Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

OpenAIRE

Li, Shilong; Yin, Chuancun; Zhao, Xia; Dai, Hongshuai

2017-01-01

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigat...

Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties

International Nuclear Information System (INIS)

Stoneking, M.R.; Den Hartog, D.J.

1996-06-01

The fitting of data by χ 2 -minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimates for the fit parameters. They compare this method with a χ 2 -minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than ∼20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers

Statistical shape analysis using 3D Poisson equation--A quantitatively validated approach.

Science.gov (United States)

Gao, Yi; Bouix, Sylvain

2016-05-01

Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures. Copyright © 2016 Elsevier B.V. All rights reserved.

Modeling laser velocimeter signals as triply stochastic Poisson processes

Science.gov (United States)

Mayo, W. T., Jr.

1976-01-01

Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

Parameter estimation and statistical test of geographically weighted bivariate Poisson inverse Gaussian regression models

Science.gov (United States)

Amalia, Junita; Purhadi, Otok, Bambang Widjanarko

2017-11-01

Poisson distribution is a discrete distribution with count data as the random variables and it has one parameter defines both mean and variance. Poisson regression assumes mean and variance should be same (equidispersion). Nonetheless, some case of the count data unsatisfied this assumption because variance exceeds mean (over-dispersion). The ignorance of over-dispersion causes underestimates in standard error. Furthermore, it causes incorrect decision in the statistical test. Previously, paired count data has a correlation and it has bivariate Poisson distribution. If there is over-dispersion, modeling paired count data is not sufficient with simple bivariate Poisson regression. Bivariate Poisson Inverse Gaussian Regression (BPIGR) model is mix Poisson regression for modeling paired count data within over-dispersion. BPIGR model produces a global model for all locations. In another hand, each location has different geographic conditions, social, cultural and economic so that Geographically Weighted Regression (GWR) is needed. The weighting function of each location in GWR generates a different local model. Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) model is used to solve over-dispersion and to generate local models. Parameter estimation of GWBPIGR model obtained by Maximum Likelihood Estimation (MLE) method. Meanwhile, hypothesis testing of GWBPIGR model acquired by Maximum Likelihood Ratio Test (MLRT) method.

Quantification of integrated HIV DNA by repetitive-sampling Alu-HIV PCR on the basis of poisson statistics.

Science.gov (United States)

De Spiegelaere, Ward; Malatinkova, Eva; Lynch, Lindsay; Van Nieuwerburgh, Filip; Messiaen, Peter; O'Doherty, Una; Vandekerckhove, Linos

2014-06-01

Quantification of integrated proviral HIV DNA by repetitive-sampling Alu-HIV PCR is a candidate virological tool to monitor the HIV reservoir in patients. However, the experimental procedures and data analysis of the assay are complex and hinder its widespread use. Here, we provide an improved and simplified data analysis method by adopting binomial and Poisson statistics. A modified analysis method on the basis of Poisson statistics was used to analyze the binomial data of positive and negative reactions from a 42-replicate Alu-HIV PCR by use of dilutions of an integration standard and on samples of 57 HIV-infected patients. Results were compared with the quantitative output of the previously described Alu-HIV PCR method. Poisson-based quantification of the Alu-HIV PCR was linearly correlated with the standard dilution series, indicating that absolute quantification with the Poisson method is a valid alternative for data analysis of repetitive-sampling Alu-HIV PCR data. Quantitative outputs of patient samples assessed by the Poisson method correlated with the previously described Alu-HIV PCR analysis, indicating that this method is a valid alternative for quantifying integrated HIV DNA. Poisson-based analysis of the Alu-HIV PCR data enables absolute quantification without the need of a standard dilution curve. Implementation of the CI estimation permits improved qualitative analysis of the data and provides a statistical basis for the required minimal number of technical replicates. © 2014 The American Association for Clinical Chemistry.

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

Science.gov (United States)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

Statistical error in simulations of Poisson processes: Example of diffusion in solids

Science.gov (United States)

Nilsson, Johan O.; Leetmaa, Mikael; Vekilova, Olga Yu.; Simak, Sergei I.; Skorodumova, Natalia V.

2016-08-01

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations.

Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Directory of Open Access Journals (Sweden)

Shilong Li

2017-01-01

Full Text Available Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

Characterization of a Compton suppression system and the applicability of Poisson statistics

International Nuclear Information System (INIS)

Nicholson, G.; Landsberger, S.; Welch, L.

2008-01-01

The Compton suppression system (CSS) has been thoroughly characterized at the University of Texas' Nuclear Engineering Teaching Laboratory (NETL). Effects of dead-time, sample displacement from primary detector, and primary energy detector position relative to the active shield detector have been measured and analyzed. Also, the applicability of Poisson counting statistics to Compton suppression spectroscopy has been evaluated. (author)

Events in time: Basic analysis of Poisson data

International Nuclear Information System (INIS)

Engelhardt, M.E.

1994-09-01

The report presents basic statistical methods for analyzing Poisson data, such as the member of events in some period of time. It gives point estimates, confidence intervals, and Bayesian intervals for the rate of occurrence per unit of time. It shows how to compare subsets of the data, both graphically and by statistical tests, and how to look for trends in time. It presents a compound model when the rate of occurrence varies randomly. Examples and SAS programs are given

Events in time: Basic analysis of Poisson data

Energy Technology Data Exchange (ETDEWEB)

Engelhardt, M.E.

1994-09-01

The report presents basic statistical methods for analyzing Poisson data, such as the member of events in some period of time. It gives point estimates, confidence intervals, and Bayesian intervals for the rate of occurrence per unit of time. It shows how to compare subsets of the data, both graphically and by statistical tests, and how to look for trends in time. It presents a compound model when the rate of occurrence varies randomly. Examples and SAS programs are given.

Intertime jump statistics of state-dependent Poisson processes.

Science.gov (United States)

Daly, Edoardo; Porporato, Amilcare

2007-01-01

A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

On the fractal characterization of Paretian Poisson processes

Science.gov (United States)

Eliazar, Iddo I.; Sokolov, Igor M.

2012-06-01

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

Lindley frailty model for a class of compound Poisson processes

Science.gov (United States)

Kadilar, Gamze Özel; Ata, Nihal

2013-10-01

The Lindley distribution gain importance in survival analysis for the similarity of exponential distribution and allowance for the different shapes of hazard function. Frailty models provide an alternative to proportional hazards model where misspecified or omitted covariates are described by an unobservable random variable. Despite of the distribution of the frailty is generally assumed to be continuous, it is appropriate to consider discrete frailty distributions In some circumstances. In this paper, frailty models with discrete compound Poisson process for the Lindley distributed failure time are introduced. Survival functions are derived and maximum likelihood estimation procedures for the parameters are studied. Then, the fit of the models to the earthquake data set of Turkey are examined.

Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints

NARCIS (Netherlands)

Kok, de A.G.; Tijms, H.C.; Duyn Schouten, van der F.A.

1984-01-01

We consider a production-inventory problem in which the production rate can be continuously controlled in order to cope with random fluctuations in the demand. The demand process for a single product is a compound Poisson process. Excess demand is backlogged. Two production rates are available and

Universal Poisson Statistics of mRNAs with Complex Decay Pathways.

Science.gov (United States)

Thattai, Mukund

2016-01-19

Messenger RNA (mRNA) dynamics in single cells are often modeled as a memoryless birth-death process with a constant probability per unit time that an mRNA molecule is synthesized or degraded. This predicts a Poisson steady-state distribution of mRNA number, in close agreement with experiments. This is surprising, since mRNA decay is known to be a complex process. The paradox is resolved by realizing that the Poisson steady state generalizes to arbitrary mRNA lifetime distributions. A mapping between mRNA dynamics and queueing theory highlights an identifiability problem: a measured Poisson steady state is consistent with a large variety of microscopic models. Here, I provide a rigorous and intuitive explanation for the universality of the Poisson steady state. I show that the mRNA birth-death process and its complex decay variants all take the form of the familiar Poisson law of rare events, under a nonlinear rescaling of time. As a corollary, not only steady-states but also transients are Poisson distributed. Deviations from the Poisson form occur only under two conditions, promoter fluctuations leading to transcriptional bursts or nonindependent degradation of mRNA molecules. These results place severe limits on the power of single-cell experiments to probe microscopic mechanisms, and they highlight the need for single-molecule measurements. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

NARCIS (Netherlands)

Lambert, A.; Simatos, F.

2015-01-01

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive Lévy process with nonzero Lévy measure. In this paper, we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

NARCIS (Netherlands)

Lambert, A.; Simatos, F.

2012-01-01

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\\'evy process with non-zero L\\'evy measure. In this paper we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two

Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes

NARCIS (Netherlands)

B. Chen (Bohan); J. Blanchet; C.H. Rhee (Chang-Han); A.P. Zwart (Bert)

2017-01-01

textabstractWe propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges

Stochastic interest model driven by compound Poisson process andBrownian motion with applications in life contingencies

Directory of Open Access Journals (Sweden)

Shilong Li

2018-03-01

Full Text Available In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model.

Testing the compounding structure of the CP-INARCH model

OpenAIRE

Weiß, Christian H.; Gonçalves, Esmeralda; Lopes, Nazaré Mendes

2017-01-01

A statistical test to distinguish between a Poisson INARCH model and a Compound Poisson INARCH model is proposed, based on the form of the probability generating function of the compounding distribution of the conditional law of the model. For first-order autoregression, the normality of the test statistics’ asymptotic distribution is established, either in the case where the model parameters are specified, or when such parameters are consistently estimated. As the test statistics’ law involv...

Application of zero-inflated poisson mixed models in prognostic factors of hepatitis C.

Science.gov (United States)

Akbarzadeh Baghban, Alireza; Pourhoseingholi, Asma; Zayeri, Farid; Jafari, Ali Akbar; Alavian, Seyed Moayed

2013-01-01

In recent years, hepatitis C virus (HCV) infection represents a major public health problem. Evaluation of risk factors is one of the solutions which help protect people from the infection. This study aims to employ zero-inflated Poisson mixed models to evaluate prognostic factors of hepatitis C. The data was collected from a longitudinal study during 2005-2010. First, mixed Poisson regression (PR) model was fitted to the data. Then, a mixed zero-inflated Poisson model was fitted with compound Poisson random effects. For evaluating the performance of the proposed mixed model, standard errors of estimators were compared. The results obtained from mixed PR showed that genotype 3 and treatment protocol were statistically significant. Results of zero-inflated Poisson mixed model showed that age, sex, genotypes 2 and 3, the treatment protocol, and having risk factors had significant effects on viral load of HCV patients. Of these two models, the estimators of zero-inflated Poisson mixed model had the minimum standard errors. The results showed that a mixed zero-inflated Poisson model was the almost best fit. The proposed model can capture serial dependence, additional overdispersion, and excess zeros in the longitudinal count data.

Extended Poisson Exponential Distribution

Directory of Open Access Journals (Sweden)

Anum Fatima

2015-09-01

Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.

Understanding poisson regression.

Science.gov (United States)

Hayat, Matthew J; Higgins, Melinda

2014-04-01

Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

International Nuclear Information System (INIS)

Lopez de la Cruz, J.; Gutierrez, M.A.

2008-01-01

This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed

A random matrix approach to the crossover of energy-level statistics from Wigner to Poisson

International Nuclear Information System (INIS)

Datta, Nilanjana; Kunz, Herve

2004-01-01

We analyze a class of parametrized random matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function of a parameter. We compute the generating function for the correlations of energy levels, in the limit of infinite matrix size. The crossover between Poisson and Wigner statistics is measured by a renormalized coupling constant. The model is exactly solved in the sense that, in the limit of infinite matrix size, the energy-level correlation functions and their generating function are given in terms of a finite set of integrals

Non-Poisson counting statistics of a hybrid G-M counter dead time model

International Nuclear Information System (INIS)

Lee, Sang Hoon; Jae, Moosung; Gardner, Robin P.

2007-01-01

The counting statistics of a G-M counter with a considerable dead time event rate deviates from Poisson statistics. Important characteristics such as observed counting rates as a function true counting rates, variances and interval distributions were analyzed for three dead time models, non-paralyzable, paralyzable and hybrid, with the help of GMSIM, a Monte Carlo dead time effect simulator. The simulation results showed good agreements with the models in observed counting rates and variances. It was found through GMSIM simulations that the interval distribution for the hybrid model showed three distinctive regions, a complete cutoff region for the duration of the total dead time, a degraded exponential and an enhanced exponential regions. By measuring the cutoff and the duration of degraded exponential from the pulse interval distribution, it is possible to evaluate the two dead times in the hybrid model

Nonparametric estimation of the heterogeneity of a random medium using compound Poisson process modeling of wave multiple scattering.

Science.gov (United States)

Le Bihan, Nicolas; Margerin, Ludovic

2009-07-01

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using compound Poisson processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.

Compound Poisson Processes and Clustered Damage of Radiation Induced DNA Double Strand Breaks

International Nuclear Information System (INIS)

Gudowska-Nowak, E.; Ritter, S.; Taucher-Scholz, G.; Kraft, G.

2000-01-01

Recent experimental data have demonstrated that DNA damage induced by densely ionizing radiation in mammalian cells is distributed along the DNA molecule in the form of clusters. The principal constituent of DNA damage are double-strand breaks (DSB) which are formed when the breaks occur in both DNA strands and are directly opposite or separated by only a few base pairs. DSBs are believed to be most important lesions produced in chromosomes by radiation; interaction between DSBs can lead to cell killing, mutation or carcinogenesis. The paper discusses a model of clustered DSB formation viewed in terms of compound Poisson process along with the predictive essay of the formalism in application to experimental data. (author)

Nonlinear Poisson equation for heterogeneous media.

Science.gov (United States)

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Poisson branching point processes

International Nuclear Information System (INIS)

Matsuo, K.; Teich, M.C.; Saleh, B.E.A.

1984-01-01

We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage. In addition, each initiating event independently contributes a nonstationary Poisson point process (whose rate is a specified function) located at that point. The additional contributions from all points of a given stage constitute a doubly stochastic Poisson point process (DSPP) whose rate is a filtered version of the initiating point process at that stage. The process studied is a generalization of a Poisson branching process in which random time delays are permitted in the generation of events. Particular attention is given to the limit in which the number of branching stages is infinite while the average number of added events per event of the previous stage is infinitesimal. In the special case when the branching is instantaneous this limit of continuous branching corresponds to the well-known Yule--Furry process with an initial Poisson population. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers

Perturbation-induced emergence of Poisson-like behavior in non-Poisson systems

International Nuclear Information System (INIS)

Akin, Osman C; Grigolini, Paolo; Paradisi, Paolo

2009-01-01

The response of a system with ON–OFF intermittency to an external harmonic perturbation is discussed. ON–OFF intermittency is described by means of a sequence of random events, i.e., the transitions from the ON to the OFF state and vice versa. The unperturbed waiting times (WTs) between two events are assumed to satisfy a renewal condition, i.e., the WTs are statistically independent random variables. The response of a renewal model with non-Poisson ON–OFF intermittency, associated with non-exponential WT distribution, is analyzed by looking at the changes induced in the WT statistical distribution by the harmonic perturbation. The scaling properties are also studied by means of diffusion entropy analysis. It is found that, in the range of fast and relatively strong perturbation, the non-Poisson system displays a Poisson-like behavior in both WT distribution and scaling. In particular, the histogram of perturbed WTs becomes a sequence of equally spaced peaks, with intensity decaying exponentially in time. Further, the diffusion entropy detects an ordinary scaling (related to normal diffusion) instead of the expected unperturbed anomalous scaling related to the inverse power-law decay. Thus, an analysis based on the WT histogram and/or on scaling methods has to be considered with some care when dealing with perturbed intermittent systems

Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson

Directory of Open Access Journals (Sweden)

Lusi Eka Afri

2017-03-01

estimation and to downward bias parameter estimation (underestimate. This study aims to compare the Negative Binomial Regression model and Conway-Maxwell-Poisson (COM- Poisson regression model to overcome over dispersion of Poisson distribution data based on deviance test statistics. The data used in this study are simulation data and applied case data. The simulation data were obtained by generating the Poisson distribution data containing over dispersion using the R programming language based on data characteristic such as ?, the probability (p of zero value and the sample size (n. The generated data is used to get the estimated parameter coefficient of the negative binomial regression and COM-Poisson. Keywords: overdispersion, negative binomial regression and Conway-Maxwell-Poisson regression

Harmonic statistics

International Nuclear Information System (INIS)

Eliazar, Iddo

2017-01-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

Harmonic statistics

Energy Technology Data Exchange (ETDEWEB)

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

2017-05-15

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

International Nuclear Information System (INIS)

Hohage, Thorsten; Werner, Frank

2016-01-01

Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years. (topical review)

On poisson-stopped-sums that are mixed poisson

OpenAIRE

Valero Baya, Jordi; Pérez Casany, Marta; Ginebra Molins, Josep

2013-01-01

Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it. Peer Reviewed

Estimating effectiveness in HIV prevention trials with a Bayesian hierarchical compound Poisson frailty model

Science.gov (United States)

Coley, Rebecca Yates; Browna, Elizabeth R.

2016-01-01

Inconsistent results in recent HIV prevention trials of pre-exposure prophylactic interventions may be due to heterogeneity in risk among study participants. Intervention effectiveness is most commonly estimated with the Cox model, which compares event times between populations. When heterogeneity is present, this population-level measure underestimates intervention effectiveness for individuals who are at risk. We propose a likelihood-based Bayesian hierarchical model that estimates the individual-level effectiveness of candidate interventions by accounting for heterogeneity in risk with a compound Poisson-distributed frailty term. This model reflects the mechanisms of HIV risk and allows that some participants are not exposed to HIV and, therefore, have no risk of seroconversion during the study. We assess model performance via simulation and apply the model to data from an HIV prevention trial. PMID:26869051

Comment on: 'A Poisson resampling method for simulating reduced counts in nuclear medicine images'.

Science.gov (United States)

de Nijs, Robin

2015-07-21

In order to be able to calculate half-count images from already acquired data, White and Lawson published their method based on Poisson resampling. They verified their method experimentally by measurements with a Co-57 flood source. In this comment their results are reproduced and confirmed by a direct numerical simulation in Matlab. Not only Poisson resampling, but also two direct redrawing methods were investigated. Redrawing methods were based on a Poisson and a Gaussian distribution. Mean, standard deviation, skewness and excess kurtosis half-count/full-count ratios were determined for all methods, and compared to the theoretical values for a Poisson distribution. Statistical parameters showed the same behavior as in the original note and showed the superiority of the Poisson resampling method. Rounding off before saving of the half count image had a severe impact on counting statistics for counts below 100. Only Poisson resampling was not affected by this, while Gaussian redrawing was less affected by it than Poisson redrawing. Poisson resampling is the method of choice, when simulating half-count (or less) images from full-count images. It simulates correctly the statistical properties, also in the case of rounding off of the images.

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

Science.gov (United States)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Statistical theory of multi-step compound and direct reactions

International Nuclear Information System (INIS)

Feshbach, H.; Kerman, A.; Koonin, S.

1980-01-01

The theory of nuclear reactions is extended so as to include a statistical treatment of multi-step processes. Two types are distinguished, the multi-step compound and the multi-step direct. The wave functions for the system are grouped according to their complexity. The multi-step direct process involves explicitly those states which are open, while the multi-step compound involves those which are bound. In addition to the random phase assumption which is applied differently to the multi-step direct and to the multi-step compound cross-sections, it is assumed that the residual interaction will have non-vanishing matrix elements between states whose complexities differ by at most one unit. This is referred to as the chaining hypothesis. Explicit expressions for the double differential cross-section giving the angular distribution and energy spectrum are obtained for both reaction types. The statistical multi-step compound cross-sections are symmetric about 90 0 . The classical statistical theory of nuclear reactions is a special limiting case. The cross-section for the statistical multi-step direct reaction consists of a set of convolutions of single-step direct cross-sections. For the many step case it is possible to derive a diffusion equation in momentum space. Application is made to the reaction 181 Ta(p,n) 181 W using the statistical multi-step compound formalism

Polynomial Poisson algebras: Gel'fand-Kirillov problem and Poisson spectra

OpenAIRE

Lecoutre, César

2014-01-01

We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras.\\ud \\ud First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to...

Statistical and heuristic image noise extraction (SHINE): a new method for processing Poisson noise in scintigraphic images

International Nuclear Information System (INIS)

Hannequin, Pascal; Mas, Jacky

2002-01-01

Poisson noise is one of the factors degrading scintigraphic images, especially at low count level, due to the statistical nature of photon detection. We have developed an original procedure, named statistical and heuristic image noise extraction (SHINE), to reduce the Poisson noise contained in the scintigraphic images, preserving the resolution, the contrast and the texture. The SHINE procedure consists in dividing the image into 4 x 4 blocks and performing a correspondence analysis on these blocks. Each block is then reconstructed using its own significant factors which are selected using an original statistical variance test. The SHINE procedure has been validated using a line numerical phantom and a hot spots and cold spots real phantom. The reference images are the noise-free simulated images for the numerical phantom and an extremely high counts image for the real phantom. The SHINE procedure has then been applied to the Jaszczak phantom and clinical data including planar bone scintigraphy, planar Sestamibi scintigraphy and Tl-201 myocardial SPECT. The SHINE procedure reduces the mean normalized error between the noisy images and the corresponding reference images. This reduction is constant and does not change with the count level. The SNR in a SHINE processed image is close to that of the corresponding raw image with twice the number of counts. The visual results with the Jaszczak phantom SPECT have shown that SHINE preserves the contrast and the resolution of the slices well. Clinical examples have shown no visual difference between the SHINE images and the corresponding raw images obtained with twice the acquisition duration. SHINE is an entirely automatic procedure which enables halving the acquisition time or the injected dose in scintigraphic acquisitions. It can be applied to all scintigraphic images, including PET data, and to all low-count photon images

An Optimization of (Q,r Inventory Policy Based on Health Care Apparel Products with Compound Poisson Demands

Directory of Open Access Journals (Sweden)

An Pan

2014-01-01

Full Text Available Addressing the problems of a health care center which produces tailor-made clothes for specific people, the paper proposes a single product continuous review model and establishes an optimal policy for the center based on (Q,r control policy to minimize expected average cost on an order cycle. A generic mathematical model to compute cost on real-time inventory level is developed to generate optimal order quantity under stochastic stock variation. The customer demands are described as compound Poisson process. Comparisons on cost between optimization method and experience-based decision on Q are made through numerical studies conducted for the inventory system of the center.

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

Science.gov (United States)

Frejlich, Pedro; Mărcuț, Ioan

2018-01-01

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

Comparison of Poisson structures and Poisson-Lie dynamical r-matrices

OpenAIRE

Enriquez, B.; Etingof, P.; Marshall, I.

2004-01-01

We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.

On Poisson functions

OpenAIRE

Terashima, Yuji

2008-01-01

In this paper, defining Poisson functions on super manifolds, we show that the graphs of Poisson functions are Dirac structures, and find Poisson functions which include as special cases both quasi-Poisson structures and twisted Poisson structures.

The applicability of the Poisson distribution in radiochemical measurements

International Nuclear Information System (INIS)

Luthardt, M.; Proesch, U.

1980-01-01

The fact that, on principle, the Poisson distribution describes the statistics of nuclear decay is generally accepted. The applicability of this distribution to nuclear radiation measurements has recently been questioned. Applying the chi-squared test for goodness of fit on the analogy of the moving average, at least 3 cases may be distinguished, which lead to an incorrect rejection of the Poisson distribution for measurements. Examples are given. Distributions, which make allowance for special parameters, should only be used after careful examination of the data with regard to other interfering effects. The Poisson distribution will further on be applicable to many simple measuring operations. Some basic equations for the analysis of poisson-distributed data are given. (author)

Formal equivalence of Poisson structures around Poisson submanifolds

NARCIS (Netherlands)

Marcut, I.T.

2012-01-01

Let (M,π) be a Poisson manifold. A Poisson submanifold P ⊂ M gives rise to a Lie algebroid AP → P. Formal deformations of π around P are controlled by certain cohomology groups associated to AP. Assuming that these groups vanish, we prove that π is formally rigid around P; that is, any other Poisson

Poisson filtering of laser ranging data

Science.gov (United States)

Ricklefs, Randall L.; Shelus, Peter J.

1993-01-01

The filtering of data in a high noise, low signal strength environment is a situation encountered routinely in lunar laser ranging (LLR) and, to a lesser extent, in artificial satellite laser ranging (SLR). The use of Poisson statistics as one of the tools for filtering LLR data is described first in a historical context. The more recent application of this statistical technique to noisy SLR data is also described.

Modeling spiking behavior of neurons with time-dependent Poisson processes.

Science.gov (United States)

Shinomoto, S; Tsubo, Y

2001-10-01

Three kinds of interval statistics, as represented by the coefficient of variation, the skewness coefficient, and the correlation coefficient of consecutive intervals, are evaluated for three kinds of time-dependent Poisson processes: pulse regulated, sinusoidally regulated, and doubly stochastic. Among these three processes, the sinusoidally regulated and doubly stochastic Poisson processes, in the case when the spike rate varies slowly compared with the mean interval between spikes, are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys.

(Quasi-)Poisson enveloping algebras

OpenAIRE

Yang, Yan-Hong; Yao, Yuan; Ye, Yu

2010-01-01

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

Comment on: 'A Poisson resampling method for simulating reduced counts in nuclear medicine images'

DEFF Research Database (Denmark)

de Nijs, Robin

2015-01-01

In order to be able to calculate half-count images from already acquired data, White and Lawson published their method based on Poisson resampling. They verified their method experimentally by measurements with a Co-57 flood source. In this comment their results are reproduced and confirmed...... by a direct numerical simulation in Matlab. Not only Poisson resampling, but also two direct redrawing methods were investigated. Redrawing methods were based on a Poisson and a Gaussian distribution. Mean, standard deviation, skewness and excess kurtosis half-count/full-count ratios were determined for all...... methods, and compared to the theoretical values for a Poisson distribution. Statistical parameters showed the same behavior as in the original note and showed the superiority of the Poisson resampling method. Rounding off before saving of the half count image had a severe impact on counting statistics...

Markov modulated Poisson process models incorporating covariates for rainfall intensity.

Science.gov (United States)

Thayakaran, R; Ramesh, N I

2013-01-01

Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.

A Poisson Cluster Stochastic Rainfall Generator That Accounts for the Interannual Variability of Rainfall Statistics: Validation at Various Geographic Locations across the United States

Directory of Open Access Journals (Sweden)

Dongkyun Kim

2014-01-01

Full Text Available A novel approach for a Poisson cluster stochastic rainfall generator was validated in its ability to reproduce important rainfall and watershed response characteristics at 104 locations in the United States. The suggested novel approach, The Hybrid Model (THM, as compared to the traditional Poisson cluster rainfall modeling approaches, has an additional capability to account for the interannual variability of rainfall statistics. THM and a traditional approach of Poisson cluster rainfall model (modified Bartlett-Lewis rectangular pulse model were compared in their ability to reproduce the characteristics of extreme rainfall and watershed response variables such as runoff and peak flow. The results of the comparison indicate that THM generally outperforms the traditional approach in reproducing the distributions of peak rainfall, peak flow, and runoff volume. In addition, THM significantly outperformed the traditional approach in reproducing extreme rainfall by 2.3% to 66% and extreme flow values by 32% to 71%.

Poisson Autoregression

DEFF Research Database (Denmark)

Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...

Poisson Autoregression

DEFF Research Database (Denmark)

Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...

Poisson Coordinates.

Science.gov (United States)

Li, Xian-Ying; Hu, Shi-Min

2013-02-01

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

Doubly stochastic Poisson processes in artificial neural learning.

Science.gov (United States)

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

A Conway-Maxwell-Poisson (CMP) model to address data dispersion on positron emission tomography.

Science.gov (United States)

Santarelli, Maria Filomena; Della Latta, Daniele; Scipioni, Michele; Positano, Vincenzo; Landini, Luigi

2016-10-01

Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

Radio pulsar glitches as a state-dependent Poisson process

Science.gov (United States)

Fulgenzi, W.; Melatos, A.; Hughes, B. D.

2017-10-01

Gross-Pitaevskii simulations of vortex avalanches in a neutron star superfluid are limited computationally to ≲102 vortices and ≲102 avalanches, making it hard to study the long-term statistics of radio pulsar glitches in realistically sized systems. Here, an idealized, mean-field model of the observed Gross-Pitaevskii dynamics is presented, in which vortex unpinning is approximated as a state-dependent, compound Poisson process in a single random variable, the spatially averaged crust-superfluid lag. Both the lag-dependent Poisson rate and the conditional distribution of avalanche-driven lag decrements are inputs into the model, which is solved numerically (via Monte Carlo simulations) and analytically (via a master equation). The output statistics are controlled by two dimensionless free parameters: α, the glitch rate at a reference lag, multiplied by the critical lag for unpinning, divided by the spin-down rate; and β, the minimum fraction of the lag that can be restored by a glitch. The system evolves naturally to a self-regulated stationary state, whose properties are determined by α/αc(β), where αc(β) ≈ β-1/2 is a transition value. In the regime α ≳ αc(β), one recovers qualitatively the power-law size and exponential waiting-time distributions observed in many radio pulsars and Gross-Pitaevskii simulations. For α ≪ αc(β), the size and waiting-time distributions are both power-law-like, and a correlation emerges between size and waiting time until the next glitch, contrary to what is observed in most pulsars. Comparisons with astrophysical data are restricted by the small sample sizes available at present, with ≤35 events observed per pulsar.

Topological Poisson Sigma models on Poisson-Lie groups

International Nuclear Information System (INIS)

Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David

2003-01-01

We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)

Simple dead-time corrections for discrete time series of non-Poisson data

International Nuclear Information System (INIS)

Larsen, Michael L; Kostinski, Alexander B

2009-01-01

The problem of dead time (instrumental insensitivity to detectable events due to electronic or mechanical reset time) is considered. Most existing algorithms to correct for event count errors due to dead time implicitly rely on Poisson counting statistics of the underlying phenomena. However, when the events to be measured are clustered in time, the Poisson statistics assumption results in underestimating both the true event count and any statistics associated with count variability; the 'busiest' part of the signal is partially missed. Using the formalism associated with the pair-correlation function, we develop first-order correction expressions for the general case of arbitrary counting statistics. The results are verified through simulation of a realistic clustering scenario

Background stratified Poisson regression analysis of cohort data.

Science.gov (United States)

Richardson, David B; Langholz, Bryan

2012-03-01

Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models.

Monitoring Poisson observations using combined applications of Shewhart and EWMA charts

Science.gov (United States)

Abujiya, Mu'azu Ramat

2017-11-01

The Shewhart and exponentially weighted moving average (EWMA) charts for nonconformities are the most widely used procedures of choice for monitoring Poisson observations in modern industries. Individually, the Shewhart EWMA charts are only sensitive to large and small shifts, respectively. To enhance the detection abilities of the two schemes in monitoring all kinds of shifts in Poisson count data, this study examines the performance of combined applications of the Shewhart, and EWMA Poisson control charts. Furthermore, the study proposes modifications based on well-structured statistical data collection technique, ranked set sampling (RSS), to detect shifts in the mean of a Poisson process more quickly. The relative performance of the proposed Shewhart-EWMA Poisson location charts is evaluated in terms of the average run length (ARL), standard deviation of the run length (SDRL), median run length (MRL), average ratio ARL (ARARL), average extra quadratic loss (AEQL) and performance comparison index (PCI). Consequently, all the new Poisson control charts based on RSS method are generally more superior than most of the existing schemes for monitoring Poisson processes. The use of these combined Shewhart-EWMA Poisson charts is illustrated with an example to demonstrate the practical implementation of the design procedure.

