A multiscale filter for noise reduction of low-dose cone beam projections.

PubMed

Yao, Weiguang; Farr, Jonathan B

2015-08-21

The Poisson or compound Poisson process governs the randomness of photon fluence in cone beam computed tomography (CBCT) imaging systems. The probability density function depends on the mean (noiseless) of the fluence at a certain detector. This dependence indicates the natural requirement of multiscale filters to smooth noise while preserving structures of the imaged object on the low-dose cone beam projection. In this work, we used a Gaussian filter, exp(-x2/2σ(2)(f)) as the multiscale filter to de-noise the low-dose cone beam projections. We analytically obtained the expression of σ(f), which represents the scale of the filter, by minimizing local noise-to-signal ratio. We analytically derived the variance of residual noise from the Poisson or compound Poisson processes after Gaussian filtering. From the derived analytical form of the variance of residual noise, optimal σ(2)(f)) is proved to be proportional to the noiseless fluence and modulated by local structure strength expressed as the linear fitting error of the structure. A strategy was used to obtain the reliable linear fitting error: smoothing the projection along the longitudinal direction to calculate the linear fitting error along the lateral direction and vice versa. The performance of our multiscale filter was examined on low-dose cone beam projections of a Catphan phantom and a head-and-neck patient. After performing the filter on the Catphan phantom projections scanned with pulse time 4 ms, the number of visible line pairs was similar to that scanned with 16 ms, and the contrast-to-noise ratio of the inserts was higher than that scanned with 16 ms about 64% in average. For the simulated head-and-neck patient projections with pulse time 4 ms, the visibility of soft tissue structures in the patient was comparable to that scanned with 20 ms. The image processing took less than 0.5 s per projection with 1024   ×   768 pixels.

A bayesian analysis for identifying DNA copy number variations using a compound poisson process.

PubMed

Chen, Jie; Yiğiter, Ayten; Wang, Yu-Ping; Deng, Hong-Wen

2010-01-01

To study chromosomal aberrations that may lead to cancer formation or genetic diseases, the array-based Comparative Genomic Hybridization (aCGH) technique is often used for detecting DNA copy number variants (CNVs). Various methods have been developed for gaining CNVs information based on aCGH data. However, most of these methods make use of the log-intensity ratios in aCGH data without taking advantage of other information such as the DNA probe (e.g., biomarker) positions/distances contained in the data. Motivated by the specific features of aCGH data, we developed a novel method that takes into account the estimation of a change point or locus of the CNV in aCGH data with its associated biomarker position on the chromosome using a compound Poisson process. We used a Bayesian approach to derive the posterior probability for the estimation of the CNV locus. To detect loci of multiple CNVs in the data, a sliding window process combined with our derived Bayesian posterior probability was proposed. To evaluate the performance of the method in the estimation of the CNV locus, we first performed simulation studies. Finally, we applied our approach to real data from aCGH experiments, demonstrating its applicability.

Properties of the Bivariate Delayed Poisson Process

DTIC Science & Technology

1974-07-01

and Lewis (1972) in their Berkeley Symposium paper and here their analysis of the bivariate Poisson processes (without Poisson noise) is carried... Poisson processes . They cannot, however, be independent Poisson processes because their events are associated in pairs by the displace- ment centres...process because its marginal processes for events of each type are themselves (univariate) Poisson processes . Cox and Lewis (1972) assumed a

Computational prediction of new auxetic materials.

PubMed

Dagdelen, John; Montoya, Joseph; de Jong, Maarten; Persson, Kristin

2017-08-22

Auxetics comprise a rare family of materials that manifest negative Poisson's ratio, which causes an expansion instead of contraction under tension. Most known homogeneously auxetic materials are porous foams or artificial macrostructures and there are few examples of inorganic materials that exhibit this behavior as polycrystalline solids. It is now possible to accelerate the discovery of materials with target properties, such as auxetics, using high-throughput computations, open databases, and efficient search algorithms. Candidates exhibiting features correlating with auxetic behavior were chosen from the set of more than 67 000 materials in the Materials Project database. Poisson's ratios were derived from the calculated elastic tensor of each material in this reduced set of compounds. We report that this strategy results in the prediction of three previously unidentified homogeneously auxetic materials as well as a number of compounds with a near-zero homogeneous Poisson's ratio, which are here denoted "anepirretic materials".There are very few inorganic materials with auxetic homogenous Poisson's ratio in polycrystalline form. Here authors develop an approach to screening materials databases for target properties such as negative Poisson's ratio by using stability and structural motifs to predict new instances of homogenous auxetic behavior as well as a number of materials with near-zero Poisson's ratio.

On the fractal characterization of Paretian Poisson processes

NASA Astrophysics Data System (ADS)

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.

Spatial event cluster detection using an approximate normal distribution.

PubMed

Torabi, Mahmoud; Rosychuk, Rhonda J

2008-12-12

In geographic surveillance of disease, areas with large numbers of disease cases are to be identified so that investigations of the causes of high disease rates can be pursued. Areas with high rates are called disease clusters and statistical cluster detection tests are used to identify geographic areas with higher disease rates than expected by chance alone. Typically cluster detection tests are applied to incident or prevalent cases of disease, but surveillance of disease-related events, where an individual may have multiple events, may also be of interest. Previously, a compound Poisson approach that detects clusters of events by testing individual areas that may be combined with their neighbours has been proposed. However, the relevant probabilities from the compound Poisson distribution are obtained from a recursion relation that can be cumbersome if the number of events are large or analyses by strata are performed. We propose a simpler approach that uses an approximate normal distribution. This method is very easy to implement and is applicable to situations where the population sizes are large and the population distribution by important strata may differ by area. We demonstrate the approach on pediatric self-inflicted injury presentations to emergency departments and compare the results for probabilities based on the recursion and the normal approach. We also implement a Monte Carlo simulation to study the performance of the proposed approach. In a self-inflicted injury data example, the normal approach identifies twelve out of thirteen of the same clusters as the compound Poisson approach, noting that the compound Poisson method detects twelve significant clusters in total. Through simulation studies, the normal approach well approximates the compound Poisson approach for a variety of different population sizes and case and event thresholds. A drawback of the compound Poisson approach is that the relevant probabilities must be determined through a recursion relation and such calculations can be computationally intensive if the cluster size is relatively large or if analyses are conducted with strata variables. On the other hand, the normal approach is very flexible, easily implemented, and hence, more appealing for users. Moreover, the concepts may be more easily conveyed to non-statisticians interested in understanding the methodology associated with cluster detection test results.

A multiscale filter for noise reduction of low-dose cone beam projections

NASA Astrophysics Data System (ADS)

Yao, Weiguang; Farr, Jonathan B.

2015-08-01

The Poisson or compound Poisson process governs the randomness of photon fluence in cone beam computed tomography (CBCT) imaging systems. The probability density function depends on the mean (noiseless) of the fluence at a certain detector. This dependence indicates the natural requirement of multiscale filters to smooth noise while preserving structures of the imaged object on the low-dose cone beam projection. In this work, we used a Gaussian filter, \\text{exp}≤ft(-{{x}2}/2σ f2\\right) as the multiscale filter to de-noise the low-dose cone beam projections. We analytically obtained the expression of {σf} , which represents the scale of the filter, by minimizing local noise-to-signal ratio. We analytically derived the variance of residual noise from the Poisson or compound Poisson processes after Gaussian filtering. From the derived analytical form of the variance of residual noise, optimal σ f2 is proved to be proportional to the noiseless fluence and modulated by local structure strength expressed as the linear fitting error of the structure. A strategy was used to obtain the reliable linear fitting error: smoothing the projection along the longitudinal direction to calculate the linear fitting error along the lateral direction and vice versa. The performance of our multiscale filter was examined on low-dose cone beam projections of a Catphan phantom and a head-and-neck patient. After performing the filter on the Catphan phantom projections scanned with pulse time 4 ms, the number of visible line pairs was similar to that scanned with 16 ms, and the contrast-to-noise ratio of the inserts was higher than that scanned with 16 ms about 64% in average. For the simulated head-and-neck patient projections with pulse time 4 ms, the visibility of soft tissue structures in the patient was comparable to that scanned with 20 ms. The image processing took less than 0.5 s per projection with 1024   ×   768 pixels.

Characterization of Nonhomogeneous Poisson Processes Via Moment Conditions.

DTIC Science & Technology

1986-08-01

Poisson processes play an important role in many fields. The Poisson process is one of the simplest counting processes and is a building block for...place of independent increments. This provides a somewhat different viewpoint for examining Poisson processes . In addition, new characterizations for

The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Shan; Liu, Zaiming

2010-03-01

In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail.

Fractional Poisson Fields and Martingales

NASA Astrophysics Data System (ADS)

Aletti, Giacomo; Leonenko, Nikolai; Merzbach, Ely

2018-02-01

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-Fractional Poisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson field on the plane.

Adiabatic reduction of a model of stochastic gene expression with jump Markov process.

PubMed

Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C

2014-04-01

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.

A Martingale Characterization of Mixed Poisson Processes.

DTIC Science & Technology

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

Stationary and non-stationary occurrences of miniature end plate potentials are well described as stationary and non-stationary Poisson processes in the mollusc Navanax inermis.

PubMed

Cappell, M S; Spray, D C; Bennett, M V

1988-06-28

Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.

[Statistical (Poisson) motor unit number estimation. Methodological aspects and normal results in the extensor digitorum brevis muscle of healthy subjects].

PubMed

Murga Oporto, L; Menéndez-de León, C; Bauzano Poley, E; Núñez-Castaín, M J

Among the differents techniques for motor unit number estimation (MUNE) there is the statistical one (Poisson), in which the activation of motor units is carried out by electrical stimulation and the estimation performed by means of a statistical analysis based on the Poisson s distribution. The study was undertaken in order to realize an approximation to the MUNE Poisson technique showing a coprehensible view of its methodology and also to obtain normal results in the extensor digitorum brevis muscle (EDB) from a healthy population. One hundred fourteen normal volunteers with age ranging from 10 to 88 years were studied using the MUNE software contained in a Viking IV system. The normal subjects were divided into two age groups (10 59 and 60 88 years). The EDB MUNE from all them was 184 49. Both, the MUNE and the amplitude of the compound muscle action potential (CMAP) were significantly lower in the older age group (p< 0.0001), showing the MUNE a better correlation with age than CMAP amplitude ( 0.5002 and 0.4142, respectively p< 0.0001). Statistical MUNE method is an important way for the assessment to the phisiology of the motor unit. The value of MUNE correlates better with the neuromuscular aging process than CMAP amplitude does.

Probabilistic Estimation of Rare Random Collisions in 3 Space

DTIC Science & Technology

2009-03-01

extended Poisson process as a feature of probability theory. With the bulk of research in extended Poisson processes going into parame- ter estimation, the...application of extended Poisson processes to spatial processes is largely untouched. Faddy performed a short study of spatial data, but overtly...the theory of extended Poisson processes . To date, the processes are limited in that the rates only depend on the number of arrivals at some time

Generation of Non-Homogeneous Poisson Processes by Thinning: Programming Considerations and Comparision with Competing Algorithms.

DTIC Science & Technology

1978-12-01

Poisson processes . The method is valid for Poisson processes with any given intensity function. The basic thinning algorithm is modified to exploit several refinements which reduce computer execution time by approximately one-third. The basic and modified thinning programs are compared with the Poisson decomposition and gap-statistics algorithm, which is easily implemented for Poisson processes with intensity functions of the form exp(a sub 0 + a sub 1t + a sub 2 t-squared. The thinning programs are competitive in both execution

Fractional properties of geophysical field variability on the example of hydrochemical parameters

NASA Astrophysics Data System (ADS)

Shevtsov, Boris; Shevtsova, Olga

2017-10-01

Using the properties of compound Poisson process and its fractional generalizations, statistical models of geophysical fields variability are considered on an example of hydrochemical parameters system. These models are universal to describe objects of different nature and allow us to explain various pulsing regime. Manifestations of non-conservatism in hydrochemical parameters system and the advantages of the system approach in the description of geophysical fields variability are discussed.

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

DTIC Science & Technology

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

Nonlinear Poisson Equation for Heterogeneous Media

PubMed Central

Hu, Langhua; Wei, Guo-Wei

2012-01-01

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. PMID:22947937

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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.

Graphic Simulations of the Poisson Process.

DTIC Science & Technology

1982-10-01

RANDOM NUMBERS AND TRANSFORMATIONS..o......... 11 Go THE RANDOM NUMBERGENERATOR....... .oo..... 15 III. POISSON PROCESSES USER GUIDE....oo.ooo ......... o...again. In the superimposed mode, two Poisson processes are active, each with a different rate parameter, (call them Type I and Type II with respective...occur. The value ’p’ is generated by the following equation where ’Li’ and ’L2’ are the rates of the two Poisson processes ; p = Li / (Li + L2) The value

Nonlinear Poisson equation for heterogeneous media.

PubMed

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.

Simulation Methods for Poisson Processes in Nonstationary Systems.

DTIC Science & Technology

1978-08-01

for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the...and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is

Identification of a Class of Filtered Poisson Processes.

DTIC Science & Technology

1981-01-01

LD-A135 371 IDENTIFICATION OF A CLASS OF FILERED POISSON PROCESSES I AU) NORTH CAROLINA UNIV AT CHAPEL HIL DEPT 0F STATISTICS D DE RRUC ET AL 1981...STNO&IO$ !tt ~ 4.s " . , ".7" -L N ~ TITLE :IDENTIFICATION OF A CLASS OF FILTERED POISSON PROCESSES Authors : DE BRUCQ Denis - GUALTIEROTTI Antonio...filtered Poisson processes is intro- duced : the amplitude has a law which is spherically invariant and the filter is real, linear and causal. It is shown

Distribution of apparent activation energy counterparts during thermo - And thermo-oxidative degradation of Aronia melanocarpa (black chokeberry).

PubMed

Janković, Bojan; Marinović-Cincović, Milena; Janković, Marija

2017-09-01

Kinetics of degradation for Aronia melanocarpa fresh fruits in argon and air atmospheres were investigated. The investigation was based on probability distributions of apparent activation energy of counterparts (ε a ). Isoconversional analysis results indicated that the degradation process in an inert atmosphere was governed by decomposition reactions of esterified compounds. Also, based on same kinetics approach, it was assumed that in an air atmosphere, the primary compound in degradation pathways could be anthocyanins, which undergo rapid chemical reactions. A new model of reactivity demonstrated that, under inert atmospheres, expectation values for ε a occured at levels of statistical probability. These values corresponded to decomposition processes in which polyphenolic compounds might be involved. ε a values obeyed laws of binomial distribution. It was established that, for thermo-oxidative degradation, Poisson distribution represented a very successful approximation for ε a values where there was additional mechanistic complexity and the binomial distribution was no longer valid. Copyright © 2017 Elsevier Ltd. All rights reserved.

Normal and compound poisson approximations for pattern occurrences in NGS reads.

PubMed

Zhai, Zhiyuan; Reinert, Gesine; Song, Kai; Waterman, Michael S; Luan, Yihui; Sun, Fengzhu

2012-06-01

Next generation sequencing (NGS) technologies are now widely used in many biological studies. In NGS, sequence reads are randomly sampled from the genome sequence of interest. Most computational approaches for NGS data first map the reads to the genome and then analyze the data based on the mapped reads. Since many organisms have unknown genome sequences and many reads cannot be uniquely mapped to the genomes even if the genome sequences are known, alternative analytical methods are needed for the study of NGS data. Here we suggest using word patterns to analyze NGS data. Word pattern counting (the study of the probabilistic distribution of the number of occurrences of word patterns in one or multiple long sequences) has played an important role in molecular sequence analysis. However, no studies are available on the distribution of the number of occurrences of word patterns in NGS reads. In this article, we build probabilistic models for the background sequence and the sampling process of the sequence reads from the genome. Based on the models, we provide normal and compound Poisson approximations for the number of occurrences of word patterns from the sequence reads, with bounds on the approximation error. The main challenge is to consider the randomness in generating the long background sequence, as well as in the sampling of the reads using NGS. We show the accuracy of these approximations under a variety of conditions for different patterns with various characteristics. Under realistic assumptions, the compound Poisson approximation seems to outperform the normal approximation in most situations. These approximate distributions can be used to evaluate the statistical significance of the occurrence of patterns from NGS data. The theory and the computational algorithm for calculating the approximate distributions are then used to analyze ChIP-Seq data using transcription factor GABP. Software is available online (www-rcf.usc.edu/∼fsun/Programs/NGS_motif_power/NGS_motif_power.html). In addition, Supplementary Material can be found online (www.liebertonline.com/cmb).

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

DTIC Science & Technology

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

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

PubMed

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.

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

PubMed Central

Poplová, Michaela; Sovka, Pavel

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. PMID:29216207

Information transmission using non-poisson regular firing.

PubMed

Koyama, Shinsuke; Omi, Takahiro; Kass, Robert E; Shinomoto, Shigeru

2013-04-01

In many cortical areas, neural spike trains do not follow a Poisson process. In this study, we investigate a possible benefit of non-Poisson spiking for information transmission by studying the minimal rate fluctuation that can be detected by a Bayesian estimator. The idea is that an inhomogeneous Poisson process may make it difficult for downstream decoders to resolve subtle changes in rate fluctuation, but by using a more regular non-Poisson process, the nervous system can make rate fluctuations easier to detect. We evaluate the degree to which regular firing reduces the rate fluctuation detection threshold. We find that the threshold for detection is reduced in proportion to the coefficient of variation of interspike intervals.

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

DTIC Science & Technology

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)

From Loss of Memory to Poisson.

ERIC Educational Resources Information Center

Johnson, Bruce R.

1983-01-01

A way of presenting the Poisson process and deriving the Poisson distribution for upper-division courses in probability or mathematical statistics is presented. The main feature of the approach lies in the formulation of Poisson postulates with immediate intuitive appeal. (MNS)

Modeling of First-Passage Processes in Financial Markets

NASA Astrophysics Data System (ADS)

Inoue, Jun-Ichi; Hino, Hikaru; Sazuka, Naoya; Scalas, Enrico

2010-03-01

In this talk, we attempt to make a microscopic modeling the first-passage process (or the first-exit process) of the BUND future by minority game with market history. We find that the first-passage process of the minority game with appropriate history length generates the same properties as the BTP future (the middle and long term Italian Government bonds with fixed interest rates), namely, both first-passage time distributions have a crossover at some specific time scale as is the case for the Mittag-Leffler function. We also provide a macroscopic (or a phenomenological) modeling of the first-passage process of the BTP future and show analytically that the first-passage time distribution of a simplest mixture of the normal compound Poisson processes does not have such a crossover.

