate-and-fire neural model. We address the question of the relationship between the timing of the synaptic inputs and the output spikes. This requires an analysis of the interspike interval distribution of the output spikes, which is obtained in the gaussian approximation. The conditional output spike density in response to noisy periodic input is evaluated as a function of the initial phase of the inputs. This enables the phase transition matrix to be calculated, which relates the phase at which the output spike is generated to the initial phase of the inputs. The interspike interval histogram and the period histogram for the neural response to ongoing periodic input are then evaluated by using the leading eigenvector of this phase transition matrix. The synchronization index of the output spikes is found to increase sharply as the inputs become synchronized. This enhancement of synchronization is most pronounced for large numbers of inputs and lower frequencies of modulation and also for rates of input near the critical input rate. However, the mutual information between the input phase of the stimulus and the timing of output spikes is found to decrease at low input rates as the number of inputs increases. The results show close agreement with those obtained from numerical simulations for large numbers of inputs.

Action Potentials↗
PubMed2005

The dual-color photon counting histogram with non-ideal photodetectors.

Dual-color photon counting histogram (PCH) analysis utilizes the photon counts in two detection channels to distinguish species by differences in brightness and color. Here we modify the existing dual-color PCH theory, which assumes ideal detectors, to include the non-ideal nature of the detector. Specifically, we address the effects of deadtime and afterpulsing. Both effects modify the shape of the dual-color PCH and thus potentially lead to incorrect values for the brightness and number of molecules if an ideal model is assumed. We use the modified theory to predict the effects of detector non-idealities on dual-color PCH as a function of concentration and brightness. In addition, we introduce a method based on moment analysis to determine the error in brightness due to non-ideal detector effects. We verify our theory experimentally by measuring a dye solution as a function of concentration and brightness. We determine the deadtime and afterpulse probability of our detectors and show that both effects play an important role in the analysis of dual-color PCH experiments. We demonstrate that resolving a mixture of CFP and YFP requires taking non-ideal detector effects into account. These corrections are also crucial for cellular measurements, as shown for GFP and RFP in mammalian cells.

Algorithms↗
PubMedDate not supplied

Modelling survival data with a cured fraction using frailty models.

Cure models have historically been utilized to analyse time-to-event data with a cured fraction. We consider the use of frailty models as an alternative approach to modelling such data. An attractive feature of the models is the allowance for heterogeneity in risk among those individuals experiencing the event of interest in addition to the incorporation of a cured component. Utilizing maximum likelihood techniques, we fit models to data concerning the recurrence of leukaemia among patients receiving autologous transplantation treatment. The analysis suggests that the gamma frailty mixture model and the compound Poisson improve on the fit of the leukaemia data as compared to the standard cure model.

Humans↗
PubMed2001

Thyroid carcinoma is characterized by genomic instability: evidence from p53 mutations.

p53 is a transcription factor with multifaceted regulatory functions in cell cycle progression, DNA repair, and programmed cell death. Inactivating mutations have been described in 50% of human cancers. These mutations appear to be important in tumor progression and response to chemotherapy and radiation treatment and thus clinical outcome. p53 mutations are found in 14% of malignant thyroid tumors and are more frequent in poorly differentiated and anaplastic tumors. Given that p53 is a late event in the notional multistep pathogenesis of cancer, we examined its mutation rates as a measure of genomic instability (hypermutability) of malignant thyroid tumors and also wondered whether radiation enhances that proclivity to genomic instability. To that end we have extracted all available data from the p53 mutation database (http://www.perso@curie.fr), verified, extended, where applicable, and supplemented that information from published reports. We were able to identify 100 entries. The distribution of the p53 mutational events--deletions/insertions, transitions versus transversion mutations--was similar to that of the database as a whole. The silent mutation rate of 17.8%, not different from the expected 25%, is consistent with a random occurrence of these mutations. The silent mutation rate is 120 times that expected and is 6 times that of the database. Moreover, the distribution of p53 mutations is compatible with Poisson's distribution, which taken with silent mutation rates indicates that p53 is particularly hypermutable in thyroid carcinomas. Epigenetic deamination of CpG dinucleotide at highly oncogenic DNA-contact residues is a feature of poorly differentiated tumors and thus associated with tumor progression. The rates of p53 mutations (15.4%) in radiation-related cancers were very similar to those in apparently spontaneously arising tumors, although there was a highly significant heterogeneity (P < 0.0005) in the residues mutated. None involved CpG deamination. It is apparent that thyroid cancer exhibits remarkable genomic instability evidenced by p53 hypermutability. Spontaneous epigenetic mutational events are involved in tumor progression and while radiation increases the absolute prevalence of thyroid cancer in the susceptible it does not increase the rate of p53 mutation and seemingly targets different non-DNA-contact residues than those in spontaneously arising tumors.

Codon↗