Poisson distribution

NARCIS (Netherlands)

Hallin, M.; Piegorsch, W.; El Shaarawi, A.

2012-01-01

The random variable X taking values 0,1,2,…,x,… with probabilities pλ(x) = e−λλx/x!, where λ∈R0+ is called a Poisson variable, and its distribution a Poisson distribution, with parameter λ. The Poisson distribution with parameter λ can be obtained as the limit, as n → ∞ and p → 0 in such a way that

On statistical analysis of compound point process

Czech Academy of Sciences Publication Activity Database

Volf, Petr

2006-01-01

Roč. 35, 2-3 (2006), s. 389-396 ISSN 1026-597X R&D Projects: GA ČR(CZ) GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : counting process * compound process * hazard function * Cox -model Subject RIV: BB - Applied Statistics, Operational Research

POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity

International Nuclear Information System (INIS)

Colman, J.

2001-01-01

1 - Description of program or function: POISSON, SUPERFISH is a group of (1) codes that solve Poisson's equation and are used to compute field quality for both magnets and fixed electric potentials and (2) RF cavity codes that calculate resonant frequencies and field distributions of the fundamental and higher modes. The group includes: POISSON, PANDIRA, SUPERFISH, AUTOMESH, LATTICE, FORCE, MIRT, PAN-T, TEKPLOT, SF01, and SHY. POISSON solves Poisson's (or Laplace's) equation for the vector (scalar) potential with nonlinear isotropic iron (dielectric) and electric current (charge) distributions for two-dimensional Cartesian or three-dimensional cylindrical symmetry. It calculates the derivatives of the potential, the stored energy, and performs harmonic (multipole) analysis of the potential. PANDIRA is similar to POISSON except it allows anisotropic and permanent magnet materials and uses a different numerical method to obtain the potential. SUPERFISH solves for the accelerating (TM) and deflecting (TE) resonant frequencies and field distributions in an RF cavity with two-dimensional Cartesian or three-dimensional cylindrical symmetry. Only the azimuthally symmetric modes are found for cylindrically symmetric cavities. AUTOMESH prepares input for LATTICE from geometrical data describing the problem, (i.e., it constructs the 'logical' mesh and generates (x,y) coordinate data for straight lines, arcs of circles, and segments of hyperbolas). LATTICE generates an irregular triangular (physical) mesh from the input data, calculates the 'point current' terms at each mesh point in regions with distributed current density, and sets up the mesh point relaxation order needed to write the binary problem file for the equation-solving POISSON, PANDIRA, or SUPERFISH. FORCE calculates forces and torques on coils and iron regions from POISSON or PANDIRA solutions for the potential. MIRT optimizes magnet profiles, coil shapes, and current densities from POISSON output based on a

The Jackson Queueing Network Model Built Using Poisson Measures. Application To A Bank Model

Directory of Open Access Journals (Sweden)

Ciuiu Daniel

2014-07-01

Full Text Available In this paper we will build a bank model using Poisson measures and Jackson queueing networks. We take into account the relationship between the Poisson and the exponential distributions, and we consider for each credit/deposit type a node where shocks are modeled as the compound Poisson processes. The transmissions of the shocks are modeled as moving between nodes in Jackson queueing networks, the external shocks are modeled as external arrivals, and the absorption of shocks as departures from the network.

Analyzing hospitalization data: potential limitations of Poisson regression.

Science.gov (United States)

Weaver, Colin G; Ravani, Pietro; Oliver, Matthew J; Austin, Peter C; Quinn, Robert R

2015-08-01

Poisson regression is commonly used to analyze hospitalization data when outcomes are expressed as counts (e.g. number of days in hospital). However, data often violate the assumptions on which Poisson regression is based. More appropriate extensions of this model, while available, are rarely used. We compared hospitalization data between 206 patients treated with hemodialysis (HD) and 107 treated with peritoneal dialysis (PD) using Poisson regression and compared results from standard Poisson regression with those obtained using three other approaches for modeling count data: negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression. We examined the appropriateness of each model and compared the results obtained with each approach. During a mean 1.9 years of follow-up, 183 of 313 patients (58%) were never hospitalized (indicating an excess of 'zeros'). The data also displayed overdispersion (variance greater than mean), violating another assumption of the Poisson model. Using four criteria, we determined that the NB and ZINB models performed best. According to these two models, patients treated with HD experienced similar hospitalization rates as those receiving PD {NB rate ratio (RR): 1.04 [bootstrapped 95% confidence interval (CI): 0.49-2.20]; ZINB summary RR: 1.21 (bootstrapped 95% CI 0.60-2.46)}. Poisson and ZIP models fit the data poorly and had much larger point estimates than the NB and ZINB models [Poisson RR: 1.93 (bootstrapped 95% CI 0.88-4.23); ZIP summary RR: 1.84 (bootstrapped 95% CI 0.88-3.84)]. We found substantially different results when modeling hospitalization data, depending on the approach used. Our results argue strongly for a sound model selection process and improved reporting around statistical methods used for modeling count data. © The Author 2015. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Background stratified Poisson regression analysis of cohort data

International Nuclear Information System (INIS)

Richardson, David B.; Langholz, Bryan

2012-01-01

Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models. (orig.)

Poisson Autoregression

DEFF Research Database (Denmark)

Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag

2009-01-01

In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

International Nuclear Information System (INIS)

Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.

2016-01-01

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

Science.gov (United States)

Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

Energy Technology Data Exchange (ETDEWEB)

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

Poisson Regression Analysis of Illness and Injury Surveillance Data

Energy Technology Data Exchange (ETDEWEB)

Frome E.L., Watkins J.P., Ellis E.D.

2012-12-12

The Department of Energy (DOE) uses illness and injury surveillance to monitor morbidity and assess the overall health of the work force. Data collected from each participating site include health events and a roster file with demographic information. The source data files are maintained in a relational data base, and are used to obtain stratified tables of health event counts and person time at risk that serve as the starting point for Poisson regression analysis. The explanatory variables that define these tables are age, gender, occupational group, and time. Typical response variables of interest are the number of absences due to illness or injury, i.e., the response variable is a count. Poisson regression methods are used to describe the effect of the explanatory variables on the health event rates using a log-linear main effects model. Results of fitting the main effects model are summarized in a tabular and graphical form and interpretation of model parameters is provided. An analysis of deviance table is used to evaluate the importance of each of the explanatory variables on the event rate of interest and to determine if interaction terms should be considered in the analysis. Although Poisson regression methods are widely used in the analysis of count data, there are situations in which over-dispersion occurs. This could be due to lack-of-fit of the regression model, extra-Poisson variation, or both. A score test statistic and regression diagnostics are used to identify over-dispersion. A quasi-likelihood method of moments procedure is used to evaluate and adjust for extra-Poisson variation when necessary. Two examples are presented using respiratory disease absence rates at two DOE sites to illustrate the methods and interpretation of the results. In the first example the Poisson main effects model is adequate. In the second example the score test indicates considerable over-dispersion and a more detailed analysis attributes the over-dispersion to extra-Poisson

Evolutionary inference via the Poisson Indel Process.

Science.gov (United States)

Bouchard-Côté, Alexandre; Jordan, Michael I

2013-01-22

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles

International Nuclear Information System (INIS)

Akemann, G.; Bender, M.

2010-01-01

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent.

Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation

International Nuclear Information System (INIS)

Bardsley, Johnathan M; Goldes, John

2009-01-01

In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is ill-posed, regularization is needed. Regularized Poisson likelihood estimation has been studied extensively by the authors, though a problem of high importance remains: the choice of the regularization parameter. We will present three statistically motivated methods for choosing the regularization parameter, and numerical examples will be presented to illustrate their effectiveness

Poisson processes

NARCIS (Netherlands)

Boxma, O.J.; Yechiali, U.; Ruggeri, F.; Kenett, R.S.; Faltin, F.W.

2007-01-01

The Poisson process is a stochastic counting process that arises naturally in a large variety of daily life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the

Poisson-event-based analysis of cell proliferation.

Science.gov (United States)

Summers, Huw D; Wills, John W; Brown, M Rowan; Rees, Paul

2015-05-01

A protocol for the assessment of cell proliferation dynamics is presented. This is based on the measurement of cell division events and their subsequent analysis using Poisson probability statistics. Detailed analysis of proliferation dynamics in heterogeneous populations requires single cell resolution within a time series analysis and so is technically demanding to implement. Here, we show that by focusing on the events during which cells undergo division rather than directly on the cells themselves a simplified image acquisition and analysis protocol can be followed, which maintains single cell resolution and reports on the key metrics of cell proliferation. The technique is demonstrated using a microscope with 1.3 μm spatial resolution to track mitotic events within A549 and BEAS-2B cell lines, over a period of up to 48 h. Automated image processing of the bright field images using standard algorithms within the ImageJ software toolkit yielded 87% accurate recording of the manually identified, temporal, and spatial positions of the mitotic event series. Analysis of the statistics of the interevent times (i.e., times between observed mitoses in a field of view) showed that cell division conformed to a nonhomogeneous Poisson process in which the rate of occurrence of mitotic events, λ exponentially increased over time and provided values of the mean inter mitotic time of 21.1 ± 1.2 hours for the A549 cells and 25.0 ± 1.1 h for the BEAS-2B cells. Comparison of the mitotic event series for the BEAS-2B cell line to that predicted by random Poisson statistics indicated that temporal synchronisation of the cell division process was occurring within 70% of the population and that this could be increased to 85% through serum starvation of the cell culture. © 2015 International Society for Advancement of Cytometry.

Singular Poisson tensors

International Nuclear Information System (INIS)

Littlejohn, R.G.

1982-01-01

The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular

Nambu–Poisson gauge theory

Energy Technology Data Exchange (ETDEWEB)

Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague 186 75 (Czech Republic); Schupp, Peter, E-mail: p.schupp@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany); Vysoký, Jan, E-mail: vysokjan@fjfi.cvut.cz [Jacobs University Bremen, 28759 Bremen (Germany); Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Prague 115 19 (Czech Republic)

2014-06-02

We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

Nambu–Poisson gauge theory

International Nuclear Information System (INIS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-01-01

We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

Science.gov (United States)

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Statistical emission of complex fragments from highly excited compound nucleus

International Nuclear Information System (INIS)

Matsuse, T.

1991-01-01

A full statistical analysis has been given in terms of the Extended Hauser-Feshbach method. The charge and kinetic energy distributions of 35 Cl+ 12 C reaction at E lab = 180, 200 MeV and 23 Na+ 24 Mg reaction at E lab = 89 MeV which form the 47 V compound nucleus are investigated as a prototype of the light mass system. The measured kinetic energy distributions of the complex fragments are shown to be well reproduced by the Extended Hauser-Feshbach method, so the observed complex fragment production is understood as the statistical binary decay from the compound nucleus induced by heavy-ion reaction. Next, this method is applied to the study of the complex production from the 111 In compound nucleus which is formed by the 84 Kr+ 27 Al reaction at E lab = 890 MeV. (K.A.) 18 refs., 10 figs

Characterizing the performance of the Conway-Maxwell Poisson generalized linear model.

Science.gov (United States)

Francis, Royce A; Geedipally, Srinivas Reddy; Guikema, Seth D; Dhavala, Soma Sekhar; Lord, Dominique; LaRocca, Sarah

2012-01-01

Count data are pervasive in many areas of risk analysis; deaths, adverse health outcomes, infrastructure system failures, and traffic accidents are all recorded as count events, for example. Risk analysts often wish to estimate the probability distribution for the number of discrete events as part of doing a risk assessment. Traditional count data regression models of the type often used in risk assessment for this problem suffer from limitations due to the assumed variance structure. A more flexible model based on the Conway-Maxwell Poisson (COM-Poisson) distribution was recently proposed, a model that has the potential to overcome the limitations of the traditional model. However, the statistical performance of this new model has not yet been fully characterized. This article assesses the performance of a maximum likelihood estimation method for fitting the COM-Poisson generalized linear model (GLM). The objectives of this article are to (1) characterize the parameter estimation accuracy of the MLE implementation of the COM-Poisson GLM, and (2) estimate the prediction accuracy of the COM-Poisson GLM using simulated data sets. The results of the study indicate that the COM-Poisson GLM is flexible enough to model under-, equi-, and overdispersed data sets with different sample mean values. The results also show that the COM-Poisson GLM yields accurate parameter estimates. The COM-Poisson GLM provides a promising and flexible approach for performing count data regression. © 2011 Society for Risk Analysis.

A Family of Poisson Processes for Use in Stochastic Models of Precipitation

Science.gov (United States)

Penland, C.

2013-12-01

Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.

Ship-Track Models Based on Poisson-Distributed Port-Departure Times

National Research Council Canada - National Science Library

Heitmeyer, Richard

2006-01-01

... of those ships, and their nominal speeds. The probability law assumes that the ship departure times are Poisson-distributed with a time-varying departure rate and that the ship speeds and ship routes are statistically independent...

A generalized right truncated bivariate Poisson regression model with applications to health data.

Science.gov (United States)

Islam, M Ataharul; Chowdhury, Rafiqul I

2017-01-01

A generalized right truncated bivariate Poisson regression model is proposed in this paper. Estimation and tests for goodness of fit and over or under dispersion are illustrated for both untruncated and right truncated bivariate Poisson regression models using marginal-conditional approach. Estimation and test procedures are illustrated for bivariate Poisson regression models with applications to Health and Retirement Study data on number of health conditions and the number of health care services utilized. The proposed test statistics are easy to compute and it is evident from the results that the models fit the data very well. A comparison between the right truncated and untruncated bivariate Poisson regression models using the test for nonnested models clearly shows that the truncated model performs significantly better than the untruncated model.

Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

International Nuclear Information System (INIS)

Grigoriu, Mircea; Samorodnitsky, Gennady

2004-01-01

Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action

Science.gov (United States)

Chekhov, L. O.; Mazzocco, M.

2017-12-01

Let \\mathscr A be the space of bilinear forms on C^N with defining matrices A endowed with a quadratic Poisson structure of reflection equation type. The paper begins with a short description of previous studies of the structure, and then this structure is extended to systems of bilinear forms whose dynamics is governed by the natural action A\\mapsto B ABT} of the {GL}_N Poisson-Lie group on \\mathscr A. A classification is given of all possible quadratic brackets on (B, A)\\in {GL}_N× \\mathscr A preserving the Poisson property of the action, thus endowing \\mathscr A with the structure of a Poisson homogeneous space. Besides the product Poisson structure on {GL}_N× \\mathscr A, there are two other (mutually dual) structures, which (unlike the product Poisson structure) admit reductions by the Dirac procedure to a space of bilinear forms with block upper triangular defining matrices. Further generalisations of this construction are considered, to triples (B,C, A)\\in {GL}_N× {GL}_N× \\mathscr A with the Poisson action A\\mapsto B ACT}, and it is shown that \\mathscr A then acquires the structure of a Poisson symmetric space. Generalisations to chains of transformations and to the quantum and quantum affine algebras are investigated, as well as the relations between constructions of Poisson symmetric spaces and the Poisson groupoid. Bibliography: 30 titles.

An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces.

Science.gov (United States)

Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying

2013-03-08

Poisson disk sampling plays an important role in a variety of visual computing, due to its useful statistical property in distribution and the absence of aliasing artifacts. While many effective techniques have been proposed to generate Poisson disk distribution in Euclidean space, relatively few work has been reported to the surface counterpart. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. We propose a new technique for parallelizing the dart throwing. Rather than the conventional approaches that explicitly partition the spatial domain to generate the samples in parallel, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. It is worth noting that our algorithm is accurate as the generated Poisson disks are uniformly and randomly distributed without bias. Our method is intrinsic in that all the computations are based on the intrinsic metric and are independent of the embedding space. This intrinsic feature allows us to generate Poisson disk distributions on arbitrary surfaces. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

Experimental investigation of statistical models describing distribution of counts

International Nuclear Information System (INIS)

Salma, I.; Zemplen-Papp, E.

1992-01-01

The binomial, Poisson and modified Poisson models which are used for describing the statistical nature of the distribution of counts are compared theoretically, and conclusions for application are considered. The validity of the Poisson and the modified Poisson statistical distribution for observing k events in a short time interval is investigated experimentally for various measuring times. The experiments to measure the influence of the significant radioactive decay were performed with 89 Y m (T 1/2 =16.06 s), using a multichannel analyser (4096 channels) in the multiscaling mode. According to the results, Poisson statistics describe the counting experiment for short measuring times (up to T=0.5T 1/2 ) and its application is recommended. However, analysis of the data demonstrated, with confidence, that for long measurements (T≥T 1/2 ) Poisson distribution is not valid and the modified Poisson function is preferable. The practical implications in calculating uncertainties and in optimizing the measuring time are discussed. Differences between the standard deviations evaluated on the basis of the Poisson and binomial models are especially significant for experiments with long measuring time (T/T 1/2 ≥2) and/or large detection efficiency (ε>0.30). Optimization of the measuring time for paired observations yields the same solution for either the binomial or the Poisson distribution. (orig.)

Experimental dead-time distortions of Poisson processes

International Nuclear Information System (INIS)

Faraci, G.; Pennisi, A.R.; Consiglio Nazionale delle Ricerche, Catania

1983-01-01

In order to check the distortions, introduced by a non-extended dead time on the Poisson statistics, accurate experiments have been made in single channel counting. At a given measuring time, the dependence on the choice of the time origin and on the width of the dead time has been verified. An excellent agreement has been found between the theoretical expressions and the experimental curves. (orig.)

Homogeneous Poisson structures

International Nuclear Information System (INIS)

Shafei Deh Abad, A.; Malek, F.

1993-09-01

We provide an algebraic definition for Schouten product and give a decomposition for any homogenenous Poisson structure in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in R k is also characterized. (author). 4 refs

Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.

Science.gov (United States)

Khazraee, S Hadi; Sáez-Castillo, Antonio Jose; Geedipally, Srinivas Reddy; Lord, Dominique

2015-05-01

The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model. © 2014 Society for Risk Analysis.

Error calculations statistics in radioactive measurements

International Nuclear Information System (INIS)

Verdera, Silvia

1994-01-01

Basic approach and procedures frequently used in the practice of radioactive measurements.Statistical principles applied are part of Good radiopharmaceutical Practices and quality assurance.Concept of error, classification as systematic and random errors.Statistic fundamentals,probability theories, populations distributions, Bernoulli, Poisson,Gauss, t-test distribution,Ξ2 test, error propagation based on analysis of variance.Bibliography.z table,t-test table, Poisson index ,Ξ2 test

Modifications to POISSON

International Nuclear Information System (INIS)

Harwood, L.H.

1981-01-01

At MSU we have used the POISSON family of programs extensively for magnetic field calculations. In the presently super-saturated computer situation, reducing the run time for the program is imperative. Thus, a series of modifications have been made to POISSON to speed up convergence. Two of the modifications aim at having the first guess solution as close as possible to the final solution. The other two aim at increasing the convergence rate. In this discussion, a working knowledge of POISSON is assumed. The amount of new code and expected time saving for each modification is discussed

Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations

DEFF Research Database (Denmark)

Sibani, Paolo

2007-01-01

in a correlated fashion and through irreversible bursts, `quakes', which punctuate reversible and equilibrium-like fluctuations of zero average. The temporal distribution of the quakes is a Poisson distribution with an average growing logarithmically on time, indicating that the quakes are triggered by record...

A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.

Science.gov (United States)

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

Information content of poisson images

International Nuclear Information System (INIS)

Cederlund, J.

1979-04-01

One major problem when producing images with the aid of Poisson distributed quanta is how best to compromise between spatial and contrast resolution. Increasing the number of image elements improves spatial resolution, but at the cost of fewer quanta per image element, which reduces contrast resolution. Information theory arguments are used to analyse this problem. It is argued that information capacity is a useful concept to describe an important property of the imaging device, but that in order to compute the information content of an image produced by this device some statistical properties (such as the a priori probability of the densities) of the object to be depicted must be taken into account. If these statistical properties are not known one cannot make a correct choice between spatial and contrast resolution. (author)

The Analysis of Corporate Bond Valuation under an Infinite Dimensional Compound Poisson Framework

Directory of Open Access Journals (Sweden)

Sheng Fan

2014-01-01

Full Text Available This paper analyzes the firm bond valuation and credit spread with an endogenous model for the pure default and callable default corporate bond. Regarding the stochastic instantaneous forward rates and the firm value as an infinite dimensional Poisson process, we provide some analytical results for the embedded American options and firm bond valuations.

Non-equal-time Poisson brackets

OpenAIRE

Nikolic, H.

1998-01-01

The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.

Branes in Poisson sigma models

International Nuclear Information System (INIS)

Falceto, Fernando

2010-01-01

In this review we discuss possible boundary conditions (branes) for the Poisson sigma model. We show how to carry out the perturbative quantization in the presence of a general pre-Poisson brane and how this is related to the deformation quantization of Poisson structures. We conclude with an open problem: the perturbative quantization of the system when the boundary has several connected components and we use a different pre-Poisson brane in every component.

Statistical properties of superimposed stationary spike trains.

Science.gov (United States)

Deger, Moritz; Helias, Moritz; Boucsein, Clemens; Rotter, Stefan

2012-06-01

The Poisson process is an often employed model for the activity of neuronal populations. It is known, though, that superpositions of realistic, non- Poisson spike trains are not in general Poisson processes, not even for large numbers of superimposed processes. Here we construct superimposed spike trains from intracellular in vivo recordings from rat neocortex neurons and compare their statistics to specific point process models. The constructed superimposed spike trains reveal strong deviations from the Poisson model. We find that superpositions of model spike trains that take the effective refractoriness of the neurons into account yield a much better description. A minimal model of this kind is the Poisson process with dead-time (PPD). For this process, and for superpositions thereof, we obtain analytical expressions for some second-order statistical quantities-like the count variability, inter-spike interval (ISI) variability and ISI correlations-and demonstrate the match with the in vivo data. We conclude that effective refractoriness is the key property that shapes the statistical properties of the superposition spike trains. We present new, efficient algorithms to generate superpositions of PPDs and of gamma processes that can be used to provide more realistic background input in simulations of networks of spiking neurons. Using these generators, we show in simulations that neurons which receive superimposed spike trains as input are highly sensitive for the statistical effects induced by neuronal refractoriness.

Statistical analysis of agarwood oil compounds in discriminating the ...

African Journals Online (AJOL)

Enhancing and improving the discrimination technique is the main aim to determine or grade the good quality of agarwood oil. In this paper, all statistical works were performed via SPSS software. Two parameters involved are abundance of compound (%) and quality of t agarwood oil either low or high quality. The result ...

On (co)homology of Frobenius Poisson algebras

OpenAIRE

Zhu, Can; Van Oystaeyen, Fred; ZHANG, Yinhuo

2014-01-01

In this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisk...

Experimental investigation of statistical density function of decaying radioactive sources

International Nuclear Information System (INIS)

Salma, I.; Zemplen-Papp, E.

1991-01-01

The validity of the Poisson and the λ P(k) modified Poisson statistical density functions of observing k events in a short time interval is investigated experimentally in radioactive decay detection for various measuring times. The experiments to measure radioactive decay were performed with 89m Y, using a multichannel analyzer. According to the results, Poisson statistics adequately describes the counting experiment for short measuring times. (author) 13 refs.; 4 figs

Normal forms in Poisson geometry

NARCIS (Netherlands)

Marcut, I.T.

2013-01-01

The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

[Application of detecting and taking overdispersion into account in Poisson regression model].

Science.gov (United States)

Bouche, G; Lepage, B; Migeot, V; Ingrand, P

2009-08-01

Researchers often use the Poisson regression model to analyze count data. Overdispersion can occur when a Poisson regression model is used, resulting in an underestimation of variance of the regression model parameters. Our objective was to take overdispersion into account and assess its impact with an illustration based on the data of a study investigating the relationship between use of the Internet to seek health information and number of primary care consultations. Three methods, overdispersed Poisson, a robust estimator, and negative binomial regression, were performed to take overdispersion into account in explaining variation in the number (Y) of primary care consultations. We tested overdispersion in the Poisson regression model using the ratio of the sum of Pearson residuals over the number of degrees of freedom (chi(2)/df). We then fitted the three models and compared parameter estimation to the estimations given by Poisson regression model. Variance of the number of primary care consultations (Var[Y]=21.03) was greater than the mean (E[Y]=5.93) and the chi(2)/df ratio was 3.26, which confirmed overdispersion. Standard errors of the parameters varied greatly between the Poisson regression model and the three other regression models. Interpretation of estimates from two variables (using the Internet to seek health information and single parent family) would have changed according to the model retained, with significant levels of 0.06 and 0.002 (Poisson), 0.29 and 0.09 (overdispersed Poisson), 0.29 and 0.13 (use of a robust estimator) and 0.45 and 0.13 (negative binomial) respectively. Different methods exist to solve the problem of underestimating variance in the Poisson regression model when overdispersion is present. The negative binomial regression model seems to be particularly accurate because of its theorical distribution ; in addition this regression is easy to perform with ordinary statistical software packages.

Extension of the application of conway-maxwell-poisson models: analyzing traffic crash data exhibiting underdispersion.

Science.gov (United States)

Lord, Dominique; Geedipally, Srinivas Reddy; Guikema, Seth D

2010-08-01

The objective of this article is to evaluate the performance of the COM-Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM-Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over- or underdispersion. Over the last year, the COM-Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson-gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM-Poisson models were estimated using crash data collected at 162 railway-highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM-Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.

Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

Science.gov (United States)

Orsingher, Enzo; Polito, Federico

2012-08-01

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

A twisted generalization of Novikov-Poisson algebras

OpenAIRE

Yau, Donald

2010-01-01

Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.

Poisson hierarchy of discrete strings

International Nuclear Information System (INIS)

Ioannidou, Theodora; Niemi, Antti J.

2016-01-01

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Poisson hierarchy of discrete strings

Energy Technology Data Exchange (ETDEWEB)

Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

2016-01-28

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere

International Nuclear Information System (INIS)

Sheu, A.J.L.

1991-01-01

We show that deformation quantizations of the Poisson structures on the Poisson Lie group SU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization of SU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure on SU(2) at the classical level is preserved under quantization. (orig.)

Cumulative Poisson Distribution Program

Science.gov (United States)

Bowerman, Paul N.; Scheuer, Ernest M.; Nolty, Robert

1990-01-01

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

A new multivariate zero-adjusted Poisson model with applications to biomedicine.

Science.gov (United States)

Liu, Yin; Tian, Guo-Liang; Tang, Man-Lai; Yuen, Kam Chuen

2018-05-25

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, ) cannot be used to fit multivariate count data with excess zero-vectors; (ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases; (iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data

KAUST Repository

Sepúlveda, Nuno

2013-02-26

Background: The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model.Results: Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates.Conclusions: In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data. 2013 Seplveda et al.; licensee BioMed Central Ltd.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data.

Science.gov (United States)

Sepúlveda, Nuno; Campino, Susana G; Assefa, Samuel A; Sutherland, Colin J; Pain, Arnab; Clark, Taane G

2013-02-26

The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data.

A Poisson hierarchical modelling approach to detecting copy number variation in sequence coverage data

KAUST Repository

Sepú lveda, Nuno; Campino, Susana G; Assefa, Samuel A; Sutherland, Colin J; Pain, Arnab; Clark, Taane G

2013-01-01

Background: The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model.Results: Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates.Conclusions: In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data. 2013 Seplveda et al.; licensee BioMed Central Ltd.

Poisson's ratio of fiber-reinforced composites

Science.gov (United States)

Christiansson, Henrik; Helsing, Johan

1996-05-01

Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the fiber fraction, are obtained numerically for hexagonal arrays of elastic circular fibers in an elastic matrix. High numerical accuracy is achieved through the use of an interface integral equation method. Questions concerning fixed point theorems and the validity of existing asymptotic relations are investigated and partially resolved. Our findings for the transverse effective Poisson's ratio, together with earlier results for random systems by other authors, make it possible to formulate a general statement for Poisson's ratio flow diagrams: For composites with circular fibers and where the phase Poisson's ratios are equal to 1/3, the system with the lowest stiffness ratio has the highest Poisson's ratio. For other choices of the elastic moduli for the phases, no simple statement can be made.

Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors

OpenAIRE

Dupé , François-Xavier; Fadili , Jalal M.; Starck , Jean-Luc

2012-01-01

International audience; In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On the other hand, as a prior, the images to restore are assumed to be positive and sparsely represented in a dictionary of waveforms such as wavelets or curvelets. Both analysis and synthesis-type spars...

Statistical features of pre-compound processes in nuclear reactions

International Nuclear Information System (INIS)

Hussein, M.S.; Rego, R.A.

1983-04-01

Several statistical aspects of multistep compound processes are discussed. The connection between the cross-section auto-correlation function and the average number of maxima is emphasized. The restrictions imposed by the non-zero value of the energy step used in measuring the excitation fuction and the experimental error are discussed. Applications are made to the system 25 Mg( 3 He,p) 27 Al. (Author) [pt

Bayesian inference on multiscale models for poisson intensity estimation: applications to photon-limited image denoising.

Science.gov (United States)

Lefkimmiatis, Stamatios; Maragos, Petros; Papandreou, George

2009-08-01

We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

Coordination of Conditional Poisson Samples

Directory of Open Access Journals (Sweden)

Grafström Anton

2015-12-01

Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

Drug Adverse Event Detection in Health Plan Data Using the Gamma Poisson Shrinker and Comparison to the Tree-based Scan Statistic

Directory of Open Access Journals (Sweden)

David Smith

2013-03-01

Full Text Available Background: Drug adverse event (AE signal detection using the Gamma Poisson Shrinker (GPS is commonly applied in spontaneous reporting. AE signal detection using large observational health plan databases can expand medication safety surveillance. Methods: Using data from nine health plans, we conducted a pilot study to evaluate the implementation and findings of the GPS approach for two antifungal drugs, terbinafine and itraconazole, and two diabetes drugs, pioglitazone and rosiglitazone. We evaluated 1676 diagnosis codes grouped into 183 different clinical concepts and four levels of granularity. Several signaling thresholds were assessed. GPS results were compared to findings from a companion study using the identical analytic dataset but an alternative statistical method—the tree-based scan statistic (TreeScan. Results: We identified 71 statistical signals across two signaling thresholds and two methods, including closely-related signals of overlapping diagnosis definitions. Initial review found that most signals represented known adverse drug reactions or confounding. About 31% of signals met the highest signaling threshold. Conclusions: The GPS method was successfully applied to observational health plan data in a distributed data environment as a drug safety data mining method. There was substantial concordance between the GPS and TreeScan approaches. Key method implementation decisions relate to defining exposures and outcomes and informed choice of signaling thresholds.