Super-stable Poissonian structures

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

In this paper we characterize classes of Poisson processes whose statistical structures are super-stable. We consider a flow generated by a one-dimensional ordinary differential equation, and an ensemble of particles ‘surfing’ the flow. The particles start from random initial positions, and are propagated along the flow by stochastic ‘wave processes’ with general statistics and general cross correlations. Setting the initial positions to be Poisson processes, we characterize the classes of Poisson processes that render the particles’ positions—at all times, and invariantly with respect to the wave processes—statistically identical to their initial positions. These Poisson processes are termed ‘super-stable’ and facilitate the generalization of the notion of stationary distributions far beyond the realm of Markov dynamics.

The Use of Crow-AMSAA Plots to Assess Mishap Trends

NASA Technical Reports Server (NTRS)

Dawson, Jeffrey W.

2011-01-01

Crow-AMSAA (CA) plots are used to model reliability growth. Use of CA plots has expanded into other areas, such as tracking events of interest to management, maintenance problems, and safety mishaps. Safety mishaps can often be successfully modeled using a Poisson probability distribution. CA plots show a Poisson process in log-log space. If the safety mishaps are a stable homogenous Poisson process, a linear fit to the points in a CA plot will have a slope of one. Slopes of greater than one indicate a nonhomogenous Poisson process, with increasing occurrence. Slopes of less than one indicate a nonhomogenous Poisson process, with decreasing occurrence. Changes in slope, known as "cusps," indicate a change in process, which could be an improvement or a degradation. After presenting the CA conceptual framework, examples are given of trending slips, trips and falls, and ergonomic incidents at NASA (from Agency-level data). Crow-AMSAA plotting is a robust tool for trending safety mishaps that can provide insight into safety performance over time.

Effect of non-Poisson samples on turbulence spectra from laser velocimetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sree, D.; Kjelgaard, S.O.; Sellers, W.L. III

1994-12-01

Spectral estimations from LV data are typically based on the assumption of a Poisson sampling process. It is demonstrated here that the sampling distribution must be considered before spectral estimates are used to infer turbulence scales. A non-Poisson sampling process can occur if there is nonhomogeneous distribution of particles in the flow. Based on the study of a simulated first-order spectrum, it has been shown that a non-Poisson sampling process causes the estimated spectrum to deviate from the true spectrum. Also, in this case the prefiltering techniques do not improve the spectral estimates at higher frequencies. 4 refs.

Evolutionary inference via the Poisson Indel Process.

PubMed

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.

Evolutionary inference via the Poisson Indel Process

PubMed Central

Bouchard-Côté, Alexandre; Jordan, Michael I.

2013-01-01

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. PMID:23275296

Monitoring Poisson observations using combined applications of Shewhart and EWMA charts

NASA Astrophysics Data System (ADS)

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.

Calculation of the Poisson cumulative distribution function

NASA Technical Reports Server (NTRS)

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

1990-01-01

A method for calculating the Poisson cdf (cumulative distribution function) is presented. The method avoids computer underflow and overflow during the process. The computer program uses this technique to calculate the Poisson cdf for arbitrary inputs. An algorithm that determines the Poisson parameter required to yield a specified value of the cdf is presented.

Poisson process stimulation of an excitable membrane cable model.

PubMed Central

Goldfinger, M D

1986-01-01

The convergence of multiple inputs within a single-neuronal substrate is a common design feature of both peripheral and central nervous systems. Typically, the result of such convergence impinges upon an intracellularly contiguous axon, where it is encoded into a train of action potentials. The simplest representation of the result of convergence of multiple inputs is a Poisson process; a general representation of axonal excitability is the Hodgkin-Huxley/cable theory formalism. The present work addressed multiple input convergence upon an axon by applying Poisson process stimulation to the Hodgkin-Huxley axonal cable. The results showed that both absolute and relative refractory periods yielded in the axonal output a random but non-Poisson process. While smaller amplitude stimuli elicited a type of short-interval conditioning, larger amplitude stimuli elicited impulse trains approaching Poisson criteria except for the effects of refractoriness. These results were obtained for stimulus trains consisting of pulses of constant amplitude and constant or variable durations. By contrast, with or without stimulus pulse shape variability, the post-impulse conditional probability for impulse initiation in the steady-state was a Poisson-like process. For stimulus variability consisting of randomly smaller amplitudes or randomly longer durations, mean impulse frequency was attenuated or potentiated, respectively. Limitations and implications of these computations are discussed. PMID:3730505

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

PubMed

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.

Universal Poisson Statistics of mRNAs with Complex Decay Pathways.

PubMed

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.

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

PubMed

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.

Poisson point process modeling for polyphonic music transcription.

PubMed

Peeling, Paul; Li, Chung-fai; Godsill, Simon

2007-04-01

Peaks detected in the frequency domain spectrum of a musical chord are modeled as realizations of a nonhomogeneous Poisson point process. When several notes are superimposed to make a chord, the processes for individual notes combine to give another Poisson process, whose likelihood is easily computable. This avoids a data association step linking individual harmonics explicitly with detected peaks in the spectrum. The likelihood function is ideal for Bayesian inference about the unknown note frequencies in a chord. Here, maximum likelihood estimation of fundamental frequencies shows very promising performance on real polyphonic piano music recordings.

Limiting Distributions of Functionals of Markov Chains.

DTIC Science & Technology

1984-08-01

limiting distributions; periodic * nonhomoger.,!ous Poisson processes . 19 ANS? MACY IConuui oe nonoe’ee if necorglooy and edern thty by block numbers...homogeneous Poisson processes is of interest in itself. The problem considered in this paper is of interest in the theory of partially observable...where we obtain the limiting distribution of the interevent times. Key Words: Markov Chains, Limiting Distributions, Periodic Nonhomogeneous Poisson

Wigner surmises and the two-dimensional homogeneous Poisson point process.

PubMed

Sakhr, Jamal; Nieminen, John M

2006-04-01

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.

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

PubMed Central

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

A spatial scan statistic for compound Poisson data.

PubMed

Rosychuk, Rhonda J; Chang, Hsing-Ming

2013-12-20

The topic of spatial cluster detection gained attention in statistics during the late 1980s and early 1990s. Effort has been devoted to the development of methods for detecting spatial clustering of cases and events in the biological sciences, astronomy and epidemiology. More recently, research has examined detecting clusters of correlated count data associated with health conditions of individuals. Such a method allows researchers to examine spatial relationships of disease-related events rather than just incident or prevalent cases. We introduce a spatial scan test that identifies clusters of events in a study region. Because an individual case may have multiple (repeated) events, we base the test on a compound Poisson model. We illustrate our method for cluster detection on emergency department visits, where individuals may make multiple disease-related visits. Copyright © 2013 John Wiley & Sons, Ltd.

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

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.

Noisy cooperative intermittent processes: From blinking quantum dots to human consciousness

NASA Astrophysics Data System (ADS)

Allegrini, Paolo; Paradisi, Paolo; Menicucci, Danilo; Bedini, Remo; Gemignani, Angelo; Fronzoni, Leone

2011-07-01

We study the superposition of a non-Poisson renewal process with the presence of a superimposed Poisson noise. The non-Poisson renewals mark the passage between meta-stable states in system with self-organization. We propose methods to measure the amount of information due to the two independent processes independently, and we see that a superficial study based on the survival probabilities yield stretched-exponential relaxations. Our method is in fact able to unravel the inverse-power law relaxation of the isolated non-Poisson processes, even when noise is present. We provide examples of this behavior in system of diverse nature, from blinking nano-crystals to weak turbulence. Finally we focus our discussion on events extracted from human electroencephalograms, and we discuss their connection with emerging properties of integrated neural dynamics, i.e. consciousness.

Markov modulated Poisson process models incorporating covariates for rainfall intensity.

PubMed

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 Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data.

PubMed

Rodrigues, Josemar; Cancho, Vicente G; de Castro, Mário; Balakrishnan, N

2012-12-01

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis--latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

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

PubMed

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.

? filtering for stochastic systems driven by Poisson processes

NASA Astrophysics Data System (ADS)

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.

Intertime jump statistics of state-dependent Poisson processes.

PubMed

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.

Dependent Neyman type A processes based on common shock Poisson approach

NASA Astrophysics Data System (ADS)

Kadilar, Gamze Özel; Kadilar, Cem

2016-04-01

The Neyman type A process is used for describing clustered data since the Poisson process is insufficient for clustering of events. In a multivariate setting, there may be dependencies between multivarite Neyman type A processes. In this study, dependent form of the Neyman type A process is considered under common shock approach. Then, the joint probability function are derived for the dependent Neyman type A Poisson processes. Then, an application based on forest fires in Turkey are given. The results show that the joint probability function of the dependent Neyman type A processes, which is obtained in this study, can be a good tool for the probabilistic fitness for the total number of burned trees in Turkey.

Retention for Stoploss reinsurance to minimize VaR in compound Poisson-Lognormal distribution

NASA Astrophysics Data System (ADS)

Soleh, Achmad Zanbar; Noviyanti, Lienda; Nurrahmawati, Irma

2015-12-01

Automobile insurance is one of the emerging general insurance's product in Indonesia. Fluctuation in total premium revenues and total claim expenses leads to a risk that insurance company can not be able to pay consumer's claims, thus reinsurance is needeed. Reinsurance is a risk transfer mechanism from the insurance company to another company called reinsurer, one of the reinsurance type is Stoploss. Because reinsurer charges premium to the insurance company, it is important to determine the retention or the total claims to be retain solely by the insurance company. Thus, retention is determined using Value at Risk (VaR) which minimize the total risk of the insurance company in the presence of Stoploss reinsurance. Retention depends only on the distribution of total claims and reinsurance loading factor. We use the compound Poisson distribution and the Log-Normal Distribution to illustrate the retention value in a collective risk model.

Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment

PubMed Central

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso

2016-01-01

ABSTRACT Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. IMPORTANCE We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation. PMID:27940547

Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2017-02-15

Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation. Copyright © 2017 Koyama et al.

Radio pulsar glitches as a state-dependent Poisson process

NASA Astrophysics Data System (ADS)

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.

Functional response and capture timing in an individual-based model: predation by northern squawfish (Ptychocheilus oregonensis) on juvenile salmonids in the Columbia River

USGS Publications Warehouse

Petersen, James H.; DeAngelis, Donald L.

1992-01-01

The behavior of individual northern squawfish (Ptychocheilus oregonensis) preying on juvenile salmonids was modeled to address questions about capture rate and the timing of prey captures (random versus contagious). Prey density, predator weight, prey weight, temperature, and diel feeding pattern were first incorporated into predation equations analogous to Holling Type 2 and Type 3 functional response models. Type 2 and Type 3 equations fit field data from the Columbia River equally well, and both models predicted predation rates on five of seven independent dates. Selecting a functional response type may be complicated by variable predation rates, analytical methods, and assumptions of the model equations. Using the Type 2 functional response, random versus contagious timing of prey capture was tested using two related models. ln the simpler model, salmon captures were assumed to be controlled by a Poisson renewal process; in the second model, several salmon captures were assumed to occur during brief "feeding bouts", modeled with a compound Poisson process. Salmon captures by individual northern squawfish were clustered through time, rather than random, based on comparison of model simulations and field data. The contagious-feeding result suggests that salmonids may be encountered as patches or schools in the river.

Exploring the existence of a stayer population with mover-stayer counting process models: application to joint damage in psoriatic arthritis.

PubMed

Yiu, Sean; Farewell, Vernon T; Tom, Brian D M

2017-08-01

Many psoriatic arthritis patients do not progress to permanent joint damage in any of the 28 hand joints, even under prolonged follow-up. This has led several researchers to fit models that estimate the proportion of stayers (those who do not have the propensity to experience the event of interest) and to characterize the rate of developing damaged joints in the movers (those who have the propensity to experience the event of interest). However, when fitted to the same data, the paper demonstrates that the choice of model for the movers can lead to widely varying conclusions on a stayer population, thus implying that, if interest lies in a stayer population, a single analysis should not generally be adopted. The aim of the paper is to provide greater understanding regarding estimation of a stayer population by comparing the inferences, performance and features of multiple fitted models to real and simulated data sets. The models for the movers are based on Poisson processes with patient level random effects and/or dynamic covariates, which are used to induce within-patient correlation, and observation level random effects are used to account for time varying unobserved heterogeneity. The gamma, inverse Gaussian and compound Poisson distributions are considered for the random effects.

Algorithm Calculates Cumulative Poisson Distribution

NASA Technical Reports Server (NTRS)

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

1992-01-01

Algorithm calculates accurate values of cumulative Poisson distribution under conditions where other algorithms fail because numbers are so small (underflow) or so large (overflow) that computer cannot process them. Factors inserted temporarily to prevent underflow and overflow. Implemented in CUMPOIS computer program described in "Cumulative Poisson Distribution Program" (NPO-17714).

On the validity of the Poisson assumption in sampling nanometer-sized aerosols

DOE Office of Scientific and Technical Information (OSTI.GOV)

Damit, Brian E; Wu, Dr. Chang-Yu; Cheng, Mengdawn

2014-01-01

A Poisson process is traditionally believed to apply to the sampling of aerosols. For a constant aerosol concentration, it is assumed that a Poisson process describes the fluctuation in the measured concentration because aerosols are stochastically distributed in space. Recent studies, however, have shown that sampling of micrometer-sized aerosols has non-Poissonian behavior with positive correlations. The validity of the Poisson assumption for nanometer-sized aerosols has not been examined and thus was tested in this study. Its validity was tested for four particle sizes - 10 nm, 25 nm, 50 nm and 100 nm - by sampling from indoor air withmore » a DMA- CPC setup to obtain a time series of particle counts. Five metrics were calculated from the data: pair-correlation function (PCF), time-averaged PCF, coefficient of variation, probability of measuring a concentration at least 25% greater than average, and posterior distributions from Bayesian inference. To identify departures from Poissonian behavior, these metrics were also calculated for 1,000 computer-generated Poisson time series with the same mean as the experimental data. For nearly all comparisons, the experimental data fell within the range of 80% of the Poisson-simulation values. Essentially, the metrics for the experimental data were indistinguishable from a simulated Poisson process. The greater influence of Brownian motion for nanometer-sized aerosols may explain the Poissonian behavior observed for smaller aerosols. Although the Poisson assumption was found to be valid in this study, it must be carefully applied as the results here do not definitively prove applicability in all sampling situations.« less

Statistical properties of superimposed stationary spike trains.

PubMed

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.

A Novel Method for Preparing Auxetic Foam from Closed-cell Polymer Foam Based on Steam Penetration and Condensation (SPC) Process.

PubMed

Fan, Donglei; Li, Minggang; Qiu, Jian; Xing, Haiping; Jiang, Zhiwei; Tang, Tao

2018-05-31

Auxetic materials are a class of materials possessing negative Poisson's ratio. Here we establish a novel method for preparing auxetic foam from closed-cell polymer foam based on steam penetration and condensation (SPC) process. Using polyethylene (PE) closed-cell foam as an example, the resultant foams treated by SPC process present negative Poisson's ratio during stretching and compression testing. The effect of steam-treated temperature and time on the conversion efficiency of negative Poisson's ratio foam is investigated, and the mechanism of SPC method for forming re-entrant structure is discussed. The results indicate that the presence of enough steam within the cells is a critical factor for the negative Poisson's ratio conversion in the SPC process. The pressure difference caused by steam condensation is the driving force for the conversion from conventional closed-cell foam to the negative Poisson's ratio foam. Furthermore, the applicability of SPC process for fabricating auxetic foam is studied by replacing PE foam by polyvinyl chloride (PVC) foam with closed-cell structure or replacing water steam by ethanol steam. The results verify the universality of SPC process for fabricating auxetic foams from conventional foams with closed-cell structure. In addition, we explored potential application of the obtained auxetic foams by SPC process in the fabrication of shape memory polymer materials.

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

PubMed

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.

The Validity of Poisson Assumptions in a Combined Loglinear/MDS Mapping Model.

ERIC Educational Resources Information Center

Everett, James E.

1993-01-01

Addresses objections to the validity of assuming a Poisson loglinear model as the generating process for citations from one journal into another. Fluctuations in citation rate, serial dependence on citations, impossibility of distinguishing between rate changes and serial dependence, evidence for changes in Poisson rate, and transitivity…

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

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.

Harmonic statistics

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-05-01

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.

Characterization of x-ray framing cameras for the National Ignition Facility using single photon pulse height analysis.

PubMed

Holder, J P; Benedetti, L R; Bradley, D K

2016-11-01

Single hit pulse height analysis is applied to National Ignition Facility x-ray framing cameras to quantify gain and gain variation in a single micro-channel plate-based instrument. This method allows the separation of gain from detectability in these photon-detecting devices. While pulse heights measured by standard-DC calibration methods follow the expected exponential distribution at the limit of a compound-Poisson process, gain-gated pulse heights follow a more complex distribution that may be approximated as a weighted sum of a few exponentials. We can reproduce this behavior with a simple statistical-sampling model.

Negative Binomial Process Count and Mixture Modeling.

PubMed

Zhou, Mingyuan; Carin, Lawrence

2015-02-01

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

NASA Technical Reports Server (NTRS)

Saleh, B. E. A.; Tavolacci, J. T.; Teich, M. C.

1981-01-01

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

Matrix decomposition graphics processing unit solver for Poisson image editing

NASA Astrophysics Data System (ADS)

Lei, Zhao; Wei, Li

2012-10-01

In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.

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

PubMed

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.

Minimum risk wavelet shrinkage operator for Poisson image denoising.

PubMed

Cheng, Wu; Hirakawa, Keigo

2015-05-01

The pixel values of images taken by an image sensor are said to be corrupted by Poisson noise. To date, multiscale Poisson image denoising techniques have processed Haar frame and wavelet coefficients--the modeling of coefficients is enabled by the Skellam distribution analysis. We extend these results by solving for shrinkage operators for Skellam that minimizes the risk functional in the multiscale Poisson image denoising setting. The minimum risk shrinkage operator of this kind effectively produces denoised wavelet coefficients with minimum attainable L2 error.

Estimating the intensity of a cyclic Poisson process in the presence of additive and multiplicative linear trend

NASA Astrophysics Data System (ADS)

Wayan Mangku, I.

2017-10-01

In this paper we survey some results on estimation of the intensity function of a cyclic Poisson process in the presence of additive and multiplicative linear trend. We do not assume any parametric form for the cyclic component of the intensity function, except that it is periodic. Moreover, we consider the case when there is only a single realization of the Poisson process is observed in a bounded interval. The considered estimators are weakly and strongly consistent when the size of the observation interval indefinitely expands. Asymptotic approximations to the bias and variance of those estimators are presented.

Gene regulation and noise reduction by coupling of stochastic processes

NASA Astrophysics Data System (ADS)

Ramos, Alexandre F.; Hornos, José Eduardo M.; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Gene regulation and noise reduction by coupling of stochastic processes

PubMed Central

Hornos, José Eduardo M.; Reinitz, John

2015-01-01

Here we characterize the low noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the the two gene states depends on protein number. This fact has a very important implication: there exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction. PMID:25768447

Gene regulation and noise reduction by coupling of stochastic processes.

PubMed

Ramos, Alexandre F; Hornos, José Eduardo M; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

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

PubMed

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.

The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability

PubMed Central

Reich, Steven

2014-01-01

Neuronal variability plays a central role in neural coding and impacts the dynamics of neuronal networks. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in response to presynaptic action potentials and are recovered stochastically in time. The dynamics of this process of vesicle release and recovery interacts with variability in the arrival times of presynaptic spikes to shape the variability of the postsynaptic response. We use continuous time Markov chain methods to analyze a model of short term synaptic depression with stochastic vesicle dynamics coupled with three different models of presynaptic spiking: one model in which the timing of presynaptic action potentials are modeled as a Poisson process, one in which action potentials occur more regularly than a Poisson process (sub-Poisson) and one in which action potentials occur more irregularly (super-Poisson). We use this analysis to investigate how variability in a presynaptic spike train is transformed by short term depression and stochastic vesicle dynamics to determine the variability of the postsynaptic response. We find that sub-Poisson presynaptic spiking increases the average rate at which vesicles are released, that the number of vesicles released over a time window is more variable for smaller time windows than larger time windows and that fast presynaptic spiking gives rise to Poisson-like variability of the postsynaptic response even when presynaptic spike times are non-Poisson. Our results complement and extend previously reported theoretical results and provide possible explanations for some trends observed in recorded data. PMID:23354693

Renewal processes based on generalized Mittag-Leffler waiting times

NASA Astrophysics Data System (ADS)

Cahoy, Dexter O.; Polito, Federico

2013-03-01

The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized the standard and fractional Poisson processes through the waiting time distribution, and showed their relations to an integral operator with a generalized Mittag-Leffler function in the kernel. The waiting times of the proposed renewal processes have the generalized Mittag-Leffler and stretched-squashed Mittag-Leffler distributions. Note that the generalizations naturally provide greater flexibility in modeling real-life renewal processes. Algorithms to simulate sample paths and to estimate the model parameters are derived. Note also that these procedures are necessary to make these models more usable in practice. State probabilities and other qualitative or quantitative features of the models are also discussed.

Birth and Death Process Modeling Leads to the Poisson Distribution: A Journey Worth Taking

ERIC Educational Resources Information Center

Rash, Agnes M.; Winkel, Brian J.

2009-01-01

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

Poisson Statistics of Combinatorial Library Sampling Predict False Discovery Rates of Screening

PubMed Central

2017-01-01

Microfluidic droplet-based screening of DNA-encoded one-bead-one-compound combinatorial libraries is a miniaturized, potentially widely distributable approach to small molecule discovery. In these screens, a microfluidic circuit distributes library beads into droplets of activity assay reagent, photochemically cleaves the compound from the bead, then incubates and sorts the droplets based on assay result for subsequent DNA sequencing-based hit compound structure elucidation. Pilot experimental studies revealed that Poisson statistics describe nearly all aspects of such screens, prompting the development of simulations to understand system behavior. Monte Carlo screening simulation data showed that increasing mean library sampling (ε), mean droplet occupancy, or library hit rate all increase the false discovery rate (FDR). Compounds identified as hits on k > 1 beads (the replicate k class) were much more likely to be authentic hits than singletons (k = 1), in agreement with previous findings. Here, we explain this observation by deriving an equation for authenticity, which reduces to the product of a library sampling bias term (exponential in k) and a sampling saturation term (exponential in ε) setting a threshold that the k-dependent bias must overcome. The equation thus quantitatively describes why each hit structure’s FDR is based on its k class, and further predicts the feasibility of intentionally populating droplets with multiple library beads, assaying the micromixtures for function, and identifying the active members by statistical deconvolution. PMID:28682059

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

PubMed

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.

A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.

PubMed

Zhao, Lei; Mi, Dong; Sun, Yeqing

2017-05-07

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory.

PubMed

Lord, Dominique; Washington, Simon P; Ivan, John N

2005-01-01

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states-perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of "excess" zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to "excess" zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed-and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros.

Sample size calculations for comparative clinical trials with over-dispersed Poisson process data.

PubMed

Matsui, Shigeyuki

2005-05-15

This paper develops a new formula for sample size calculations for comparative clinical trials with Poisson or over-dispersed Poisson process data. The criteria for sample size calculations is developed on the basis of asymptotic approximations for a two-sample non-parametric test to compare the empirical event rate function between treatment groups. This formula can accommodate time heterogeneity, inter-patient heterogeneity in event rate, and also, time-varying treatment effects. An application of the formula to a trial for chronic granulomatous disease is provided. Copyright 2004 John Wiley & Sons, Ltd.

A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

PubMed

Wan, Wai-Yin; Chan, Jennifer S K

2009-08-01

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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 thismore » 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.« less

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

PubMed Central

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

2014-01-01

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. PMID:22684587

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

PubMed

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.

Poisson Coordinates.

PubMed

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.

Poissonian renormalizations, exponentials, and power laws.

PubMed

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Poisson mixture model for measurements using counting.

PubMed

Miller, Guthrie; Justus, Alan; Vostrotin, Vadim; Dry, Donald; Bertelli, Luiz

2010-03-01

Starting with the basic Poisson statistical model of a counting measurement process, 'extraPoisson' variance or 'overdispersion' are included by assuming that the Poisson parameter representing the mean number of counts itself comes from another distribution. The Poisson parameter is assumed to be given by the quantity of interest in the inference process multiplied by a lognormally distributed normalising coefficient plus an additional lognormal background that might be correlated with the normalising coefficient (shared uncertainty). The example of lognormal environmental background in uranium urine data is discussed. An additional uncorrelated background is also included. The uncorrelated background is estimated from a background count measurement using Bayesian arguments. The rather complex formulas are validated using Monte Carlo. An analytical expression is obtained for the probability distribution of gross counts coming from the uncorrelated background, which allows straightforward calculation of a classical decision level in the form of a gross-count alarm point with a desired false-positive rate. The main purpose of this paper is to derive formulas for exact likelihood calculations in the case of various kinds of backgrounds.

Thermoelectric Materials

NASA Astrophysics Data System (ADS)

Gao, Peng; Berkun, Isil; Schmidt, Robert D.; Luzenski, Matthew F.; Lu, Xu; Bordon Sarac, Patricia; Case, Eldon D.; Hogan, Timothy P.

2014-06-01

Mg2(Si,Sn) compounds are promising candidate low-cost, lightweight, nontoxic thermoelectric materials made from abundant elements and are suited for power generation applications in the intermediate temperature range of 600 K to 800 K. Knowledge on the transport and mechanical properties of Mg2(Si,Sn) compounds is essential to the design of Mg2(Si,Sn)-based thermoelectric devices. In this work, such materials were synthesized using the molten-salt sealing method and were powder processed, followed by pulsed electric sintering densification. A set of Mg2.08Si0.4- x Sn0.6Sb x (0 ≤ x ≤ 0.072) compounds were investigated, and a peak ZT of 1.50 was obtained at 716 K in Mg2.08Si0.364Sn0.6Sb0.036. The high ZT is attributed to a high electrical conductivity in these samples, possibly caused by a magnesium deficiency in the final product. The mechanical response of the material to stresses is a function of the elastic moduli. The temperature-dependent Young's modulus, shear modulus, bulk modulus, Poisson's ratio, acoustic wave speeds, and acoustic Debye temperature of the undoped Mg2(Si,Sn) compounds were measured using resonant ultrasound spectroscopy from 295 K to 603 K. In addition, the hardness and fracture toughness were measured at room temperature.

A Comparative Study of Structural Stability and Mechanical and Optical Properties of Fluorapatite (Ca5(PO4)3F) and Lithium Disilicate (Li2Si2O5) Components Forming Dental Glass-Ceramics: First Principles Study

NASA Astrophysics Data System (ADS)

Biskri, Z. E.; Rached, H.; Bouchear, M.; Rached, D.; Aida, M. S.

2016-10-01

The aim of this paper is a comparative study of structural stability and mechanical and optical properties of fluorapatite (FA) (Ca5(PO4)3F) and lithium disilicate (LD) (Li2Si2O5), using the first principles pseudopotential method based on density functional theory (DFT) within the generalized gradient approximation (GGA). The stability of fluorapatite and lithium disilicate compounds has been evaluated on the basis of their formation enthalpies. The results show that fluorapatite is more energetically stable than lithium disilicate. The independent elastic constants and related mechanical properties, including bulk modulus ( B), shear modulus ( G), Young's modulus ( E) and Poisson's ratio ( ν) as well as the Vickers hardness ( H v), have been calculated for fluorapatite compound and compared with other theoretical and experimental results. The obtained values of the shear modulus, Young's modulus and Vickers hardness are smaller in comparison with those of lithium disilicate compound, implying that lithium disilicate is more rigid than fluorapatite. The brittle and ductile properties were also discussed using B/ G ratio and Poisson's ratio. Optical properties such as refractive index n( ω), extinction coefficient k( ω), absorption coefficient α( ω) and optical reflectivity R( ω) have been determined from the calculations of the complex dielectric function ɛ( ω), and interpreted on the basis of the electronic structures of both compounds. The calculated values of static dielectric constant ɛ 1(0) and static refractive index n(0) show that the Li2Si2O5 compound has larger values compared to those of the Ca5(PO4)3F compound. The results of the extinction coefficient show that Li2Si2O5 compound exhibits a much stronger ultraviolet absorption. According to the absorption and reflectivity spectra, we inferred that both compounds are theoretically the best visible and infrared transparent materials.

Paretian Poisson Processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2008-05-01

Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ` Paretian Poisson processes'. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.

Long-term statistics of extreme tsunami height at Crescent City

NASA Astrophysics Data System (ADS)

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.

Time distributions of solar energetic particle events: Are SEPEs really random?

NASA Astrophysics Data System (ADS)

Jiggens, P. T. A.; Gabriel, S. B.

2009-10-01

Solar energetic particle events (SEPEs) can exhibit flux increases of several orders of magnitude over background levels and have always been considered to be random in nature in statistical models with no dependence of any one event on the occurrence of previous events. We examine whether this assumption of randomness in time is correct. Engineering modeling of SEPEs is important to enable reliable and efficient design of both Earth-orbiting and interplanetary spacecraft and future manned missions to Mars and the Moon. All existing engineering models assume that the frequency of SEPEs follows a Poisson process. We present analysis of the event waiting times using alternative distributions described by Lévy and time-dependent Poisson processes and compared these with the usual Poisson distribution. The results show significant deviation from a Poisson process and indicate that the underlying physical processes might be more closely related to a Lévy-type process, suggesting that there is some inherent “memory” in the system. Inherent Poisson assumptions of stationarity and event independence are investigated, and it appears that they do not hold and can be dependent upon the event definition used. SEPEs appear to have some memory indicating that events are not completely random with activity levels varying even during solar active periods and are characterized by clusters of events. This could have significant ramifications for engineering models of the SEP environment, and it is recommended that current statistical engineering models of the SEP environment should be modified to incorporate long-term event dependency and short-term system memory.

The contribution of simple random sampling to observed variations in faecal egg counts.

PubMed

Torgerson, Paul R; Paul, Michaela; Lewis, Fraser I

2012-09-10

It has been over 100 years since the classical paper published by Gosset in 1907, under the pseudonym "Student", demonstrated that yeast cells suspended in a fluid and measured by a haemocytometer conformed to a Poisson process. Similarly parasite eggs in a faecal suspension also conform to a Poisson process. Despite this there are common misconceptions how to analyse or interpret observations from the McMaster or similar quantitative parasitic diagnostic techniques, widely used for evaluating parasite eggs in faeces. The McMaster technique can easily be shown from a theoretical perspective to give variable results that inevitably arise from the random distribution of parasite eggs in a well mixed faecal sample. The Poisson processes that lead to this variability are described and illustrative examples of the potentially large confidence intervals that can arise from observed faecal eggs counts that are calculated from the observations on a McMaster slide. Attempts to modify the McMaster technique, or indeed other quantitative techniques, to ensure uniform egg counts are doomed to failure and belie ignorance of Poisson processes. A simple method to immediately identify excess variation/poor sampling from replicate counts is provided. Copyright © 2012 Elsevier B.V. All rights reserved.

Pattern analysis of community health center location in Surabaya using spatial Poisson point process

NASA Astrophysics Data System (ADS)

Kusumaningrum, Choriah Margareta; Iriawan, Nur; Winahju, Wiwiek Setya

2017-11-01

Community health center (puskesmas) is one of the closest health service facilities for the community, which provide healthcare for population on sub-district level as one of the government-mandated community health clinics located across Indonesia. The increasing number of this puskesmas does not directly comply the fulfillment of basic health services needed in such region. Ideally, a puskesmas has to cover up to maximum 30,000 people. The number of puskesmas in Surabaya indicates an unbalance spread in all of the area. This research aims to analyze the spread of puskesmas in Surabaya using spatial Poisson point process model in order to get the effective location of Surabaya's puskesmas which based on their location. The results of the analysis showed that the distribution pattern of puskesmas in Surabaya is non-homogeneous Poisson process and is approched by mixture Poisson model. Based on the estimated model obtained by using Bayesian mixture model couple with MCMC process, some characteristics of each puskesmas have no significant influence as factors to decide the addition of health center in such location. Some factors related to the areas of sub-districts have to be considered as covariate to make a decision adding the puskesmas in Surabaya.

Poissonian renormalizations, exponentials, and power laws

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Developing an economical and reliable test for measuring the resilient modulus and Poisson's ratio of subgrade.

DOT National Transportation Integrated Search

2010-11-01

The resilient modulus and Poissons ratio of base and sublayers in highway use are : important parameters in design and quality control process. The currently used techniques : include CBR (California Bearing Ratio) test, resilient modulus test,...

Theory of earthquakes interevent times applied to financial markets

NASA Astrophysics Data System (ADS)

Jagielski, Maciej; Kutner, Ryszard; Sornette, Didier

2017-10-01

We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account how past events influence the occurrence of future events. By analyzing the empirical data for 15 different financial assets, we show that the formalism of the Hawkes process used for earthquakes can successfully model the PDF of interevent times between successive market losses.

Equivalence of MAXENT and Poisson point process models for species distribution modeling in ecology.

PubMed

Renner, Ian W; Warton, David I

2013-03-01

Modeling the spatial distribution of a species is a fundamental problem in ecology. A number of modeling methods have been developed, an extremely popular one being MAXENT, a maximum entropy modeling approach. In this article, we show that MAXENT is equivalent to a Poisson regression model and hence is related to a Poisson point process model, differing only in the intercept term, which is scale-dependent in MAXENT. We illustrate a number of improvements to MAXENT that follow from these relations. In particular, a point process model approach facilitates methods for choosing the appropriate spatial resolution, assessing model adequacy, and choosing the LASSO penalty parameter, all currently unavailable to MAXENT. The equivalence result represents a significant step in the unification of the species distribution modeling literature. Copyright © 2013, The International Biometric Society.

Does the U.S. exercise contagion on Italy? A theoretical model and empirical evidence

NASA Astrophysics Data System (ADS)

Cerqueti, Roy; Fenga, Livio; Ventura, Marco

2018-06-01

This paper deals with the theme of contagion in financial markets. At this aim, we develop a model based on Mixed Poisson Processes to describe the abnormal returns of financial markets of two considered countries. In so doing, the article defines the theoretical conditions to be satisfied in order to state that one of them - the so-called leader - exercises contagion on the others - the followers. Specifically, we employ an invariant probabilistic result stating that a suitable transformation of a Mixed Poisson Process is still a Mixed Poisson Process. The theoretical claim is validated by implementing an extensive simulation analysis grounded on empirical data. The countries considered are the U.S. (as the leader) and Italy (as the follower) and the period under scrutiny is very large, ranging from 1970 to 2014.

Seasonally adjusted birth frequencies follow the Poisson distribution.

PubMed

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 < 0.01). The fundamental model with year and month as explanatory variables is significantly improved (p < 0.001) by adding day of the week as an explanatory variable. Altogether 7.5% more children are born on Tuesdays than on Sundays. The digit sum of the date is non-significant as an explanatory variable (p = 0.23), nor does it increase the explained variance. INERPRETATION: Spontaneous births are well modelled by a time-dependent 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.

Noise parameter estimation for poisson corrupted images using variance stabilization transforms.

PubMed

Jin, Xiaodan; Xu, Zhenyu; Hirakawa, Keigo

2014-03-01

Noise is present in all images captured by real-world image sensors. Poisson distribution is said to model the stochastic nature of the photon arrival process and agrees with the distribution of measured pixel values. We propose a method for estimating unknown noise parameters from Poisson corrupted images using properties of variance stabilization. With a significantly lower computational complexity and improved stability, the proposed estimation technique yields noise parameters that are comparable in accuracy to the state-of-art methods.

NON-HOMOGENEOUS POISSON PROCESS MODEL FOR GENETIC CROSSOVER INTERFERENCE.

PubMed

Leu, Szu-Yun; Sen, Pranab K

2014-01-01

The genetic crossover interference is usually modeled with a stationary renewal process to construct the genetic map. We propose two non-homogeneous, also dependent, Poisson process models applied to the known physical map. The crossover process is assumed to start from an origin and to occur sequentially along the chromosome. The increment rate depends on the position of the markers and the number of crossover events occurring between the origin and the markers. We show how to obtain parameter estimates for the process and use simulation studies and real Drosophila data to examine the performance of the proposed models.