Statistical properties of earthquakes clustering

Directory of Open Access Journals (Sweden)

A. Vecchio

2008-04-01

Full Text Available Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of earthquakes. We show that this process strongly departs from a Poisson statistics for both catalogue and sequence data sets. This indicate the presence of correlations in the system probably related to the stressing perturbation characterizing the seismicity in the area under analysis. As shown by this analysis, the catalogues, at variance with sequences, show common statistical properties.

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

Science.gov (United States)

Konno, Hidetoshi; Tamura, Yoshiyasu

2018-01-01

In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance.

Science.gov (United States)

Poplová, Michaela; Sovka, Pavel; Cifra, Michal

2017-01-01

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal.

Dirichlet forms methods for Poisson point measures and Lévy processes with emphasis on the creation-annihilation techniques

CERN Document Server

Bouleau, Nicolas

2015-01-01

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calcul...

Non-holonomic dynamics and Poisson geometry

International Nuclear Information System (INIS)

Borisov, A V; Mamaev, I S; Tsiganov, A V

2014-01-01

This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie-Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles

A dynamic bivariate Poisson model for analysing and forecasting match results in the English Premier League

NARCIS (Netherlands)

Koopman, S.J.; Lit, R.

2015-01-01

Summary: We develop a statistical model for the analysis and forecasting of football match results which assumes a bivariate Poisson distribution with intensity coefficients that change stochastically over time. The dynamic model is a novelty in the statistical time series analysis of match results

Poisson brackets of orthogonal polynomials

OpenAIRE

Cantero, María José; Simon, Barry

2009-01-01

For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.

Constructions and classifications of projective Poisson varieties.

Science.gov (United States)

Pym, Brent

2018-01-01

This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

Constructions and classifications of projective Poisson varieties

Science.gov (United States)

Pym, Brent

2018-03-01

This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

Nonlocal Poisson-Fermi model for ionic solvent.

Science.gov (United States)

Xie, Dexuan; Liu, Jinn-Liang; Eisenberg, Bob

2016-07-01

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process

Directory of Open Access Journals (Sweden)

Hidetoshi Konno

2018-01-01

Full Text Available In neural spike counting experiments, it is known that there are two main features: (i the counting number has a fractional power-law growth with time and (ii the waiting time (i.e., the inter-spike-interval distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii can be modeled by the method of SSPPs. Namely, the first one (i associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP.

Image deblurring with Poisson data: from cells to galaxies

International Nuclear Information System (INIS)

Bertero, M; Boccacci, P; Desiderà, G; Vicidomini, G

2009-01-01

Image deblurring is an important topic in imaging science. In this review, we consider together fluorescence microscopy and optical/infrared astronomy because of two common features: in both cases the imaging system can be described, with a sufficiently good approximation, by a convolution operator, whose kernel is the so-called point-spread function (PSF); moreover, the data are affected by photon noise, described by a Poisson process. This statistical property of the noise, that is common also to emission tomography, is the basis of maximum likelihood and Bayesian approaches introduced in the mid eighties. From then on, a huge amount of literature has been produced on these topics. This review is a tutorial and a review of a relevant part of this literature, including some of our previous contributions. We discuss the mathematical modeling of the process of image formation and detection, and we introduce the so-called Bayesian paradigm that provides the basis of the statistical treatment of the problem. Next, we describe and discuss the most frequently used algorithms as well as other approaches based on a different description of the Poisson noise. We conclude with a review of other topics related to image deblurring such as boundary effect correction, space-variant PSFs, super-resolution, blind deconvolution and multiple-image deconvolution. (topical review)

Nonextensive statistical mechanics of ionic solutions

International Nuclear Information System (INIS)

Varela, L.M.; Carrete, J.; Munoz-Sola, R.; Rodriguez, J.R.; Gallego, J.

2007-01-01

Classical mean-field Poisson-Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson-Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye-Hueckel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q

Monte Carlo Simulation for Statistical Decay of Compound Nucleus

Directory of Open Access Journals (Sweden)

Chadwick M.B.

2012-02-01

Full Text Available We perform Monte Carlo simulations for neutron and γ-ray emissions from a compound nucleus based on the Hauser-Feshbach statistical theory. This Monte Carlo Hauser-Feshbach (MCHF method calculation, which gives us correlated information between emitted particles and γ-rays. It will be a powerful tool in many applications, as nuclear reactions can be probed in a more microscopic way. We have been developing the MCHF code, CGM, which solves the Hauser-Feshbach theory with the Monte Carlo method. The code includes all the standard models that used in a standard Hauser-Feshbach code, namely the particle transmission generator, the level density module, interface to the discrete level database, and so on. CGM can emit multiple neutrons, as long as the excitation energy of the compound nucleus is larger than the neutron separation energy. The γ-ray competition is always included at each compound decay stage, and the angular momentum and parity are conserved. Some calculations for a fission fragment 140Xe are shown as examples of the MCHF method, and the correlation between the neutron and γ-ray is discussed.

Counting statistics in radioactivity measurements

International Nuclear Information System (INIS)

Martin, J.

1975-01-01

The application of statistical methods to radioactivity measurement problems is analyzed in several chapters devoted successively to: the statistical nature of radioactivity counts; the application to radioactive counting of two theoretical probability distributions, Poisson's distribution law and the Laplace-Gauss law; true counting laws; corrections related to the nature of the apparatus; statistical techniques in gamma spectrometry [fr

Singular reduction of Nambu-Poisson manifolds

Science.gov (United States)

Das, Apurba

The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.

Bayesian Estimation Of Shift Point In Poisson Model Under Asymmetric Loss Functions

Directory of Open Access Journals (Sweden)

uma srivastava

2012-01-01

Full Text Available The paper deals with estimating  shift point which occurs in any sequence of independent observations  of Poisson model in statistical process control. This shift point occurs in the sequence when  i.e. m  life data are observed. The Bayes estimator on shift point 'm' and before and after shift process means are derived for symmetric and asymmetric loss functions under informative and non informative priors. The sensitivity analysis of Bayes estimators are carried out by simulation and numerical comparisons with  R-programming. The results shows the effectiveness of shift in sequence of Poisson disribution .

Neutron fluctuation analysis in a subcritical multiplying system with a stochastically pulsed poisson source

International Nuclear Information System (INIS)

Kostic, Lj.

2003-01-01

The influence of the stochastically pulsed Poisson source to the statistical properties of the subcritical multiplying system is analyzed in the paper. It is shown a strong dependence on the pulse period and pulse width of the source (author)

Statistical molecular design of balanced compound libraries for QSAR modeling.

Science.gov (United States)

Linusson, A; Elofsson, M; Andersson, I E; Dahlgren, M K

2010-01-01

A fundamental step in preclinical drug development is the computation of quantitative structure-activity relationship (QSAR) models, i.e. models that link chemical features of compounds with activities towards a target macromolecule associated with the initiation or progression of a disease. QSAR models are computed by combining information on the physicochemical and structural features of a library of congeneric compounds, typically assembled from two or more building blocks, and biological data from one or more in vitro assays. Since the models provide information on features affecting the compounds' biological activity they can be used as guides for further optimization. However, in order for a QSAR model to be relevant to the targeted disease, and drug development in general, the compound library used must contain molecules with balanced variation of the features spanning the chemical space believed to be important for interaction with the biological target. In addition, the assays used must be robust and deliver high quality data that are directly related to the function of the biological target and the associated disease state. In this review, we discuss and exemplify the concept of statistical molecular design (SMD) in the selection of building blocks and final synthetic targets (i.e. compounds to synthesize) to generate information-rich, balanced libraries for biological testing and computation of QSAR models.

Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light

Energy Technology Data Exchange (ETDEWEB)

Volovich, Igor V., E-mail: volovich@mi.ras.ru

2016-01-08

We discuss non-classicality of photon antibunching and sub-Poisson photon statistics. The difference K between the variance and the mean of the particle number operator as a measure of non-classicality of a state is discussed. The non-classicality of quantum states, discussed here, is different from another non-classicality, related with Bell's inequalities and entanglement though both can be traced to the violation of an inequality implied by an assumption of classicality that utilized the Cauchy–Schwarz inequality in the derivation. - Highlights: • Non-classicality of photon antibunching and sub-Poisson statistics are discussed. • The Cauchy–Schwarz inequality provides criteria for the non-classicality. • The vacuum contribution makes the superposition of quantum states more classical. • Experiments to generate non-classical superpositions of the Fock states are suggested.

Hazard rate model and statistical analysis of a compound point process

Czech Academy of Sciences Publication Activity Database

Volf, Petr

2005-01-01

Roč. 41, č. 6 (2005), s. 773-786 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : couting process * compound process * Cox regression model * intensity Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.343, year: 2005

Quasars, companion galaxies and Poisson statistics

International Nuclear Information System (INIS)

Webster, A.

1982-01-01

Arp has presented a sample of quasars lying close to the companion galaxies of bright spirals, from which he estimates a value of 10 -17 for the probability that the galaxies and quasars are sited independently on the celestial sphere; Browne, however, has found a simple fallacy in the statistics which accounts for about 10 of the 17 orders of magnitude. Here we draw attention to an obscure part of Arp's calculation which we have been unable to repeat; if it is carried out in what seems to be the most straightforward way, about five more orders may be accounted for. In consequence, it is not clear that the sample contains any evidence damaging to the popular notion that the redshifts of quasars indicate distance through the Hubble Law. (author)

Generalized master equations for non-Poisson dynamics on networks.

Science.gov (United States)

Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM

Science.gov (United States)

Bowerman, P. N.

1994-01-01

The cumulative poisson distribution program, NEWTPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714), can be used independently of one another. NEWTPOIS determines percentiles for gamma distributions with integer shape parameters and calculates percentiles for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. NEWTPOIS determines the Poisson parameter (lambda), that is; the mean (or expected) number of events occurring in a given unit of time, area, or space. Given that the user already knows the cumulative probability for a specific number of occurrences (n) it is usually a simple matter of substitution into the Poisson distribution summation to arrive at lambda. However, direct calculation of the Poisson parameter becomes difficult for small positive values of n and unmanageable for large values. NEWTPOIS uses Newton's iteration method to extract lambda from the initial value condition of the Poisson distribution where n=0, taking successive estimations until some user specified error term (epsilon) is reached. The NEWTPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting epsilon, n, and the cumulative probability of the occurrence of n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 30K. NEWTPOIS was developed in 1988.

Avoiding negative populations in explicit Poisson tau-leaping.

Science.gov (United States)

Cao, Yang; Gillespie, Daniel T; Petzold, Linda R

2005-08-01

The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure.

Particle-hole state densities for statistical multi-step compound reactions

International Nuclear Information System (INIS)

Oblozinsky, P.

1986-01-01

An analytical relation is derived for the density of particle-hole bound states applying the equidistant-spacing approximation and the Darwin-Fowler statistical method. The Pauli exclusion principle as well as the finite depth of the potential well are taken into account. The set of densities needed for calculations of multi-step compound reactions is completed by deriving the densities of accessible final states for escape and damping. (orig.)

Integrate-and-fire vs Poisson models of LGN input to V1 cortex: noisier inputs reduce orientation selectivity.

Science.gov (United States)

Lin, I-Chun; Xing, Dajun; Shapley, Robert

2012-12-01

One of the reasons the visual cortex has attracted the interest of computational neuroscience is that it has well-defined inputs. The lateral geniculate nucleus (LGN) of the thalamus is the source of visual signals to the primary visual cortex (V1). Most large-scale cortical network models approximate the spike trains of LGN neurons as simple Poisson point processes. However, many studies have shown that neurons in the early visual pathway are capable of spiking with high temporal precision and their discharges are not Poisson-like. To gain an understanding of how response variability in the LGN influences the behavior of V1, we study response properties of model V1 neurons that receive purely feedforward inputs from LGN cells modeled either as noisy leaky integrate-and-fire (NLIF) neurons or as inhomogeneous Poisson processes. We first demonstrate that the NLIF model is capable of reproducing many experimentally observed statistical properties of LGN neurons. Then we show that a V1 model in which the LGN input to a V1 neuron is modeled as a group of NLIF neurons produces higher orientation selectivity than the one with Poisson LGN input. The second result implies that statistical characteristics of LGN spike trains are important for V1's function. We conclude that physiologically motivated models of V1 need to include more realistic LGN spike trains that are less noisy than inhomogeneous Poisson processes.

Differential expression analysis for RNAseq using Poisson mixed models.

Science.gov (United States)

Sun, Shiquan; Hood, Michelle; Scott, Laura; Peng, Qinke; Mukherjee, Sayan; Tung, Jenny; Zhou, Xiang

2017-06-20

Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Statistical windows in angular momentum space: the basis of heavy-ion compound cross section

International Nuclear Information System (INIS)

Hussein, M.S.; Toledo, A.S. de.

1981-04-01

The concept of statistical windows in angular momentum space is introduced and utilized to develop a practical model for the heavy-ion compound cross section. Closed expressions for the average differential cross-section are derived and compared with Hauser-Feshbach calculations. The effects of the statistical windows are isolated and discussed. (Author) [pt

Poisson Mixture Regression Models for Heart Disease Prediction.

Science.gov (United States)

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

Science.gov (United States)

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

Singularities of Poisson structures and Hamiltonian bifurcations

NARCIS (Netherlands)

Meer, van der J.C.

2010-01-01

Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom

Relationship between the generalized equivalent uniform dose formulation and the Poisson statistics-based tumor control probability model

International Nuclear Information System (INIS)

Zhou Sumin; Das, Shiva; Wang Zhiheng; Marks, Lawrence B.

2004-01-01

The generalized equivalent uniform dose (GEUD) model uses a power-law formalism, where the outcome is related to the dose via a power law. We herein investigate the mathematical compatibility between this GEUD model and the Poisson statistics based tumor control probability (TCP) model. The GEUD and TCP formulations are combined and subjected to a compatibility constraint equation. This compatibility constraint equates tumor control probability from the original heterogeneous target dose distribution to that from the homogeneous dose from the GEUD formalism. It is shown that this constraint equation possesses a unique, analytical closed-form solution which relates radiation dose to the tumor cell survival fraction. It is further demonstrated that, when there is no positive threshold or finite critical dose in the tumor response to radiation, this relationship is not bounded within the realistic cell survival limits of 0%-100%. Thus, the GEUD and TCP formalisms are, in general, mathematically inconsistent. However, when a threshold dose or finite critical dose exists in the tumor response to radiation, there is a unique mathematical solution for the tumor cell survival fraction that allows the GEUD and TCP formalisms to coexist, provided that all portions of the tumor are confined within certain specific dose ranges

Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems

International Nuclear Information System (INIS)

Chang, Liu; Peng, Chang; Shi-Xing, Liu; Yong-Xin, Guo

2010-01-01

This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost-Poisson structure for generalised Chaplygin's systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noncanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion

Poisson Spot with Magnetic Levitation

Science.gov (United States)

Hoover, Matthew; Everhart, Michael; D'Arruda, Jose

2010-01-01

In this paper we describe a unique method for obtaining the famous Poisson spot without adding obstacles to the light path, which could interfere with the effect. A Poisson spot is the interference effect from parallel rays of light diffracting around a solid spherical object, creating a bright spot in the center of the shadow.

A note on optimal (s,S) and (R,nQ) policies under a stuttering Poisson demand process

DEFF Research Database (Denmark)

Larsen, Christian

2015-01-01

In this note, a new efficient algorithm is proposed to find an optimal (s, S) replenishment policy for inventory systems with continuous reviews and where the demand follows a stuttering Poisson process (the compound element is geometrically distributed). We also derive three upper bounds...

Poisson goodness-of-fit tests for radiation-induced chromosome aberrations

International Nuclear Information System (INIS)

Merkle, W.

1981-01-01

Asymptotic and exact Poisson goodness-to-fit tests have been reviewed with regard to their applicability in analysing distributional properties of data on chromosome aberrations. It has been demonstrated that for typical cytogenetic samples, i.e. when the average number of aberrations per cell is smaller than one, results of asymptotic tests, especially of the most commonly used u-test, differ greatly from results of corresponding exact tests. While the u-statistic can serve as a qualitative index to indicate a tendency towards under- or over-dispersion, exact tests should be used if the assumption of a Poisson distribution is crucial, e.g. in investigating induction mechanisms. If the main interest is to detect a difference between the mean and the variance of a sample it is furthermore important to realize that a much larger sample size is required to detect underdispersion than it is to detect overdispersion. (author)

Newton/Poisson-Distribution Program

Science.gov (United States)

Bowerman, Paul N.; Scheuer, Ernest M.

1990-01-01

NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.

A Martingale Characterization of Mixed Poisson Processes.

Science.gov (United States)

1985-10-01

03LA A 11. TITLE (Inciuae Security Clanafication, ",A martingale characterization of mixed Poisson processes " ________________ 12. PERSONAL AUTHOR... POISSON PROCESSES Jostification .......... . ... . . Di.;t ib,,jtion by Availability Codes Dietmar Pfeifer* Technical University Aachen Dist Special and...Mixed Poisson processes play an important role in many branches of applied probability, for instance in insurance mathematics and physics (see Albrecht

Pricing Zero-Coupon Catastrophe Bonds Using EVT with Doubly Stochastic Poisson Arrivals

Directory of Open Access Journals (Sweden)

Zonggang Ma

2017-01-01

Full Text Available The frequency and severity of climate abnormal change displays an irregular upward cycle as global warming intensifies. Therefore, this paper employs a doubly stochastic Poisson process with Black Derman Toy (BDT intensity to describe the catastrophic characteristics. By using the Property Claim Services (PCS loss index data from 2001 to 2010 provided by the US Insurance Services Office (ISO, the empirical result reveals that the BDT arrival rate process is superior to the nonhomogeneous Poisson and lognormal intensity process due to its smaller RMSE, MAE, MRPE, and U and larger E and d. Secondly, to depict extreme features of catastrophic risks, this paper adopts the Peak Over Threshold (POT in extreme value theory (EVT to characterize the tail characteristics of catastrophic loss distribution. And then the loss distribution is analyzed and assessed using a quantile-quantile (QQ plot to visually check whether the PCS index observations meet the generalized Pareto distribution (GPD assumption. Furthermore, this paper derives a pricing formula for zero-coupon catastrophe bonds with a stochastic interest rate environment and aggregate losses generated by a compound doubly stochastic Poisson process under the forward measure. Finally, simulation results verify pricing model predictions and show how catastrophic risks and interest rate risk affect the prices of zero-coupon catastrophe bonds.

Poisson-Hopf limit of quantum algebras

International Nuclear Information System (INIS)

Ballesteros, A; Celeghini, E; Olmo, M A del

2009-01-01

The Poisson-Hopf analogue of an arbitrary quantum algebra U z (g) is constructed by introducing a one-parameter family of quantizations U z,ℎ (g) depending explicitly on ℎ and by taking the appropriate ℎ → 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su q P (3) case is introduced. The q-Serre relations are also extended to the Poisson limit. This approach opens the perspective for possible applications of higher rank q-deformed Hopf algebras in semiclassical contexts

Reduction of Nambu-Poisson Manifolds by Regular Distributions

Science.gov (United States)

Das, Apurba

2018-03-01

The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.

Poisson's spot and Gouy phase

Science.gov (United States)

da Paz, I. G.; Soldati, Rodolfo; Cabral, L. A.; de Oliveira, J. G. G.; Sampaio, Marcos

2016-12-01

Recently there have been experimental results on Poisson spot matter-wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for Poisson's spot with matter waves based on the Babinet principle, in which we use the results for free propagation and single-slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter-wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium (D2) molecules.

Unimodularity criteria for Poisson structures on foliated manifolds

Science.gov (United States)

Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

2018-03-01

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

Non-isothermal Smoluchowski-Poisson equation as a singular limit of the Navier-Stokes-Fourier-Poisson system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Laurençot, P.

2007-01-01

Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007

Principles of applying Poisson units in radiology

International Nuclear Information System (INIS)

Benyumovich, M.S.

2000-01-01

The probability that radioactive particles hit particular space patterns (e.g. cells in the squares of a count chamber net) and time intervals (e.g. radioactive particles hit a given area per time unit) follows the Poisson distribution. The mean is the only parameter from which all this distribution depends. A metrological base of counting the cells and radioactive particles is a property of the Poisson distribution assuming equality of a standard deviation to a root square of mean (property 1). The application of Poisson units in counting of blood formed elements and cultured cells was proposed by us (Russian Federation Patent No. 2126230). Poisson units relate to the means which make the property 1 valid. In a case of cells counting, the square of these units is equal to 1/10 of one of count chamber net where they count the cells. Thus one finds the means from the single cell count rate divided by 10. Finding the Poisson units when counting the radioactive particles should assume determination of a number of these particles sufficient to make equality 1 valid. To this end one should subdivide a time interval used in counting a single particle count rate into different number of equal portions (count numbers). Next one should pick out the count number ensuring the satisfaction of equality 1. Such a portion is taken as a Poisson unit in the radioactive particles count. If the flux of particles is controllable one should set up a count rate sufficient to make equality 1 valid. Operations with means obtained by with the use of Poisson units are performed on the base of approximation of the Poisson distribution by a normal one. (author)

A Seemingly Unrelated Poisson Regression Model

OpenAIRE

King, Gary

1989-01-01

This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.

Poisson geometry from a Dirac perspective

Science.gov (United States)

Meinrenken, Eckhard

2018-03-01

We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.

Analisis Faktor – Faktor yang Mempengaruhi Jumlah Kejahatan Pencurian Kendaraan Bermotor (Curanmor) Menggunakan Model Geographically Weighted Poisson Regression (Gwpr)

OpenAIRE

Haris, Muhammad; Yasin, Hasbi; Hoyyi, Abdul

2015-01-01

Theft is an act taking someone else's property, partially or entierely, with intention to have it illegally. Motor vehicle theft is one of the most highlighted crime type and disturbing the communities. Regression analysis is a statistical analysis for modeling the relationships between response variable and predictor variable. If the response variable follows a Poisson distribution or categorized as a count data, so the regression model used is Poisson regression. Geographically Weighted Poi...

Statistical methods of spin assignment in compound nuclear reactions

International Nuclear Information System (INIS)

Mach, H.; Johns, M.W.

1984-01-01

Spin assignment to nuclear levels can be obtained from standard in-beam gamma-ray spectroscopy techniques and in the case of compound nuclear reactions can be complemented by statistical methods. These are based on a correlation pattern between level spin and gamma-ray intensities feeding low-lying levels. Three types of intensity and level spin correlations are found suitable for spin assignment: shapes of the excitation functions, ratio of intensity at two beam energies or populated in two different reactions, and feeding distributions. Various empirical attempts are examined and the range of applicability of these methods as well as the limitations associated with them are given. 12 references

Statistical methods of spin assignment in compound nuclear reactions

International Nuclear Information System (INIS)

Mach, H.; Johns, M.W.

1985-01-01

Spin assignment to nuclear levels can be obtained from standard in-beam gamma-ray spectroscopy techniques and in the case of compound nuclear reactions can be complemented by statistical methods. These are based on a correlation pattern between level spin and gamma-ray intensities feeding low-lying levels. Three types of intensity and level spin correlations are found suitable for spin assignment: shapes of the excitation functions, ratio of intensity at two beam energies or populated in two different reactions, and feeding distributions. Various empirical attempts are examined and the range of applicability of these methods as well as the limitations associated with them are given

Fundamentals of statistics

CERN Document Server

Mulholland, Henry

1968-01-01

Fundamentals of Statistics covers topics on the introduction, fundamentals, and science of statistics. The book discusses the collection, organization and representation of numerical data; elementary probability; the binomial Poisson distributions; and the measures of central tendency. The text describes measures of dispersion for measuring the spread of a distribution; continuous distributions for measuring on a continuous scale; the properties and use of normal distribution; and tests involving the normal or student's 't' distributions. The use of control charts for sample means; the ranges

Log-normal frailty models fitted as Poisson generalized linear mixed models.

Science.gov (United States)

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

The Fractional Poisson Process and the Inverse Stable Subordinator

OpenAIRE

Meerschaert, Mark; Nane, Erkan; Vellaisamy, P.

2011-01-01

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extend...

Evaluating the double Poisson generalized linear model.

Science.gov (United States)

Zou, Yaotian; Geedipally, Srinivas Reddy; Lord, Dominique

2013-10-01

The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. Copyright © 2013 Elsevier Ltd. All rights reserved.

Two-state Markov-chain Poisson nature of individual cellphone call statistics

Science.gov (United States)

Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier

2016-07-01

Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.

A test of inflated zeros for Poisson regression models.

Science.gov (United States)

He, Hua; Zhang, Hui; Ye, Peng; Tang, Wan

2017-01-01

Excessive zeros are common in practice and may cause overdispersion and invalidate inference when fitting Poisson regression models. There is a large body of literature on zero-inflated Poisson models. However, methods for testing whether there are excessive zeros are less well developed. The Vuong test comparing a Poisson and a zero-inflated Poisson model is commonly applied in practice. However, the type I error of the test often deviates seriously from the nominal level, rendering serious doubts on the validity of the test in such applications. In this paper, we develop a new approach for testing inflated zeros under the Poisson model. Unlike the Vuong test for inflated zeros, our method does not require a zero-inflated Poisson model to perform the test. Simulation studies show that when compared with the Vuong test our approach not only better at controlling type I error rate, but also yield more power.

Football goal distributions and extremal statistics

Science.gov (United States)

Greenhough, J.; Birch, P. C.; Chapman, S. C.; Rowlands, G.

2002-12-01

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored are too heavy-tailed to be fitted over their entire ranges by Poisson or negative binomial distributions which would be expected for uncorrelated processes. Log-normal distributions cannot include zero scores and here we find that the PDFs are consistent with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71-2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.

Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.

Science.gov (United States)

Hougaard, P; Lee, M L; Whitmore, G A

1997-12-01

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

Relaxed Poisson cure rate models.

Science.gov (United States)

Rodrigues, Josemar; Cordeiro, Gauss M; Cancho, Vicente G; Balakrishnan, N

2016-03-01

The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Poisson denoising on the sphere

Science.gov (United States)

Schmitt, J.; Starck, J. L.; Fadili, J.; Grenier, I.; Casandjian, J. M.

2009-08-01

In the scope of the Fermi mission, Poisson noise removal should improve data quality and make source detection easier. This paper presents a method for Poisson data denoising on sphere, called Multi-Scale Variance Stabilizing Transform on Sphere (MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a transform which aims to stabilize a Poisson data set such that each stabilized sample has an (asymptotically) constant variance. In addition, for the VST used in the method, the transformed data are asymptotically Gaussian. Thus, MS-VSTS consists in decomposing the data into a sparse multi-scale dictionary (wavelets, curvelets, ridgelets...), and then applying a VST on the coefficients in order to get quasi-Gaussian stabilized coefficients. In this present article, the used multi-scale transform is the Isotropic Undecimated Wavelet Transform. Then, hypothesis tests are made to detect significant coefficients, and the denoised image is reconstructed with an iterative method based on Hybrid Steepest Descent (HST). The method is tested on simulated Fermi data.

Zero inflated Poisson and negative binomial regression models: application in education.

Science.gov (United States)

Salehi, Masoud; Roudbari, Masoud

2015-01-01

The number of failed courses and semesters in students are indicators of their performance. These amounts have zero inflated (ZI) distributions. Using ZI Poisson and negative binomial distributions we can model these count data to find the associated factors and estimate the parameters. This study aims at to investigate the important factors related to the educational performance of students. This cross-sectional study performed in 2008-2009 at Iran University of Medical Sciences (IUMS) with a population of almost 6000 students, 670 students selected using stratified random sampling. The educational and demographical data were collected using the University records. The study design was approved at IUMS and the students' data kept confidential. The descriptive statistics and ZI Poisson and negative binomial regressions were used to analyze the data. The data were analyzed using STATA. In the number of failed semesters, Poisson and negative binomial distributions with ZI, students' total average and quota system had the most roles. For the number of failed courses, total average, and being in undergraduate or master levels had the most effect in both models. In all models the total average have the most effect on the number of failed courses or semesters. The next important factor is quota system in failed semester and undergraduate and master levels in failed courses. Therefore, average has an important inverse effect on the numbers of failed courses and semester.

Selective Contrast Adjustment by Poisson Equation

Directory of Open Access Journals (Sweden)

Ana-Belen Petro

2013-09-01

Full Text Available Poisson Image Editing is a new technique permitting to modify the gradient vector field of an image, and then to recover an image with a gradient approaching this modified gradient field. This amounts to solve a Poisson equation, an operation which can be efficiently performed by Fast Fourier Transform (FFT. This paper describes an algorithm applying this technique, with two different variants. The first variant enhances the contrast by increasing the gradient in the dark regions of the image. This method is well adapted to images with back light or strong shadows, and reveals details in the shadows. The second variant of the same Poisson technique enhances all small gradients in the image, thus also sometimes revealing details and texture.

PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON

Directory of Open Access Journals (Sweden)

PUTU SUSAN PRADAWATI

2013-09-01

Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution.

Science.gov (United States)

Womack, James C; Anton, Lucian; Dziedzic, Jacek; Hasnip, Phil J; Probert, Matt I J; Skylaris, Chris-Kriton

2018-03-13

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10 9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

The quantum poisson-Lie T-duality and mirror symmetry

International Nuclear Information System (INIS)

Parkhomenko, S.E.

1999-01-01

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also

Noncommutative gauge theory for Poisson manifolds

Energy Technology Data Exchange (ETDEWEB)

Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

2000-09-25

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Noncommutative gauge theory for Poisson manifolds

International Nuclear Information System (INIS)

Jurco, Branislav; Schupp, Peter; Wess, Julius

2000-01-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

Almost Poisson integration of rigid body systems

International Nuclear Information System (INIS)

Austin, M.A.; Krishnaprasad, P.S.; Li-Sheng Wang

1993-01-01

In this paper we discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by lie group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is an O(h 3 ) error estimate for the Lie-Poisson structure, where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored. 24 refs., 9 figs

Photon statistics in scintillation crystals

Science.gov (United States)

Bora, Vaibhav Joga Singh

Scintillation based gamma-ray detectors are widely used in medical imaging, high-energy physics, astronomy and national security. Scintillation gamma-ray detectors are eld-tested, relatively inexpensive, and have good detection eciency. Semi-conductor detectors are gaining popularity because of their superior capability to resolve gamma-ray energies. However, they are relatively hard to manufacture and therefore, at this time, not available in as large formats and much more expensive than scintillation gamma-ray detectors. Scintillation gamma-ray detectors consist of: a scintillator, a material that emits optical (scintillation) photons when it interacts with ionization radiation, and an optical detector that detects the emitted scintillation photons and converts them into an electrical signal. Compared to semiconductor gamma-ray detectors, scintillation gamma-ray detectors have relatively poor capability to resolve gamma-ray energies. This is in large part attributed to the "statistical limit" on the number of scintillation photons. The origin of this statistical limit is the assumption that scintillation photons are either Poisson distributed or super-Poisson distributed. This statistical limit is often dened by the Fano factor. The Fano factor of an integer-valued random process is dened as the ratio of its variance to its mean. Therefore, a Poisson process has a Fano factor of one. The classical theory of light limits the Fano factor of the number of photons to a value greater than or equal to one (Poisson case). However, the quantum theory of light allows for Fano factors to be less than one. We used two methods to look at the correlations between two detectors looking at same scintillation pulse to estimate the Fano factor of the scintillation photons. The relationship between the Fano factor and the correlation between the integral of the two signals detected was analytically derived, and the Fano factor was estimated using the measurements for SrI2:Eu, YAP

Square root approximation to the poisson channel

NARCIS (Netherlands)

Tsiatmas, A.; Willems, F.M.J.; Baggen, C.P.M.J.