Irreversible thermodynamics of Poisson processes with reaction.

PubMed

Méndez, V; Fort, J

1999-11-01

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.

A Hands-on Activity for Teaching the Poisson Distribution Using the Stock Market

ERIC Educational Resources Information Center

Dunlap, Mickey; Studstill, Sharyn

2014-01-01

The number of increases a particular stock makes over a fixed period follows a Poisson distribution. This article discusses using this easily-found data as an opportunity to let students become involved in the data collection and analysis process.

Modeling environmental noise exceedances using non-homogeneous Poisson processes.

PubMed

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.

Simple and Hierarchical Models for Stochastic Test Misgrading.

ERIC Educational Resources Information Center

Wang, Jianjun

1993-01-01

Test misgrading is treated as a stochastic process. The expected number of misgradings, inter-occurrence time of misgradings, and waiting time for the "n"th misgrading are discussed based on a simple Poisson model and a hierarchical Beta-Poisson model. Examples of model construction are given. (SLD)

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun Wei, E-mail: wsun@mathstat.concordia.ca; Zeng Yong, E-mail: zengy@umkc.edu; Zhang Shu, E-mail: zhangshuisme@hotmail.com

2013-06-15

We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical schememore » based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.« less

Study on reservoir time-varying design flood of inflow based on Poisson process with time-dependent parameters

NASA Astrophysics Data System (ADS)

Li, Jiqing; Huang, Jing; Li, Jianchang

2018-06-01

The time-varying design flood can make full use of the measured data, which can provide the reservoir with the basis of both flood control and operation scheduling. This paper adopts peak over threshold method for flood sampling in unit periods and Poisson process with time-dependent parameters model for simulation of reservoirs time-varying design flood. Considering the relationship between the model parameters and hypothesis, this paper presents the over-threshold intensity, the fitting degree of Poisson distribution and the design flood parameters are the time-varying design flood unit period and threshold discriminant basis, deduced Longyangxia reservoir time-varying design flood process at 9 kinds of design frequencies. The time-varying design flood of inflow is closer to the reservoir actual inflow conditions, which can be used to adjust the operating water level in flood season and make plans for resource utilization of flood in the basin.

Using the Gamma-Poisson Model to Predict Library Circulations.

ERIC Educational Resources Information Center

Burrell, Quentin L.

1990-01-01

Argues that the gamma mixture of Poisson processes, for all its perceived defects, can be used to make predictions regarding future library book circulations of a quality adequate for general management requirements. The use of the model is extensively illustrated with data from two academic libraries. (Nine references) (CLB)

Questionable Validity of Poisson Assumptions in a Combined Loglinear/MDS Mapping Model.

ERIC Educational Resources Information Center

Gleason, John M.

1993-01-01

This response to an earlier article on a combined log-linear/MDS model for mapping journals by citation analysis discusses the underlying assumptions of the Poisson model with respect to characteristics of the citation process. The importance of empirical data analysis is also addressed. (nine references) (LRW)

Extensions of Rasch's Multiplicative Poisson Model.

ERIC Educational Resources Information Center

Jansen, Margo G. H.; van Duijn, Marijtje A. J.

1992-01-01

A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)

Transport of Multivalent Electrolyte Mixtures in Micro- and Nanochannels

DTIC Science & Technology

2013-11-08

equations for this process are the unsteady Navier-Stokes equations along with continuity and the Poisson- Nernst -Planck system for the electro- static part...about five times the Debye screening length D (the 1/e lengthscale for the potential from the solution of the linearized Poisson- Boltzmann equation

Do bacterial cell numbers follow a theoretical Poisson distribution? Comparison of experimentally obtained numbers of single cells with random number generation via computer simulation.

PubMed

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu

2016-12-01

We investigated a bacterial sample preparation procedure for single-cell studies. In the present study, we examined whether single bacterial cells obtained via 10-fold dilution followed a theoretical Poisson distribution. Four serotypes of Salmonella enterica, three serotypes of enterohaemorrhagic Escherichia coli and one serotype of Listeria monocytogenes were used as sample bacteria. An inoculum of each serotype was prepared via a 10-fold dilution series to obtain bacterial cell counts with mean values of one or two. To determine whether the experimentally obtained bacterial cell counts follow a theoretical Poisson distribution, a likelihood ratio test between the experimentally obtained cell counts and Poisson distribution which parameter estimated by maximum likelihood estimation (MLE) was conducted. The bacterial cell counts of each serotype sufficiently followed a Poisson distribution. Furthermore, to examine the validity of the parameters of Poisson distribution from experimentally obtained bacterial cell counts, we compared these with the parameters of a Poisson distribution that were estimated using random number generation via computer simulation. The Poisson distribution parameters experimentally obtained from bacterial cell counts were within the range of the parameters estimated using a computer simulation. These results demonstrate that the bacterial cell counts of each serotype obtained via 10-fold dilution followed a Poisson distribution. The fact that the frequency of bacterial cell counts follows a Poisson distribution at low number would be applied to some single-cell studies with a few bacterial cells. In particular, the procedure presented in this study enables us to develop an inactivation model at the single-cell level that can estimate the variability of survival bacterial numbers during the bacterial death process. Copyright © 2016 Elsevier Ltd. All rights reserved.

The distribution of catchment coverage by stationary rainstorms

NASA Technical Reports Server (NTRS)

Eagleson, P. S.

1984-01-01

The occurrence of wetted rainstorm area within a catchment is modeled as a Poisson arrival process in which each storm is composed of stationary, nonoverlapping, independent random cell clusters whose centers are Poisson-distributed in space and whose areas are fractals. The two Poisson parameters and hence the first two moments of the wetted fraction are derived in terms of catchment average characteristics of the (observable) station precipitation. The model is used to estimate spatial properties of tropical air mass thunderstorms on six tropical catchments in the Sudan.

Generalized Poisson-Kac Processes: Basic Properties and Implications in Extended Thermodynamics and Transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2016-04-01

We introduce a new class of stochastic processes in Rn,{{{mathbb R}}^n}, referred to as generalized Poisson-Kac (GPK) processes, that generalizes the Poisson-Kac telegrapher's random motion in higher dimensions. These stochastic processes possess finite propagation velocity, almost everywhere smooth trajectories, and converge in the Kac limit to Brownian motion. GPK processes are defined by coupling the selection of a bounded velocity vector from a family of N distinct ones with a Markovian dynamics controlling probabilistically this selection. This model can be used as a probabilistic tool for a stochastically consistent formulation of extended thermodynamic theories far from equilibrium.

Applying the Anderson-Darling test to suicide clusters: evidence of contagion at U. S. universities?

PubMed

MacKenzie, Donald W

2013-01-01

Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Suicide dates were collected for MIT and Cornell for 1990-2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

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

PubMed Central

Naya, Hugo; Urioste, Jorge I; Chang, Yu-Mei; Rodrigues-Motta, Mariana; Kremer, Roberto; Gianola, Daniel

2008-01-01

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. PMID:18558072

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

PubMed

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.

General methodology for nonlinear modeling of neural systems with Poisson point-process inputs.

PubMed

Marmarelis, V Z; Berger, T W

2005-07-01

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process inputs. It shows that only the Wiener kernels can be estimated via cross-correlation, but must be defined as zero along the diagonals. The Volterra kernels can be estimated far more accurately (and from shorter data-records) by use of the Laguerre expansion technique adapted to point-process inputs, and they are independent of the mean rate of stimulation (unlike their P-W counterparts that depend on it). The Volterra kernels can also be estimated for broadband point-process inputs that are not Poisson. Useful applications of this modeling approach include cases where we seek to determine (model) the transfer characteristics between one neuronal axon (a point-process 'input') and another axon (a point-process 'output') or some other measure of neuronal activity (a continuous 'output', such as population activity) with which a causal link exists.

A Mixed-Effects Heterogeneous Negative Binomial Model for Postfire Conifer Regeneration in Northeastern California, USA

Treesearch

Justin S. Crotteau; Martin W. Ritchie; J. Morgan Varner

2014-01-01

Many western USA fire regimes are typified by mixed-severity fire, which compounds the variability inherent to natural regeneration densities in associated forests. Tree regeneration data are often discrete and nonnegative; accordingly, we fit a series of Poisson and negative binomial variation models to conifer seedling counts across four distinct burn severities and...

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

An unbiased risk estimator for image denoising in the presence of mixed poisson-gaussian noise.

PubMed

Le Montagner, Yoann; Angelini, Elsa D; Olivo-Marin, Jean-Christophe

2014-03-01

The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.

Compound estimation procedures in reliability

NASA Technical Reports Server (NTRS)

Barnes, Ron

1990-01-01

At NASA, components and subsystems of components in the Space Shuttle and Space Station generally go through a number of redesign stages. While data on failures for various design stages are sometimes available, the classical procedures for evaluating reliability only utilize the failure data on the present design stage of the component or subsystem. Often, few or no failures have been recorded on the present design stage. Previously, Bayesian estimators for the reliability of a single component, conditioned on the failure data for the present design, were developed. These new estimators permit NASA to evaluate the reliability, even when few or no failures have been recorded. Point estimates for the latter evaluation were not possible with the classical procedures. Since different design stages of a component (or subsystem) generally have a good deal in common, the development of new statistical procedures for evaluating the reliability, which consider the entire failure record for all design stages, has great intuitive appeal. A typical subsystem consists of a number of different components and each component has evolved through a number of redesign stages. The present investigations considered compound estimation procedures and related models. Such models permit the statistical consideration of all design stages of each component and thus incorporate all the available failure data to obtain estimates for the reliability of the present version of the component (or subsystem). A number of models were considered to estimate the reliability of a component conditioned on its total failure history from two design stages. It was determined that reliability estimators for the present design stage, conditioned on the complete failure history for two design stages have lower risk than the corresponding estimators conditioned only on the most recent design failure data. Several models were explored and preliminary models involving bivariate Poisson distribution and the Consael Process (a bivariate Poisson process) were developed. Possible short comings of the models are noted. An example is given to illustrate the procedures. These investigations are ongoing with the aim of developing estimators that extend to components (and subsystems) with three or more design stages.

Elasticity, slowness, thermal conductivity and the anisotropies in the Mn3Cu1-xGexN compounds

NASA Astrophysics Data System (ADS)

Li, Guan-Nan; Chen, Zhi-Qian; Lu, Yu-Ming; Hu, Meng; Jiao, Li-Na; Zhao, Hao-Ting

2018-03-01

We perform the first-principles to systematically investigate the elastic properties, minimum thermal conductivity and anisotropy of the negative thermal expansion compounds Mn3Cu1-xGexN. The elastic constant, bulk modulus, shear modulus, Young’s modulus and Poisson ratio are calculated for all the compounds. The results of the elastic constant indicate that all the compounds are mechanically stable and the doped Ge can adjust the ductile character of the compounds. According to the values of the percent ratio of the elastic anisotropy AB, AE and AG, shear anisotropic factors A1, A2 and A3, all the Mn3Cu1-xGexN compounds are elastic anisotropy. The three-dimensional diagrams of elastic moduli in space also show that all the compounds are elastic anisotropy. In addition, the acoustic wave speed, slowness, minimum thermal conductivity and Debye temperature are also calculated. When the ratio of content for Cu and Ge arrived to 1:1, the compound has the lowest thermal conductivity and the highest Debye temperature.

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

NASA Astrophysics Data System (ADS)

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.

Fractional Brownian motion and long term clinical trial recruitment

PubMed Central

Zhang, Qiang; Lai, Dejian

2015-01-01

Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations. PMID:26347306

Fractional Brownian motion and long term clinical trial recruitment.

PubMed

Zhang, Qiang; Lai, Dejian

2011-05-01

Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations.

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

PubMed

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.

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

PubMed

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.

An empirical Bayesian and Buhlmann approach with non-homogenous Poisson process

NASA Astrophysics Data System (ADS)

Noviyanti, Lienda

2015-12-01

All general insurance companies in Indonesia have to adjust their current premium rates according to maximum and minimum limit rates in the new regulation established by the Financial Services Authority (Otoritas Jasa Keuangan / OJK). In this research, we estimated premium rate by means of the Bayesian and the Buhlmann approach using historical claim frequency and claim severity in a five-group risk. We assumed a Poisson distributed claim frequency and a Normal distributed claim severity. Particularly, we used a non-homogenous Poisson process for estimating the parameters of claim frequency. We found that estimated premium rates are higher than the actual current rate. Regarding to the OJK upper and lower limit rates, the estimates among the five-group risk are varied; some are in the interval and some are out of the interval.

The Dependent Poisson Race Model and Modeling Dependence in Conjoint Choice Experiments

ERIC Educational Resources Information Center

Ruan, Shiling; MacEachern, Steven N.; Otter, Thomas; Dean, Angela M.

2008-01-01

Conjoint choice experiments are used widely in marketing to study consumer preferences amongst alternative products. We develop a class of choice models, belonging to the class of Poisson race models, that describe a "random utility" which lends itself to a process-based description of choice. The models incorporate a dependence structure which…

Generalized master equations for non-Poisson dynamics on networks.

PubMed

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.

Generalized master equations for non-Poisson dynamics on networks

NASA Astrophysics Data System (ADS)

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.

Weber's law implies neural discharge more regular than a Poisson process.

PubMed

Kang, Jing; Wu, Jianhua; Smerieri, Anteo; Feng, Jianfeng

2010-03-01

Weber's law is one of the basic laws in psychophysics, but the link between this psychophysical behavior and the neuronal response has not yet been established. In this paper, we carried out an analysis on the spike train statistics when Weber's law holds, and found that the efferent spike train of a single neuron is less variable than a Poisson process. For population neurons, Weber's law is satisfied only when the population size is small (< 10 neurons). However, if the population neurons share a weak correlation in their discharges and individual neuronal spike train is more regular than a Poisson process, Weber's law is true without any restriction on the population size. Biased competition attractor network also demonstrates that the coefficient of variation of interspike interval in the winning pool should be less than one for the validity of Weber's law. Our work links Weber's law with neural firing property quantitatively, shedding light on the relation between psychophysical behavior and neuronal responses.

Pareto genealogies arising from a Poisson branching evolution model with selection.

PubMed

Huillet, Thierry E

2014-02-01

We study a class of coalescents derived from a sampling procedure out of N i.i.d. Pareto(α) random variables, normalized by their sum, including β-size-biasing on total length effects (β < α). Depending on the range of α we derive the large N limit coalescents structure, leading either to a discrete-time Poisson-Dirichlet (α, -β) Ξ-coalescent (α ε[0, 1)), or to a family of continuous-time Beta (2 - α, α - β)Λ-coalescents (α ε[1, 2)), or to the Kingman coalescent (α ≥ 2). We indicate that this class of coalescent processes (and their scaling limits) may be viewed as the genealogical processes of some forward in time evolving branching population models including selection effects. In such constant-size population models, the reproduction step, which is based on a fitness-dependent Poisson Point Process with scaling power-law(α) intensity, is coupled to a selection step consisting of sorting out the N fittest individuals issued from the reproduction step.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Clustered mixed nonhomogeneous Poisson process spline models for the analysis of recurrent event panel data.

PubMed

Nielsen, J D; Dean, C B

2008-09-01

A flexible semiparametric model for analyzing longitudinal panel count data arising from mixtures is presented. Panel count data refers here to count data on recurrent events collected as the number of events that have occurred within specific follow-up periods. The model assumes that the counts for each subject are generated by mixtures of nonhomogeneous Poisson processes with smooth intensity functions modeled with penalized splines. Time-dependent covariate effects are also incorporated into the process intensity using splines. Discrete mixtures of these nonhomogeneous Poisson process spline models extract functional information from underlying clusters representing hidden subpopulations. The motivating application is an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth. Mature moths arise from hidden, but distinct, subpopulations and monitoring the subpopulation responses was of interest. Within-cluster random effects are used to account for correlation structures and heterogeneity common to this type of data. An estimating equation approach to inference requiring only low moment assumptions is developed and the finite sample properties of the proposed estimating functions are investigated empirically by simulation.

Option pricing for stochastic volatility model with infinite activity Lévy jumps

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2016-08-01

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.

Orientational analysis of planar fibre systems observed as a Poisson shot-noise process.

PubMed

Kärkkäinen, Salme; Lantuéjoul, Christian

2007-10-01

We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Kärkkäinen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampling lines is constant. This assumption is proved to be valid asymptotically for Boolean models and dead leaves models, under some regularity conditions. In this work, we derive the scaled variogram and its approximations for a planar Poisson shot-noise process using the modified Bessel function. In the case of reasonable high resolution of the observed image, the scaled variogram has an approximate functional relation to the point intensity, and in the case of high resolution the relation is proportional. As the obtained relations are approximative, they are tested on simulations. The existing orientation analysis method based on the proportional relation is further experimented on images with different resolutions. The new result, the asymptotic proportionality between the scaled variograms and the point intensities for a Poisson shot-noise process, completes the earlier results for the Boolean models and for the dead leaves models.

A Bayesian method for inferring transmission chains in a partially observed epidemic.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef M.; Ray, Jaideep

2008-10-01

We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historicalmore » data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.« less

Brain, music, and non-Poisson renewal processes

NASA Astrophysics Data System (ADS)

Bianco, Simone; Ignaccolo, Massimiliano; Rider, Mark S.; Ross, Mary J.; Winsor, Phil; Grigolini, Paolo

2007-06-01

In this paper we show that both music composition and brain function, as revealed by the electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a technique of statistical analysis recently developed by our group, the aging experiment (AE). First, we find that in both cases the distances between two consecutive events are described by nonexponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities Ψ(t) are well fitted by stretched exponentials [ Ψ(t)∝exp (-(γt)α) , with 0.5<α<1 .] The second step rests on the adoption of AE, which shows that these are renewal processes. We show that the stretched exponential, due to its renewal character, is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index μ=1+α . Adopting the AE procedure we find that both EEG and music composition yield μ<2 . On the basis of the recently discovered complexity matching effect, according to which a complex system S with μS<2 responds only to a complex driving signal P with μP⩽μS , we conclude that the results of our analysis may explain the influence of music on the human brain.

Analysis of single-molecule fluorescence spectroscopic data with a Markov-modulated Poisson process.

PubMed

Jäger, Mark; Kiel, Alexander; Herten, Dirk-Peter; Hamprecht, Fred A

2009-10-05

We present a photon-by-photon analysis framework for the evaluation of data from single-molecule fluorescence spectroscopy (SMFS) experiments using a Markov-modulated Poisson process (MMPP). A MMPP combines a discrete (and hidden) Markov process with an additional Poisson process reflecting the observation of individual photons. The algorithmic framework is used to automatically analyze the dynamics of the complex formation and dissociation of Cu2+ ions with the bidentate ligand 2,2'-bipyridine-4,4'dicarboxylic acid in aqueous media. The process of association and dissociation of Cu2+ ions is monitored with SMFS. The dcbpy-DNA conjugate can exist in two or more distinct states which influence the photon emission rates. The advantage of a photon-by-photon analysis is that no information is lost in preprocessing steps. Different model complexities are investigated in order to best describe the recorded data and to determine transition rates on a photon-by-photon basis. The main strength of the method is that it allows to detect intermittent phenomena which are masked by binning and that are difficult to find using correlation techniques when they are short-lived.

Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation.

PubMed

Gustafsson, Leif; Sternad, Mikael

2007-10-01

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

Morphology and linear-elastic moduli of random network solids.

PubMed

Nachtrab, Susan; Kapfer, Sebastian C; Arns, Christoph H; Madadi, Mahyar; Mecke, Klaus; Schröder-Turk, Gerd E

2011-06-17

The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A random-censoring Poisson model for underreported data.

PubMed

de Oliveira, Guilherme Lopes; Loschi, Rosangela Helena; Assunção, Renato Martins

2017-12-30

A major challenge when monitoring risks in socially deprived areas of under developed countries is that economic, epidemiological, and social data are typically underreported. Thus, statistical models that do not take the data quality into account will produce biased estimates. To deal with this problem, counts in suspected regions are usually approached as censored information. The censored Poisson model can be considered, but all censored regions must be precisely known a priori, which is not a reasonable assumption in most practical situations. We introduce the random-censoring Poisson model (RCPM) which accounts for the uncertainty about both the count and the data reporting processes. Consequently, for each region, we will be able to estimate the relative risk for the event of interest as well as the censoring probability. To facilitate the posterior sampling process, we propose a Markov chain Monte Carlo scheme based on the data augmentation technique. We run a simulation study comparing the proposed RCPM with 2 competitive models. Different scenarios are considered. RCPM and censored Poisson model are applied to account for potential underreporting of early neonatal mortality counts in regions of Minas Gerais State, Brazil, where data quality is known to be poor. Copyright © 2017 John Wiley & Sons, Ltd.

On Subset Selection Procedures for Poisson Processes and Some Applications to the Binomial and Multinomial Problems

DTIC Science & Technology

1976-07-01

PURDUE UNIVERSITY DEPARTMENT OF STATISTICS DIVISION OF MATHEMATICAL SCIENCES ON SUBSET SELECTION PROCEDURES FOR POISSON PROCESSES AND SOME...Mathematical Sciences Mimeograph Series #457, July 1976 This research was supported by the Office of Naval Research under Contract NOOO14-75-C-0455 at Purdue...11 CON PC-111 riFIC-F ,A.F ANO ADDPFS Office of INaval ResearchJu#07 Washington, DC07 36AE 14~~~ rjCr; NF A ’ , A FAA D F 6 - I S it 9 i 1, - ,1 I

Crystalline nucleation in undercooled liquids: a Bayesian data-analysis approach for a nonhomogeneous Poisson process.

PubMed

Filipponi, A; Di Cicco, A; Principi, E

2012-12-01

A Bayesian data-analysis approach to data sets of maximum undercooling temperatures recorded in repeated melting-cooling cycles of high-purity samples is proposed. The crystallization phenomenon is described in terms of a nonhomogeneous Poisson process driven by a temperature-dependent sample nucleation rate J(T). The method was extensively tested by computer simulations and applied to real data for undercooled liquid Ge. It proved to be particularly useful in the case of scarce data sets where the usage of binned data would degrade the available experimental information.

Extended Poisson process modelling and analysis of grouped binary data.

PubMed

Faddy, Malcolm J; Smith, David M

2012-05-01

A simple extension of the Poisson process results in binomially distributed counts of events in a time interval. A further extension generalises this to probability distributions under- or over-dispersed relative to the binomial distribution. Substantial levels of under-dispersion are possible with this modelling, but only modest levels of over-dispersion - up to Poisson-like variation. Although simple analytical expressions for the moments of these probability distributions are not available, approximate expressions for the mean and variance are derived, and used to re-parameterise the models. The modelling is applied in the analysis of two published data sets, one showing under-dispersion and the other over-dispersion. More appropriate assessment of the precision of estimated parameters and reliable model checking diagnostics follow from this more general modelling of these data sets. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Measurement of Poisson's ratio of nonmetallic materials by laser holographic interferometry

NASA Astrophysics Data System (ADS)

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.

Reduction of Poisson noise in measured time-resolved data for time-domain diffuse optical tomography.

PubMed

Okawa, S; Endo, Y; Hoshi, Y; Yamada, Y

2012-01-01

A method to reduce noise for time-domain diffuse optical tomography (DOT) is proposed. Poisson noise which contaminates time-resolved photon counting data is reduced by use of maximum a posteriori estimation. The noise-free data are modeled as a Markov random process, and the measured time-resolved data are assumed as Poisson distributed random variables. The posterior probability of the occurrence of the noise-free data is formulated. By maximizing the probability, the noise-free data are estimated, and the Poisson noise is reduced as a result. The performances of the Poisson noise reduction are demonstrated in some experiments of the image reconstruction of time-domain DOT. In simulations, the proposed method reduces the relative error between the noise-free and noisy data to about one thirtieth, and the reconstructed DOT image was smoothed by the proposed noise reduction. The variance of the reconstructed absorption coefficients decreased by 22% in a phantom experiment. The quality of DOT, which can be applied to breast cancer screening etc., is improved by the proposed noise reduction.

Approximations to camera sensor noise

NASA Astrophysics Data System (ADS)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

Image denoising in mixed Poisson-Gaussian noise.

PubMed

Luisier, Florian; Blu, Thierry; Unser, Michael

2011-03-01

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds (LET) that we optimize by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE), derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate). We provide a practical approximation of this theoretical MSE estimate for the tractable optimization of arbitrary transform-domain thresholding. We then propose a pointwise estimator for undecimated filterbank transforms, which consists of subband-adaptive thresholding functions with signal-dependent thresholds that are globally optimized in the image domain. We finally demonstrate the potential of the proposed approach through extensive comparisons with state-of-the-art techniques that are specifically tailored to the estimation of Poisson intensities. We also present denoising results obtained on real images of low-count fluorescence microscopy.

Calculation of the compounded uncertainty of 14C AMS measurements

NASA Astrophysics Data System (ADS)

Nadeau, Marie-Josée; Grootes, Pieter M.

2013-01-01

The correct method to calculate conventional 14C ages from the carbon isotopic ratios was summarised 35 years ago by Stuiver and Polach (1977) and is now accepted as the only method to calculate 14C ages. There is, however, no consensus regarding the treatment of AMS data, mainly of the uncertainty of the final result. The estimation and treatment of machine background, process blank, and/or in situ contamination is not uniform between laboratories, leading to differences in 14C results, mainly for older ages. As Donahue (1987) and Currie (1994), among others, mentioned, some laboratories find it important to use the scatter of several measurements as uncertainty while others prefer to use Poisson statistics. The contribution of the scatter of the standards, machine background, process blank, and in situ contamination to the uncertainty of the final 14C result is also treated in different ways. In the early years of AMS, several laboratories found it important to describe their calculation process in details. In recent years, this practise has declined. We present an overview of the calculation process for 14C AMS measurements looking at calculation practises published from the beginning of AMS until present.

Statistical modeling of storm-level Kp occurrences

USGS Publications Warehouse

Remick, K.J.; Love, J.J.

2006-01-01

We consider the statistical modeling of the occurrence in time of large Kp magnetic storms as a Poisson process, testing whether or not relatively rare, large Kp events can be considered to arise from a stochastic, sequential, and memoryless process. For a Poisson process, the wait times between successive events occur statistically with an exponential density function. Fitting an exponential function to the durations between successive large Kp events forms the basis of our analysis. Defining these wait times by calculating the differences between times when Kp exceeds a certain value, such as Kp ??? 5, we find the wait-time distribution is not exponential. Because large storms often have several periods with large Kp values, their occurrence in time is not memoryless; short duration wait times are not independent of each other and are often clumped together in time. If we remove same-storm large Kp occurrences, the resulting wait times are very nearly exponentially distributed and the storm arrival process can be characterized as Poisson. Fittings are performed on wait time data for Kp ??? 5, 6, 7, and 8. The mean wait times between storms exceeding such Kp thresholds are 7.12, 16.55, 42.22, and 121.40 days respectively.

Analyzing hospitalization data: potential limitations of Poisson regression.

PubMed

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.

Evolving Scale-Free Networks by Poisson Process: Modeling and Degree Distribution.

PubMed

Feng, Minyu; Qu, Hong; Yi, Zhang; Xie, Xiurui; Kurths, Jurgen

2016-05-01

Since the great mathematician Leonhard Euler initiated the study of graph theory, the network has been one of the most significant research subject in multidisciplinary. In recent years, the proposition of the small-world and scale-free properties of complex networks in statistical physics made the network science intriguing again for many researchers. One of the challenges of the network science is to propose rational models for complex networks. In this paper, in order to reveal the influence of the vertex generating mechanism of complex networks, we propose three novel models based on the homogeneous Poisson, nonhomogeneous Poisson and birth death process, respectively, which can be regarded as typical scale-free networks and utilized to simulate practical networks. The degree distribution and exponent are analyzed and explained in mathematics by different approaches. In the simulation, we display the modeling process, the degree distribution of empirical data by statistical methods, and reliability of proposed networks, results show our models follow the features of typical complex networks. Finally, some future challenges for complex systems are discussed.

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method

PubMed Central

Zhang, Tingting; Kou, S. C.

2010-01-01

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure. PMID:21258615

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.

PubMed

Zhang, Tingting; Kou, S C

2010-01-01

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

Investigating on the Differences between Triggered and Background Seismicity in Italy and Southern California.

NASA Astrophysics Data System (ADS)

Stallone, A.; Marzocchi, W.

2017-12-01

Earthquake occurrence may be approximated by a multidimensional Poisson clustering process, where each point of the Poisson process is replaced by a cluster of points, the latter corresponding to the well-known aftershock sequence (triggered events). Earthquake clusters and their parents are assumed to occur according to a Poisson process at a constant temporal rate proportional to the tectonic strain rate, while events within a cluster are modeled as generations of dependent events reproduced by a branching process. Although the occurrence of such space-time clusters is a general feature in different tectonic settings, seismic sequences seem to have marked differences from region to region: one example, among many others, is that seismic sequences of moderate magnitude in Italian Apennines seem to last longer than similar seismic sequences in California. In this work we investigate on the existence of possible differences in the earthquake clustering process in these two areas. At first, we separate the triggered and background components of seismicity in the Italian and Southern California seismic catalog. Then we study the space-time domain of the triggered earthquakes with the aim to identify possible variations in the triggering properties across the two regions. In the second part of the work we focus our attention on the characteristics of the background seismicity in both seismic catalogs. The assumption of time stationarity of the background seismicity (which includes both cluster parents and isolated events) is still under debate. Some authors suggest that the independent component of seismicity could undergo transient perturbations at various time scales due to different physical mechanisms, such as, for example, viscoelastic relaxation, presence of fluids, non-stationary plate motion, etc, whose impact may depend on the tectonic setting. Here we test if the background seismicity in the two regions can be satisfactorily described by the time-homogeneous Poisson process, and, in case, we characterize quantitatively possible discrepancies with this reference process, and the differences between the two regions.

Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries

NASA Astrophysics Data System (ADS)

Gillis, T.; Winckelmans, G.; Chatelain, P.

2018-02-01

We present a fast and efficient Fourier-based solver for the Poisson problem around an arbitrary geometry in an unbounded 3D domain. This solver merges two rewarding approaches, the lattice Green's function method and the immersed interface method, using the Sherman-Morrison-Woodbury decomposition formula. The method is intended to be second order up to the boundary. This is verified on two potential flow benchmarks. We also further analyse the iterative process and the convergence behavior of the proposed algorithm. The method is applicable to a wide range of problems involving a Poisson equation around inner bodies, which goes well beyond the present validation on potential flows.

An ab-initio investigation on SrLa intermetallic compound

NASA Astrophysics Data System (ADS)

Kumar, S. Ramesh; Jaiganesh, G.; Jayalakshmi, V.

2018-05-01

The electronic, elastic and thermodynamic property of CsCl-type SrLa are investigated through density functional theory. The energy-volume relation for this compound has been obtained. The band structure, density of states and charge density in (110) plane are also examined. The elastic constants (C11, C12 and C44) of SrLa is computed, then, using these elastic constants, the bulk moduli, shear moduli, Young's moduli and Poisson's ratio are also derived. The calculated results showed that CsCl-type SrLa is ductile at ambient conditions. The thermodynamic quantities such as free energy, entropy and heat capacity as a function of temperature are estimated and the results obtained are discussed.

Order-disorder effects on the elastic properties of CuMPt6 (M=Cr and Co) compounds

NASA Astrophysics Data System (ADS)

Huang, Shuo; Li, Rui-Zi; Qi, San-Tao; Chen, Bao; Shen, Jiang

2014-04-01

The elastic properties of CuMPt6 (M=Cr and Co) in disordered face-centered cubic (fcc) structure and ordered Cu3Au-type structure are studied with lattice inversion embedded-atom method. The calculated lattice constant and Debye temperature agree quite well with the comparable experimental data. The obtained formation enthalpy demonstrates that the Cu3Au-type structure is energetically more favorable. Numerical estimates of the elastic constants, bulk/shear modulus, Young's modulus, Poisson's ratio, elastic anisotropy, and Debye temperature for both compounds are performed, and the results suggest that the disordered fcc structure is much softer than the ordered Cu3Au-type structure.

Waiting-time distributions of magnetic discontinuities: clustering or Poisson process?

PubMed

Greco, A; Matthaeus, W H; Servidio, S; Dmitruk, P

2009-10-01

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

The Poisson Random Process. Applications of Probability Theory to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 340.

ERIC Educational Resources Information Center

Wilde, Carroll O.

The Poisson probability distribution is seen to provide a mathematical model from which useful information can be obtained in practical applications. The distribution and some situations to which it applies are studied, and ways to find answers to practical questions are noted. The unit includes exercises and a model exam, and provides answers to…

Waiting-time distributions of magnetic discontinuities: Clustering or Poisson process?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Greco, A.; Matthaeus, W. H.; Servidio, S.

2009-10-15

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Wavelets, ridgelets, and curvelets for Poisson noise removal.

PubMed

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.

Clinical characterization of 2D pressure field in human left ventricles

NASA Astrophysics Data System (ADS)

Borja, Maria; Rossini, Lorenzo; Martinez-Legazpi, Pablo; Benito, Yolanda; Alhama, Marta; Yotti, Raquel; Perez Del Villar, Candelas; Gonzalez-Mansilla, Ana; Barrio, Alicia; Fernandez-Aviles, Francisco; Bermejo, Javier; Khan, Andrew; Del Alamo, Juan Carlos

2014-11-01

The evaluation of left ventricle (LV) function in the clinical setting remains a challenge. Pressure gradient is a reliable and reproducible indicator of the LV function. We obtain 2D relative pressure field in the LV using in-vivo measurements obtained by processing Doppler-echocardiography images of healthy and dilated hearts. Exploiting mass conservation, we solve the Poisson pressure equation (PPE) dropping the time derivatives and viscous terms. The flow acceleration appears only in the boundary conditions, making our method weakly sensible to the time resolution of in-vivo acquisitions. To ensure continuity with respect to the discrete operator and grid used, a potential flow correction is applied beforehand, which gives another Poisson equation. The new incompressible velocity field ensures that the compatibility equation for the PPE is satisfied. Both Poisson equations are efficiently solved on a Cartesian grid using a multi-grid method and immersed boundary for the LV wall. The whole process is computationally inexpensive and could play a diagnostic role in the clinical assessment of LV function.

Eruption patterns of the chilean volcanoes Villarrica, Llaima, and Tupungatito

NASA Astrophysics Data System (ADS)

Muñoz, Miguel

1983-09-01

The historical eruption records of three Chilean volcanoes have been subjected to many statistical tests, and none have been found to differ significantly from random, or Poissonian, behaviour. The statistical analysis shows rough conformity with the descriptions determined from the eruption rate functions. It is possible that a constant eruption rate describes the activity of Villarrica; Llaima and Tupungatito present complex eruption rate patterns that appear, however, to have no statistical significance. Questions related to loading and extinction processes and to the existence of shallow secondary magma chambers to which magma is supplied from a deeper system are also addressed. The analysis and the computation of the serial correlation coefficients indicate that the three series may be regarded as stationary renewal processes. None of the test statistics indicates rejection of the Poisson hypothesis at a level less than 5%, but the coefficient of variation for the eruption series at Llaima is significantly different from the value expected for a Poisson process. Also, the estimates of the normalized spectrum of the counting process for the three series suggest a departure from the random model, but the deviations are not found to be significant at the 5% level. Kolmogorov-Smirnov and chi-squared test statistics, applied directly to ascertaining to which probability P the random Poisson model fits the data, indicate that there is significant agreement in the case of Villarrica ( P=0.59) and Tupungatito ( P=0.3). Even though the P-value for Llaima is a marginally significant 0.1 (which is equivalent to rejecting the Poisson model at the 90% confidence level), the series suggests that nonrandom features are possibly present in the eruptive activity of this volcano.

Filling of a Poisson trap by a population of random intermittent searchers.

PubMed

Bressloff, Paul C; Newby, Jay M

2012-03-01

We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→∞, in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f(n)(t). The latter is determined by the integrated Poisson rate μ(t)=∫(0)(t)λ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n.

Automatic detection of key innovations, rate shifts, and diversity-dependence on phylogenetic trees.