2013-01-01

Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding

Duality and modular class of a Nambu-Poisson structure

International Nuclear Information System (INIS)

Ibanez, R.; Leon, M. de; Lopez, B.; Marrero, J.C.; Padron, E.

2001-01-01

In this paper we introduce cohomology and homology theories for Nambu-Poisson manifolds. Also we study the relation between the existence of a duality for these theories and the vanishing of a particular Nambu-Poisson cohomology class, the modular class. The case of a regular Nambu-Poisson structure and some singular examples are discussed. (author)

Scaling the Poisson Distribution

Science.gov (United States)

Farnsworth, David L.

2014-01-01

We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.

Selecting the right statistical model for analysis of insect count data by using information theoretic measures.

Science.gov (United States)

Sileshi, G

2006-10-01

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Poisson-Lie T-plurality

International Nuclear Information System (INIS)

Unge, Rikard von

2002-01-01

We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the literature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants. (author)

Associative and Lie deformations of Poisson algebras

OpenAIRE

Remm, Elisabeth

2011-01-01

Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.

Some functional limit theorems for compound Cox processes

Energy Technology Data Exchange (ETDEWEB)

Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Some functional limit theorems for compound Cox processes

International Nuclear Information System (INIS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-01-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.

Science.gov (United States)

Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew

2014-12-26

Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

Laplace-Laplace analysis of the fractional Poisson process

OpenAIRE

Gorenflo, Rudolf; Mainardi, Francesco

2013-01-01

We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.

The Poisson equation at second order in relativistic cosmology

International Nuclear Information System (INIS)

Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.

2013-01-01

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field

On Poisson Nonlinear Transformations

Directory of Open Access Journals (Sweden)

Nasir Ganikhodjaev

2014-01-01

Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

Network Traffic Monitoring Using Poisson Dynamic Linear Models

Energy Technology Data Exchange (ETDEWEB)

Merl, D. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2011-05-09

In this article, we discuss an approach for network forensics using a class of nonstationary Poisson processes with embedded dynamic linear models. As a modeling strategy, the Poisson DLM (PoDLM) provides a very flexible framework for specifying structured effects that may influence the evolution of the underlying Poisson rate parameter, including diurnal and weekly usage patterns. We develop a novel particle learning algorithm for online smoothing and prediction for the PoDLM, and demonstrate the suitability of the approach to real-time deployment settings via a new application to computer network traffic monitoring.

Test of Poisson Process for Earthquakes in and around Korea

International Nuclear Information System (INIS)

Noh, Myunghyun; Choi, Hoseon

2015-01-01

Since Cornell's work on the probabilistic seismic hazard analysis (hereafter, PSHA), majority of PSHA computer codes are assuming that the earthquake occurrence is Poissonian. To the author's knowledge, it is uncertain who first opened the issue of the Poisson process for the earthquake occurrence. The systematic PSHA in Korea, led by the nuclear industry, were carried out for more than 25 year with the assumption of the Poisson process. However, the assumption of the Poisson process has never been tested. Therefore, the test is of significance. We tested whether the Korean earthquakes follow the Poisson process or not. The Chi-square test with the significance level of 5% was applied. The test turned out that the Poisson process could not be rejected for the earthquakes of magnitude 2.9 or larger. However, it was still observed in the graphical comparison that some portion of the observed distribution significantly deviated from the Poisson distribution. We think this is due to the small earthquake data. The earthquakes of magnitude 2.9 or larger occurred only 376 times during 34 years. Therefore, the judgment on the Poisson process derived in the present study is not conclusive

On the application of nonhomogeneous Poisson process to the reliability analysis of service water pumps of nuclear power plants

International Nuclear Information System (INIS)

Cruz Saldanha, Pedro Luiz da.

1995-12-01

The purpose of this study is to evaluate the nonhomogeneous Poisson process as a model to rate of occurrence of failures when it is not constant, and the times between failures are not independent nor identically distributed. To this evaluation, an analyse of reliability of service water pumps of a typical nuclear power plant is made considering the model discussed in the last paragraph, as long as the pumps are effectively repairable components. Standard statistical techniques, such as maximum likelihood and linear regression, are applied to estimate parameters of nonhomogeneous Poisson process model. As a conclusion of the study, the nonhomogeneous Poisson process is adequate to model rate of occurrence of failures that are function of time, and can be used where the aging mechanisms are present in operation of repairable systems. (author). 72 refs., 45 figs., 21 tabs

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

Science.gov (United States)

Neti, Prasad V.S.V.; Howell, Roger W.

2010-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log-normal (LN) distribution function (J Nucl Med. 2006;47:1049–1058) with the aid of autoradiography. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analysis of these earlier data. Methods The measured distributions of α-particle tracks per cell were subjected to statistical tests with Poisson, LN, and Poisson-lognormal (P-LN) models. Results The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL of 210Po-citrate. When cells were exposed to 67 kBq/mL, the P-LN distribution function gave a better fit; however, the underlying activity distribution remained log-normal. Conclusion The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution. PMID:18483086

Poisson sigma model with branes and hyperelliptic Riemann surfaces

International Nuclear Information System (INIS)

Ferrario, Andrea

2008-01-01

We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions

Method of Poisson's ratio imaging within a material part

Science.gov (United States)

Roth, Don J. (Inventor)

1996-01-01

The present invention is directed to a method of displaying the Poisson's ratio image of a material part. In the present invention longitudinal data is produced using a longitudinal wave transducer and shear wave data is produced using a shear wave transducer. The respective data is then used to calculate the Poisson's ratio for the entire material part. The Poisson's ratio approximations are then used to displayed the image.

Accounting for undetected compounds in statistical analyses of mass spectrometry 'omic studies.

Science.gov (United States)

Taylor, Sandra L; Leiserowitz, Gary S; Kim, Kyoungmi

2013-12-01

Mass spectrometry is an important high-throughput technique for profiling small molecular compounds in biological samples and is widely used to identify potential diagnostic and prognostic compounds associated with disease. Commonly, this data generated by mass spectrometry has many missing values resulting when a compound is absent from a sample or is present but at a concentration below the detection limit. Several strategies are available for statistically analyzing data with missing values. The accelerated failure time (AFT) model assumes all missing values result from censoring below a detection limit. Under a mixture model, missing values can result from a combination of censoring and the absence of a compound. We compare power and estimation of a mixture model to an AFT model. Based on simulated data, we found the AFT model to have greater power to detect differences in means and point mass proportions between groups. However, the AFT model yielded biased estimates with the bias increasing as the proportion of observations in the point mass increased while estimates were unbiased with the mixture model except if all missing observations came from censoring. These findings suggest using the AFT model for hypothesis testing and mixture model for estimation. We demonstrated this approach through application to glycomics data of serum samples from women with ovarian cancer and matched controls.

Contravariant gravity on Poisson manifolds and Einstein gravity

International Nuclear Information System (INIS)

Kaneko, Yukio; Watamura, Satoshi; Muraki, Hisayoshi

2017-01-01

A relation between gravity on Poisson manifolds proposed in Asakawa et al (2015 Fortschr. Phys . 63 683–704) and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein–Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner. (paper)

Modified Regression Correlation Coefficient for Poisson Regression Model

Science.gov (United States)

Kaengthong, Nattacha; Domthong, Uthumporn

2017-09-01

This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).

A comparison of Poisson-one-inflated power series distributions for ...

African Journals Online (AJOL)

A class of Poisson-one-inflated power series distributions (the binomial, the Poisson, the negative binomial, the geometric, the log-series and the misrecorded Poisson) are proposed for modeling rural out-migration at the household level. The probability mass functions of the mixture distributions are derived and fitted to the ...

Poisson-Jacobi reduction of homogeneous tensors

International Nuclear Information System (INIS)

Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P

2004-01-01

The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N

Poisson solvers for self-consistent multi-particle simulations

International Nuclear Information System (INIS)

Qiang, J; Paret, S

2014-01-01

Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density distribution in the multi-particle simulation. In this paper, we review a number of numerical methods that can be used to solve the Poisson equation efficiently. The computational complexity of those numerical methods will be O(N log(N)) or O(N) instead of O(N2), where N is the total number of grid points used to solve the Poisson equation

Poisson image reconstruction with Hessian Schatten-norm regularization.

Science.gov (United States)

Lefkimmiatis, Stamatios; Unser, Michael

2013-11-01

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupted by Poisson noise. In this paper, we propose an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators. In particular, the employed regularizers involve the Hessian as the regularization operator and Schatten matrix norms as the potential functions. For the solution of the problem, we propose two optimization algorithms that are specifically tailored to the Poisson nature of the noise. These algorithms are based on an augmented-Lagrangian formulation of the problem and correspond to two variants of the alternating direction method of multipliers. Further, we derive a link that relates the proximal map of an l(p) norm with the proximal map of a Schatten matrix norm of order p. This link plays a key role in the development of one of the proposed algorithms. Finally, we provide experimental results on natural and biological images for the task of Poisson image deblurring and demonstrate the practical relevance and effectiveness of the proposed framework.

Seasonally adjusted birth frequencies follow the Poisson distribution.

Science.gov (United States)

Barra, Mathias; Lindstrøm, Jonas C; Adams, Samantha S; Augestad, Liv A

2015-12-15

Variations in birth frequencies have an impact on activity planning in maternity wards. Previous studies of this phenomenon have commonly included elective births. A Danish study of spontaneous births found that birth frequencies were well modelled by a Poisson process. Somewhat unexpectedly, there were also weekly variations in the frequency of spontaneous births. Another study claimed that birth frequencies follow the Benford distribution. Our objective was to test these results. We analysed 50,017 spontaneous births at Akershus University Hospital in the period 1999-2014. To investigate the Poisson distribution of these births, we plotted their variance over a sliding average. We specified various Poisson regression models, with the number of births on a given day as the outcome variable. The explanatory variables included various combinations of years, months, days of the week and the digit sum of the date. The relationship between the variance and the average fits well with an underlying Poisson process. A Benford distribution was disproved by a goodness-of-fit test (p Poisson process when monthly and day-of-the-week variation is included. The frequency is highest in summer towards June and July, Friday and Tuesday stand out as particularly busy days, and the activity level is at its lowest during weekends.

Quest for consistent modelling of statistical decay of the compound nucleus

Science.gov (United States)

Banerjee, Tathagata; Nath, S.; Pal, Santanu

2018-01-01

A statistical model description of heavy ion induced fusion-fission reactions is presented where shell effects, collective enhancement of level density, tilting away effect of compound nuclear spin and dissipation are included. It is shown that the inclusion of all these effects provides a consistent picture of fission where fission hindrance is required to explain the experimental values of both pre-scission neutron multiplicities and evaporation residue cross-sections in contrast to some of the earlier works where a fission hindrance is required for pre-scission neutrons but a fission enhancement for evaporation residue cross-sections.

A high order solver for the unbounded Poisson equation

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

2013-01-01

. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied......A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field...... and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain....

Some applications of the fractional Poisson probability distribution

International Nuclear Information System (INIS)

Laskin, Nick

2009-01-01

Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.

A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep

Directory of Open Access Journals (Sweden)

Rodrigues-Motta Mariana

2008-07-01

Full Text Available Abstract Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep.

The spin-statistics connection in classical field theory

International Nuclear Information System (INIS)

Morgan, J A

2006-01-01

The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group corresponding to general causal fields is reviewed. The connection is obtained by imposing local commutativity on the fields and exploiting the parity operation to exchange spatial coordinates in the scalar product of classical field evaluated at one spatial location with the same field evaluated at a distinct location. The spin-statistics connection for irreducible canonical realizations of the Poincare group of spin j is obtained in the form: classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2j even and fundamental Poisson antibracket relations for 2j odd

Measuring mouse retina response near the detection threshold to direct stimulation of photons with sub-poisson statistics

Science.gov (United States)

Tavala, Amir; Dovzhik, Krishna; Schicker, Klaus; Koschak, Alexandra; Zeilinger, Anton

Probing the visual system of human and animals at very low photon rate regime has recently attracted the quantum optics community. In an experiment on the isolated photoreceptor cells of Xenopus, the cell output signal was measured while stimulating it by pulses with sub-poisson distributed photons. The results showed single photon detection efficiency of 29 +/-4.7% [1]. Another behavioral experiment on human suggests a less detection capability at perception level with the chance of 0.516 +/-0.01 (i.e. slightly better than random guess) [2]. Although the species are different, both biological models and experimental observations with classical light stimuli expect that a fraction of single photon responses is filtered somewhere within the retina network and/or during the neural processes in the brain. In this ongoing experiment, we look for a quantitative answer to this question by measuring the output signals of the last neural layer of WT mouse retina using microelectrode arrays. We use a heralded downconversion single-photon source. We stimulate the retina directly since the eye lens (responsible for 20-50% of optical loss and scattering [2]) is being removed. Here, we demonstrate our first results that confirms the response to the sub-poisson distributied pulses. This project was supported by Austrian Academy of Sciences, SFB FoQuS F 4007-N23 funded by FWF and ERC QIT4QAD 227844 funded by EU Commission.

Pendugaan Angka Kematian Bayi dengan Menggunakan Model Poisson Bayes Berhirarki Dua-Level

Directory of Open Access Journals (Sweden)

Nusar Hajarisman

2013-06-01

Full Text Available Official institutions of national data providers such as the BPS-Statistics Indonesia is required to produce and present the statistical information, as necessary as a form of contributory BPS region in support of regional development policy and planning. There are survey conducted by BPS capability estimation techniques are still limited, due to the resulting estimators have not been able to directly assumed for small areas. In this article we propose the hierarchical Bayesian models, especially for count data which are Poisson distributed, in small area estimation problem. The model was developed by combining concept of generalized linear model and Fay-Herriot model. The results of the development of this model is implemented to estimate the infant mortality rate in Bojonegoro district, East Java Province.

Sensitivity study of poisson corruption in tomographic measurements for air-water flows

International Nuclear Information System (INIS)

Munshi, P.; Vaidya, M.S.

1993-01-01

An application of computerized tomography (CT) for measuring void fraction profiles in two-phase air-water flows was reported earlier. Those attempts involved some special radial methods for tomographic reconstruction and the popular convolution backprojection (CBP) method. The CBP method is capable of reconstructing void profiles for nonsymmetric flows also. In this paper, we investigate the effect of corrupted CT data for gamma-ray sources and aCBP algorithm. The corruption in such a case is due to the statistical (Poisson) nature of the source

Cluster X-varieties, amalgamation, and Poisson-Lie groups

DEFF Research Database (Denmark)

Fock, V. V.; Goncharov, A. B.

2006-01-01

In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as cluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varie...

Hidden Markov models for zero-inflated Poisson counts with an application to substance use.

Science.gov (United States)

DeSantis, Stacia M; Bandyopadhyay, Dipankar

2011-06-30

Paradigms for substance abuse cue-reactivity research involve pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress-and cue-reactivity study. The hypothesized latent state corresponds to 'high' or 'low' use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week's state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data. Copyright © 2011 John Wiley & Sons, Ltd.

Leptospirosis disease mapping with standardized morbidity ratio and Poisson-Gamma model: An analysis of Leptospirosis disease in Kelantan, Malaysia

Science.gov (United States)

Che Awang, Aznida; Azah Samat, Nor

2017-09-01

Leptospirosis is a disease caused by the infection of pathogenic species from the genus of Leptospira. Human can be infected by the leptospirosis from direct or indirect exposure to the urine of infected animals. The excretion of urine from the animal host that carries pathogenic Leptospira causes the soil or water to be contaminated. Therefore, people can become infected when they are exposed to contaminated soil and water by cut on the skin as well as open wound. It also can enter the human body by mucous membrane such nose, eyes and mouth, for example by splashing contaminated water or urine into the eyes or swallowing contaminated water or food. Currently, there is no vaccine available for the prevention or treatment of leptospirosis disease but this disease can be treated if it is diagnosed early to avoid any complication. The disease risk mapping is important in a way to control and prevention of disease. Using a good choice of statistical model will produce a good disease risk map. Therefore, the aim of this study is to estimate the relative risk for leptospirosis disease based initially on the most common statistic used in disease mapping called Standardized Morbidity Ratio (SMR) and Poisson-gamma model. This paper begins by providing a review of the SMR method and Poisson-gamma model, which we then applied to leptospirosis data of Kelantan, Malaysia. Both results are displayed and compared using graph, tables and maps. The result shows that the second method Poisson-gamma model produces better relative risk estimates compared to the SMR method. This is because the Poisson-gamma model can overcome the drawback of SMR where the relative risk will become zero when there is no observed leptospirosis case in certain regions. However, the Poisson-gamma model also faced problems where the covariate adjustment for this model is difficult and no possibility for allowing spatial correlation between risks in neighbouring areas. The problems of this model have

Poisson traces, D-modules, and symplectic resolutions.

Science.gov (United States)

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions

Science.gov (United States)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

Science.gov (United States)

Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

2011-01-01

Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

Particle-wave discrimination in Poisson spot experiments

International Nuclear Information System (INIS)

Reisinger, T; Bracco, G; Holst, B

2011-01-01

Matter-wave interferometry has been used extensively over the last few years to demonstrate the quantum-mechanical wave nature of increasingly larger and more massive particles. We have recently suggested the use of the historical Poisson spot setup to test the diffraction properties of larger objects. In this paper, we present the results of a classical particle van der Waals (vdW) force model for a Poisson spot experimental setup and compare these to Fresnel diffraction calculations with a vdW phase term. We include the effect of disc-edge roughness in both models. Calculations are performed with D 2 and with C 70 using realistic parameters. We find that the sensitivity of the on-axis interference/focus spot to disc-edge roughness is very different in the two cases. We conclude that by measuring the intensity on the optical axis as a function of disc-edge roughness, it can be determined whether the objects behave as de Broglie waves or classical particles. The scaling of the Poisson spot experiment to larger molecular masses is, however, not as favorable as in the case of near-field light-grating-based interferometers. Instead, we discuss the possibility of studying the Casimir-Polder potential using the Poisson spot setup.

Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets

Science.gov (United States)

Carlet, Guido; Casati, Matteo; Shadrin, Sergey

2017-04-01

We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D > 1. Hence, in contrast with the D = 1 case, the deformation theory in the multivariable case is non-trivial.

Quantum algebras and Poisson geometry in mathematical physics

CERN Document Server

Karasev, M V

2005-01-01

This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.

Poisson's ratio and Young's modulus of lipid bilayers in different phases

Directory of Open Access Journals (Sweden)

Tayebeh eJadidi

2014-04-01

Full Text Available A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness.In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distancesin one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in orderto predict the temperature dependence of its Poisson's ratio and Young's modulus.

Estimating Bird / Aircraft Collision Probabilities and Risk Utilizing Spatial Poisson Processes

Science.gov (United States)

2012-06-10

ESTIMATING BIRD/AIRCRAFT COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE...AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE RESEARCH PAPER Presented to the Faculty Department of Operational Sciences...COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES Brady J. Vaira, BS, MS Major, USAF Approved

Improving EWMA Plans for Detecting Unusual Increases in Poisson Counts

Directory of Open Access Journals (Sweden)

R. S. Sparks

2009-01-01

adaptive exponentially weighted moving average (EWMA plan is developed for signalling unusually high incidence when monitoring a time series of nonhomogeneous daily disease counts. A Poisson transitional regression model is used to fit background/expected trend in counts and provides “one-day-ahead” forecasts of the next day's count. Departures of counts from their forecasts are monitored. The paper outlines an approach for improving early outbreak data signals by dynamically adjusting the exponential weights to be efficient at signalling local persistent high side changes. We emphasise outbreak signals in steady-state situations; that is, changes that occur after the EWMA statistic had run through several in-control counts.

Statistical methods in nuclear theory

International Nuclear Information System (INIS)

Shubin, Yu.N.

1974-01-01

The paper outlines statistical methods which are widely used for describing properties of excited states of nuclei and nuclear reactions. It discusses physical assumptions lying at the basis of known distributions between levels (Wigner, Poisson distributions) and of widths of highly excited states (Porter-Thomas distribution, as well as assumptions used in the statistical theory of nuclear reactions and in the fluctuation analysis. The author considers the random matrix method, which consists in replacing the matrix elements of a residual interaction by random variables with a simple statistical distribution. Experimental data are compared with results of calculations using the statistical model. The superfluid nucleus model is considered with regard to superconducting-type pair correlations

Poisson structures for reduced non-holonomic systems

International Nuclear Information System (INIS)

Ramos, Arturo

2004-01-01

Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank 2 and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of the Poisson structures and extend their domain of definition. We apply the theory to the rolling disc, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder

High order Poisson Solver for unbounded flows

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

2015-01-01

This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing...

Estimation of Poisson noise in spatial domain

Science.gov (United States)

Švihlík, Jan; Fliegel, Karel; Vítek, Stanislav; Kukal, Jaromír.; Krbcová, Zuzana

2017-09-01

This paper deals with modeling of astronomical images in the spatial domain. We consider astronomical light images contaminated by the dark current which is modeled by Poisson random process. Dark frame image maps the thermally generated charge of the CCD sensor. In this paper, we solve the problem of an addition of two Poisson random variables. At first, the noise analysis of images obtained from the astronomical camera is performed. It allows estimating parameters of the Poisson probability mass functions in every pixel of the acquired dark frame. Then the resulting distributions of the light image can be found. If the distributions of the light image pixels are identified, then the denoising algorithm can be applied. The performance of the Bayesian approach in the spatial domain is compared with the direct approach based on the method of moments and the dark frame subtraction.

Failure of the statistical hypothesis for compound nucleus decay

International Nuclear Information System (INIS)

Chrien, R.E.

1976-01-01

In the past five years, conclusive evidence has accumulated that channel correlations are important in resonance reactions. Experiments showing the failure of the statistical hypothesis for compound nucleus decay are described. The emphasis is on the radiative neutron capture reaction, where much detailed work has been done. A short summary of the theory of the (n,γ) reaction is presented; it is demonstrated that this reaction is a sensitive probe of the wave functions for highly excited nuclear states. Various experimental techniques using reactor and accelerator-based neutron sources are presented. The experiments have shown that both resonant and non-resonant reactions can show single particle effects where the external part of configuration space is dominant. In the non-resonant case, hard sphere capture is important; on resonances, valence particle motion and the contributions of 1 and 3 quasi-particle doorway states make up a significant fraction of the radiative width

On covariant Poisson brackets in classical field theory

International Nuclear Information System (INIS)

Forger, Michael; Salles, Mário O.

2015-01-01

How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra

On covariant Poisson brackets in classical field theory

Energy Technology Data Exchange (ETDEWEB)

Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)

2015-10-15

How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.

Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data.

Science.gov (United States)

Rakitzis, Athanasios C; Castagliola, Philippe; Maravelakis, Petros E

2018-02-01

In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.

Exact solution for the Poisson field in a semi-infinite strip.

Science.gov (United States)

Cohen, Yossi; Rothman, Daniel H

2017-04-01

The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

A Method of Poisson's Ration Imaging Within a Material Part

Science.gov (United States)

Roth, Don J. (Inventor)

1994-01-01

The present invention is directed to a method of displaying the Poisson's ratio image of a material part. In the present invention, longitudinal data is produced using a longitudinal wave transducer and shear wave data is produced using a shear wave transducer. The respective data is then used to calculate the Poisson's ratio for the entire material part. The Poisson's ratio approximations are then used to display the data.

Fractional poisson--a simple dose-response model for human norovirus.

Science.gov (United States)

Messner, Michael J; Berger, Philip; Nappier, Sharon P

2014-10-01

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.

Microergodicity effects on ebullition of methane modelled by Mixed Poisson process with Pareto mixing variable

Czech Academy of Sciences Publication Activity Database

Jordanova, P.; Dušek, Jiří; Stehlík, M.

2013-01-01

Roč. 128, OCT 15 (2013), s. 124-134 ISSN 0169-7439 R&D Projects: GA ČR(CZ) GAP504/11/1151; GA MŠk(CZ) ED1.1.00/02.0073 Institutional support: RVO:67179843 Keywords : environmental chemistry * ebullition of methane * mixed poisson processes * renewal process * pareto distribution * moving average process * robust statistics * sedge–grass marsh Subject RIV: EH - Ecology, Behaviour Impact factor: 2.381, year: 2013

Action-angle variables and a KAM theorem for b-Poisson manifolds

OpenAIRE

Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

2015-01-01

In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

Non-Poisson Processes: Regression to Equilibrium Versus Equilibrium Correlation Functions

Science.gov (United States)

2004-07-07

ARTICLE IN PRESSPhysica A 347 (2005) 268–2880378-4371/$ - doi:10.1016/j Correspo E-mail adwww.elsevier.com/locate/physaNon- Poisson processes : regression...05.40.a; 89.75.k; 02.50.Ey Keywords: Stochastic processes; Non- Poisson processes ; Liouville and Liouville-like equations; Correlation function...which is not legitimate with renewal non- Poisson processes , is a correct property if the deviation from the exponential relaxation is obtained by time

Multi-parameter full waveform inversion using Poisson

KAUST Repository

Oh, Juwon

2016-07-21

In multi-parameter full waveform inversion (FWI), the success of recovering each parameter is dependent on characteristics of the partial derivative wavefields (or virtual sources), which differ according to parameterisation. Elastic FWIs based on the two conventional parameterisations (one uses Lame constants and density; the other employs P- and S-wave velocities and density) have low resolution of gradients for P-wave velocities (or ). Limitations occur because the virtual sources for P-wave velocity or (one of the Lame constants) are related only to P-P diffracted waves, and generate isotropic explosions, which reduce the spatial resolution of the FWI for these parameters. To increase the spatial resolution, we propose a new parameterisation using P-wave velocity, Poisson\\'s ratio, and density for frequency-domain multi-parameter FWI for isotropic elastic media. By introducing Poisson\\'s ratio instead of S-wave velocity, the virtual source for the P-wave velocity generates P-S and S-S diffracted waves as well as P-P diffracted waves in the partial derivative wavefields for the P-wave velocity. Numerical examples of the cross-triangle-square (CTS) model indicate that the new parameterisation provides highly resolved descent directions for the P-wave velocity. Numerical examples of noise-free and noisy data synthesised for the elastic Marmousi-II model support the fact that the new parameterisation is more robust for noise than the two conventional parameterisations.

Study on two-dimensional POISSON design of large-scale FFAG magnet

International Nuclear Information System (INIS)

Ouyang Huafu

2006-01-01

In order to decrease the edge effect of the field, the designed magnetic field distribution in a large-scale FFAG magnet is realized by both the trim coil and the shape of the magnet pole-face. Through two-dimensional POISSON simulations, the distribution about the current and the position of the trim coil and the shape of the magnet pole are determined. In order to facilitate the POISSON design, two codes are writteen to automatically adjust the current and the position of the trim coil and the shape of magnet pole-face appeared in the POISSON input file. With the two codes, the efficiency of POISSON simulations is improved and the mistakes which might occur in writing and adjusting the POISSON input file manually could be avoided. (authors)

Double asymptotics for the chi-square statistic.

Science.gov (United States)

Rempała, Grzegorz A; Wesołowski, Jacek

2016-12-01

Consider distributional limit of the Pearson chi-square statistic when the number of classes m n increases with the sample size n and [Formula: see text]. Under mild moment conditions, the limit is Gaussian for λ = ∞, Poisson for finite λ > 0, and degenerate for λ = 0.

Boundary Lax pairs from non-ultra-local Poisson algebras

International Nuclear Information System (INIS)

Avan, Jean; Doikou, Anastasia

2009-01-01

We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.

Statistical hadronization and hadronic micro-canonical ensemble II

International Nuclear Information System (INIS)

Becattini, F.; Ferroni, L.

2004-01-01

We present a Monte Carlo calculation of the micro-canonical ensemble of the ideal hadron-resonance gas including all known states up to a mass of about 1.8 GeV and full quantum statistics. The micro-canonical average multiplicities of the various hadron species are found to converge to the canonical ones for moderately low values of the total energy, around 8 GeV, thus bearing out previous analyses of hadronic multiplicities in the canonical ensemble. The main numerical computing method is an importance sampling Monte Carlo algorithm using the product of Poisson distributions to generate multi-hadronic channels. It is shown that the use of this multi-Poisson distribution allows for an efficient and fast computation of averages, which can be further improved in the limit of very large clusters. We have also studied the fitness of a previously proposed computing method, based on the Metropolis Monte Carlo algorithm, for event generation in the statistical hadronization model. We find that the use of the multi-Poisson distribution as proposal matrix dramatically improves the computation performance. However, due to the correlation of subsequent samples, this method proves to be generally less robust and effective than the importance sampling method. (orig.)

Eigenfunction statistics for Anderson model with Hölder continuous ...

Indian Academy of Sciences (India)

The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India ... Anderson model; Hölder continuous measure; Poisson statistics. ...... [4] Combes J-M, Hislop P D and Klopp F, An optimal Wegner estimate and its application to.

The BRST complex of homological Poisson reduction

Science.gov (United States)

Müller-Lennert, Martin

2017-02-01

BRST complexes are differential graded Poisson algebras. They are associated with a coisotropic ideal J of a Poisson algebra P and provide a description of the Poisson algebra (P/J)^J as their cohomology in degree zero. Using the notion of stable equivalence introduced in Felder and Kazhdan (Contemporary Mathematics 610, Perspectives in representation theory, 2014), we prove that any two BRST complexes associated with the same coisotropic ideal are quasi-isomorphic in the case P = R[V] where V is a finite-dimensional symplectic vector space and the bracket on P is induced by the symplectic structure on V. As a corollary, the cohomology of the BRST complexes is canonically associated with the coisotropic ideal J in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal J. We finally quantize the BRST complex rigorously in the presence of infinitely many ghost variables and discuss the uniqueness of the quantization procedure.

Poisson's Ratio and Auxetic Properties of Natural Rocks

Science.gov (United States)

Ji, Shaocheng; Li, Le; Motra, Hem Bahadur; Wuttke, Frank; Sun, Shengsi; Michibayashi, Katsuyoshi; Salisbury, Matthew H.

2018-02-01

Here we provide an appraisal of the Poisson's ratios (υ) for natural elements, common oxides, silicate minerals, and rocks with the purpose of searching for naturally auxetic materials. The Poisson's ratios of equivalently isotropic polycrystalline aggregates were calculated from dynamically measured elastic properties. Alpha-cristobalite is currently the only known naturally occurring mineral that has exclusively negative υ values at 20-1,500°C. Quartz and potentially berlinite (AlPO4) display auxetic behavior in the vicinity of their α-β structure transition. None of the crystalline igneous and metamorphic rocks (e.g., amphibolite, gabbro, granite, peridotite, and schist) display auxetic behavior at pressures of >5 MPa and room temperature. Our experimental measurements showed that quartz-rich sedimentary rocks (i.e., sandstone and siltstone) are most likely to be the only rocks with negative Poisson's ratios at low confining pressures (≤200 MPa) because their main constituent mineral, α-quartz, already has extremely low Poisson's ratio (υ = 0.08) and they contain microcracks, micropores, and secondary minerals. This finding may provide a new explanation for formation of dome-and-basin structures in quartz-rich sedimentary rocks in response to a horizontal compressional stress in the upper crust.