PubMed

Rabosky, Daniel L

2014-01-01

A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify heterogeneous mixtures of dynamic processes within single phylogenies. I developed a method that can identify arbitrary numbers of time-varying diversification processes on phylogenies without specifying their locations in advance. The method uses reversible-jump Markov Chain Monte Carlo to move between model subspaces that vary in the number of distinct diversification regimes. The model assumes that changes in evolutionary regimes occur across the branches of phylogenetic trees under a compound Poisson process and explicitly accounts for rate variation through time and among lineages. Using simulated datasets, I demonstrate that the method can be used to quantify complex mixtures of time-dependent, diversity-dependent, and constant-rate diversification processes. I compared the performance of the method to the MEDUSA model of rate variation among lineages. As an empirical example, I analyzed the history of speciation and extinction during the radiation of modern whales. The method described here will greatly facilitate the exploration of macroevolutionary dynamics across large phylogenetic trees, which may have been shaped by heterogeneous mixtures of distinct evolutionary processes.

Automatic Detection of Key Innovations, Rate Shifts, and Diversity-Dependence on Phylogenetic Trees

PubMed Central

Rabosky, Daniel L.

2014-01-01

A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify heterogeneous mixtures of dynamic processes within single phylogenies. I developed a method that can identify arbitrary numbers of time-varying diversification processes on phylogenies without specifying their locations in advance. The method uses reversible-jump Markov Chain Monte Carlo to move between model subspaces that vary in the number of distinct diversification regimes. The model assumes that changes in evolutionary regimes occur across the branches of phylogenetic trees under a compound Poisson process and explicitly accounts for rate variation through time and among lineages. Using simulated datasets, I demonstrate that the method can be used to quantify complex mixtures of time-dependent, diversity-dependent, and constant-rate diversification processes. I compared the performance of the method to the MEDUSA model of rate variation among lineages. As an empirical example, I analyzed the history of speciation and extinction during the radiation of modern whales. The method described here will greatly facilitate the exploration of macroevolutionary dynamics across large phylogenetic trees, which may have been shaped by heterogeneous mixtures of distinct evolutionary processes. PMID:24586858

Joseph eleve des poissons au Gabon. Guide pour l'elevage des poissons (Joseph Raises Fish in Gabon. Guide for Raising Fish).

ERIC Educational Resources Information Center

Needham, Scott

A guide, in French, to raising fish for food and profit is designed to instruct and encourage Gabonese natives to establish family fisheries. It describes and illustrates in story form the process used to plan the fishery, clear the land, seek help from an agricultural agent, create a dam, make compost, plan and build the pond, feed the fish,…

A stochastic model for stationary dynamics of prices in real estate markets. A case of random intensity for Poisson moments of prices changes

NASA Astrophysics Data System (ADS)

Rusakov, Oleg; Laskin, Michael

2017-06-01

We consider a stochastic model of changes of prices in real estate markets. We suppose that in a book of prices the changes happen in points of jumps of a Poisson process with a random intensity, i.e. moments of changes sequently follow to a random process of the Cox process type. We calculate cumulative mathematical expectations and variances for the random intensity of this point process. In the case that the process of random intensity is a martingale the cumulative variance has a linear grows. We statistically process a number of observations of real estate prices and accept hypotheses of a linear grows for estimations as well for cumulative average, as for cumulative variance both for input and output prises that are writing in the book of prises.

First-principles study on the structure, elastic properties, hardness and electronic structure of TMB4 (TM=Cr, Re, Ru and Os) compounds

NASA Astrophysics Data System (ADS)

Pan, Y.; Zheng, W. T.; Guan, W. M.; Zhang, K. H.; Fan, X. F.

2013-11-01

The structural formation, elastic properties, hardness and electronic structure of TMB4 (TM=Cr, Re, Ru and Os) compounds are investigated using first-principles approach. The value of C22 for these compounds is almost two times bigger than the C11 and C33. The intrinsic hardness, shear modulus and Young's modulus are calculated to be in a sequence of CrB4>ReB4>RuB4>OsB4, and the Poisson's ratio and B/G ratio of TMB4 follow the order of CrB4

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

PubMed

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 (ν<1) or under-dispersion (ν>1) 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.

Information transfer with rate-modulated Poisson processes: a simple model for nonstationary stochastic resonance.

PubMed

Goychuk, I

2001-08-01

Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.

A Poisson process approximation for generalized K-5 confidence regions

NASA Technical Reports Server (NTRS)

Arsham, H.; Miller, D. R.

1982-01-01

One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.

Mixed-Poisson Point Process with Partially-Observed Covariates: Ecological Momentary Assessment of Smoking.

PubMed

Neustifter, Benjamin; Rathbun, Stephen L; Shiffman, Saul

2012-01-01

Ecological Momentary Assessment is an emerging method of data collection in behavioral research that may be used to capture the times of repeated behavioral events on electronic devices, and information on subjects' psychological states through the electronic administration of questionnaires at times selected from a probability-based design as well as the event times. A method for fitting a mixed Poisson point process model is proposed for the impact of partially-observed, time-varying covariates on the timing of repeated behavioral events. A random frailty is included in the point-process intensity to describe variation among subjects in baseline rates of event occurrence. Covariate coefficients are estimated using estimating equations constructed by replacing the integrated intensity in the Poisson score equations with a design-unbiased estimator. An estimator is also proposed for the variance of the random frailties. Our estimators are robust in the sense that no model assumptions are made regarding the distribution of the time-varying covariates or the distribution of the random effects. However, subject effects are estimated under gamma frailties using an approximate hierarchical likelihood. The proposed approach is illustrated using smoking data.

Toward negative Poisson's ratio composites: Investigation of the auxetic behavior of fibrous networks

NASA Astrophysics Data System (ADS)

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.

De Rham-Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space

NASA Astrophysics Data System (ADS)

Privault, Nicolas

2016-05-01

We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-Hodge-Kodaira decomposition as well as Weitzenböck and Clark-Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms.

Prediction study of structural, elastic and electronic properties of FeMP (M = Ti, Zr, Hf) compounds

NASA Astrophysics Data System (ADS)

Tanto, A.; Chihi, T.; Ghebouli, M. A.; Reffas, M.; Fatmi, M.; Ghebouli, B.

2018-06-01

First principles calculations are applied in the study of FeMP (M = Ti, Zr, Hf) compounds. We investigate the structural, elastic, mechanical and electronic properties by combining first-principles calculations with the CASTEP approach. For ideal polycrystalline FeMP (M = Ti, Zr, Hf) the shear modulus, Young's modulus, Poisson's ratio, elastic anisotropy indexes, Pugh's criterion, elastic wave velocities and Debye temperature are also calculated from the single crystal elastic constants. The shear anisotropic factors and anisotropy are obtained from the single crystal elastic constants. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal.

Optical Signal Processing: Poisson Image Restoration and Shearing Interferometry

NASA Technical Reports Server (NTRS)

Hong, Yie-Ming

1973-01-01

Optical signal processing can be performed in either digital or analog systems. Digital computers and coherent optical systems are discussed as they are used in optical signal processing. Topics include: image restoration; phase-object visualization; image contrast reversal; optical computation; image multiplexing; and fabrication of spatial filters. Digital optical data processing deals with restoration of images degraded by signal-dependent noise. When the input data of an image restoration system are the numbers of photoelectrons received from various areas of a photosensitive surface, the data are Poisson distributed with mean values proportional to the illuminance of the incoherently radiating object and background light. Optical signal processing using coherent optical systems is also discussed. Following a brief review of the pertinent details of Ronchi's diffraction grating interferometer, moire effect, carrier-frequency photography, and achromatic holography, two new shearing interferometers based on them are presented. Both interferometers can produce variable shear.

Generic Schemes for Single-Molecule Kinetics. 2: Information Content of the Poisson Indicator.

PubMed

Avila, Thomas R; Piephoff, D Evan; Cao, Jianshu

2017-08-24

Recently, we described a pathway analysis technique (paper 1) for analyzing generic schemes for single-molecule kinetics based upon the first-passage time distribution. Here, we employ this method to derive expressions for the Poisson indicator, a normalized measure of stochastic variation (essentially equivalent to the Fano factor and Mandel's Q parameter), for various renewal (i.e., memoryless) enzymatic reactions. We examine its dependence on substrate concentration, without assuming all steps follow Poissonian kinetics. Based upon fitting to the functional forms of the first two waiting time moments, we show that, to second order, the non-Poissonian kinetics are generally underdetermined but can be specified in certain scenarios. For an enzymatic reaction with an arbitrary intermediate topology, we identify a generic minimum of the Poisson indicator as a function of substrate concentration, which can be used to tune substrate concentration to the stochastic fluctuations and to estimate the largest number of underlying consecutive links in a turnover cycle. We identify a local maximum of the Poisson indicator (with respect to substrate concentration) for a renewal process as a signature of competitive binding, either between a substrate and an inhibitor or between multiple substrates. Our analysis explores the rich connections between Poisson indicator measurements and microscopic kinetic mechanisms.

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

NASA Astrophysics Data System (ADS)

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.

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals

NASA Astrophysics Data System (ADS)

Frejlich, Pedro; Mărcuț, Ioan

2018-03-01

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.

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

PubMed

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.

Prognostics-based qualification of high-power white LEDs using Lévy process approach

NASA Astrophysics Data System (ADS)

Yung, Kam-Chuen; Sun, Bo; Jiang, Xiaopeng

2017-01-01

Due to their versatility in a variety of applications and the growing market demand, high-power white light-emitting diodes (LEDs) have attracted considerable attention. Reliability qualification testing is an essential part of the product development process to ensure the reliability of a new LED product before its release. However, the widely used IES-TM-21 method does not provide comprehensive reliability information. For more accurate and effective qualification, this paper presents a novel method based on prognostics techniques. Prognostics is an engineering technology predicting the future reliability or determining the remaining useful lifetime (RUL) of a product by assessing the extent of deviation or degradation from its expected normal operating conditions. A Lévy subordinator of a mixed Gamma and compound Poisson process is used to describe the actual degradation process of LEDs characterized by random sporadic small jumps of degradation degree, and the reliability function is derived for qualification with different distribution forms of jump sizes. The IES LM-80 test results reported by different LED vendors are used to develop and validate the qualification methodology. This study will be helpful for LED manufacturers to reduce the total test time and cost required to qualify the reliability of an LED product.

Probabilistic reasoning in data analysis.

PubMed

Sirovich, Lawrence

2011-09-20

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on probabilistic reasoning in the analysis of biological data. General probabilistic frameworks are introduced, and a number of standard probability distributions are described using simple intuitive ideas. Particular attention is focused on random arrivals that are independent of prior history (Markovian events), with an emphasis on waiting times, Poisson processes, and Poisson probability distributions. The use of these various probability distributions is applied to biomedical problems, including several classic experimental studies.

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

NASA Astrophysics Data System (ADS)

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.

Overdispersion of the Molecular Clock: Temporal Variation of Gene-Specific Substitution Rates in Drosophila

PubMed Central

Hartl, Daniel L.

2008-01-01

Simple models of molecular evolution assume that sequences evolve by a Poisson process in which nucleotide or amino acid substitutions occur as rare independent events. In these models, the expected ratio of the variance to the mean of substitution counts equals 1, and substitution processes with a ratio greater than 1 are called overdispersed. Comparing the genomes of 10 closely related species of Drosophila, we extend earlier evidence for overdispersion in amino acid replacements as well as in four-fold synonymous substitutions. The observed deviation from the Poisson expectation can be described as a linear function of the rate at which substitutions occur on a phylogeny, which implies that deviations from the Poisson expectation arise from gene-specific temporal variation in substitution rates. Amino acid sequences show greater temporal variation in substitution rates than do four-fold synonymous sequences. Our findings provide a general phenomenological framework for understanding overdispersion in the molecular clock. Also, the presence of substantial variation in gene-specific substitution rates has broad implications for work in phylogeny reconstruction and evolutionary rate estimation. PMID:18480070

Computation of solar perturbations with Poisson series

NASA Technical Reports Server (NTRS)

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.

Application of spatial Poisson process models to air mass thunderstorm rainfall

NASA Technical Reports Server (NTRS)

Eagleson, P. S.; Fennessy, N. M.; Wang, Qinliang; Rodriguez-Iturbe, I.

1987-01-01

Eight years of summer storm rainfall observations from 93 stations in and around the 154 sq km Walnut Gulch catchment of the Agricultural Research Service, U.S. Department of Agriculture, in Arizona are processed to yield the total station depths of 428 storms. Statistical analysis of these random fields yields the first two moments, the spatial correlation and variance functions, and the spatial distribution of total rainfall for each storm. The absolute and relative worth of three Poisson models are evaluated by comparing their prediction of the spatial distribution of storm rainfall with observations from the second half of the sample. The effect of interstorm parameter variation is examined.

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

NASA Astrophysics Data System (ADS)

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 slightly outperformed the other MRC models with respect to the intensity-frequency relationship. To assess the performance of the coupled Poisson rectangular pulse and constrained cascade model, precipitation events were stochastically generated by the Poisson rectangular pulse model and then disaggregated by the constrained cascade model. We found that the coupled model performs satisfactorily in terms of the temporal pattern of the precipitation time series, event characteristics and the intensity-frequency relationship.

Weak convergence to isotropic complex [Formula: see text] random measure.

PubMed

Wang, Jun; Li, Yunmeng; Sang, Liheng

2017-01-01

In this paper, we prove that an isotropic complex symmetric α -stable random measure ([Formula: see text]) can be approximated by a complex process constructed by integrals based on the Poisson process with random intensity.

Estimation of parameters in Shot-Noise-Driven Doubly Stochastic Poisson processes using the EM algorithm--modeling of pre- and postsynaptic spike trains.

PubMed

Mino, H

2007-01-01

To estimate the parameters, the impulse response (IR) functions of some linear time-invariant systems generating intensity processes, in Shot-Noise-Driven Doubly Stochastic Poisson Process (SND-DSPP) in which multivariate presynaptic spike trains and postsynaptic spike trains can be assumed to be modeled by the SND-DSPPs. An explicit formula for estimating the IR functions from observations of multivariate input processes of the linear systems and the corresponding counting process (output process) is derived utilizing the expectation maximization (EM) algorithm. The validity of the estimation formula was verified through Monte Carlo simulations in which two presynaptic spike trains and one postsynaptic spike train were assumed to be observable. The IR functions estimated on the basis of the proposed identification method were close to the true IR functions. The proposed method will play an important role in identifying the input-output relationship of pre- and postsynaptic neural spike trains in practical situations.

Determining the Uncertainty of X-Ray Absorption Measurements

PubMed Central

Wojcik, Gary S.

2004-01-01

X-ray absorption (or more properly, x-ray attenuation) techniques have been applied to study the moisture movement in and moisture content of materials like cement paste, mortar, and wood. An increase in the number of x-ray counts with time at a location in a specimen may indicate a decrease in moisture content. The uncertainty of measurements from an x-ray absorption system, which must be known to properly interpret the data, is often assumed to be the square root of the number of counts, as in a Poisson process. No detailed studies have heretofore been conducted to determine the uncertainty of x-ray absorption measurements or the effect of averaging data on the uncertainty. In this study, the Poisson estimate was found to adequately approximate normalized root mean square errors (a measure of uncertainty) of counts for point measurements and profile measurements of water specimens. The Poisson estimate, however, was not reliable in approximating the magnitude of the uncertainty when averaging data from paste and mortar specimens. Changes in uncertainty from differing averaging procedures were well-approximated by a Poisson process. The normalized root mean square errors decreased when the x-ray source intensity, integration time, collimator size, and number of scanning repetitions increased. Uncertainties in mean paste and mortar count profiles were kept below 2 % by averaging vertical profiles at horizontal spacings of 1 mm or larger with counts per point above 4000. Maximum normalized root mean square errors did not exceed 10 % in any of the tests conducted. PMID:27366627

Structural, electronic, elastic, thermoelectric and thermodynamic properties of the NbMSb half heusler (M=Fe, Ru, Os) compounds with first principle calculations

NASA Astrophysics Data System (ADS)

Abid, O. Miloud; Menouer, S.; Yakoubi, A.; Khachai, H.; Omran, S. Bin; Murtaza, G.; Prakash, Deo; Khenata, R.; Verma, K. D.

2016-05-01

The structural, electronic, elastic, thermoelectric and thermodynamic properties of NbMSb (M = Fe, Ru, Os) half heusler compounds are reported. The full-potential linearized augmented plane wave (FP-LAPW) plus local orbital (lo) method, based on the density functional theory (DFT) was employed for the present study. The equilibrium lattice parameter results are in good compliance with the available experimental measurements. The electronic band structure and Boltzmann transport calculations indicated a narrow indirect energy band gap for the compound having electronic structure favorable for thermoelectric performance as well as with substantial thermopowers at temperature ranges from 300 K to 800 K. Furthermore, good potential for thermoelectric performance (thermopower S ≥ 500 μeV) was found at higher temperature. In addition, the analysis of the charge density, partial and total densities of states (DOS) of three compounds demonstrate their semiconducting, ionic and covalent characters. Conversely, the calculated values of the Poisson's ratio and the B/G ratio indicate their ductile makeup. The thermal properties of the compounds were calculated by quasi-harmonic Debye model as implemented in the GIBBS code.

A dictionary learning approach for Poisson image deblurring.

PubMed

Ma, Liyan; Moisan, Lionel; Yu, Jian; Zeng, Tieyong

2013-07-01

The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a maximum a posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patch-based sparse representation prior over a learned dictionary, the pixel-based total variation regularization term and a data-fidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio value and the method noise, the proposed algorithm outperforms state-of-the-art methods.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

First Principles Investigation of Fluorine Based Strontium Series of Perovskites

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2016-11-01

Density functional theory is used to explore structural, elastic, and mechanical properties of SrLiF3, SrNaF3, SrKF3 and SrRbF3 fluoroperovskite compounds by means of an ab-initio Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method. Several lattice parameters are employed to obtain accurate equilibrium volume (Vo). The resultant quantities include ground state energy, elastic constants, shear modulus, bulk modulus, young's modulus, cauchy's pressure, poisson's ratio, shear constant, ratio of elastic anisotropy factor, kleinman's parameter, melting temperature, and lame's coefficient. The calculated structural parameters via DFT as well as analytical methods are found to be consistent with experimental findings. Chemical bonding is used to investigate corresponding chemical trends which authenticate combination of covalent-ionic behavior. Furthermore electron density plots as well as elastic and mechanical properties are reported for the first time which reveals that fluorine based strontium series of perovskites are mechanically stable and posses weak resistance towards shear deformation as compared to resistance towards unidirectional compression while brittleness and ionic behavior is dominated in them which decreases from SrLiF3 to SrRbF3. Calculated cauchy's pressure, poisson's ratio and B/G ratio also proves ionic nature in these compounds. The present methodology represents an effective and influential approach to calculate the whole set of elastic and mechanical parameters which would support to understand various physical phenomena and empower device engineers for implementing these materials in numerous applications.

Ab Initio Study of Electronic Structure, Elastic and Transport Properties of Fluoroperovskite LiBeF3

NASA Astrophysics Data System (ADS)

Benmhidi, H.; Rached, H.; Rached, D.; Benkabou, M.

2017-04-01

The aim of this work is to investigate the electronic, mechanical, and transport properties of the fluoroperovskite compound LiBeF3 by first-principles calculations using the full-potential linear muffin-tin orbital method based on density functional theory within the local density approximation. The independent elastic constants and related mechanical properties including the bulk modulus ( B), shear modulus ( G), Young's modulus ( E), and Poisson's ratio ( ν) have been studied, yielding the elastic moduli, shear wave velocities, and Debye temperature. According to the electronic properties, this compound is an indirect-bandgap material, in good agreement with available theoretical data. The electron effective mass, hole effective mass, and energy bandgaps with their volume and pressure dependence are investigated for the first time.

First principles predictions of electronic and elastic properties of BaPb2As2 in the ThCr2Si2-type structure

NASA Astrophysics Data System (ADS)

Bourourou, Y.; Amari, S.; Yahiaoui, I. E.; Bouhafs, B.

2018-01-01

A first-principles approach is used to predicts the electronic and elastic properties of BaPb2As2 superconductor compound, using full-potential linearized augmented plane wave plus local orbitals (FP-L/APW+lo) scheme within the local density approximation LDA. The calculated equilibrium structural parameter a agree well with the experiment while the c/a ratio is far away from the experimental result. The band structure, density of states, together with the charge density and chemical bonding are discussed. The calculated elastic constants for our compound indicate that it is mechanically stable at ambient pressure. Polycrystalline elastic moduli (Young's, Bulk, shear Modulus and the Poisson's ratio) were calculated according to the Voigte-Reusse-Hill (VRH) average.

Structural stability, elastic and thermodynamic properties of Au-Cu alloys from first-principles calculations

NASA Astrophysics Data System (ADS)

Kong, Ge-Xing; Ma, Xiao-Juan; Liu, Qi-Jun; Li, Yong; Liu, Zheng-Tang

2018-03-01

Using first-principles calculations method based on density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE) implementation of the generalized gradient approximation (GGA), we investigate the structural, elastic and thermodynamic properties of gold-copper intermetallic compounds (Au-Cu ICs). The calculated lattice parameters are in excellent agreement with experimental data. The elastic constants show that all the investigated Au-Cu alloys are mechanically stable. Elastic properties, including the shear modulus, Young's modulus, Poisson's ratio and Pugh's indicator, of the intermetallic compounds are evaluated and discussed, with special attention to the remarkable anisotropy displayed by Au-Cu ICs. Thermodynamic and transport properties including the Debye temperature, thermal conductivity and melting point are predicted from the averaged sound velocity and elastic moduli, using semi-empirical formulas.

Yes, the GIGP Really Does Work--And Is Workable!

ERIC Educational Resources Information Center

Burrell, Quentin L.; Fenton, Michael R.

1993-01-01

Discusses the generalized inverse Gaussian-Poisson (GIGP) process for informetric modeling. Negative binomial distribution is discussed, construction of the GIGP process is explained, zero-truncated GIGP is considered, and applications of the process with journals, library circulation statistics, and database index terms are described. (50…

Exploring the evolutionary mechanism of complex supply chain systems using evolving hypergraphs

NASA Astrophysics Data System (ADS)

Suo, Qi; Guo, Jin-Li; Sun, Shiwei; Liu, Han

2018-01-01

A new evolutionary model is proposed to describe the characteristics and evolution pattern of supply chain systems using evolving hypergraphs, in which nodes represent enterprise entities while hyperedges represent the relationships among diverse trades. The nodes arrive at the system in accordance with a Poisson process, with the evolving process incorporating the addition of new nodes, linking of old nodes, and rewiring of links. Grounded in the Poisson process theory and continuum theory, the stationary average hyperdegree distribution is shown to follow a shifted power law (SPL), and the theoretical predictions are consistent with the results of numerical simulations. Testing the impact of parameters on the model yields a positive correlation between hyperdegree and degree. The model also uncovers macro characteristics of the relationships among enterprises due to the microscopic interactions among individuals.

Study of photon correlation techniques for processing of laser velocimeter signals

NASA Technical Reports Server (NTRS)

Mayo, W. T., Jr.

1977-01-01

The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.

Stochastic description of geometric phase for polarized waves in random media

NASA Astrophysics Data System (ADS)

Boulanger, Jérémie; Le Bihan, Nicolas; Rossetto, Vincent

2013-01-01

We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible to measure an outgoing polarization distribution. We consider thin scattering media illuminated by a polarized source and compute the probability distribution function of the polarization on the exit surface. We solve the direct problem using compound Poisson processes on the rotation group SO(3) and non-commutative harmonic analysis. We obtain an exact expression for the polarization distribution which generalizes previous works and design an algorithm solving the inverse problem of estimating the scattering properties of the medium from the measured polarization distribution. This technique applies to thin disordered layers, spatially fluctuating media and multiple scattering systems and is based on the polarization but not on the signal amplitude. We suggest that it can be used as a non-invasive testing method.

Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

PubMed Central

Moore, Brian R.; Höhna, Sebastian; May, Michael R.; Rannala, Bruce; Huelsenbeck, John P.

2016-01-01

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversification-rate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM. PMID:27512038

Inhomogeneous Poisson process rate function inference from dead-time limited observations.

PubMed

Verma, Gunjan; Drost, Robert J

2017-05-01

The estimation of an inhomogeneous Poisson process (IHPP) rate function from a set of process observations is an important problem arising in optical communications and a variety of other applications. However, because of practical limitations of detector technology, one is often only able to observe a corrupted version of the original process. In this paper, we consider how inference of the rate function is affected by dead time, a period of time after the detection of an event during which a sensor is insensitive to subsequent IHPP events. We propose a flexible nonparametric Bayesian approach to infer an IHPP rate function given dead-time limited process realizations. Simulation results illustrate the effectiveness of our inference approach and suggest its ability to extend the utility of existing sensor technology by permitting more accurate inference on signals whose observations are dead-time limited. We apply our inference algorithm to experimentally collected optical communications data, demonstrating the practical utility of our approach in the context of channel modeling and validation.

Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events.

PubMed

Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon

2016-01-01

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.

Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events

PubMed Central

Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon

2016-01-01

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate. PMID:28066225

FIND: difFerential chromatin INteractions Detection using a spatial Poisson process

PubMed Central

Chen, Yang; Zhang, Michael Q.

2018-01-01

Polymer-based simulations and experimental studies indicate the existence of a spatial dependency between the adjacent DNA fibers involved in the formation of chromatin loops. However, the existing strategies for detecting differential chromatin interactions assume that the interacting segments are spatially independent from the other segments nearby. To resolve this issue, we developed a new computational method, FIND, which considers the local spatial dependency between interacting loci. FIND uses a spatial Poisson process to detect differential chromatin interactions that show a significant difference in their interaction frequency and the interaction frequency of their neighbors. Simulation and biological data analysis show that FIND outperforms the widely used count-based methods and has a better signal-to-noise ratio. PMID:29440282

Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation

NASA Astrophysics Data System (ADS)

Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo

2014-03-01

Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.

Replication of Cancellation Orders Using First-Passage Time Theory in Foreign Currency Market

NASA Astrophysics Data System (ADS)

Boilard, Jean-François; Kanazawa, Kiyoshi; Takayasu, Hideki; Takayasu, Misako

Our research focuses on the annihilation dynamics of limit orders in a spot foreign currency market for various currency pairs. We analyze the cancellation order distribution conditioned on the normalized distance from the mid-price; where the normalized distance is defined as the final distance divided by the initial distance. To reproduce real data, we introduce two simple models that assume the market price moves randomly and cancellation occurs either after fixed time t or following the Poisson process. Results of our model qualitatively reproduce basic statistical properties of cancellation orders of the data when limit orders are cancelled according to the Poisson process. We briefly discuss implication of our findings in the construction of more detailed microscopic models.

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

NASA Astrophysics Data System (ADS)

Radev, Dimitar; Lokshina, Izabella

2010-11-01

The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.

Quasi-neutral limit of Euler–Poisson system of compressible fluids coupled to a magnetic field

NASA Astrophysics Data System (ADS)

Yang, Jianwei

2018-06-01

In this paper, we consider the quasi-neutral limit of a three-dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field. We prove that, as Debye length tends to zero, periodic initial-value problems of the model have unique smooth solutions existing in the time interval where the ideal incompressible magnetohydrodynamic equations has smooth solution. Meanwhile, it is proved that smooth solutions converge to solutions of incompressible magnetohydrodynamic equations with a sharp convergence rate in the process of quasi-neutral limit.

Effect of non-Poisson samples on turbulence spectra from laser velocimetry

NASA Technical Reports Server (NTRS)

Sree, Dave; Kjelgaard, Scott O.; Sellers, William L., III

1994-01-01

Spectral analysis of laser velocimetry (LV) data plays an important role in characterizing a turbulent flow and in estimating the associated turbulence scales, which can be helpful in validating theoretical and numerical turbulence models. The determination of turbulence scales is critically dependent on the accuracy of the spectral estimates. Spectral estimations from 'individual realization' laser velocimetry data are typically based on the assumption of a Poisson sampling process. What this Note has demonstrated is that the sampling distribution must be considered before spectral estimates are used to infer turbulence scales.

Fission meter and neutron detection using poisson distribution comparison

DOEpatents

Rowland, Mark S; Snyderman, Neal J

2014-11-18

A neutron detector system and method for discriminating fissile material from non-fissile material wherein a digital data acquisition unit collects data at high rate, and in real-time processes large volumes of data directly into information that a first responder can use to discriminate materials. The system comprises counting neutrons from the unknown source and detecting excess grouped neutrons to identify fission in the unknown source. Comparison of the observed neutron count distribution with a Poisson distribution is performed to distinguish fissile material from non-fissile material.

Method for resonant measurement

DOEpatents

Rhodes, G.W.; Migliori, A.; Dixon, R.D.

1996-03-05

A method of measurement of objects to determine object flaws, Poisson`s ratio ({sigma}) and shear modulus ({mu}) is shown and described. First, the frequency for expected degenerate responses is determined for one or more input frequencies and then splitting of degenerate resonant modes are observed to identify the presence of flaws in the object. Poisson`s ratio and the shear modulus can be determined by identification of resonances dependent only on the shear modulus, and then using that shear modulus to find Poisson`s ratio using other modes dependent on both the shear modulus and Poisson`s ratio. 1 fig.

Formulation of the Multi-Hit Model With a Non-Poisson Distribution of Hits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassiliev, Oleg N., E-mail: Oleg.Vassiliev@albertahealthservices.ca

2012-07-15

Purpose: We proposed a formulation of the multi-hit single-target model in which the Poisson distribution of hits was replaced by a combination of two distributions: one for the number of particles entering the target and one for the number of hits a particle entering the target produces. Such an approach reflects the fact that radiation damage is a result of two different random processes: particle emission by a radiation source and interaction of particles with matter inside the target. Methods and Materials: Poisson distribution is well justified for the first of the two processes. The second distribution depends on howmore » a hit is defined. To test our approach, we assumed that the second distribution was also a Poisson distribution. The two distributions combined resulted in a non-Poisson distribution. We tested the proposed model by comparing it with previously reported data for DNA single- and double-strand breaks induced by protons and electrons, for survival of a range of cell lines, and variation of the initial slopes of survival curves with radiation quality for heavy-ion beams. Results: Analysis of cell survival equations for this new model showed that they had realistic properties overall, such as the initial and high-dose slopes of survival curves, the shoulder, and relative biological effectiveness (RBE) In most cases tested, a better fit of survival curves was achieved with the new model than with the linear-quadratic model. The results also suggested that the proposed approach may extend the multi-hit model beyond its traditional role in analysis of survival curves to predicting effects of radiation quality and analysis of DNA strand breaks. Conclusions: Our model, although conceptually simple, performed well in all tests. The model was able to consistently fit data for both cell survival and DNA single- and double-strand breaks. It correctly predicted the dependence of radiation effects on parameters of radiation quality.« less

Including long-range dependence in integrate-and-fire models of the high interspike-interval variability of cortical neurons.

PubMed

Jackson, B Scott

2004-10-01

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (nonPoissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have long-range dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

A Random Variable Transformation Process.

ERIC Educational Resources Information Center

Scheuermann, Larry

1989-01-01

Provides a short BASIC program, RANVAR, which generates random variates for various theoretical probability distributions. The seven variates include: uniform, exponential, normal, binomial, Poisson, Pascal, and triangular. (MVL)

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

PubMed Central

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

Log Normal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of Alpha Particle Track Autoradiography

PubMed Central

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

2008-01-01

Recently, the distribution of radioactivity among a population of cells labeled with 210Po was shown to be well described by a log normal distribution function (J Nucl Med 47, 6 (2006) 1049-1058) with the aid of an autoradiographic approach. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analyses of these data. Methods The measured distributions of alpha particle tracks per cell were subjected to statistical tests with Poisson (P), log normal (LN), and Poisson – log normal (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 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. Conclusions 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:16741316

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

PubMed Central

Yang, Sejung; Lee, Byung-Uk

2015-01-01

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138

Numerical solutions for patterns statistics on Markov chains.

PubMed

Nuel, Gregory

2006-01-01

We propose here a review of the methods available to compute pattern statistics on text generated by a Markov source. Theoretical, but also numerical aspects are detailed for a wide range of techniques (exact, Gaussian, large deviations, binomial and compound Poisson). The SPatt package (Statistics for Pattern, free software available at http://stat.genopole.cnrs.fr/spatt) implementing all these methods is then used to compare all these approaches in terms of computational time and reliability in the most complete pattern statistics benchmark available at the present time.

Mapping species abundance by a spatial zero-inflated Poisson model: a case study in the Wadden Sea, the Netherlands.

PubMed

Lyashevska, Olga; Brus, Dick J; van der Meer, Jaap

2016-01-01

The objective of the study was to provide a general procedure for mapping species abundance when data are zero-inflated and spatially correlated counts. The bivalve species Macoma balthica was observed on a 500×500 m grid in the Dutch part of the Wadden Sea. In total, 66% of the 3451 counts were zeros. A zero-inflated Poisson mixture model was used to relate counts to environmental covariates. Two models were considered, one with relatively fewer covariates (model "small") than the other (model "large"). The models contained two processes: a Bernoulli (species prevalence) and a Poisson (species intensity, when the Bernoulli process predicts presence). The model was used to make predictions for sites where only environmental data are available. Predicted prevalences and intensities show that the model "small" predicts lower mean prevalence and higher mean intensity, than the model "large". Yet, the product of prevalence and intensity, which might be called the unconditional intensity, is very similar. Cross-validation showed that the model "small" performed slightly better, but the difference was small. The proposed methodology might be generally applicable, but is computer intensive.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

Sojourning with the Homogeneous Poisson Process.

PubMed

Liu, Piaomu; Peña, Edsel A

2016-01-01

In this pedagogical article, distributional properties, some surprising, pertaining to the homogeneous Poisson process (HPP), when observed over a possibly random window, are presented. Properties of the gap-time that covered the termination time and the correlations among gap-times of the observed events are obtained. Inference procedures, such as estimation and model validation, based on event occurrence data over the observation window, are also presented. We envision that through the results in this paper, a better appreciation of the subtleties involved in the modeling and analysis of recurrent events data will ensue, since the HPP is arguably one of the simplest among recurrent event models. In addition, the use of the theorem of total probability, Bayes theorem, the iterated rules of expectation, variance and covariance, and the renewal equation could be illustrative when teaching distribution theory, mathematical statistics, and stochastic processes at both the undergraduate and graduate levels. This article is targeted towards both instructors and students.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Atomic Charge Parameters for the Finite Difference Poisson-Boltzmann Method Using Electronegativity Neutralization.

PubMed

Yang, Qingyi; Sharp, Kim A

2006-07-01

An optimization of Rappe and Goddard's charge equilibration (QEq) method of assigning atomic partial charges is described. This optimization is designed for fast and accurate calculation of solvation free energies using the finite difference Poisson-Boltzmann (FDPB) method. The optimization is performed against experimental small molecule solvation free energies using the FDPB method and adjusting Rappe and Goddard's atomic electronegativity values. Using a test set of compounds for which experimental solvation energies are available and a rather small number of parameters, very good agreement was obtained with experiment, with a mean unsigned error of about 0.5 kcal/mol. The QEq atomic partial charge assignment method can reflect the effects of the conformational changes and solvent induction on charge distribution in molecules. In the second section of the paper we examined this feature with a study of the alanine dipeptide conformations in water solvent. The different contributions to the energy surface of the dipeptide were examined and compared with the results from fixed CHARMm charge potential, which is widely used for molecular dynamics studies.

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

NASA Technical Reports Server (NTRS)

Erkmen, Baris I.; Moision, Bruce E.