Introduction to Bayesian statistics

CERN Document Server

Bolstad, William M

2017-01-01

There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...

Estimation of a Non-homogeneous Poisson Model: An Empirical ...

African Journals Online (AJOL)

This article aims at applying the Nonhomogeneous Poisson process to trends of economic development. For this purpose, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean ...

NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes

Directory of Open Access Journals (Sweden)

Ana C. Cebrián

2015-03-01

Full Text Available NHPoisson is an R package for the modeling of nonhomogeneous Poisson processes in one dimension. It includes functions for data preparation, maximum likelihood estimation, covariate selection and inference based on asymptotic distributions and simulation methods. It also provides specific methods for the estimation of Poisson processes resulting from a peak over threshold approach. In addition, the package supports a wide range of model validation tools and functions for generating nonhomogenous Poisson process trajectories. This paper is a description of the package and aims to help those interested in modeling data using nonhomogeneous Poisson processes.

Adaptive maximal poisson-disk sampling on surfaces

KAUST Repository

Yan, Dongming

2012-01-01

In this paper, we study the generation of maximal Poisson-disk sets with varying radii on surfaces. Based on the concepts of power diagram and regular triangulation, we present a geometric analysis of gaps in such disk sets on surfaces, which is the key ingredient of the adaptive maximal Poisson-disk sampling framework. Moreover, we adapt the presented sampling framework for remeshing applications. Several novel and efficient operators are developed for improving the sampling/meshing quality over the state-of-theart. © 2012 ACM.

Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes

NARCIS (Netherlands)

Belitser, E.N.; Serra, P.; van Zanten, H.

2015-01-01

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. To motivate our results we start by analyzing count data coming from a call center which we model as a Poisson process. This analysis is carried out using a certain

Fractional Poisson process (II)

International Nuclear Information System (INIS)

Wang Xiaotian; Wen Zhixiong; Zhang Shiying

2006-01-01

In this paper, we propose a stochastic process W H (t)(H-bar (12,1)) which we call fractional Poisson process. The process W H (t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution

Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.

Science.gov (United States)

Zhang, Jiachao; Hirakawa, Keigo

2017-04-01

This paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs. A quantile analysis in pixel, wavelet transform, and variance stabilization domains reveal that the tails of Poisson, signal-dependent Gaussian, and Poisson-Gaussian models are too short to capture real sensor noise behavior. A new Poisson mixture noise model is proposed to correct the mismatch of tail behavior. Based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data, we propose a mixture of Poisson denoising method to remove the denoising artifacts without affecting image details, such as edge and textures. Experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique.

Exploring factors associated with traumatic dental injuries in preschool children: a Poisson regression analysis.

Science.gov (United States)

Feldens, Carlos Alberto; Kramer, Paulo Floriani; Ferreira, Simone Helena; Spiguel, Mônica Hermann; Marquezan, Marcela

2010-04-01

This cross-sectional study aimed to investigate the factors associated with dental trauma in preschool children using Poisson regression analysis with robust variance. The study population comprised 888 children aged 3- to 5-year-old attending public nurseries in Canoas, southern Brazil. Questionnaires assessing information related to the independent variables (age, gender, race, mother's educational level and family income) were completed by the parents. Clinical examinations were carried out by five trained examiners in order to assess traumatic dental injuries (TDI) according to Andreasen's classification. One of the five examiners was calibrated to assess orthodontic characteristics (open bite and overjet). Multivariable Poisson regression analysis with robust variance was used to determine the factors associated with dental trauma as well as the strengths of association. Traditional logistic regression was also performed in order to compare the estimates obtained by both methods of statistical analysis. 36.4% (323/888) of the children suffered dental trauma and there was no difference in prevalence rates from 3 to 5 years of age. Poisson regression analysis showed that the probability of the outcome was almost 30% higher for children whose mothers had more than 8 years of education (Prevalence Ratio = 1.28; 95% CI = 1.03-1.60) and 63% higher for children with an overjet greater than 2 mm (Prevalence Ratio = 1.63; 95% CI = 1.31-2.03). Odds ratios clearly overestimated the size of the effect when compared with prevalence ratios. These findings indicate the need for preventive orientation regarding TDI, in order to educate parents and caregivers about supervising infants, particularly those with increased overjet and whose mothers have a higher level of education. Poisson regression with robust variance represents a better alternative than logistic regression to estimate the risk of dental trauma in preschool children.

Statistical Methods for Unusual Count Data

DEFF Research Database (Denmark)

Guthrie, Katherine A.; Gammill, Hilary S.; Kamper-Jørgensen, Mads

2016-01-01

microchimerism data present challenges for statistical analysis, including a skewed distribution, excess zero values, and occasional large values. Methods for comparing microchimerism levels across groups while controlling for covariates are not well established. We compared statistical models for quantitative...... microchimerism values, applied to simulated data sets and 2 observed data sets, to make recommendations for analytic practice. Modeling the level of quantitative microchimerism as a rate via Poisson or negative binomial model with the rate of detection defined as a count of microchimerism genome equivalents per...

Bayesian regression of piecewise homogeneous Poisson processes

Directory of Open Access Journals (Sweden)

Diego Sevilla

2015-12-01

Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015

Gyrokinetic energy conservation and Poisson-bracket formulation

International Nuclear Information System (INIS)

Brizard, A.

1989-01-01

An integral expression for the gyrokinetic total energy of a magnetized plasma, with general magnetic field configuration perturbed by fully electromagnetic fields, was recently derived through the use of a gyrocenter Lie transformation. It is shown that the gyrokinetic energy is conserved by the gyrokinetic Hamiltonian flow to all orders in perturbed fields. An explicit demonstration that a gyrokinetic Hamiltonian containing quadratic nonlinearities preserves the gyrokinetic energy up to third order is given. The Poisson-bracket formulation greatly facilitates this demonstration with the help of the Jacobi identity and other properties of the Poisson brackets

Hamiltonian field description of the one-dimensional Poisson-Vlasov equations

International Nuclear Information System (INIS)

Morrison, P.J.

1981-07-01

The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained

Poisson-type inequalities for growth properties of positive superharmonic functions.

Science.gov (United States)

Luan, Kuan; Vieira, John

2017-01-01

In this paper, we present new Poisson-type inequalities for Poisson integrals with continuous data on the boundary. The obtained inequalities are used to obtain growth properties at infinity of positive superharmonic functions in a smooth cone.

Soft network materials with isotropic negative Poisson's ratios over large strains.

Science.gov (United States)

Liu, Jianxing; Zhang, Yihui

2018-01-31

Auxetic materials with negative Poisson's ratios have important applications across a broad range of engineering areas, such as biomedical devices, aerospace engineering and automotive engineering. A variety of design strategies have been developed to achieve artificial auxetic materials with controllable responses in the Poisson's ratio. The development of designs that can offer isotropic negative Poisson's ratios over large strains can open up new opportunities in emerging biomedical applications, which, however, remains a challenge. Here, we introduce deterministic routes to soft architected materials that can be tailored precisely to yield the values of Poisson's ratio in the range from -1 to 1, in an isotropic manner, with a tunable strain range from 0% to ∼90%. The designs rely on a network construction in a periodic lattice topology, which incorporates zigzag microstructures as building blocks to connect lattice nodes. Combined experimental and theoretical studies on broad classes of network topologies illustrate the wide-ranging utility of these concepts. Quantitative mechanics modeling under both infinitesimal and finite deformations allows the development of a rigorous design algorithm that determines the necessary network geometries to yield target Poisson ratios over desired strain ranges. Demonstrative examples in artificial skin with both the negative Poisson's ratio and the nonlinear stress-strain curve precisely matching those of the cat's skin and in unusual cylindrical structures with engineered Poisson effect and shape memory effect suggest potential applications of these network materials.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

Science.gov (United States)

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

Science.gov (United States)

Yu, Pei; Li, Zi-Yuan; Xu, Hong-Ya; Huang, Liang; Dietz, Barbara; Grebogi, Celso; Lai, Ying-Cheng

2016-12-01

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular-sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

Optimized thick-wall cylinders by virtue of Poisson's ratio selection

International Nuclear Information System (INIS)

Whitty, J.P.M.; Henderson, B.; Francis, J.; Lloyd, N.

2011-01-01

The principal stress distributions in thick-wall cylinders due to variation in the Poisson's ratio are predicted using analytical and finite element methods. Analyses of appropriate brittle and ductile failure criteria show that under the isochoric pressure conditions investigated that auextic (i.e. those possessing a negative Poisson's ratio) materials act as stress concentrators; hence they are predicted to fail before their conventional (i.e. possessing a positive Poisson's ratio) material counterparts. The key finding of the work presented shows that for constrained thick-wall cylinders the maximum tensile principal stress can vanish at a particular Poisson's ratio and aspect ratio. This phenomenon is exploited in order to present an optimized design criterion for thick-wall cylinders. Moreover, via the use of a cogent finite element model, this criterion is also shown to be applicable for the design of micro-porous materials.

The Lie-Poisson structure of integrable classical non-linear sigma models

International Nuclear Information System (INIS)

Bordemann, M.; Forger, M.; Schaeper, U.; Laartz, J.

1993-01-01

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into the r-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matrices r and s are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrix c. It is proposed that all these Poisson brackets taken together are representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed. (orig.)

Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data.

Science.gov (United States)

Sim, Shin Zhu; Gupta, Ramesh C; Ong, Seng Huat

2018-01-09

In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.

Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers

Science.gov (United States)

Neshveyev, Sergey; Tuset, Lars

2012-05-01

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0 topology on the spectrum of C( G q / K q ). Next we show that the family of C*-algebras C( G q / K q ), 0 < q ≤ 1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra {{C}[G/K]} . Finally, extending a result of Nagy, we show that C( G q / K q ) is canonically KK-equivalent to C( G/ K).

Poisson-Lie T-duality open strings and D-branes

CERN Document Server

Klimcik, C.

1996-01-01

Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold G are dual to D-brane - anti-D-brane pairs propagating on the dual group manifold \\ti G. The D-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group \\ti G by the dressing action of the group G. T-duality maps the momentum of the open string into the mutual distance of the D-branes in the pair. The whole picture is then extended to the full modular space M(D) of the Poisson-Lie equivalent \\si-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of D-branes living on targets belonging to M(D). In this more general case the D-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.

Exterior differentials in superspace and Poisson brackets

International Nuclear Information System (INIS)

Soroka, Dmitrij V.; Soroka, Vyacheslav A.

2003-01-01

It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity to another bracket is introduced. It is also indicated that the resulting bracket leads to generalization of the Schouten-Nijenhuis bracket for the cases of superspace and brackets of diverse Grassmann parities. It is shown that in the case of the Grassmann-odd exterior differential the resulting bracket is the bracket given on exterior forms. The above-mentioned transition with the use of the odd exterior differential applied to the linear even/odd Poisson brackets, that correspond to semi-simple Lie groups, results, respectively, in also linear odd/even brackets which are naturally connected with the Lie superalgebra. The latter contains the BRST and anti-BRST charges and can be used for calculation of the BRST operator cogomology. (author)

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

International Nuclear Information System (INIS)

Nutku, Yavuz

2003-01-01

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems

Modeling of RO/NF membrane rejections of PhACs and organic compounds: a statistical analysis

Directory of Open Access Journals (Sweden)

G. Amy

2008-07-01

Full Text Available Rejections of pharmaceutical compounds (Ibuprofen, Diclofenac, Clofibric acid, Naproxen, Primidone, Phenacetin and organic compounds (Dichloroacetic acid, Trichloroacetic acid, Chloroform, Bromoform, Trichloroethene, Perchloroethene, Carbontetrachloride, Carbontetrabromide by NF (Filmtec, Saehan and RO (Filmtec, Saehan, Toray, Koch membranes were studied. Chloroform presented the lowest rejection due to small molar volume, equivalent width and length. Diclofenac and Primidone showed high rejections related to high molar volume and length. Dichloroacetic acid and Trichloroacetic acid presented good rejections caused by charge exclusion instead of steric hindrance mechanism influencing rejection. Bromoform and Trichloroethene showed low rejections due to small length and equivalent width. Carbontetrabromide, Perchloroethene and Carbontetrachloride with higher equivalent width than BF and TCE presented better rejections. A qualitative analysis of variables using Principal Component Analysis was successfully implemented for reduction of physical-chemical compound properties that influence membrane rejection of PhACs and organic compounds. Properties such as dipole moment, molar volume, hydrophobicity/hydrophilicity, molecular length and equivalent width were found to be important descriptors for simulation of membrane rejection. For membranes used in the experiments, we may conclude that charge repulsion was an important mechanism of rejection for ionic compounds. After analysis with Multiple Linear Regression, we also may conclude that membrane rejection of neutral compounds was well predicted by molar volume, length, equivalent width, hydrophobicity/hydrophilicity and dipole moment. Molecular weight was a poor descriptor variable for rejection modelling. We were able to provide acceptable statistical significance for important results.

Numerical methods for realizing nonstationary Poisson processes with piecewise-constant instantaneous-rate functions

DEFF Research Database (Denmark)

Harrod, Steven; Kelton, W. David

2006-01-01

Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. The authors review the risks of ignoring nonstationarity in Poisson processes and demonstrate three algorithms for generation of Poisson processes...

Statistical properties of several models of fractional random point processes

Science.gov (United States)

Bendjaballah, C.

2011-08-01

Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.

Quadratic Hamiltonians on non-symmetric Poisson structures

International Nuclear Information System (INIS)

Arribas, M.; Blesa, F.; Elipe, A.

2007-01-01

Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases

Formality theory from Poisson structures to deformation quantization

CERN Document Server

Esposito, Chiara

2015-01-01

This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

GEPOIS: a two dimensional nonuniform mesh Poisson solver

International Nuclear Information System (INIS)

Quintenz, J.P.; Freeman, J.R.

1979-06-01

A computer code is described which solves Poisson's equation for the electric potential over a two dimensional cylindrical (r,z) nonuniform mesh which can contain internal electrodes. Poisson's equation is solved over a given region subject to a specified charge distribution with either Neumann or Dirichlet perimeter boundary conditions and with Dirichlet boundary conditions on internal surfaces. The static electric field is also computed over the region with special care given to normal electric field components at boundary surfaces

The cylindrical K-function and Poisson line cluster point processes

DEFF Research Database (Denmark)

Møller, Jesper; Safavimanesh, Farzaneh; Rasmussen, Jakob G.

Poisson line cluster point processes, is also introduced. Parameter estimation based on moment methods or Bayesian inference for this model is discussed when the underlying Poisson line process and the cluster memberships are treated as hidden processes. To illustrate the methodologies, we analyze two...

Estimating the period of a cyclic non-homogeneous Poisson process

NARCIS (Netherlands)

Belitser, E.; Andrade Serra, De P.J.; Zanten, van J.H.

2013-01-01

Motivated by applications of Poisson processes for modelling periodic time-varying phenomena, we study a semi-parametric estimator of the period of cyclic intensity function of a non-homogeneous Poisson process. There are no parametric assumptions on the intensity function which is treated as an

Formulation of Hamiltonian mechanics with even and odd Poisson brackets

International Nuclear Information System (INIS)

Khudaverdyan, O.M.; Nersesyan, A.P.

1987-01-01

A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs

Efficiency optimization of a fast Poisson solver in beam dynamics simulation

Science.gov (United States)

Zheng, Dawei; Pöplau, Gisela; van Rienen, Ursula

2016-01-01

Calculating the solution of Poisson's equation relating to space charge force is still the major time consumption in beam dynamics simulations and calls for further improvement. In this paper, we summarize a classical fast Poisson solver in beam dynamics simulations: the integrated Green's function method. We introduce three optimization steps of the classical Poisson solver routine: using the reduced integrated Green's function instead of the integrated Green's function; using the discrete cosine transform instead of discrete Fourier transform for the Green's function; using a novel fast convolution routine instead of an explicitly zero-padded convolution. The new Poisson solver routine preserves the advantages of fast computation and high accuracy. This provides a fast routine for high performance calculation of the space charge effect in accelerators.

Control Multivariante Estadístico de Variables Discretas tipo Poisson

OpenAIRE

GARCIA BUSTOS, SANDRA LORENA

2016-01-01

En algunos casos, cuando el número de defectos de un proceso de producción tiene que ser controlada, la distribución de Poisson se emplea para modelar la frecuencia de estos defectos y para desarrollar un gráfico de control. En este trabajo se analiza el control de características de calidad p> 1 de Poisson . Cuando este control se necesita, hay dos enfoques principales: 1 - Un gráfico para cada variable de Poisson, el esquema múltiple.. 2 -. Sólo una gráfico para todas las variables, el sist...

Pêche thonière et dispositifs de concentration de poissons

OpenAIRE

Le Gall, Jean-yves; Cayre, Patrice; Taquet, Marc

2000-01-01

Le colloque international « Pêche thonière et dispositifs de concentration de poissons» organisé en octobre 1999, en Martinique, permet de dresser un bilan, sous forme de synthèses régionales, de l'exploitation des grands poissons pélagiques à l'aide de DCP dans les trois océans et en Méditerranée. La technologie, les méthodes de pêche, l'impact sur les ressources, le comportement agrégatif des poissons et les aspects socio-économiques de l'utilisation des DCP sont les principaux thèmes dével...

The coupling of Poisson sigma models to topological backgrounds

Energy Technology Data Exchange (ETDEWEB)

Rosa, Dario [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)

2016-12-13

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

An intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces.

Science.gov (United States)

Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying

2013-09-01

Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in IR(n). To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

Complete synchronization of the global coupled dynamical network induced by Poisson noises.

Science.gov (United States)

Guo, Qing; Wan, Fangyi

2017-01-01

The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.

Transforming spatial point processes into Poisson processes using random superposition

DEFF Research Database (Denmark)

Møller, Jesper; Berthelsen, Kasper Klitgaaard

with a complementary spatial point process Y  to obtain a Poisson process X∪Y  with intensity function β. Underlying this is a bivariate spatial birth-death process (Xt,Yt) which converges towards the distribution of (X,Y). We study the joint distribution of X and Y, and their marginal and conditional distributions....... In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson...... process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking...

Long-term statistics of extreme tsunami height at Crescent City

Science.gov (United States)

Dong, Sheng; Zhai, Jinjin; Tao, Shanshan

2017-06-01

Historically, Crescent City is one of the most vulnerable communities impacted by tsunamis along the west coast of the United States, largely attributed to its offshore geography. Trans-ocean tsunamis usually produce large wave runup at Crescent Harbor resulting in catastrophic damages, property loss and human death. How to determine the return values of tsunami height using relatively short-term observation data is of great significance to assess the tsunami hazards and improve engineering design along the coast of Crescent City. In the present study, the extreme tsunami heights observed along the coast of Crescent City from 1938 to 2015 are fitted using six different probabilistic distributions, namely, the Gumbel distribution, the Weibull distribution, the maximum entropy distribution, the lognormal distribution, the generalized extreme value distribution and the generalized Pareto distribution. The maximum likelihood method is applied to estimate the parameters of all above distributions. Both Kolmogorov-Smirnov test and root mean square error method are utilized for goodness-of-fit test and the better fitting distribution is selected. Assuming that the occurrence frequency of tsunami in each year follows the Poisson distribution, the Poisson compound extreme value distribution can be used to fit the annual maximum tsunami amplitude, and then the point and interval estimations of return tsunami heights are calculated for structural design. The results show that the Poisson compound extreme value distribution fits tsunami heights very well and is suitable to determine the return tsunami heights for coastal disaster prevention.

Four-dimensional gravity as an almost-Poisson system

Science.gov (United States)

Ita, Eyo Eyo

2015-04-01

In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

Poisson-Like Spiking in Circuits with Probabilistic Synapses

Science.gov (United States)

Moreno-Bote, Rubén

2014-01-01

Neuronal activity in cortex is variable both spontaneously and during stimulation, and it has the remarkable property that it is Poisson-like over broad ranges of firing rates covering from virtually zero to hundreds of spikes per second. The mechanisms underlying cortical-like spiking variability over such a broad continuum of rates are currently unknown. We show that neuronal networks endowed with probabilistic synaptic transmission, a well-documented source of variability in cortex, robustly generate Poisson-like variability over several orders of magnitude in their firing rate without fine-tuning of the network parameters. Other sources of variability, such as random synaptic delays or spike generation jittering, do not lead to Poisson-like variability at high rates because they cannot be sufficiently amplified by recurrent neuronal networks. We also show that probabilistic synapses predict Fano factor constancy of synaptic conductances. Our results suggest that synaptic noise is a robust and sufficient mechanism for the type of variability found in cortex. PMID:25032705

2D Poisson sigma models with gauged vectorial supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Bonezzi, Roberto [Dipartimento di Fisica ed Astronomia, Università di Bologna and INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)

2015-08-12

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.

Remarks on 'Poisson ratio beyond the limits of the elasticity theory'

International Nuclear Information System (INIS)

Wojciechowski, K.W.

2002-12-01

The non-chiral, elastically isotropic model exhibits Poison ratios in the range -1 ≤ σ ≤ 1 without any molecular rotation. The centres of discs-atoms are replaced in the vertices of a perfect triangle of the side length equal to σ. The positive sign of the Lame constant λ is not necessary for the stability of an isotropic system at any dimensionality. As the upper limit for the Poisson ratio in 2D isotropic systems is 1, crystalline or polycrystalline 2D systems can be obtained having the Poisson ratio exceeding 1/2. Both the traditional theory of elasticity and the Cosserat one exclude Poisson ratios exceeding 1/2 in 3D isotropic systems. Neighter anisotropy nor rotation are necessary to obtain extreme values of the Poisson ratio (author)

Computation of solar perturbations with Poisson series

Science.gov (United States)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

Blind beam-hardening correction from Poisson measurements

Science.gov (United States)

Gu, Renliang; Dogandžić, Aleksandar

2016-02-01

We develop a sparse image reconstruction method for Poisson-distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements and express the mass- attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate-descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov's proximal-gradient (NPG) step for estimating the density map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) step for estimating the incident-spectrum parameters. To accelerate convergence of the density- map NPG steps, we apply function restart and a step-size selection scheme that accounts for varying local Lipschitz constants of the Poisson NLL. Real X-ray CT reconstruction examples demonstrate the performance of the proposed scheme.

The Poisson equation on Klein surfaces

Directory of Open Access Journals (Sweden)

Monica Rosiu

2016-04-01

Full Text Available We obtain a formula for the solution of the Poisson equation with Dirichlet boundary condition on a region of a Klein surface. This formula reveals the symmetric character of the solution.

Linear odd Poisson bracket on Grassmann variables

International Nuclear Information System (INIS)

Soroka, V.A.

1999-01-01

A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson bracket having the only Grassmann-odd nilpotent differential Δ-operator of the second order. It is shown that these Δ-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Fiber-wise linear Poisson structures related to W∗-algebras

Science.gov (United States)

Odzijewicz, Anatol; Jakimowicz, Grzegorz; Sliżewska, Aneta

2018-01-01

In the framework of Banach differential geometry we investigate the fiber-wise linear Poisson structures as well as the Lie groupoid and Lie algebroid structures which are defined in the canonical way by the structure of a W∗-algebra (von Neumann algebra) M. The main role in this theory is played by the complex Banach-Lie groupoid G(M) ⇉ L(M) of partially invertible elements of M over the lattice L(M) of orthogonal projections of M. The Atiyah sequence and the predual Atiyah sequence corresponding to this groupoid are investigated from the point of view of Banach Poisson geometry. In particular we show that the predual Atiyah sequence fits in a short exact sequence of complex Banach sub-Poisson V B-groupoids with G(M) ⇉ L(M) as the side groupoid.

A relation between Liapunov stability, non-wanderingness and Poisson stability

International Nuclear Information System (INIS)

Ahmad, K.H.

1985-07-01

In this work, some of the relations among Liapunov stability, non-wanderingness and Poisson stability are considered. In particular it is shown that for a non-wandering point in a set, positive (resp. negative) Liapunov stability in that set implies positive (resp. negative) Poisson stability in the same set. (author)

Statistics for experimentalists

CERN Document Server

Cooper, B E

2014-01-01

Statistics for Experimentalists aims to provide experimental scientists with a working knowledge of statistical methods and search approaches to the analysis of data. The book first elaborates on probability and continuous probability distributions. Discussions focus on properties of continuous random variables and normal variables, independence of two random variables, central moments of a continuous distribution, prediction from a normal distribution, binomial probabilities, and multiplication of probabilities and independence. The text then examines estimation and tests of significance. Topics include estimators and estimates, expected values, minimum variance linear unbiased estimators, sufficient estimators, methods of maximum likelihood and least squares, and the test of significance method. The manuscript ponders on distribution-free tests, Poisson process and counting problems, correlation and function fitting, balanced incomplete randomized block designs and the analysis of covariance, and experiment...

Poisson INAR(1)过程的质量控制%Quality control chart for poisson INAR(1) process

Institute of Scientific and Technical Information of China (English)

睢立伟; 宋向东

2017-01-01

为解决在实际生产中,过程数据并不总能满足彼此独立的假设前提,从而使得一些控制图不再适用于具有相关性的过程的问题,以免在监控过程中出现大量的虚假警报.论文采用取整法研究一阶自回归泊松计数过程模型,首先将一阶自回归模型与泊松计数过程结合起来,然后对原有的模型就行修正,在新模型的基础上重新构造了c控制图和残差控制图的控制限,以使得这两种控制图能够适应新的模型.研究结果表明:两种控制图都只是在一定的情况下使用,研究结论对于研究具有相关性的统计过程有着重要的推进作用.%To solve the problem that in actual production,the process data is not always satisfied with the assumption of independence,which makes some control charts no longer suitable for the process of correlation,so as to avoid a large number of false alarm.This paper studied the poisson INAR(1) process with rounding method.Firstly,the AR(1) process was combined with the poisson counting process,and the original model was corrected.Based on the new model,the control limits of c-chart and residual chart were constructed,in order to adapt the new model.The results of the study indicate the application of the two control charts.The research results have important promoting effect on the study of statistical process.

The negative binomial distribution as a model for external corrosion defect counts in buried pipelines

International Nuclear Information System (INIS)

Valor, Alma; Alfonso, Lester; Caleyo, Francisco; Vidal, Julio; Perez-Baruch, Eloy; Hallen, José M.

2015-01-01

Highlights: • Observed external-corrosion defects in underground pipelines revealed a tendency to cluster. • The Poisson distribution is unable to fit extensive count data for these type of defects. • In contrast, the negative binomial distribution provides a suitable count model for them. • Two spatial stochastic processes lead to the negative binomial distribution for defect counts. • They are the Gamma-Poisson mixed process and the compound Poisson process. • A Rogeŕs process also arises as a plausible temporal stochastic process leading to corrosion defect clustering and to negative binomially distributed defect counts. - Abstract: The spatial distribution of external corrosion defects in buried pipelines is usually described as a Poisson process, which leads to corrosion defects being randomly distributed along the pipeline. However, in real operating conditions, the spatial distribution of defects considerably departs from Poisson statistics due to the aggregation of defects in groups or clusters. In this work, the statistical analysis of real corrosion data from underground pipelines operating in southern Mexico leads to conclude that the negative binomial distribution provides a better description for defect counts. The origin of this distribution from several processes is discussed. The analysed processes are: mixed Gamma-Poisson, compound Poisson and Roger’s processes. The physical reasons behind them are discussed for the specific case of soil corrosion.

? filtering for stochastic systems driven by Poisson processes

Science.gov (United States)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Poisson's theorem and integrals of KdV equation

International Nuclear Information System (INIS)

Tasso, H.

1978-01-01

Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)

Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis.

Science.gov (United States)

Armstrong, Ben G; Gasparrini, Antonio; Tobias, Aurelio

2014-11-24

The time stratified case cross-over approach is a popular alternative to conventional time series regression for analysing associations between time series of environmental exposures (air pollution, weather) and counts of health outcomes. These are almost always analyzed using conditional logistic regression on data expanded to case-control (case crossover) format, but this has some limitations. In particular adjusting for overdispersion and auto-correlation in the counts is not possible. It has been established that a Poisson model for counts with stratum indicators gives identical estimates to those from conditional logistic regression and does not have these limitations, but it is little used, probably because of the overheads in estimating many stratum parameters. The conditional Poisson model avoids estimating stratum parameters by conditioning on the total event count in each stratum, thus simplifying the computing and increasing the number of strata for which fitting is feasible compared with the standard unconditional Poisson model. Unlike the conditional logistic model, the conditional Poisson model does not require expanding the data, and can adjust for overdispersion and auto-correlation. It is available in Stata, R, and other packages. By applying to some real data and using simulations, we demonstrate that conditional Poisson models were simpler to code and shorter to run than are conditional logistic analyses and can be fitted to larger data sets than possible with standard Poisson models. Allowing for overdispersion or autocorrelation was possible with the conditional Poisson model but when not required this model gave identical estimates to those from conditional logistic regression. Conditional Poisson regression models provide an alternative to case crossover analysis of stratified time series data with some advantages. The conditional Poisson model can also be used in other contexts in which primary control for confounding is by fine

Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria

International Nuclear Information System (INIS)

Ling, K.; Abraham-Shrauner, B.

1981-01-01

The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically

A high order solver for the unbounded Poisson equation

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...... of convergence consistent with the moments conserved by the applied smoothing function. In the hybrid particle-mesh method of Hockney and Eastwood (HE) the particles are interpolated onto a regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values...... and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight...

Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

Directory of Open Access Journals (Sweden)

Liu Jinn-Liang

2017-10-01

Full Text Available We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.

A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture

OpenAIRE

Van Nguyen, Thu

2011-01-01

In the present paper we prove the following conjecture in Kingman, J.F.C., Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerning a famous Raikov's theorem of decomposition of Poisson random variables: "If a radial sum of two independent random variables X and Y is radial Poisson, then each of them must be radial Poisson."

Use of Statistics for Data Evaluation in Environmental Radioactivity Measurements

International Nuclear Information System (INIS)

Sutarman

2001-01-01

Counting statistics will give a correction on environmental radioactivity measurement result. Statistics provides formulas to determine standard deviation (S B ) and minimum detectable concentration (MDC) according to the Poisson distribution. Both formulas depend on the background count rate, counting time, counting efficiency, gamma intensity, and sample size. A long time background counting results in relatively low S B and MDC that can present relatively accurate measurement results. (author)

A multiresolution method for solving the Poisson equation using high order regularization

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Walther, Jens Honore

2016-01-01

We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regulari......We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches...... and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poisson solver produces convergence rates...

Classifying next-generation sequencing data using a zero-inflated Poisson model.

Science.gov (United States)

Zhou, Yan; Wan, Xiang; Zhang, Baoxue; Tong, Tiejun

2018-04-15

With the development of high-throughput techniques, RNA-sequencing (RNA-seq) is becoming increasingly popular as an alternative for gene expression analysis, such as RNAs profiling and classification. Identifying which type of diseases a new patient belongs to with RNA-seq data has been recognized as a vital problem in medical research. As RNA-seq data are discrete, statistical methods developed for classifying microarray data cannot be readily applied for RNA-seq data classification. Witten proposed a Poisson linear discriminant analysis (PLDA) to classify the RNA-seq data in 2011. Note, however, that the count datasets are frequently characterized by excess zeros in real RNA-seq or microRNA sequence data (i.e. when the sequence depth is not enough or small RNAs with the length of 18-30 nucleotides). Therefore, it is desired to develop a new model to analyze RNA-seq data with an excess of zeros. In this paper, we propose a Zero-Inflated Poisson Logistic Discriminant Analysis (ZIPLDA) for RNA-seq data with an excess of zeros. The new method assumes that the data are from a mixture of two distributions: one is a point mass at zero, and the other follows a Poisson distribution. We then consider a logistic relation between the probability of observing zeros and the mean of the genes and the sequencing depth in the model. Simulation studies show that the proposed method performs better than, or at least as well as, the existing methods in a wide range of settings. Two real datasets including a breast cancer RNA-seq dataset and a microRNA-seq dataset are also analyzed, and they coincide with the simulation results that our proposed method outperforms the existing competitors. The software is available at http://www.math.hkbu.edu.hk/∼tongt. xwan@comp.hkbu.edu.hk or tongt@hkbu.edu.hk. Supplementary data are available at Bioinformatics online.

Graded geometry and Poisson reduction

OpenAIRE

Cattaneo, A S; Zambon, M

2009-01-01

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

Science.gov (United States)

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

A Note On the Estimation of the Poisson Parameter

Directory of Open Access Journals (Sweden)

S. S. Chitgopekar

1985-01-01

distribution when there are errors in observing the zeros and ones and obtains both the maximum likelihood and moments estimates of the Poisson mean and the error probabilities. It is interesting to note that either method fails to give unique estimates of these parameters unless the error probabilities are functionally related. However, it is equally interesting to observe that the estimate of the Poisson mean does not depend on the functional relationship between the error probabilities.

Efficient triangulation of Poisson-disk sampled point sets

KAUST Repository

Guo, Jianwei

2014-05-06

In this paper, we present a simple yet efficient algorithm for triangulating a 2D input domain containing a Poisson-disk sampled point set. The proposed algorithm combines a regular grid and a discrete clustering approach to speedup the triangulation. Moreover, our triangulation algorithm is flexible and performs well on more general point sets such as adaptive, non-maximal Poisson-disk sets. The experimental results demonstrate that our algorithm is robust for a wide range of input domains and achieves significant performance improvement compared to the current state-of-the-art approaches. © 2014 Springer-Verlag Berlin Heidelberg.

Poisson equation for weak gravitational lensing

International Nuclear Information System (INIS)

Kling, Thomas P.; Campbell, Bryan

2008-01-01

Using the Newman and Penrose [E. T. Newman and R. Penrose, J. Math. Phys. (N.Y.) 3, 566 (1962).] spin-coefficient formalism, we examine the full Bianchi identities of general relativity in the context of gravitational lensing, where the matter and space-time curvature are projected into a lens plane perpendicular to the line of sight. From one component of the Bianchi identity, we provide a rigorous, new derivation of a Poisson equation for the projected matter density where the source term involves second derivatives of the observed weak gravitational lensing shear. We also show that the other components of the Bianchi identity reveal no new results. Numerical integration of the Poisson equation in test cases shows an accurate mass map can be constructed from the combination of a ground-based, wide-field image and a Hubble Space Telescope image of the same system

Generalized Hamiltonians, functional integration and statistics of continuous fluids and plasmas

International Nuclear Information System (INIS)

Tasso, H.

1985-05-01

Generalized Hamiltonian formalism including generalized Poisson brackets and Lie-Poisson brackets is presented in Section II. Gyroviscous magnetohydrodynamics is treated as a relevant example in Euler and Clebsch variables. Section III is devoted to a short review of functional integration containing the definition and a discussion of ambiguities and methods of evaluation. The main part of the contribution is given in Section IV, where some of the content of the previous sections is applied to Gibbs statistics of continuous fluids and plasmas. In particular, exact fluctuation spectra are calculated for relevant equations in fluids and plasmas. (orig.)

Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

Science.gov (United States)

Wang, Fengwen

2018-05-01

This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson's ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson's ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson's ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson's ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson's ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson's ratios, material architectures for any Poisson's ratio in the interval of ν ∈ [ - 0.78 , 0.00 ] are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson's ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson's ratio are achievable.

Area-to-Area Poisson Kriging and Spatial Bayesian Analysis

Science.gov (United States)

Asmarian, Naeimehossadat; Jafari-Koshki, Tohid; Soleimani, Ali; Taghi Ayatollahi, Seyyed Mohammad

2016-10-01

Background: In many countries gastric cancer has the highest incidence among the gastrointestinal cancers and is the second most common cancer in Iran. The aim of this study was to identify and map high risk gastric cancer regions at the county-level in Iran. Methods: In this study we analyzed gastric cancer data for Iran in the years 2003-2010. Areato- area Poisson kriging and Besag, York and Mollie (BYM) spatial models were applied to smoothing the standardized incidence ratios of gastric cancer for the 373 counties surveyed in this study. The two methods were compared in term of accuracy and precision in identifying high risk regions. Result: The highest smoothed standardized incidence rate (SIR) according to area-to-area Poisson kriging was in Meshkinshahr county in Ardabil province in north-western Iran (2.4,SD=0.05), while the highest smoothed standardized incidence rate (SIR) according to the BYM model was in Ardabil, the capital of that province (2.9,SD=0.09). Conclusion: Both methods of mapping, ATA Poisson kriging and BYM, showed the gastric cancer incidence rate to be highest in north and north-west Iran. However, area-to-area Poisson kriging was more precise than the BYM model and required less smoothing. According to the results obtained, preventive measures and treatment programs should be focused on particular counties of Iran. Creative Commons Attribution License

Identification d’une Classe de Processus de Poisson Filtres (Identification of a Class of Filtered Poisson Processes).

Science.gov (United States)

1983-05-20

Poisson processes is introduced: the amplitude has a law which is spherically invariant and the filter is real, linear and causal. It is shown how such a model can be identified from experimental data. (Author)

Generalization of Poisson distribution for the case of changing probability of consequential events

International Nuclear Information System (INIS)

Kushnirenko, E.

1995-01-01

The generalization of the Poisson distribution for the case of changing probabilities of the consequential events is done. It is shown that the classical Poisson distribution is the special case of this generalized distribution when the probabilities of the consequential events are constant. The using of the generalized Poisson distribution gives the possibility in some cases to obtain analytical result instead of making Monte-Carlo calculation

Dilaton gravity, Poisson sigma models and loop quantum gravity

International Nuclear Information System (INIS)

Bojowald, Martin; Reyes, Juan D

2009-01-01

Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum-corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D spacetime dimensions.

Efficient maximal Poisson-disk sampling and remeshing on surfaces

KAUST Repository

Guo, Jianwei; Yan, Dongming; Jia, Xiaohong; Zhang, Xiaopeng

2015-01-01

Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.

Efficient maximal Poisson-disk sampling and remeshing on surfaces

KAUST Repository

Guo, Jianwei

2015-02-01

Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.

Coupling Poisson rectangular pulse and multiplicative microcanonical random cascade models to generate sub-daily precipitation timeseries

Science.gov (United States)

Pohle, Ina; Niebisch, Michael; Müller, Hannes; Schümberg, Sabine; Zha, Tingting; Maurer, Thomas; Hinz, Christoph

2018-07-01

To simulate the impacts of within-storm rainfall variabilities on fast hydrological processes, long precipitation time series with high temporal resolution are required. Due to limited availability of observed data such time series are typically obtained from stochastic models. However, most existing rainfall models are limited in their ability to conserve rainfall event statistics which are relevant for hydrological processes. Poisson rectangular pulse models are widely applied to generate long time series of alternating precipitation events durations and mean intensities as well as interstorm period durations. Multiplicative microcanonical random cascade (MRC) models are used to disaggregate precipitation time series from coarse to fine temporal resolution. To overcome the inconsistencies between the temporal structure of the Poisson rectangular pulse model and the MRC model, we developed a new coupling approach by introducing two modifications to the MRC model. These modifications comprise (a) a modified cascade model ("constrained cascade") which preserves the event durations generated by the Poisson rectangular model by constraining the first and last interval of a precipitation event to contain precipitation and (b) continuous sigmoid functions of the multiplicative weights to consider the scale-dependency in the disaggregation of precipitation events of different durations. The constrained cascade model was evaluated in its ability to disaggregate observed precipitation events in comparison to existing MRC models. For that, we used a 20-year record of hourly precipitation at six stations across Germany. The constrained cascade model showed a pronounced better agreement with the observed data in terms of both the temporal pattern of the precipitation time series (e.g. the dry and wet spell durations and autocorrelations) and event characteristics (e.g. intra-event intermittency and intensity fluctuation within events). The constrained cascade model also

Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

International Nuclear Information System (INIS)

Czachor, M.

1996-01-01

Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

A generalized Poisson solver for first-principles device simulations

Energy Technology Data Exchange (ETDEWEB)

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch [Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland); Brück, Sascha; Luisier, Mathieu [Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)

2016-01-28

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.

Poisson point processes imaging, tracking, and sensing

CERN Document Server

Streit, Roy L

2010-01-01

This overview of non-homogeneous and multidimensional Poisson point processes and their applications features mathematical tools and applications from emission- and transmission-computed tomography to multiple target tracking and distributed sensor detection.

The Hitchin model, Poisson-quasi-Nijenhuis, geometry and symmetry reduction

International Nuclear Information System (INIS)

Zucchini, Roberto

2007-01-01

We revisit our earlier work on the AKSZ-like formulation of topological sigma model on generalized complex manifolds, or Hitchin model, [20]. We show that the target space geometry geometry implied by the BV master equations is Poisson-quasi-Nijenhuis geometry recently introduced and studied by Stienon and Xu (in the untwisted case) in [44]. Poisson-quasi-Nijenhuis geometry is more general than generalized complex geometry and comprises it as a particular case. Next, we show how gauging and reduction can be implemented in the Hitchin model. We find that the geometry resulting form the BV master equation is closely related to but more general than that recently described by Lin and Tolman in [40, 41], suggesting a natural framework for the study of reduction of Poisson-quasi-Nijenhuis manifolds

A Statistical Learning Framework for Materials Science: Application to Elastic Moduli of k-nary Inorganic Polycrystalline Compounds.

Science.gov (United States)

de Jong, Maarten; Chen, Wei; Notestine, Randy; Persson, Kristin; Ceder, Gerbrand; Jain, Anubhav; Asta, Mark; Gamst, Anthony

2016-10-03

Materials scientists increasingly employ machine or statistical learning (SL) techniques to accelerate materials discovery and design. Such pursuits benefit from pooling training data across, and thus being able to generalize predictions over, k-nary compounds of diverse chemistries and structures. This work presents a SL framework that addresses challenges in materials science applications, where datasets are diverse but of modest size, and extreme values are often of interest. Our advances include the application of power or Hölder means to construct descriptors that generalize over chemistry and crystal structure, and the incorporation of multivariate local regression within a gradient boosting framework. The approach is demonstrated by developing SL models to predict bulk and shear moduli (K and G, respectively) for polycrystalline inorganic compounds, using 1,940 compounds from a growing database of calculated elastic moduli for metals, semiconductors and insulators. The usefulness of the models is illustrated by screening for superhard materials.

On the Fedosov deformation quantization beyond the regular Poisson manifolds

International Nuclear Information System (INIS)

Dolgushev, V.A.; Isaev, A.P.; Lyakhovich, S.L.; Sharapov, A.A.

2002-01-01

A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane

Modeling the number of car theft using Poisson regression

Science.gov (United States)

Zulkifli, Malina; Ling, Agnes Beh Yen; Kasim, Maznah Mat; Ismail, Noriszura

2016-10-01

Regression analysis is the most popular statistical methods used to express the relationship between the variables of response with the covariates. The aim of this paper is to evaluate the factors that influence the number of car theft using Poisson regression model. This paper will focus on the number of car thefts that occurred in districts in Peninsular Malaysia. There are two groups of factor that have been considered, namely district descriptive factors and socio and demographic factors. The result of the study showed that Bumiputera composition, Chinese composition, Other ethnic composition, foreign migration, number of residence with the age between 25 to 64, number of employed person and number of unemployed person are the most influence factors that affect the car theft cases. These information are very useful for the law enforcement department, insurance company and car owners in order to reduce and limiting the car theft cases in Peninsular Malaysia.

METHOD OF FOREST FIRES PROBABILITY ASSESSMENT WITH POISSON LAW

Directory of Open Access Journals (Sweden)

A. S. Plotnikova

2016-01-01

Full Text Available The article describes the method for the forest fire burn probability estimation on a base of Poisson distribution. The λ parameter is assumed to be a mean daily number of fires detected for each Forest Fire Danger Index class within specific period of time. Thus, λ was calculated for spring, summer and autumn seasons separately. Multi-annual daily Forest Fire Danger Index values together with EO-derived hot spot map were input data for the statistical analysis. The major result of the study is generation of the database on forest fire burn probability. Results were validated against EO daily data on forest fires detected over Irkutsk oblast in 2013. Daily weighted average probability was shown to be linked with the daily number of detected forest fires. Meanwhile, there was found a number of fires which were developed when estimated probability was low. The possible explanation of this phenomenon was provided.

Measuring Poisson Ratios at Low Temperatures

Science.gov (United States)

Boozon, R. S.; Shepic, J. A.

1987-01-01

Simple extensometer ring measures bulges of specimens in compression. New method of measuring Poisson's ratio used on brittle ceramic materials at cryogenic temperatures. Extensometer ring encircles cylindrical specimen. Four strain gauges connected in fully active Wheatstone bridge self-temperature-compensating. Used at temperatures as low as liquid helium.

Efficient information transfer by Poisson neurons

Czech Academy of Sciences Publication Activity Database

Košťál, Lubomír; Shinomoto, S.

2016-01-01

Roč. 13, č. 3 (2016), s. 509-520 ISSN 1547-1063 R&D Projects: GA ČR(CZ) GA15-08066S Institutional support: RVO:67985823 Keywords : information capacity * Poisson neuron * metabolic cost * decoding error Subject RIV: BD - Theory of Information Impact factor: 1.035, year: 2016

Quantization of Poisson Manifolds from the Integrability of the Modular Function

Science.gov (United States)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

Poisson structure of dynamical systems with three degrees of freedom

Science.gov (United States)

Gümral, Hasan; Nutku, Yavuz

1993-12-01

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.

Theory of overdispersion in counting statistics caused by fluctuating probabilities

International Nuclear Information System (INIS)

Semkow, Thomas M.

1999-01-01

It is shown that the random Lexis fluctuations of probabilities such as probability of decay or detection cause the counting statistics to be overdispersed with respect to the classical binomial, Poisson, or Gaussian distributions. The generating and the distribution functions for the overdispersed counting statistics are derived. Applications to radioactive decay with detection and more complex experiments are given, as well as distinguishing between the source and background, in the presence of overdispersion. Monte-Carlo verifications are provided

LOR-OSEM: statistical PET reconstruction from raw line-of-response histograms

International Nuclear Information System (INIS)

Kadrmas, Dan J

2004-01-01

Iterative statistical reconstruction methods are becoming the standard in positron emission tomography (PET). Conventional maximum-likelihood expectation-maximization (MLEM) and ordered-subsets (OSEM) algorithms act on data which have been pre-processed into corrected, evenly-spaced histograms; however, such pre-processing corrupts the Poisson statistics. Recent advances have incorporated attenuation, scatter and randoms compensation into the iterative reconstruction. The objective of this work was to incorporate the remaining pre-processing steps, including arc correction, to reconstruct directly from raw unevenly-spaced line-of-response (LOR) histograms. This exactly preserves Poisson statistics and full spatial information in a manner closely related to listmode ML, making full use of the ML statistical model. The LOR-OSEM algorithm was implemented using a rotation-based projector which maps directly to the unevenly-spaced LOR grid. Simulation and phantom experiments were performed to characterize resolution, contrast and noise properties for 2D PET. LOR-OSEM provided a beneficial noise-resolution tradeoff, outperforming AW-OSEM by about the same margin that AW-OSEM outperformed pre-corrected OSEM. The relationship between LOR-ML and listmode ML algorithms was explored, and implementation differences are discussed. LOR-OSEM is a viable alternative to AW-OSEM for histogram-based reconstruction with improved spatial resolution and noise properties

Performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data.

Science.gov (United States)

Yelland, Lisa N; Salter, Amy B; Ryan, Philip

2011-10-15

Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.

Null canonical formalism 1, Maxwell field. [Poisson brackets, boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Wodkiewicz, K [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej

1975-01-01

The purpose of this paper is to formulate the canonical formalism on null hypersurfaces for the Maxwell electrodynamics. The set of the Poisson brackets relations for null variables of the Maxwell field is obtained. The asymptotic properties of the theory are investigated. The Poisson bracket relations for the news-functions of the Maxwell field are computed. The Hamiltonian form of the asymptotic Maxwell equations in terms of these news-functions is obtained.

Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems

Directory of Open Access Journals (Sweden)

Hailiang Li

2003-09-01

Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.

State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.

Science.gov (United States)

1978-12-01

The state estimation problem of linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered, especially the case...where the incident intensities of the Poisson processes are low and the system is observed in an additive white Gaussian noise. The minimum mean squared

Elementary Statistical Models for Vector Collision-Sequence Interference Effects with Poisson-Distributed Collision Times

International Nuclear Information System (INIS)

Lewis, J.C.

2011-01-01

In a recent paper (Lewis, 2008) a class of models suitable for application to collision-sequence interference was introduced. In these models velocities are assumed to be completely randomized in each collision. The distribution of velocities was assumed to be Gaussian. The integrated induced dipole moment μk, for vector interference, or the scalar modulation μk, for scalar interference, was assumed to be a function of the impulse (integrated force) fk, or its magnitude fk, experienced by the molecule in a collision. For most of (Lewis, 2008) it was assumed that μk fk and μk fk, but it proved to be possible to extend the models, so that the magnitude of the induced dipole moment is equal to an arbitrary power or sum of powers of the intermolecular force. This allows estimates of the in filling of the interference dip by the dis proportionality of the induced dipole moment and force. One particular such model, using data from (Herman and Lewis, 2006), leads to the most realistic estimate for the in filling of the vector interference dip yet obtained. In (Lewis, 2008) the drastic assumption was made that collision times occurred at equal intervals. In the present paper that assumption is removed: the collision times are taken to form a Poisson process. This is much more realistic than the equal-intervals assumption. The interference dip is found to be a Lorentzian in this model

Statistical fluctuations of the number of neutrons in a pile

International Nuclear Information System (INIS)

Raievski, V.

1958-01-01

The theory of the statistical fluctuations in a pile is extended to the space dependent case, and gives the fluctuations of the number of neutrons in a cell of the core or reflector of the pile. This number changes through elementary processes occurring at random, which are, capture, source, fission and scattering. Of all these processes, fission is the only one which changes more than one neutron at a time and so is responsible of the deviation of the fluctuations from a Poisson law. The importance of this deviation depends on the dimensions of the cell compared to the slowing down length. When the dimensions are small, the fluctuations close to a Poisson law. (author) [fr

Independent production and Poisson distribution

International Nuclear Information System (INIS)

Golokhvastov, A.I.

1994-01-01

The well-known statement of factorization of inclusive cross-sections in case of independent production of particles (or clusters, jets etc.) and the conclusion of Poisson distribution over their multiplicity arising from it do not follow from the probability theory in any way. Using accurately the theorem of the product of independent probabilities, quite different equations are obtained and no consequences relative to multiplicity distributions are obtained. 11 refs

A generalized gyrokinetic Poisson solver

International Nuclear Information System (INIS)

Lin, Z.; Lee, W.W.

1995-03-01

A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms

Penyelesaian Persamaan Poisson 2D dengan Menggunakan Metode Gauss-Seidel dan Conjugate Gradien

OpenAIRE

Mahmudah, Dewi Erla; Naf'an, Muhammad Zidny

2017-01-01

In this paper we focus on solution of 2D Poisson equation numerically. 2D Poisson equation is a partial differential equation of second order elliptical type. This equation is a particular form or non-homogeneous form of the Laplace equation. The solution of 2D Poisson equation is performed numerically using Gauss Seidel method and Conjugate Gradient method. The result is the value using Gauss Seidel method and Conjugate Gradient method is same. But, consider the iteration process, the conver...

Sanskrit Compound Processor

Science.gov (United States)

Kumar, Anil; Mittal, Vipul; Kulkarni, Amba

Sanskrit is very rich in compound formation. Typically a compound does not code the relation between its components explicitly. To understand the meaning of a compound, it is necessary to identify its components, discover the relations between them and finally generate a paraphrase of the compound. In this paper, we discuss the automatic segmentation and type identification of a compound using simple statistics that results from the manually annotated data.

Les poissons de Guyane

OpenAIRE

Ifremer

1992-01-01

Vous trouverez dans ce document les 24 poissons les plus courants de Guyane (sur un nombre d'espèces approchant les 200) avec leurs principales caractéristiques, leurs noms scientifiques, français, anglais et espagnol et leurs photographies. Ils sont classés, de l'acoupa au vivaneau ti yeux, par ordre alphabétique. Si vous ne trouvez pas de chiffres sur la production de telle ou telle espèce, c'est parce qu'ils n'existent pas, mais aussi et surtout parce qu'ils ne signifieraient rien, l...

Poisson regression for modeling count and frequency outcomes in trauma research.

Science.gov (United States)

Gagnon, David R; Doron-LaMarca, Susan; Bell, Margret; O'Farrell, Timothy J; Taft, Casey T

2008-10-01

The authors describe how the Poisson regression method for analyzing count or frequency outcome variables can be applied in trauma studies. The outcome of interest in trauma research may represent a count of the number of incidents of behavior occurring in a given time interval, such as acts of physical aggression or substance abuse. Traditional linear regression approaches assume a normally distributed outcome variable with equal variances over the range of predictor variables, and may not be optimal for modeling count outcomes. An application of Poisson regression is presented using data from a study of intimate partner aggression among male patients in an alcohol treatment program and their female partners. Results of Poisson regression and linear regression models are compared.

Repairable-conditionally repairable damage model based on dual Poisson processes.

Science.gov (United States)

Lind, B K; Persson, L M; Edgren, M R; Hedlöf, I; Brahme, A

2003-09-01

The advent of intensity-modulated radiation therapy makes it increasingly important to model the response accurately when large volumes of normal tissues are irradiated by controlled graded dose distributions aimed at maximizing tumor cure and minimizing normal tissue toxicity. The cell survival model proposed here is very useful and flexible for accurate description of the response of healthy tissues as well as tumors in classical and truly radiobiologically optimized radiation therapy. The repairable-conditionally repairable (RCR) model distinguishes between two different types of damage, namely the potentially repairable, which may also be lethal, i.e. if unrepaired or misrepaired, and the conditionally repairable, which may be repaired or may lead to apoptosis if it has not been repaired correctly. When potentially repairable damage is being repaired, for example by nonhomologous end joining, conditionally repairable damage may require in addition a high-fidelity correction by homologous repair. The induction of both types of damage is assumed to be described by Poisson statistics. The resultant cell survival expression has the unique ability to fit most experimental data well at low doses (the initial hypersensitive range), intermediate doses (on the shoulder of the survival curve), and high doses (on the quasi-exponential region of the survival curve). The complete Poisson expression can be approximated well by a simple bi-exponential cell survival expression, S(D) = e(-aD) + bDe(-cD), where the first term describes the survival of undamaged cells and the last term represents survival after complete repair of sublethal damage. The bi-exponential expression makes it easy to derive D(0), D(q), n and alpha, beta values to facilitate comparison with classical cell survival models.

Effect of Poisson's loss factor of rubbery material on underwater sound absorption of anechoic coatings

Science.gov (United States)

Zhong, Jie; Zhao, Honggang; Yang, Haibin; Yin, Jianfei; Wen, Jihong

2018-06-01

Rubbery coatings embedded with air cavities are commonly used on underwater structures to reduce reflection of incoming sound waves. In this paper, the relationships between Poisson's and modulus loss factors of rubbery materials are theoretically derived, the different effects of the tiny Poisson's loss factor on characterizing the loss factors of shear and longitudinal moduli are revealed. Given complex Young's modulus and dynamic Poisson's ratio, it is found that the shear loss factor has almost invisible variation with the Poisson's loss factor and is very close to the loss factor of Young's modulus, while the longitudinal loss factor almost linearly decreases with the increase of Poisson's loss factor. Then, a finite element (FE) model is used to investigate the effect of the tiny Poisson's loss factor, which is generally neglected in some FE models, on the underwater sound absorption of rubbery coatings. Results show that the tiny Poisson's loss factor has a significant effect on the sound absorption of homogeneous coatings within the concerned frequency range, while it has both frequency- and structure-dependent influence on the sound absorption of inhomogeneous coatings with embedded air cavities. Given the material parameters and cavity dimensions, more obvious effect can be observed for the rubbery coating with a larger lattice constant and/or a thicker cover layer.

Adaptive maximal poisson-disk sampling on surfaces

KAUST Repository

Yan, Dongming; Wonka, Peter

2012-01-01

In this paper, we study the generation of maximal Poisson-disk sets with varying radii on surfaces. Based on the concepts of power diagram and regular triangulation, we present a geometric analysis of gaps in such disk sets on surfaces, which

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

Science.gov (United States)

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2017-07-01

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 (22α̂)0.50 for 0.020.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 Poisson model dose-response curve. © 2016 Society for Risk Analysis.

Poisson regression approach for modeling fatal injury rates amongst Malaysian workers

International Nuclear Information System (INIS)

Kamarulzaman Ibrahim; Heng Khai Theng

2005-01-01

Many safety studies are based on the analysis carried out on injury surveillance data. The injury surveillance data gathered for the analysis include information on number of employees at risk of injury in each of several strata where the strata are defined in terms of a series of important predictor variables. Further insight into the relationship between fatal injury rates and predictor variables may be obtained by the poisson regression approach. Poisson regression is widely used in analyzing count data. In this study, poisson regression is used to model the relationship between fatal injury rates and predictor variables which are year (1995-2002), gender, recording system and industry type. Data for the analysis were obtained from PERKESO and Jabatan Perangkaan Malaysia. It is found that the assumption that the data follow poisson distribution has been violated. After correction for the problem of over dispersion, the predictor variables that are found to be significant in the model are gender, system of recording, industry type, two interaction effects (interaction between recording system and industry type and between year and industry type). Introduction Regression analysis is one of the most popular

Easy Demonstration of the Poisson Spot

Science.gov (United States)

Gluck, Paul

2010-01-01

Many physics teachers have a set of slides of single, double and multiple slits to show their students the phenomena of interference and diffraction. Thomas Young's historic experiments with double slits were indeed a milestone in proving the wave nature of light. But another experiment, namely the Poisson spot, was also important historically and…

Modifications in the AUTOMESH and other POISSON Group Codes

International Nuclear Information System (INIS)

Gupta, R.C.

1986-01-01

Improvements in the POISSON Group Codes are discussed. These improvements allow one to compute magnetic field to an accuracy of a few parts in 100,000 in quite complicated geometries with a reduced requirement on computational time and computer memory. This can be accomplished mainly by making the mesh dense at some places and sparse at other places. AUTOMESH has been modified so that one can use variable mesh size conveniently and efficiently at a number of places. We will present an example to illustrate these techniques. Several other improvements in the codes AUTOMESH, LATTICE and POISSON will also be discussed

Statistical thermodynamics -- A tool for understanding point defects in intermetallic compounds

International Nuclear Information System (INIS)

Ipser, H.; Krachler, R.

1996-01-01

The principles of the derivation of statistical-thermodynamic models to interpret the compositional variation of thermodynamic properties in non-stoichiometric intermetallic compounds are discussed. Two types of models are distinguished: the Bragg-Williams type, where the total energy of the crystal is taken as the sum of the interaction energies of all nearest-neighbor pairs of atoms, and the Wagner-Schottky type, where the internal energy, the volume, and the vibrational entropy of the crystal are assumed to be linear functions of the numbers of atoms or vacancies on the different sublattices. A Wagner-Schottky type model is used for the description of two examples with different crystal structures: for β'-FeAl (with B2-structure) defect concentrations and their variation with composition are derived from the results of measurements of the aluminum vapor pressure, the resulting values are compared with results of other independent experimental methods; for Rh 3 Te 4 (with an NiAs-derivative structure) the defect mechanism responsible for non-stoichiometry is worked out by application of a theoretical model to the results of tellurium vapor pressure measurements. In addition it is shown that the shape of the activity curve indicates a certain sequence of superstructures. In principle, there are no limitations to the application of statistical thermodynamics to experimental thermodynamic data as long as these are available with sufficient accuracy, and as long as it is ensured that the distribution of the point defects is truly random, i.e. that there are no aggregates of defects

Modeling Repeated Count Data : Some Extensions of the Rasch Poisson Counts Model

NARCIS (Netherlands)

van Duijn, M.A.J.; Jansen, Margo

1995-01-01

We consider data that can be summarized as an N X K table of counts-for example, test data obtained by administering K tests to N subjects. The cell entries y(ij) are assumed to be conditionally independent Poisson-distributed random variables, given the NK Poisson intensity parameters mu(ij). The

Zero-inflated Poisson model based likelihood ratio test for drug safety signal detection.

Science.gov (United States)

Huang, Lan; Zheng, Dan; Zalkikar, Jyoti; Tiwari, Ram

2017-02-01

In recent decades, numerous methods have been developed for data mining of large drug safety databases, such as Food and Drug Administration's (FDA's) Adverse Event Reporting System, where data matrices are formed by drugs such as columns and adverse events as rows. Often, a large number of cells in these data matrices have zero cell counts and some of them are "true zeros" indicating that the drug-adverse event pairs cannot occur, and these zero counts are distinguished from the other zero counts that are modeled zero counts and simply indicate that the drug-adverse event pairs have not occurred yet or have not been reported yet. In this paper, a zero-inflated Poisson model based likelihood ratio test method is proposed to identify drug-adverse event pairs that have disproportionately high reporting rates, which are also called signals. The maximum likelihood estimates of the model parameters of zero-inflated Poisson model based likelihood ratio test are obtained using the expectation and maximization algorithm. The zero-inflated Poisson model based likelihood ratio test is also modified to handle the stratified analyses for binary and categorical covariates (e.g. gender and age) in the data. The proposed zero-inflated Poisson model based likelihood ratio test method is shown to asymptotically control the type I error and false discovery rate, and its finite sample performance for signal detection is evaluated through a simulation study. The simulation results show that the zero-inflated Poisson model based likelihood ratio test method performs similar to Poisson model based likelihood ratio test method when the estimated percentage of true zeros in the database is small. Both the zero-inflated Poisson model based likelihood ratio test and likelihood ratio test methods are applied to six selected drugs, from the 2006 to 2011 Adverse Event Reporting System database, with varying percentages of observed zero-count cells.

Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

OpenAIRE

Haas, F.; Shukla, P. K.

2008-01-01

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved p...

Poisson structure of the equations of ideal multispecies fluid electrodynamics

International Nuclear Information System (INIS)

Spencer, R.G.

1984-01-01

The equations of the two- (or multi-) fluid model of plasma physics are recast in Hamiltonian form, following general methods of symplectic geometry. The dynamical variables are the fields of physical interest, but are noncanonical, so that the Poisson bracket in the theory is not the standard one. However, it is a skew-symmetric bilinear form which, from the method of derivation, automatically satisfies the Jacobi identity; therefore, this noncanonical structure has all the essential properties of a canonical Poisson bracket

Modelling infant mortality rate in Central Java, Indonesia use generalized poisson regression method

Science.gov (United States)

Prahutama, Alan; Sudarno

2018-05-01

The infant mortality rate is the number of deaths under one year of age occurring among the live births in a given geographical area during a given year, per 1,000 live births occurring among the population of the given geographical area during the same year. This problem needs to be addressed because it is an important element of a country’s economic development. High infant mortality rate will disrupt the stability of a country as it relates to the sustainability of the population in the country. One of regression model that can be used to analyze the relationship between dependent variable Y in the form of discrete data and independent variable X is Poisson regression model. Recently The regression modeling used for data with dependent variable is discrete, among others, poisson regression, negative binomial regression and generalized poisson regression. In this research, generalized poisson regression modeling gives better AIC value than poisson regression. The most significant variable is the Number of health facilities (X1), while the variable that gives the most influence to infant mortality rate is the average breastfeeding (X9).

Affine Poisson Groups and WZW Model

Directory of Open Access Journals (Sweden)

Ctirad Klimcík

2008-01-01

Full Text Available We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the q → ∞ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.

Poisson brackets for fluids and plasmas

International Nuclear Information System (INIS)

Morrison, P.J.

1982-01-01

Noncanonical yet Hamiltonian descriptions are presented of many of the non-dissipative field equations that govern fluids and plasmas. The dynamical variables are the usually encountered physical variables. These descriptions have the advantage that gauge conditions are absent, but at the expense of introducing peculiar Poisson brackets. Clebsch-like potential descriptions that reverse this situations are also introduced

Coherent transform, quantization, and Poisson geometry

CERN Document Server

Novikova, E; Itskov, V; Karasev, M V

1998-01-01

This volume contains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.

Invariants and labels for Lie-Poisson Systems

International Nuclear Information System (INIS)

Thiffeault, J.L.; Morrison, P.J.

1998-04-01

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system

Approximation by some combinations of Poisson integrals for Hermite and Laguerre expansions

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Grażyna Krech

2013-02-01

Full Text Available The aim of this paper is the study of a rate of convergence of some combinations of Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over the Poisson integrals. We prove also the Voronovskaya type theorem for these new operators.

Predictors of the number of under-five malnourished children in Bangladesh: application of the generalized poisson regression model.

Science.gov (United States)

Islam, Mohammad Mafijul; Alam, Morshed; Tariquzaman, Md; Kabir, Mohammad Alamgir; Pervin, Rokhsona; Begum, Munni; Khan, Md Mobarak Hossain

2013-01-08

Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and (ii) to find some predictors of this outcome variable. The data is extracted from the Bangladesh Demographic and Health Survey (BDHS) 2007. Briefly, this survey employs a nationally representative sample which is based on a two-stage stratified sample of households. A total of 4,460 under-five children is analysed using various statistical techniques namely Chi-square test and GPR model. The GPR model (as compared to the standard Poisson regression and negative Binomial regression) is found to be justified to study the above-mentioned outcome variable because of its under-dispersion (variance variable namely mother's education, father's education, wealth index, sanitation status, source of drinking water, and total number of children ever born to a woman. Consistencies of our findings in light of many other studies suggest that the GPR model is an ideal alternative of other statistical models to analyse the number of under-five malnourished children in a family. Strategies based on significant predictors may improve the nutritional status of children in Bangladesh.

Statistical properties of a filtered Poisson process with additive random noise: distributions, correlations and moment estimation

International Nuclear Information System (INIS)

Theodorsen, A; Garcia, O E; Rypdal, M

2017-01-01

Filtered Poisson processes are often used as reference models for intermittent fluctuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical term in a stochastic differential equation. The lowest order moments, probability density function, auto-correlation function and power spectral density are derived and used to identify and compare the effects of the two different noise terms. Monte-Carlo studies of synthetic time series are used to investigate the accuracy of model parameter estimation and to identify methods for distinguishing the noise types. It is shown that the probability density function and the three lowest order moments provide accurate estimations of the model parameters, but are unable to separate the noise types. The auto-correlation function and the power spectral density also provide methods for estimating the model parameters, as well as being capable of identifying the noise type. The number of times the signal crosses a prescribed threshold level in the positive direction also promises to be able to differentiate the noise type. (paper)

Tests of a homogeneous Poisson process against clustering and other alternatives

International Nuclear Information System (INIS)

Atwood, C.L.

1994-05-01

This report presents three closely related tests of the hypothesis that data points come from a homogeneous Poisson process. If there is too much observed variation among the log-transformed between-point distances, the hypothesis is rejected. The tests are more powerful than the standard chi-squared test against the alternative hypothesis of event clustering, but not against the alternative hypothesis of a Poisson process with smoothly varying intensity

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics

Directory of Open Access Journals (Sweden)

Dongming Li

2017-04-01

Full Text Available An adaptive optics (AO system provides real-time compensation for atmospheric turbulence. However, an AO image is usually of poor contrast because of the nature of the imaging process, meaning that the image contains information coming from both out-of-focus and in-focus planes of the object, which also brings about a loss in quality. In this paper, we present a robust multi-frame adaptive optics image restoration algorithm via maximum likelihood estimation. Our proposed algorithm uses a maximum likelihood method with image regularization as the basic principle, and constructs the joint log likelihood function for multi-frame AO images based on a Poisson distribution model. To begin with, a frame selection method based on image variance is applied to the observed multi-frame AO images to select images with better quality to improve the convergence of a blind deconvolution algorithm. Then, by combining the imaging conditions and the AO system properties, a point spread function estimation model is built. Finally, we develop our iterative solutions for AO image restoration addressing the joint deconvolution issue. We conduct a number of experiments to evaluate the performances of our proposed algorithm. Experimental results show that our algorithm produces accurate AO image restoration results and outperforms the current state-of-the-art blind deconvolution methods.

Equal-Time and Equal-Space Poisson Brackets of the N -Component Coupled NLS Equation

International Nuclear Information System (INIS)

Zhou Ru-Guang; Li Pei-Yao; Gao Yuan

2017-01-01

Two Poisson brackets for the N-component coupled nonlinear Schrödinger (NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation. (paper)

Modeling environmental noise exceedances using non-homogeneous Poisson processes.

Science.gov (United States)

Guarnaccia, Claudio; Quartieri, Joseph; Barrios, Juan M; Rodrigues, Eliane R

2014-10-01

In this work a non-homogeneous Poisson model is considered to study noise exposure. The Poisson process, counting the number of times that a sound level surpasses a threshold, is used to estimate the probability that a population is exposed to high levels of noise a certain number of times in a given time interval. The rate function of the Poisson process is assumed to be of a Weibull type. The presented model is applied to community noise data from Messina, Sicily (Italy). Four sets of data are used to estimate the parameters involved in the model. After the estimation and tuning are made, a way of estimating the probability that an environmental noise threshold is exceeded a certain number of times in a given time interval is presented. This estimation can be very useful in the study of noise exposure of a population and also to predict, given the current behavior of the data, the probability of occurrence of high levels of noise in the near future. One of the most important features of the model is that it implicitly takes into account different noise sources, which need to be treated separately when using usual models.

Robust iterative observer for source localization for Poisson equation

KAUST Repository

Majeed, Muhammad Usman

2017-01-05

Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

Robust iterative observer for source localization for Poisson equation

KAUST Repository

Majeed, Muhammad Usman; Laleg-Kirati, Taous-Meriem

2017-01-01

Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

Comparison between two bivariate Poisson distributions through the ...

African Journals Online (AJOL)

These two models express themselves by their probability mass function. ... To remedy this problem, Berkhout and Plug proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive.

Detecting overdispersion in count data: A zero-inflated Poisson regression analysis

Science.gov (United States)

Afiqah Muhamad Jamil, Siti; Asrul Affendi Abdullah, M.; Kek, Sie Long; Nor, Maria Elena; Mohamed, Maryati; Ismail, Norradihah

2017-09-01

This study focusing on analysing count data of butterflies communities in Jasin, Melaka. In analysing count dependent variable, the Poisson regression model has been known as a benchmark model for regression analysis. Continuing from the previous literature that used Poisson regression analysis, this study comprising the used of zero-inflated Poisson (ZIP) regression analysis to gain acute precision on analysing the count data of butterfly communities in Jasin, Melaka. On the other hands, Poisson regression should be abandoned in the favour of count data models, which are capable of taking into account the extra zeros explicitly. By far, one of the most popular models include ZIP regression model. The data of butterfly communities which had been called as the number of subjects in this study had been taken in Jasin, Melaka and consisted of 131 number of subjects visits Jasin, Melaka. Since the researchers are considering the number of subjects, this data set consists of five families of butterfly and represent the five variables involve in the analysis which are the types of subjects. Besides, the analysis of ZIP used the SAS procedure of overdispersion in analysing zeros value and the main purpose of continuing the previous study is to compare which models would be better than when exists zero values for the observation of the count data. The analysis used AIC, BIC and Voung test of 5% level significance in order to achieve the objectives. The finding indicates that there is a presence of over-dispersion in analysing zero value. The ZIP regression model is better than Poisson regression model when zero values exist.

The Poisson model limits in NBA basketball: Complexity in team sports

Science.gov (United States)

Martín-González, Juan Manuel; de Saá Guerra, Yves; García-Manso, Juan Manuel; Arriaza, Enrique; Valverde-Estévez, Teresa

2016-12-01

Team sports are frequently studied by researchers. There is presumption that scoring in basketball is a random process and that can be described using the Poisson Model. Basketball is a collaboration-opposition sport, where the non-linear local interactions among players are reflected in the evolution of the score that ultimately determines the winner. In the NBA, the outcomes of close games are often decided in the last minute, where fouls play a main role. We examined 6130 NBA games in order to analyze the time intervals between baskets and scoring dynamics. Most numbers of baskets (n) over a time interval (ΔT) follow a Poisson distribution, but some (e.g., ΔT = 10 s, n > 3) behave as a Power Law. The Poisson distribution includes most baskets in any game, in most game situations, but in close games in the last minute, the numbers of events are distributed following a Power Law. The number of events can be adjusted by a mixture of two distributions. In close games, both teams try to maintain their advantage solely in order to reach the last minute: a completely different game. For this reason, we propose to use the Poisson model as a reference. The complex dynamics will emerge from the limits of this model.

Poisson/Superfish codes for personal computers

International Nuclear Information System (INIS)

Humphries, S.

1992-01-01

The Poisson/Superfish codes calculate static E or B fields in two-dimensions and electromagnetic fields in resonant structures. New versions for 386/486 PCs and Macintosh computers have capabilities that exceed the mainframe versions. Notable improvements are interactive graphical post-processors, improved field calculation routines, and a new program for charged particle orbit tracking. (author). 4 refs., 1 tab., figs

Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus

Science.gov (United States)

Buring, Ricardo; Kiselev, Arthemy V.; Rutten, Nina

2018-02-01

Let \\mathscr{P} be a Poisson structure on a finite-dimensional affine real manifold. Can \\mathscr{P} be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach - with respect to all affine Poisson manifolds - to finding a class of solutions to this deformation problem. For that reasoning, several types of graphs are needed. In this paper we outline the algorithms to generate those graphs. The graphs that encode deformations are classified by the number of internal vertices k; for k ≤ 4 we present all solutions of the deformation problem. For k ≥ 5, first reproducing the pentagon-wheel picture suggested at k = 6 by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that yields a new unique solution without 2-loops and tadpoles at k = 8.

Testing independence between two Poisson-generated multinomial variables in case-series and cohort studies.

Science.gov (United States)

Hocine, Mounia; Guillemot, Didier; Tubert-Bitter, Pascale; Moreau, Thierry

2005-12-30

In case-series or cohort studies, we propose a test of independence between the occurrences of two types of recurrent events (such as two repeated infections) related to an intermittent exposure (such as an antibiotic treatment). The test relies upon an extension of a recent method for analysing case-series data, in the presence of one type of recurrent event. The test statistic is derived from a bivariate Poisson generated-multinomial distribution. Simulations for checking the validity of the test concerning the type I error and the power properties are presented. The test is illustrated using data from a cohort on antibiotics bacterial resistance in schoolchildren. Copyright 2005 John Wiley & Sons, Ltd.

A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

DEFF Research Database (Denmark)

Spietz, Henrik Juul; Mølholm Hejlesen, Mads; Walther, Jens Honoré

2018-01-01

the regularized unbounded-periodic Green's functions can be implemented in an FFT-based Poisson solver to obtain a convergence rate corresponding to the regularization order of the Green's function. The high order is achieved without any additional computational cost from the conventional FFT-based Poisson solver...... and enables the calculation of the derivative of the solution to the same high order by direct spectral differentiation. We illustrate an application of the FFT-based Poisson solver by using it with a vortex particle mesh method for the approximation of incompressible flow for a problem with a single periodic...

Interpretation of some (p,n), (n,p), and (3He, p) reactions by means of the statistical multistep compound emission theory

International Nuclear Information System (INIS)

Bonetti, R.; Milazzo, L.C.; Melanotte, M.

1983-01-01

A number of (p,n), (n,p), and ( 3 He, p) reactions have been interpreted on the basis of the statistical multistep compound emission mechanism. Good agreement with experiment is found both in spectrum shape and in the value of the coherence widths

Renewal characterization of Markov modulated Poisson processes

Directory of Open Access Journals (Sweden)

Marcel F. Neuts

1989-01-01

Full Text Available A Markov Modulated Poisson Process (MMPP M(t defined on a Markov chain J(t is a pure jump process where jumps of M(t occur according to a Poisson process with intensity λi whenever the Markov chain J(t is in state i. M(t is called strongly renewal (SR if M(t is a renewal process for an arbitrary initial probability vector of J(t with full support on P={i:λi>0}. M(t is called weakly renewal (WR if there exists an initial probability vector of J(t such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t,M(t]. Relevance to the lumpability of J(t is also studied.

Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

International Nuclear Information System (INIS)

Haas, F.; Shukla, P. K.

2008-01-01

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed.

Numerical solution of continuous-time DSGE models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...... classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very...

A new non-commutative representation of the Wiener and Poisson processes

International Nuclear Information System (INIS)

Privault, N.

1996-01-01

Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs

Nonlocal surface plasmons by Poisson Green's function matching

International Nuclear Information System (INIS)

Morgenstern Horing, Norman J

2006-01-01

The Poisson Green's function for all space is derived for the case in which an interface divides space into two separate semi-infinite media, using the Green's function matching method. Each of the separate semi-infinite constituent parts has its own dynamic, nonlocal polarizability, which is taken to be unaffected by the presence of the interface and is represented by the corresponding bulk response property. While this eliminates Friedel oscillatory phenomenology near the interface with p ∼ 2p F , it is nevertheless quite reasonable and useful for a broad range of lower (nonvanishing) wavenumbers, p F . The resulting full-space Poisson Green's function is dynamic, nonlocal and spatially inhomogeneous, and its frequency pole yields the surface plasmon dispersion relation, replete with dynamic and nonlocal features. It also accommodates an ambient magnetic field

Elastic properties of a material composed of alternating layers of negative and positive Poisson's ratio

International Nuclear Information System (INIS)

Kocer, C.; McKenzie, D.R.; Bilek, M.M.

2009-01-01

The theory of elasticity predicts a variety of phenomena associated with solids that possess a negative Poisson's ratio. The fabrication of metamaterials with a 'designed' microstructure that exhibit a Poisson's ratio approaching the thermodynamic limits of 1/2 and -1 increases the likelihood of realising these phenomena for applications. In this work, we investigate the properties of a layered composite, with alternating layers of materials with negative and positive Poisson's ratio approaching the thermodynamic limits. Using the finite element method to simulate uniaxial loading and indentation of a free standing composite, we observed an increase in the resistance to mechanical deformation above the average value of the two materials. Even though the greatest increase in stiffness is gained as the thermodynamic limits are approached, a significant amount of added stiffness can be attained, provided that the Young's modulus of the negative Poisson's ratio material is not less than that of the positive Poisson's ratio material

Quaternionic and Poisson-Lie structures in three-dimensional gravity: The cosmological constant as deformation parameter

International Nuclear Information System (INIS)

Meusburger, C.; Schroers, B. J.

2008-01-01

Each of the local isometry groups arising in three-dimensional (3d) gravity can be viewed as a group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement and use it as a unifying framework for studying Poisson structures associated with the local isometry groups. We show that, in all cases except for the case of Euclidean signature with positive cosmological constant, the local isometry groups are equipped with the Poisson-Lie structure of a classical double. We calculate the dressing action of the factor groups on each other and find, among others, a simple and unified description of the symplectic leaves of SU(2) and SL(2,R). We also compute the Poisson structure on the dual Poisson-Lie groups of the local isometry groups and on their Heisenberg doubles; together, they determine the Poisson structure of the phase space of 3d gravity in the so-called combinatorial description

Concurrent topological design of composite structures and materials containing multiple phases of distinct Poisson's ratios

Science.gov (United States)

Long, Kai; Yuan, Philip F.; Xu, Shanqing; Xie, Yi Min

2018-04-01

Most studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson's ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson's ratios. The proposed method aims to minimize the mean compliance of the macrostructure with a given mass of base materials. In contrast to the traditional interpolation of the stiffness matrix through numerical results, an interpolation scheme of the Young's modulus and Poisson's ratio using different parameters is adopted. The numerical results demonstrate that the Poisson effect plays a key role in reducing the mean compliance of the final design. An important contribution of the present study is that the proposed concurrent optimization method can automatically distribute base materials with distinct Poisson's ratios between the macrostructural and microstructural levels under a single constraint of the total mass.

Critical statistics for non-Hermitian matrices

International Nuclear Information System (INIS)

Garcia-Garcia, A.M.; Verbaarschot, J.J.M.; Nishigaki, S.M.

2002-01-01

We introduce a generalized ensemble of non-Hermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble, and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak non-Hermiticity and in the case of strong non-Hermiticity. In the weak non-Hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of non-Hermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong non-Hermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

International Nuclear Information System (INIS)

Laurence, T.; Chromy, B.

2010-01-01

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms of counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE

Reference manual for the POISSON/SUPERFISH Group of Codes

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

The POISSON/SUPERFISH Group codes were set up to solve two separate problems: the design of magnets and the design of rf cavities in a two-dimensional geometry. The first stage of either problem is to describe the layout of the magnet or cavity in a way that can be used as input to solve the generalized Poisson equation for magnets or the Helmholtz equations for cavities. The computer codes require that the problems be discretized by replacing the differentials (dx,dy) by finite differences ({delta}X,{delta}Y). Instead of defining the function everywhere in a plane, the function is defined only at a finite number of points on a mesh in the plane.

Dataset for acrylate/silica nanoparticles formulations and photocured composites: Viscosity, filler dispersion and bulk Poisson׳s ratio

Directory of Open Access Journals (Sweden)

Hubert Gojzewski

2017-06-01

Full Text Available UV-curable polymer composites are of importance in industry, biomedical applications, scientific fields, and daily life. Outstanding physical properties of polymer composites were achieved with nanoparticles as filler, primarily in enhancing mechanical strength or barrier properties. Structure-property relationships of the resulting nanocomposites are dictated by the polymer-filler molecular architecture, i.e. interactions between polymer matrix and filler, and high surface area to volume ratio of the filler particles. Among monomers, acrylates and methacrylates attracted wide attention due to their ease of polymerization and excellent physicochemical and mechanical properties of the derived polymers. We prepared and photopolymerized two series of formulations containing hydrophobized silica nanofiller (Aerosil R7200 dispersed in 2-hydroxyethyl acrylate (HEA or polyethylene glycol diacrylate (PEGDA monomers. We compared selected physical properties of the formulations, both before and after photocuring; specifically the viscosity of formulations and dispersion of the filler in the polymer matrices. Additionally, we estimated the bulk Poisson׳s ratio of the investigated nanocomposites. This article contains data related to the research article entitled “Nanoscale Young׳s modulus and surface morphology in photocurable polyacrylate/nanosilica composites” (Gojzewski et al., 2017 [1].

High-Order Finite-Difference Solution of the Poisson Equation Involving Complex Geometries in Embedded Meshes

Science.gov (United States)

Marques, Alexandre; Nave, Jean-Christophe; Rosales, Ruben

2011-11-01

The Poisson equation is of central importance in the description of fluid flows and other physical phenomena. In prior work, Marques, Nave, and Rosales introduced the Correction Function Method (CFM) to obtain fourth-order accurate solutions for the constant coefficient Poisson problem with prescribed jump conditions for the solution and its normal derivative across arbitrary interfaces. Here we combine this method with the ideas introduced by Mayo to solve other Poisson problems involving complex geometries. In summary, we are able to rewrite the problem as a boundary integral equation in terms of a potential distribution over the boundary or interface. The solution of this integral equation is discontinuous across the boundary or interface. Hence, after this integral equation is solved using standard techniques, the potential distribution can be used to determine the jump discontinuities. We are then able to use the CFM to solve the resulting Poisson equation with jump discontinuities. The outcome is a fourth-order accurate scheme to solve general Poisson problems which, over arbitrary geometries, has a cost that is approximately twice that of a fast Poisson solver using FFT on a rectangular geometry of the same size. Details of the method and applications will be presented.

Variance to mean ratio, R(t), for poisson processes on phylogenetic trees.

Science.gov (United States)

Goldman, N

1994-09-01

The ratio of expected variance to mean, R(t), of numbers of DNA base substitutions for contemporary sequences related by a "star" phylogeny is widely seen as a measure of the adherence of the sequences' evolution to a Poisson process with a molecular clock, as predicted by the "neutral theory" of molecular evolution under certain conditions. A number of estimators of R(t) have been proposed, all predicted to have mean 1 and distributions based on the chi 2. Various genes have previously been analyzed and found to have values of R(t) far in excess of 1, calling into question important aspects of the neutral theory. In this paper, I use Monte Carlo simulation to show that the previously suggested means and distributions of estimators of R(t) are highly inaccurate. The analysis is applied to star phylogenies and to general phylogenetic trees, and well-known gene sequences are reanalyzed. For star phylogenies the results show that Kimura's estimators ("The Neutral Theory of Molecular Evolution," Cambridge Univ. Press, Cambridge, 1983) are unsatisfactory for statistical testing of R(t), but confirm the accuracy of Bulmer's correction factor (Genetics 123: 615-619, 1989). For all three nonstar phylogenies studied, attained values of all three estimators of R(t), although larger than 1, are within their true confidence limits under simple Poisson process models. This shows that lineage effects can be responsible for high estimates of R(t), restoring some limited confidence in the molecular clock and showing that the distinction between lineage and molecular clock effects is vital.(ABSTRACT TRUNCATED AT 250 WORDS)

Application of Poisson random effect models for highway network screening.

Science.gov (United States)

Jiang, Ximiao; Abdel-Aty, Mohamed; Alamili, Samer

2014-02-01

In recent years, Bayesian random effect models that account for the temporal and spatial correlations of crash data became popular in traffic safety research. This study employs random effect Poisson Log-Normal models for crash risk hotspot identification. Both the temporal and spatial correlations of crash data were considered. Potential for Safety Improvement (PSI) were adopted as a measure of the crash risk. Using the fatal and injury crashes that occurred on urban 4-lane divided arterials from 2006 to 2009 in the Central Florida area, the random effect approaches were compared to the traditional Empirical Bayesian (EB) method and the conventional Bayesian Poisson Log-Normal model. A series of method examination tests were conducted to evaluate the performance of different approaches. These tests include the previously developed site consistence test, method consistence test, total rank difference test, and the modified total score test, as well as the newly proposed total safety performance measure difference test. Results show that the Bayesian Poisson model accounting for both temporal and spatial random effects (PTSRE) outperforms the model that with only temporal random effect, and both are superior to the conventional Poisson Log-Normal model (PLN) and the EB model in the fitting of crash data. Additionally, the method evaluation tests indicate that the PTSRE model is significantly superior to the PLN model and the EB model in consistently identifying hotspots during successive time periods. The results suggest that the PTSRE model is a superior alternative for road site crash risk hotspot identification. Copyright © 2013 Elsevier Ltd. All rights reserved.

Bases chimiosensorielles du comportement alimentaire chez les poissons

Directory of Open Access Journals (Sweden)

SAGLIO Ph.

1981-07-01

Full Text Available Le comportement alimentaire, indispensable à la survie de l'individu et donc de l'espèce, occupe à ce titre une position de première importance dans la hiérarchie des comportements fondamentaux qui tous en dépendent très étroitement. Chez les poissons, cette prééminence se trouve illustrée par l'extrême diversité des supports sensoriels impliqués et des expressions comportementales qui leur sont liées. A la suite d'un certain nombre de mises en évidence neurophysiologiques et éthologiques de l'importance du sens chimique (olfaction, gustation dans le comportement alimentaire des poissons, de très importants secteurs d'études électrophysiologiques et d'analyses physico-chimiques visant à en déterminer la nature exacte (en termes de substances actives se sont développés ces vingt dernières années. De tous ces travaux dont les plus avancés sont présentés ici, il ressort que les acides aminés de série L plus ou moins associés à d'autres composés de poids moléculaires < 1000 constituent des composés chimiques jouant un rôle déterminant dans le comportement alimentaire de nombreuses espèces de poissons carnivores.

A covariant Poisson deformation quantization with separation of variables up to the third order

OpenAIRE

Karabegov, Alexander

2002-01-01

We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a K\\"ahler manifold M. Unlike C_1 and C_2, this operator can not be expressed in terms of the K\\"ahler-Poisson tensor on M. We modify C_3 to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and thus can be defined on an arbitrary complex manifold endowed with a Poisson bivecto...

Generalized results on the role of new-time transformations in finite-dimensional Poisson systems

Energy Technology Data Exchange (ETDEWEB)

Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)

2010-01-25

The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.

Poisson's equation in de Sitter space-time

Energy Technology Data Exchange (ETDEWEB)

Pessa, E [Rome Univ. (Italy). Ist. di Matematica

1980-11-01

Based on a suitable generalization of Poisson's equation for de Sitter space-time the form of gravitation's law in 'projective relativity' is examined; it is found that, in the interior case, a small difference with the customary Newtonian law arises. This difference, of a repulsive character, can be very important in cosmological problems.

Elastic and thermal properties of silicon compounds from first-principles calculations

Energy Technology Data Exchange (ETDEWEB)

Hou, Haijun; Zhu, H.J. [Yancheng Institute of Technology (China). School of Materials Engineering; Cheng, W.H. [Yancheng Institute of Technology (China). Dept. of Light Chemical Engineering; Xie, L.H. [Sichuan Normal Univ., Chengdu (China). Inst. of Solid State Physics and School of Physics and Electronic Engineering

2016-11-01

The structural and elastic properties of V-Si (V{sub 3}Si, VSi{sub 2}, V{sub 5}Si{sub 3}, and V{sub 6}Si{sub 5}) compounds are studied by using first-principles method. The calculated equilibrium lattice parameters and formation enthalpy are in good agreement with the available experimental data and other theoretical results. The calculated results indicate that the V-Si compounds are mechanically stable. Elastic properties including bulk modulus, shear modulus, Young's modulus, and Poisson's ratio are also obtained. The elastic anisotropies of V-Si compounds are investigated via the three-dimensional (3D) figures of directional dependences of reciprocals of Young's modulus. Finally, based on the quasi-harmonic Debye model, the internal energy, Helmholtz free energy, entropy, heat capacity, thermal expansion coefficient, Grueneisen parameter, and Debye temperature of V-Si compounds have been calculated.

Statistical analysis of the sustained lava dome emplacement and destruction processes at Popocatépetl volcano, Central México

Science.gov (United States)

Mendoza-Rosas, Ana Teresa; Gómez-Vázquez, Ángel; De la Cruz-Reyna, Servando

2017-06-01

Popocatépetl volcano reawakened in 1994 after nearly 70 years of quiescence. Between 1996 and 2015, a succession of at least 38 lava domes have been irregularly emplaced and destroyed, with each dome reaching particular volumes at specific emplacement rates. The complexity of this sequence is analyzed using statistical methods in an attempt to gain insight into the physics and dynamics of the lava dome emplacement and destruction process and to objectively assess the hazards related to that volcano. The time series of emplacements, dome residences, lava effusion lulls, and emplaced dome volumes and thicknesses are modeled using the simple exponential and Weibull distributions, the compound non-homogeneous generalized Pareto-Poisson process (NHPPP), and the mixture of exponentials distribution (MOED). The statistical analysis reveals that the sequence of dome emplacements is a non-stationary, self-regulating process most likely controlled by the balance between buoyancy-driven magma ascent and volatile exsolution crystallization. This balance has supported the sustained effusive activity for decades and may persist for an undetermined amount of time. However, the eruptive history of Popocatépetl includes major Plinian phases that may have resulted from a breach in that balance. Certain criteria to recognize such breaching conditions are inferred from this statistical analysis.

Quasineutral Limit of the Schrödinger-Poisson System in Coulomb Gauge

OpenAIRE

Lin, Chi-Kun; Wong, Yau-Shu; Wu, Kung-Chien

2012-01-01

The zero Debye length asymptotic of the Schrödinger-Poisson system in Coulomb gauge for ill-prepared initial data is studied. We prove that when the scaled Debye length λ → 0, the current density defined by the solution of the Schrödinger-Poisson system in the Coulomb gauge converges to the solution of the rotating incompressible Euler equation plus a fast singular oscillating gradient vector field.

Poisson processes and a Bessel function integral

NARCIS (Netherlands)

Steutel, F.W.

1985-01-01

The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily

Histogram bin width selection for time-dependent Poisson processes

International Nuclear Information System (INIS)

Koyama, Shinsuke; Shinomoto, Shigeru

2004-01-01

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method

Histogram bin width selection for time-dependent Poisson processes

Energy Technology Data Exchange (ETDEWEB)

Koyama, Shinsuke; Shinomoto, Shigeru [Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan)

2004-07-23

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.

Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969-2007.

Science.gov (United States)

Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo

2015-08-01

Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Risk Estimation for Lung Cancer in Libya: Analysis Based on Standardized Morbidity Ratio, Poisson-Gamma Model, BYM Model and Mixture Model

Science.gov (United States)

Alhdiri, Maryam Ahmed; Samat, Nor Azah; Mohamed, Zulkifley

2017-03-01

Cancer is the most rapidly spreading disease in the world, especially in developing countries, including Libya. Cancer represents a significant burden on patients, families, and their societies. This disease can be controlled if detected early. Therefore, disease mapping has recently become an important method in the fields of public health research and disease epidemiology. The correct choice of statistical model is a very important step to producing a good map of a disease. Libya was selected to perform this work and to examine its geographical variation in the incidence of lung cancer. The objective of this paper is to estimate the relative risk for lung cancer. Four statistical models to estimate the relative risk for lung cancer and population censuses of the study area for the time period 2006 to 2011 were used in this work. They are initially known as Standardized Morbidity Ratio, which is the most popular statistic, which used in the field of disease mapping, Poisson-gamma model, which is one of the earliest applications of Bayesian methodology, Besag, York and Mollie (BYM) model and Mixture model. As an initial step, this study begins by providing a review of all proposed models, which we then apply to lung cancer data in Libya. Maps, tables and graph, goodness-of-fit (GOF) were used to compare and present the preliminary results. This GOF is common in statistical modelling to compare fitted models. The main general results presented in this study show that the Poisson-gamma model, BYM model, and Mixture model can overcome the problem of the first model (SMR) when there is no observed lung cancer case in certain districts. Results show that the Mixture model is most robust and provides better relative risk estimates across a range of models. Creative Commons Attribution License

Variational Gaussian approximation for Poisson data

Science.gov (United States)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

A novel method for the accurate evaluation of Poisson's ratio of soft polymer materials.

Science.gov (United States)

Lee, Jae-Hoon; Lee, Sang-Soo; Chang, Jun-Dong; Thompson, Mark S; Kang, Dong-Joong; Park, Sungchan; Park, Seonghun

2013-01-01

A new method with a simple algorithm was developed to accurately measure Poisson's ratio of soft materials such as polyvinyl alcohol hydrogel (PVA-H) with a custom experimental apparatus consisting of a tension device, a micro X-Y stage, an optical microscope, and a charge-coupled device camera. In the proposed method, the initial positions of the four vertices of an arbitrarily selected quadrilateral from the sample surface were first measured to generate a 2D 1st-order 4-node quadrilateral element for finite element numerical analysis. Next, minimum and maximum principal strains were calculated from differences between the initial and deformed shapes of the quadrilateral under tension. Finally, Poisson's ratio of PVA-H was determined by the ratio of minimum principal strain to maximum principal strain. This novel method has an advantage in the accurate evaluation of Poisson's ratio despite misalignment between specimens and experimental devices. In this study, Poisson's ratio of PVA-H was 0.44 ± 0.025 (n = 6) for 2.6-47.0% elongations with a tendency to decrease with increasing elongation. The current evaluation method of Poisson's ratio with a simple measurement system can be employed to a real-time automated vision-tracking system which is used to accurately evaluate the material properties of various soft materials.

Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach.

Science.gov (United States)

Mohammadi, Tayeb; Kheiri, Soleiman; Sedehi, Morteza

2016-01-01

Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.

2D sigma models and differential Poisson algebras

International Nuclear Information System (INIS)

Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander

2015-01-01

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

Improved mesh generator for the POISSON Group Codes

International Nuclear Information System (INIS)

Gupta, R.C.

1987-01-01

This paper describes the improved mesh generator of the POISSON Group Codes. These improvements enable one to have full control over the way the mesh is generated and in particular the way the mesh density is distributed throughout this model. A higher mesh density in certain regions coupled with a successively lower mesh density in others keeps the accuracy of the field computation high and the requirements on the computer time and computer memory low. The mesh is generated with the help of codes AUTOMESH and LATTICE; both have gone through a major upgrade. Modifications have also been made in the POISSON part of these codes. We shall present an example of a superconducting dipole magnet to explain how to use this code. The results of field computations are found to be reliable within a few parts in a hundred thousand even in such complex geometries

Beta-Poisson model for single-cell RNA-seq data analyses.

Science.gov (United States)

Vu, Trung Nghia; Wills, Quin F; Kalari, Krishna R; Niu, Nifang; Wang, Liewei; Rantalainen, Mattias; Pawitan, Yudi

2016-07-15

Single-cell RNA-sequencing technology allows detection of gene expression at the single-cell level. One typical feature of the data is a bimodality in the cellular distribution even for highly expressed genes, primarily caused by a proportion of non-expressing cells. The standard and the over-dispersed gamma-Poisson models that are commonly used in bulk-cell RNA-sequencing are not able to capture this property. We introduce a beta-Poisson mixture model that can capture the bimodality of the single-cell gene expression distribution. We further integrate the model into the generalized linear model framework in order to perform differential expression analyses. The whole analytical procedure is called BPSC. The results from several real single-cell RNA-seq datasets indicate that ∼90% of the transcripts are well characterized by the beta-Poisson model; the model-fit from BPSC is better than the fit of the standard gamma-Poisson model in > 80% of the transcripts. Moreover, in differential expression analyses of simulated and real datasets, BPSC performs well against edgeR, a conventional method widely used in bulk-cell RNA-sequencing data, and against scde and MAST, two recent methods specifically designed for single-cell RNA-seq data. An R package BPSC for model fitting and differential expression analyses of single-cell RNA-seq data is available under GPL-3 license at https://github.com/nghiavtr/BPSC CONTACT: yudi.pawitan@ki.se or mattias.rantalainen@ki.se Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Development of planning level transportation safety tools using Geographically Weighted Poisson Regression.

Science.gov (United States)

Hadayeghi, Alireza; Shalaby, Amer S; Persaud, Bhagwant N

2010-03-01

A common technique used for the calibration of collision prediction models is the Generalized Linear Modeling (GLM) procedure with the assumption of Negative Binomial or Poisson error distribution. In this technique, fixed coefficients that represent the average relationship between the dependent variable and each explanatory variable are estimated. However, the stationary relationship assumed may hide some important spatial factors of the number of collisions at a particular traffic analysis zone. Consequently, the accuracy of such models for explaining the relationship between the dependent variable and the explanatory variables may be suspected since collision frequency is likely influenced by many spatially defined factors such as land use, demographic characteristics, and traffic volume patterns. The primary objective of this study is to investigate the spatial variations in the relationship between the number of zonal collisions and potential transportation planning predictors, using the Geographically Weighted Poisson Regression modeling technique. The secondary objective is to build on knowledge comparing the accuracy of Geographically Weighted Poisson Regression models to that of Generalized Linear Models. The results show that the Geographically Weighted Poisson Regression models are useful for capturing spatially dependent relationships and generally perform better than the conventional Generalized Linear Models. Copyright 2009 Elsevier Ltd. All rights reserved.

Quantum fields and Poisson processes. Pt. 2

International Nuclear Information System (INIS)

Bertrand, J.; Gaveau, B.; Rideau, G.

1985-01-01

Quantum field evolutions are written as expectation values with respect to Poisson processes in two simple models; interaction of two boson fields (with conservation of the number of particles in one field) and interaction of a boson with a fermion field. The introduction of a cutt-off ensures that the expectation values are well-defined. (orig.)

Nonhomogeneous fractional Poisson processes

International Nuclear Information System (INIS)

Wang Xiaotian; Zhang Shiying; Fan Shen

2007-01-01

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W H (j) (t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W H (j) (t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function λ(t) strongly influences the existence of the highest finite moment of W H (j) (t) and the behaviour of the tail probability of W H (j) (t)

POISSON, Analysis Solution of Poisson Problems in Probabilistic Risk Assessment

International Nuclear Information System (INIS)

Froehner, F.H.

1986-01-01

1 - Description of program or function: Purpose of program: Analytic treatment of two-stage Poisson problem in Probabilistic Risk Assessment. Input: estimated a-priori mean failure rate and error factor of system considered (for calculation of stage-1 prior), number of failures and operating times for similar systems (for calculation of stage-2 prior). Output: a-posteriori probability distributions on linear and logarithmic time scale (on specified time grid) and expectation values of failure rate and error factors are calculated for: - stage-1 a-priori distribution, - stage-1 a-posteriori distribution, - stage-2 a-priori distribution, - stage-2 a-posteriori distribution. 2 - Method of solution: Bayesian approach with conjugate stage-1 prior, improved with experience from similar systems to yield stage-2 prior, and likelihood function from experience with system under study (documentation see below under 10.). 3 - Restrictions on the complexity of the problem: Up to 100 similar systems (including the system considered), arbitrary number of problems (failure types) with same grid

Models for probability and statistical inference theory and applications

CERN Document Server

Stapleton, James H

2007-01-01

This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models

OpenAIRE

Evangelista, Luiz Roberto; Lenzi, Ervin Kaminski; Barbero, Giovanni

2013-01-01

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual (PNP) or anomalous (PNPA) diffusional models that satisfy Poisson's equation in a finite-length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these re...

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models.

Science.gov (United States)

Evangelista, Luiz Roberto; Lenzi, Ervin Kaminski; Barbero, Giovanni

2013-11-20

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

High-Order Finite-Difference Solution of the Poisson Equation with Interface Jump Conditions II

Science.gov (United States)

Marques, Alexandre; Nave, Jean-Christophe; Rosales, Rodolfo

2010-11-01

The Poisson equation with jump discontinuities across an interface is of central importance in Computational Fluid Dynamics. In prior work, Marques, Nave, and Rosales have introduced a method to obtain fourth-order accurate solutions for the constant coefficient Poisson problem. Here we present an extension of this method to solve the variable coefficient Poisson problem to fourth-order of accuracy. The extended method is based on local smooth extrapolations of the solution field across the interface. The extrapolation procedure uses a combination of cubic Hermite interpolants and a high-order representation of the interface using the Gradient-Augmented Level-Set technique. This procedure is compatible with the use of standard discretizations for the Laplace operator, and leads to modified linear systems which have the same sparsity pattern as the standard discretizations. As a result, standard Poisson solvers can be used with only minimal modifications. Details of the method and applications will be presented.

Overdispersion in nuclear statistics

International Nuclear Information System (INIS)

Semkow, Thomas M.

1999-01-01

The modern statistical distribution theory is applied to the development of the overdispersion theory in ionizing-radiation statistics for the first time. The physical nuclear system is treated as a sequence of binomial processes, each depending on a characteristic probability, such as probability of decay, detection, etc. The probabilities fluctuate in the course of a measurement, and the physical reasons for that are discussed. If the average values of the probabilities change from measurement to measurement, which originates from the random Lexis binomial sampling scheme, then the resulting distribution is overdispersed. The generating functions and probability distribution functions are derived, followed by a moment analysis. The Poisson and Gaussian limits are also given. The distribution functions belong to a family of generalized hypergeometric factorial moment distributions by Kemp and Kemp, and can serve as likelihood functions for the statistical estimations. An application to radioactive decay with detection is described and working formulae are given, including a procedure for testing the counting data for overdispersion. More complex experiments in nuclear physics (such as solar neutrino) can be handled by this model, as well as distinguishing between the source and background

Doubly stochastic Poisson process models for precipitation at fine time-scales

Science.gov (United States)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Is neutron evaporation from highly excited nuclei a poisson random process

International Nuclear Information System (INIS)

Simbel, M.H.

1982-01-01

It is suggested that neutron emission from highly excited nuclei follows a Poisson random process. The continuous variable of the process is the excitation energy excess over the binding energy of the emitted neutrons and the discrete variable is the number of emitted neutrons. Cross sections for (HI,xn) reactions are analyzed using a formula containing a Poisson distribution function. The post- and pre-equilibrium components of the cross section are treated separately. The agreement between the predictions of this formula and the experimental results is very good. (orig.)

Measurements of the Poisson ratio and fragility of glass-forming liquids

DEFF Research Database (Denmark)

Christensen, Tage Emil; Olsen, Niels Boye

Recently much attention has been given to models and phenomenology of glass-forming liquids that correlates fast and slow degrees of freedom . In particular the Poisson ratio has been correlated with fragility. We present data on shear - and bulk modulus obtained by the techniques...... of the piezoelectric transducers PBG and PSG on a number of glass-forming liquids. Hereby the Poisson ratio can be found. Furthermore the PSG also gives the temperature dependence of shear viscosity and thereby the fragility. The validity of the conjectured relation is discussed...

Família composta Poisson-Truncada: propriedades e aplicações

OpenAIRE

ARAÚJO, Raphaela Lima Belchior de

2015-01-01

Este trabalho analisa propriedades da família de distribuições de probabilidade Composta N e propõe a sub-família Composta Poisson-Truncada como um meio de compor distribuições de probabilidade. Suas propriedades foram estudadas e uma nova distribuição foi investigada: a distribuição Composta Poisson-Truncada Normal. Esta distribuição possui três parâmetros e tem uma flexibilidade para modelar dados multimodais. Demonstramos que sua densidade é dada por uma mistura infinita de densidades norm...

WAITING TIME DISTRIBUTION OF SOLAR ENERGETIC PARTICLE EVENTS MODELED WITH A NON-STATIONARY POISSON PROCESS

International Nuclear Information System (INIS)

Li, C.; Su, W.; Fang, C.; Zhong, S. J.; Wang, L.

2014-01-01

We present a study of the waiting time distributions (WTDs) of solar energetic particle (SEP) events observed with the spacecraft WIND and GOES. The WTDs of both solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail of ∼Δt –γ . The SEEs display a broken power-law WTD. The power-law index is γ 1 = 0.99 for the short waiting times (<70 hr) and γ 2 = 1.92 for large waiting times (>100 hr). The break of the WTD of SEEs is probably due to the modulation of the corotating interaction regions. The power-law index, γ ∼ 1.82, is derived for the WTD of the SPEs which is consistent with the WTD of type II radio bursts, indicating a close relationship between the shock wave and the production of energetic protons. The WTDs of SEP events can be modeled with a non-stationary Poisson process, which was proposed to understand the waiting time statistics of solar flares. We generalize the method and find that, if the SEP event rate λ = 1/Δt varies as the time distribution of event rate f(λ) = Aλ –α exp (– βλ), the time-dependent Poisson distribution can produce a power-law tail WTD of ∼Δt α –3 , where 0 ≤ α < 2

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Directory of Open Access Journals (Sweden)

Chi Zhang

2015-05-01

Full Text Available To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP distributions by incorporating a multiplicative factor (or dependency parameter λ, named as Type I and Type II bivariate ZIGP distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over- or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.

Association between large strongyle genera in larval cultures--using rare-event poisson regression.

Science.gov (United States)

Cao, X; Vidyashankar, A N; Nielsen, M K

2013-09-01

Decades of intensive anthelmintic treatment has caused equine large strongyles to become quite rare, while the cyathostomins have developed resistance to several drug classes. The larval culture has been associated with low to moderate negative predictive values for detecting Strongylus vulgaris infection. It is unknown whether detection of other large strongyle species can be statistically associated with presence of S. vulgaris. This remains a statistical challenge because of the rare occurrence of large strongyle species. This study used a modified Poisson regression to analyse a dataset for associations between S. vulgaris infection and simultaneous occurrence of Strongylus edentatus and Triodontophorus spp. In 663 horses on 42 Danish farms, the individual prevalences of S. vulgaris, S. edentatus and Triodontophorus spp. were 12%, 3% and 12%, respectively. Both S. edentatus and Triodontophorus spp. were significantly associated with S. vulgaris infection with relative risks above 1. Further, S. edentatus was associated with use of selective therapy on the farms, as well as negatively associated with anthelmintic treatment carried out within 6 months prior to the study. The findings illustrate that occurrence of S. vulgaris in larval cultures can be interpreted as indicative of other large strongyles being likely to be present.

Optimal linear filtering of Poisson process with dead time

International Nuclear Information System (INIS)

Glukhova, E.V.

1993-01-01

The paper presents a derivation of an integral equation defining the impulsed transient of optimum linear filtering for evaluation of the intensity of the fluctuating Poisson process with allowance for dead time of transducers

Statistical characteristics of serious network failures in Japan

International Nuclear Information System (INIS)

Uchida, Masato

2014-01-01

Due to significant environmental changes in the telecommunications market, network failures affect socioeconomic activities more than ever before. However, the health of public networks at a national level has not been investigated in detail. In this paper, we investigate the statistical characteristics of interval, duration, and the number of users affected for serious network failures, which are defined as network failures that last for more than two hours and affect more than 30,000 users, that occurred in Japan during Japanese fiscal years 2008–2012 (April 2008–March 2013). The results show that (i) the interval follows a Poisson process, (ii) the duration follows a Pareto distribution, (iii) the number of users affected follows a piecewise Pareto distribution, (iv) the product of duration and the number of users affected roughly follow a distribution that can be derived from a convolution of two distributions of duration and the number of users affected, and (v) the relationship between duration and the number of users affected differs from service to service. - Highlights: • The statistical characteristics of serious network failures in Japan are analyzed. • The analysis is based on public information that is available at the moment. • The interval follows a Poisson process. • The duration follows a Pareto distribution. • The number of users affected follows a piecewise Pareto distribution

Confidence Level Computation for Combining Searches with Small Statistics

OpenAIRE

Junk, Thomas

1999-01-01

This article describes an efficient procedure for computing approximate confidence levels for searches for new particles where the expected signal and background levels are small enough to require the use of Poisson statistics. The results of many independent searches for the same particle may be combined easily, regardless of the discriminating variables which may be measured for the candidate events. The effects of systematic uncertainty in the signal and background models are incorporated ...

Poisson equation in the Kohn-Sham Coulomb problem

OpenAIRE

Manby, F. R.; Knowles, Peter James

2001-01-01

We apply the Poisson equation to the quantum mechanical Coulomb problem for many-particle systems. By introducing a suitable basis set, the two-electron Coulomb integrals become simple overlaps. This offers the possibility of very rapid linear-scaling treatment of the Coulomb contribution to Kohn-Sham theory.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

International Nuclear Information System (INIS)

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-01

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations

Hyperbolically Patterned 3D Graphene Metamaterial with Negative Poisson's Ratio and Superelasticity.

Science.gov (United States)

Zhang, Qiangqiang; Xu, Xiang; Lin, Dong; Chen, Wenli; Xiong, Guoping; Yu, Yikang; Fisher, Timothy S; Li, Hui

2016-03-16

A hyperbolically patterned 3D graphene metamaterial (GM) with negative Poisson's ratio and superelasticity is highlighted. It is synthesized by a modified hydrothermal approach and subsequent oriented freeze-casting strategy. GM presents a tunable Poisson's ratio by adjusting the structural porosity, macroscopic aspect ratio (L/D), and freeze-casting conditions. Such a GM suggests promising applications as soft actuators, sensors, robust shock absorbers, and environmental remediation. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Wavelets, ridgelets, and curvelets for Poisson noise removal.

Science.gov (United States)

Zhang, Bo; Fadili, Jalal M; Starck, Jean-Luc

2008-07-01

In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. This new transform, which can be deemed as an extension of the Anscombe transform to filtered data, is simple, fast, and efficient in (very) low-count situations. We combine this VST with the filter banks of wavelets, ridgelets and curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes. By doing so, the noise-contaminated coefficients of these MS-VST-modified transforms are asymptotically normally distributed with known variances. A classical hypothesis-testing framework is adopted to detect the significant coefficients, and a sparsity-driven iterative scheme reconstructs properly the final estimate. A range of examples show the power of this MS-VST approach for recovering important structures of various morphologies in (very) low-count images. These results also demonstrate that the MS-VST approach is competitive relative to many existing denoising methods.

Natural Poisson structures of nonlinear plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-01-01

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)

Natural Poisson structures of nonlinear plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-06-01

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering

Non-chiral, molecular model of negative Poisson ratio in two dimensions

International Nuclear Information System (INIS)

Wojciechowski, K W

2003-01-01

A two-dimensional model of tri-atomic molecules (in which 'atoms' are distributed on vertices of equilateral triangles, and which are further referred to as cyclic trimers) is solved exactly in the static (zero-temperature) limit for the nearest-neighbour site-site interactions. It is shown that the cyclic trimers form a mechanically stable and elastically isotropic non-chiral phase of negative Poisson ratio. The properties of the system are illustrated by three examples of atom-atom interaction potentials: (i) the purely repulsive (n-inverse-power) potential, (ii) the purely attractive (n-power) potential and (iii) the Lennard-Jones potential which shows both the repulsive and the attractive part. The analytic form of the dependence of the Poisson ratio on the interatomic potential is obtained. It is shown that the Poisson ratio depends, in a universal way, only on the trimer anisotropy parameter both (1) in the limit of n → ∞ for cases (i) and (ii), as well as (2) at the zero external pressure for any potential with a doubly differentiable minimum, case (iii) is an example

Bayesian spatial modeling of HIV mortality via zero-inflated Poisson models.

Science.gov (United States)

Musal, Muzaffer; Aktekin, Tevfik

2013-01-30

In this paper, we investigate the effects of poverty and inequality on the number of HIV-related deaths in 62 New York counties via Bayesian zero-inflated Poisson models that exhibit spatial dependence. We quantify inequality via the Theil index and poverty via the ratios of two Census 2000 variables, the number of people under the poverty line and the number of people for whom poverty status is determined, in each Zip Code Tabulation Area. The purpose of this study was to investigate the effects of inequality and poverty in addition to spatial dependence between neighboring regions on HIV mortality rate, which can lead to improved health resource allocation decisions. In modeling county-specific HIV counts, we propose Bayesian zero-inflated Poisson models whose rates are functions of both covariate and spatial/random effects. To show how the proposed models work, we used three different publicly available data sets: TIGER Shapefiles, Census 2000, and mortality index files. In addition, we introduce parameter estimation issues of Bayesian zero-inflated Poisson models and discuss MCMC method implications. Copyright © 2012 John Wiley & Sons, Ltd.

Toward negative Poisson's ratio composites: Investigation of the auxetic behavior of fibrous networks

Science.gov (United States)

Tatlier, Mehmet Seha

Random fibrous can be found among natural and synthetic materials. Some of these random fibrous networks possess negative Poisson's ratio and they are extensively called auxetic materials. The governing mechanisms behind this counter intuitive property in random networks are yet to be understood and this kind of auxetic material remains widely under-explored. However, most of synthetic auxetic materials suffer from their low strength. This shortcoming can be rectified by developing high strength auxetic composites. The process of embedding auxetic random fibrous networks in a polymer matrix is an attractive alternate route to the manufacture of auxetic composites, however before such an approach can be developed, a methodology for designing fibrous networks with the desired negative Poisson's ratios must first be established. This requires an understanding of the factors which bring about negative Poisson's ratios in these materials. In this study, a numerical model is presented in order to investigate the auxetic behavior in compressed random fiber networks. Finite element analyses of three-dimensional stochastic fiber networks were performed to gain insight into the effects of parameters such as network anisotropy, network density, and degree of network compression on the out-of-plane Poisson's ratio and Young's modulus. The simulation results suggest that the compression is the critical parameter that gives rise to negative Poisson's ratio while anisotropy significantly promotes the auxetic behavior. This model can be utilized to design fibrous auxetic materials and to evaluate feasibility of developing auxetic composites by using auxetic fibrous networks as the reinforcing layer.

Statistical analysis of natural radiation levels inside the UNICAMP campus through the use of Geiger-Muller counter

International Nuclear Information System (INIS)

Fontolan, Juliana A.; Biral, Antonio Renato P.

2013-01-01

It is known that the distribution at time intervals of random and unrelated events leads to the Poisson distribution . This work aims to study the distribution in time intervals of events resulting from radioactive decay of atoms present in the UNICAMP where activities involving the use of ionizing radiation are performed environments . The proposal is that the distribution surveys at intervals of these events in different locations of the university are carried out through the use of a Geiger-Mueller tube . In a next step , the evaluation of distributions obtained by using non- parametric statistics (Chi- square and Kolmogorov Smirnoff) will be taken . For analyzes involving correlations we intend to use the ANOVA (Analysis of Variance) statistical tool . Measured in six different places within the Campinas , with the use of Geiger- Muller its count mode and a time window of 20 seconds was performed . Through statistical tools chi- square and Kolmogorov Smirnoff tests, using the EXCEL program , it was observed that the distributions actually refer to a Poisson distribution. Finally, the next step is to perform analyzes involving correlations using the statistical tool ANOVA

Poisson processes on groups and Feynman path integrals

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.

1979-09-01

An expression is given for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems

Monitoring Poisson time series using multi-process models

DEFF Research Database (Denmark)

Engebjerg, Malene Dahl Skov; Lundbye-Christensen, Søren; Kjær, Birgitte B.

aspects of health resource management may also be addressed. In this paper we center on the detection of outbreaks of infectious diseases. This is achieved by a multi-process Poisson state space model taking autocorrelation and overdispersion into account, which has been applied to a data set concerning...

Poisson-generalized gamma empirical Bayes model for disease ...

African Journals Online (AJOL)

In spatial disease mapping, the use of Bayesian models of estimation technique is becoming popular for smoothing relative risks estimates for disease mapping. The most common Bayesian conjugate model for disease mapping is the Poisson-Gamma Model (PG). To explore further the activity of smoothing of relative risk ...

Nonhomogeneous fractional Poisson processes

Energy Technology Data Exchange (ETDEWEB)

Wang Xiaotian [School of Management, Tianjin University, Tianjin 300072 (China)]. E-mail: swa001@126.com; Zhang Shiying [School of Management, Tianjin University, Tianjin 300072 (China); Fan Shen [Computer and Information School, Zhejiang Wanli University, Ningbo 315100 (China)

2007-01-15

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W{sub H}{sup (j)}(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W{sub H}{sup (j)}(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function {lambda}(t) strongly influences the existence of the highest finite moment of W{sub H}{sup (j)}(t) and the behaviour of the tail probability of W{sub H}{sup (j)}(t)

Casimir meets Poisson: improved quark/gluon discrimination with counting observables

Science.gov (United States)

Frye, Christopher; Larkoski, Andrew J.; Thaler, Jesse; Zhou, Kevin

2017-09-01

Charged track multiplicity is among the most powerful observables for discriminating quark- from gluon-initiated jets. Despite its utility, it is not infrared and collinear (IRC) safe, so perturbative calculations are limited to studying the energy evolution of multiplicity moments. While IRC-safe observables, like jet mass, are perturbatively calculable, their distributions often exhibit Casimir scaling, such that their quark/gluon discrimination power is limited by the ratio of quark to gluon color factors. In this paper, we introduce new IRC-safe counting observables whose discrimination performance exceeds that of jet mass and approaches that of track multiplicity. The key observation is that track multiplicity is approximately Poisson distributed, with more suppressed tails than the Sudakov peak structure from jet mass. By using an iterated version of the soft drop jet grooming algorithm, we can define a "soft drop multiplicity" which is Poisson distributed at leading-logarithmic accuracy. In addition, we calculate the next-to-leading-logarithmic corrections to this Poisson structure. If we allow the soft drop groomer to proceed to the end of the jet branching history, we can define a collinear-unsafe (but still infrared-safe) counting observable. Exploiting the universality of the collinear limit, we define generalized fragmentation functions to study the perturbative energy evolution of collinear-unsafe multiplicity.

On Poisson's ratio for metal matrix composite laminates. [aluminum boron composites

Science.gov (United States)

Herakovich, C. T.; Shuart, M. J.

1978-01-01

The definition of Poisson's ratio for nonlinear behavior of metal matrix composite laminates is discussed and experimental results for tensile and compressive loading of five different boron-aluminum laminates are presented. It is shown that there may be considerable difference in the value of Poisson's ratio as defined by a total strain or an incremental strain definition. It is argued that the incremental definition is more appropriate for nonlinear material behavior. Results from a (0) laminate indicate that the incremental definition provides a precursor to failure which is not evident if the total strain definition is used.

Measurement of Poisson's ratio of nonmetallic materials by laser holographic interferometry

Science.gov (United States)

Zhu, Jian T.

1991-12-01

By means of the off-axis collimated plane wave coherent light arrangement and a loading device by pure bending, Poisson's ratio values of CFRP (carbon fiber-reinforced plactics plates, lay-up 0 degree(s), 90 degree(s)), GFRP (glass fiber-reinforced plactics plates, radial direction) and PMMA (polymethyl methacrylate, x, y direction) have been measured. In virtue of this study, the ministry standard for the Ministry of Aeronautical Industry (Testing method for the measurement of Poisson's ratio of non-metallic by laser holographic interferometry) has been published. The measurement process is fast and simple. The measuring results are reliable and accurate.

The Rasch Poisson counts model for incomplete data : An application of the EM algorithm

NARCIS (Netherlands)

Jansen, G.G.H.

Rasch's Poisson counts model is a latent trait model for the situation in which K tests are administered to N examinees and the test score is a count [e.g., the repeated occurrence of some event, such as the number of items completed or the number of items answered (in)correctly]. The Rasch Poisson

Poisson processes on groups and Feynamn path integrals

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Aix-Marseille-2 Univ., 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.

1980-01-01

We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems. (orig.)

Population activity statistics dissect subthreshold and spiking variability in V1.

Science.gov (United States)

Bányai, Mihály; Koman, Zsombor; Orbán, Gergő

2017-07-01

Response variability, as measured by fluctuating responses upon repeated performance of trials, is a major component of neural responses, and its characterization is key to interpret high dimensional population recordings. Response variability and covariability display predictable changes upon changes in stimulus and cognitive or behavioral state, providing an opportunity to test the predictive power of models of neural variability. Still, there is little agreement on which model to use as a building block for population-level analyses, and models of variability are often treated as a subject of choice. We investigate two competing models, the doubly stochastic Poisson (DSP) model assuming stochasticity at spike generation, and the rectified Gaussian (RG) model tracing variability back to membrane potential variance, to analyze stimulus-dependent modulation of both single-neuron and pairwise response statistics. Using a pair of model neurons, we demonstrate that the two models predict similar single-cell statistics. However, DSP and RG models have contradicting predictions on the joint statistics of spiking responses. To test the models against data, we build a population model to simulate stimulus change-related modulations in pairwise response statistics. We use single-unit data from the primary visual cortex (V1) of monkeys to show that while model predictions for variance are qualitatively similar to experimental data, only the RG model's predictions are compatible with joint statistics. These results suggest that models using Poisson-like variability might fail to capture important properties of response statistics. We argue that membrane potential-level modeling of stochasticity provides an efficient strategy to model correlations. NEW & NOTEWORTHY Neural variability and covariability are puzzling aspects of cortical computations. For efficient decoding and prediction, models of information encoding in neural populations hinge on an appropriate model of

Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems

International Nuclear Information System (INIS)

Hernandez-Bermejo, Benito

2011-01-01

A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: → A new family of Poisson structures is globally characterized and analyzed. → Such family is globally defined for arbitrary values of the dimension and the rank. → Global construction of Casimir invariants and Darboux canonical form is provided. → Very diverse and previously known solutions of physical interest are generalized.

Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems

Energy Technology Data Exchange (ETDEWEB)

Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)

2011-05-09

A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: A new family of Poisson structures is globally characterized and analyzed. Such family is globally defined for arbitrary values of the dimension and the rank. Global construction of Casimir invariants and Darboux canonical form is provided. Very diverse and previously known solutions of physical interest are generalized.

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

Science.gov (United States)

Blossey, R.; Maggs, A. C.; Podgornik, R.

2017-06-01

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

A spatial scan statistic for survival data based on Weibull distribution.

Science.gov (United States)

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

The spatial scan statistic has been developed as a geographical cluster detection analysis tool for different types of data sets such as Bernoulli, Poisson, ordinal, normal and exponential. We propose a scan statistic for survival data based on Weibull distribution. It may also be used for other survival distributions, such as exponential, gamma, and log normal. The proposed method is applied on the survival data of tuberculosis patients for the years 2004-2005 in Nainital district of Uttarakhand, India. Simulation studies reveal that the proposed method performs well for different survival distribution functions. Copyright © 2013 John Wiley & Sons, Ltd.