2010-01-01

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Environmental heterogeneity blurs the signature of dispersal syndromes on spatial patterns of woody species in a moist tropical forest

PubMed Central

Velázquez, Eduardo; Escudero, Adrián; de la Cruz, Marcelino

2018-01-01

We assessed the relative importance of dispersal limitation, environmental heterogeneity and their joint effects as determinants of the spatial patterns of 229 species in the moist tropical forest of Barro Colorado Island (Panama). We differentiated five types of species according to their dispersal syndrome; autochorous, anemochorous, and zoochorous species with small, medium-size and large fruits. We characterized the spatial patterns of each species and we checked whether they were best fitted by Inhomogeneous Poisson (IPP), Homogeneous Poisson cluster (HPCP) and Inhomogeneous Poisson cluster processes (IPCP) by means of the Akaike Information Criterion. We also assessed the influence of species’ dispersal mode in the average cluster size. We found that 63% of the species were best fitted by IPCP regardless of their dispersal syndrome, although anemochorous species were best described by HPCP. Our results indicate that spatial patterns of tree species in this forest cannot be explained only by dispersal limitation, but by the joint effects of dispersal limitation and environmental heterogeneity. The absence of relationships between dispersal mode and degree of clustering suggests that several processes modify the original spatial pattern generated by seed dispersal. These findings emphasize the importance of fitting point process models with a different biological meaning when studying the main determinants of spatial structure in plant communities. PMID:29451871

Applying Flammability Limit Probabilities and the Normoxic Upward Limiting Pressure Concept to NASA STD-6001 Test 1

NASA Technical Reports Server (NTRS)

Olson, Sandra L.; Beeson, Harold; Fernandez-Pello, A. Carlos

2014-01-01

Repeated Test 1 extinction tests near the upward flammability limit are expected to follow a Poisson process trend. This Poisson process trend suggests that rather than define a ULOI and MOC (which requires two limits to be determined), it might be better to define a single upward limit as being where 1/e (where e (approx. equal to 2.7183) is the characteristic time of the normalized Poisson process) of the materials burn, or, rounding, where approximately 1/3 of the samples fail the test (and burn). Recognizing that spacecraft atmospheres will not bound the entire oxygen-pressure parameter space, but actually lie along the normoxic atmosphere control band, we can focus the materials flammability testing along this normoxic band. A Normoxic Upward Limiting Pressure (NULP) is defined that determines the minimum safe total pressure for a material within the constant partial pressure control band. Then, increasing this pressure limit by a factor of safety, we can define the material as being safe to use at the NULP + SF (where SF is on the order of 10 kilopascal, based on existing flammability data). It is recommended that the thickest material to be tested with the current Test 1 igniter should be 3 mm thick (1/8 inches) to avoid the problem of differentiating between an ignition limit and a true flammability limit.

77 FR 13691 - Qualification of Drivers; Exemption Applications; Vision

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-07

..., ocular hypertension, retinal detachment, cataracts and corneal scaring. In most cases, their eye... Application of Multiple Regression Analysis of a Poisson Process,'' Journal of American Statistical...

Internal Stress Distribution Measurement of TIG Welded SUS304 Samples Using Neutron Diffraction Technique

NASA Astrophysics Data System (ADS)

Muslih, M. Refai; Sumirat, I.; Sairun; Purwanta

2008-03-01

The distribution of residual stress of SUS304 samples that were undergone TIG welding process with four different electric currents has been measured. The welding has been done in the middle part of the samples that was previously grooved by milling machine. Before they were welded the samples were annealed at 650 degree Celsius for one hour. The annealing process was done to eliminate residual stress generated by grooving process so that the residual stress within the samples was merely produced from welding process. The calculation of distribution of residual stress was carried out by measuring the strains within crystal planes of Fe(220) SUS304. Strain, Young modulus, and Poisson ratio of Fe(220) SUS304 were measured using DN1-M neutron diffractometer. Young modulus and Poisson ratio of Fe(220) SUS304 sample were measured in-situ. The result of calculations showed that distribution of residual stress of SUS304 in the vicinity of welded area is influenced both by treatments given at the samples-making process and by the electric current used during welding process.

First principle study of structural, elastic and electronic properties of APt3 (A=Mg, Sc, Y and Zr)

NASA Astrophysics Data System (ADS)

Benamer, A.; Roumili, A.; Medkour, Y.; Charifi, Z.

2018-02-01

We report results obtained from first principle calculations on APt3 compounds with A=Mg, Sc, Y and Zr. Our results of the lattice parameter a are in good agreement with experimental data, with deviations less than 0.8%. Single crystal elastic constants are calculated, then polycrystalline elastic moduli (bulk, shear and Young moduli, Poisson ration, anisotropy factor) are presented. Based on Debye model, Debye temperature ϴD is calculated from the sound velocities Vl, Vt and Vm. Band structure results show that the studied compounds are electrical conductors, the conduction mechanism is assured by Pt-d electrons. Different hybridisation states are observed between Pt-d and A-d orbitals. The study of the charge density distribution and the population analysis shows the coexistence of ionic, covalent and metallic bonds.

The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks.

PubMed

Guo, Jin-Li; Suo, Qi; Shen, Ai-Zhong; Forrest, Jeffrey

2016-09-27

To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution of hyperedge cardinalities is studied. The Poisson process theory is used to describe the arrival process of new node batches. And, by using the Poisson process theory and a continuity technique, the hypernetwork is analyzed and the characteristic equation of hyperedge cardinalities is obtained. Additionally, an analytical expression for the stationary average hyperedge cardinality distribution is derived by employing the characteristic equation, from which Bose-Einstein condensation in the hypernetwork is obtained. The theoretical analyses in this paper agree with the conducted numerical simulations. This is the first study on the hyperedge cardinality in hypernetworks, where Bose-Einstein condensation can be regarded as a special case of hypernetworks. Moreover, a condensation degree is also discussed with which Bose-Einstein condensation can be classified.

Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

NASA Astrophysics Data System (ADS)

Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János

2014-01-01

Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

FIND: difFerential chromatin INteractions Detection using a spatial Poisson process.

PubMed

Djekidel, Mohamed Nadhir; Chen, Yang; Zhang, Michael Q

2018-02-12

Polymer-based simulations and experimental studies indicate the existence of a spatial dependency between the adjacent DNA fibers involved in the formation of chromatin loops. However, the existing strategies for detecting differential chromatin interactions assume that the interacting segments are spatially independent from the other segments nearby. To resolve this issue, we developed a new computational method, FIND, which considers the local spatial dependency between interacting loci. FIND uses a spatial Poisson process to detect differential chromatin interactions that show a significant difference in their interaction frequency and the interaction frequency of their neighbors. Simulation and biological data analysis show that FIND outperforms the widely used count-based methods and has a better signal-to-noise ratio. © 2018 Djekidel et al.; Published by Cold Spring Harbor Laboratory Press.

Simulation of diffuse-charge capacitance in electric double layer capacitors

NASA Astrophysics Data System (ADS)

Sun, Ning; Gersappe, Dilip

2017-01-01

We use a Lattice Boltzmann Model (LBM) in order to simulate diffuse-charge dynamics in Electric Double Layer Capacitors (EDLCs). Simulations are carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). The steric effect of concentrated solutions is considered by using a Modified Poisson-Nernst-Planck (MPNP) equations and compared with regular Poisson-Nernst-Planck (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. Our studies show how electrode morphology can be used to tailor the properties of supercapacitors.

A stochastical event-based continuous time step rainfall generator based on Poisson rectangular pulse and microcanonical random cascade models

NASA Astrophysics Data System (ADS)

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

2017-04-01

Rainfall variability within a storm is of major importance for fast hydrological processes, e.g. surface runoff, erosion and solute dissipation from surface soils. To investigate and simulate the impacts of within-storm variabilities on these processes, long time series of rainfall with high resolution are required. Yet, observed precipitation records of hourly or higher resolution are in most cases available only for a small number of stations and only for a few years. To obtain long time series of alternating rainfall events and interstorm periods while conserving the statistics of observed rainfall events, the Poisson model can be used. Multiplicative microcanonical random cascades have been widely applied to disaggregate rainfall time series from coarse to fine temporal resolution. We present a new coupling approach of the Poisson rectangular pulse model and the multiplicative microcanonical random cascade model that preserves the characteristics of rainfall events as well as inter-storm periods. In the first step, a Poisson rectangular pulse model is applied to generate discrete rainfall events (duration and mean intensity) and inter-storm periods (duration). The rainfall events are subsequently disaggregated to high-resolution time series (user-specified, e.g. 10 min resolution) by a multiplicative microcanonical random cascade model. One of the challenges of coupling these models is to parameterize the cascade model for the event durations generated by the Poisson model. In fact, the cascade model is best suited to downscale rainfall data with constant time step such as daily precipitation data. Without starting from a fixed time step duration (e.g. daily), the disaggregation of events requires some modifications of the multiplicative microcanonical random cascade model proposed by Olsson (1998): Firstly, the parameterization of the cascade model for events of different durations requires continuous functions for the probabilities of the multiplicative weights, which we implemented through sigmoid functions. Secondly, the branching of the first and last box is constrained to preserve the rainfall event durations generated by the Poisson rectangular pulse model. The event-based continuous time step rainfall generator has been developed and tested using 10 min and hourly rainfall data of four stations in North-Eastern Germany. The model performs well in comparison to observed rainfall in terms of event durations and mean event intensities as well as wet spell and dry spell durations. It is currently being tested using data from other stations across Germany and in different climate zones. Furthermore, the rainfall event generator is being applied in modelling approaches aimed at understanding the impact of rainfall variability on hydrological processes. Reference Olsson, J.: Evaluation of a scaling cascade model for temporal rainfall disaggregation, Hydrology and Earth System Sciences, 2, 19.30

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

NASA Astrophysics Data System (ADS)

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.

Poisson-event-based analysis of cell proliferation.

PubMed

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.

Statistical properties of several models of fractional random point processes

NASA Astrophysics Data System (ADS)

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.

Stability and Elastic, Electronic, and Thermodynamic Properties of Fe2TiSi1- x Sn x Compounds

NASA Astrophysics Data System (ADS)

Jong, Ju-Yong; Yan, Jihong; Zhu, Jingchuan; Kim, Chol-Jin

2017-10-01

We have systematically studied the structural, phase, and mechanical stability and elastic, electronic, and thermodynamic properties of Fe2TiSi1- x Sn x ( x = 0, 0.25, 0.5, 0.75, 1) compounds using first-principles calculations. The structural and phase stability and elastic properties of Fe2TiSi1- x Sn x ( x = 0, 0.25, 0.5, 0.75, 1) indicated that all of the compounds are thermodynamically and mechanically stable. The shear modulus, bulk modulus, Young's modulus, Poisson's ratio, electronic band structure, density of states, Debye temperature, and Grüneisen parameter of all the substituted compounds were studied. The results show that Sn substitution in Fe2TiSi enhances its stability and mechanical and thermoelectric properties. The Fe2TiSi1- x Sn x compounds have narrow bandgap from 0.144 eV and 0.472 eV for Sn substitution from 0 to 1. The calculated band structure and density of states (DOS) of Fe2TiSi1- x Sn x show that the thermoelectric properties can be improved at substituent concentration x of 0.75. The lattice thermal conductivity was significantly decreased in the Sn-substituted compounds, and all the results indicate that Fe2TiSi0.25Sn0.75 could be a new candidate high-performance thermoelectric material.

On the Singularity of the Vlasov-Poisson System

DOE Office of Scientific and Technical Information (OSTI.GOV)

and Hong Qin, Jian Zheng

2013-04-26

The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker- Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency v approaches zero. However, we show that the colllisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the approaching zero from the positive side.

On the singularity of the Vlasov-Poisson system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Jian; Qin, Hong; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08550

2013-09-15

The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker-Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency ν approaches zero. However, we show that the collisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the ν approaches zero from the positive side.

Stochastic Processes as True-Score Models for Highly Speeded Mental Tests.

ERIC Educational Resources Information Center

Moore, William E.

The previous theoretical development of the Poisson process as a strong model for the true-score theory of mental tests is discussed, and additional theoretical properties of the model from the standpoint of individual examinees are developed. The paper introduces the Erlang process as a family of test theory models and shows in the context of…

Bayesian semi-parametric analysis of Poisson change-point regression models: application to policy making in Cali, Colombia.

PubMed

Park, Taeyoung; Krafty, Robert T; Sánchez, Alvaro I

2012-07-27

A Poisson regression model with an offset assumes a constant baseline rate after accounting for measured covariates, which may lead to biased estimates of coefficients in an inhomogeneous Poisson process. To correctly estimate the effect of time-dependent covariates, we propose a Poisson change-point regression model with an offset that allows a time-varying baseline rate. When the nonconstant pattern of a log baseline rate is modeled with a nonparametric step function, the resulting semi-parametric model involves a model component of varying dimension and thus requires a sophisticated varying-dimensional inference to obtain correct estimates of model parameters of fixed dimension. To fit the proposed varying-dimensional model, we devise a state-of-the-art MCMC-type algorithm based on partial collapse. The proposed model and methods are used to investigate an association between daily homicide rates in Cali, Colombia and policies that restrict the hours during which the legal sale of alcoholic beverages is permitted. While simultaneously identifying the latent changes in the baseline homicide rate which correspond to the incidence of sociopolitical events, we explore the effect of policies governing the sale of alcohol on homicide rates and seek a policy that balances the economic and cultural dependencies on alcohol sales to the health of the public.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

Library Book Circulation and the Beta-Binomial Distribution.

ERIC Educational Resources Information Center

Gelman, E.; Sichel, H. S.

1987-01-01

Argues that library book circulation is a binomial rather than a Poisson process, and that individual book popularities are continuous beta distributions. Three examples demonstrate the superiority of beta over negative binomial distribution, and it is suggested that a bivariate-binomial process would be helpful in predicting future book…

A Generalized QMRA Beta-Poisson Dose-Response Model.

PubMed

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

2016-10-01

Quantitative microbial risk assessment (QMRA) is widely accepted for characterizing the microbial risks associated with food, water, and wastewater. Single-hit dose-response models are the most commonly used dose-response models in QMRA. Denoting PI(d) as the probability of infection at a given mean dose d, a three-parameter generalized QMRA beta-Poisson dose-response model, PI(d|α,β,r*), is proposed in which the minimum number of organisms required for causing infection, K min , is not fixed, but a random variable following a geometric distribution with parameter 0

Nambu-Poisson gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-06-01

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.

STDP allows fast rate-modulated coding with Poisson-like spike trains.

PubMed

Gilson, Matthieu; Masquelier, Timothée; Hugues, Etienne

2011-10-01

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (~10-20 ms) for sufficiently many inputs (~100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.

A modified Poisson-Boltzmann equation applied to protein adsorption.

PubMed

Gama, Marlon de Souza; Santos, Mirella Simões; Lima, Eduardo Rocha de Almeida; Tavares, Frederico Wanderley; Barreto, Amaro Gomes Barreto

2018-01-05

Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects. Copyright © 2017 Elsevier B.V. All rights reserved.

STDP Allows Fast Rate-Modulated Coding with Poisson-Like Spike Trains

PubMed Central

Hugues, Etienne

2011-01-01

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (∼10–20 ms) for sufficiently many inputs (∼100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks. PMID:22046113

How to deal with the Poisson-gamma model to forecast patients' recruitment in clinical trials when there are pauses in recruitment dynamic?

PubMed

Minois, Nathan; Savy, Stéphanie; Lauwers-Cances, Valérie; Andrieu, Sandrine; Savy, Nicolas

2017-03-01

Recruiting patients is a crucial step of a clinical trial. Estimation of the trial duration is a question of paramount interest. Most techniques are based on deterministic models and various ad hoc methods neglecting the variability in the recruitment process. To overpass this difficulty the so-called Poisson-gamma model has been introduced involving, for each centre, a recruitment process modelled by a Poisson process whose rate is assumed constant in time and gamma-distributed. The relevancy of this model has been widely investigated. In practice, rates are rarely constant in time, there are breaks in recruitment (for instance week-ends or holidays). Such information can be collected and included in a model considering piecewise constant rate functions yielding to an inhomogeneous Cox model. The estimation of the trial duration is much more difficult. Three strategies of computation of the expected trial duration are proposed considering all the breaks, considering only large breaks and without considering breaks. The bias of these estimations procedure are assessed by means of simulation studies considering three scenarios of breaks simulation. These strategies yield to estimations with a very small bias. Moreover, the strategy with the best performances in terms of prediction and with the smallest bias is the one which does not take into account of breaks. This result is important as, in practice, collecting breaks data is pretty hard to manage.

Sparsity-based Poisson denoising with dictionary learning.

PubMed

Giryes, Raja; Elad, Michael

2014-12-01

The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging, and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive-independent identically distributed. Gaussian noise, for which many effective algorithms are available. However, in a low-SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. Salmon et al took this route, proposing a patch-based exponential image representation model based on Gaussian mixture model, leading to state-of-the-art results. In this paper, we propose to harness sparse-representation modeling to the image patches, adopting the same exponential idea. Our scheme uses a greedy pursuit with boot-strapping-based stopping condition and dictionary learning within the denoising process. The reconstruction performance of the proposed scheme is competitive with leading methods in high SNR and achieving state-of-the-art results in cases of low SNR.

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient.

PubMed

Bian, Liheng; Suo, Jinli; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei; Chen, Feng; Dai, Qionghai

2016-06-10

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.

Poisson property of the occurrence of flip-flops in a model membrane.

PubMed

Arai, Noriyoshi; Akimoto, Takuma; Yamamoto, Eiji; Yasui, Masato; Yasuoka, Kenji

2014-02-14

How do lipid molecules in membranes perform a flip-flop? The flip-flops of lipid molecules play a crucial role in the formation and flexibility of membranes. However, little has been determined about the behavior of flip-flops, either experimentally, or in molecular dynamics simulations. Here, we provide numerical results of the flip-flops of model lipid molecules in a model membrane and investigate the statistical properties, using millisecond-order coarse-grained molecular simulations (dissipative particle dynamics). We find that there are three different ways of flip-flops, which can be clearly characterized by their paths on the free energy surface. Furthermore, we found that the probability of the number of the flip-flops is well fitted by the Poisson distribution, and the probability density function for the inter-occurrence times of flip-flops coincides with that of the forward recurrence times. These results indicate that the occurrence of flip-flops is a Poisson process, which will play an important role in the flexibilities of membranes.

Modeling motor vehicle crashes using Poisson-gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter.

PubMed

Lord, Dominique

2006-07-01

There has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution; when crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the "low mean problem" (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies and should, therefore, be reliably estimated. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of an unreliably estimated dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used by transportation safety modelers for estimating the dispersion parameter of Poisson-gamma models were evaluated: the method of moments, the weighted regression, and the maximum likelihood method. In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes unreliably estimated increases significantly as the sample mean and sample size decrease. Consequently, the results show that an unreliably estimated dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with an unreliable dispersion parameter for modeling motor vehicle crashes.

Effects of biaxial strains on electronic and elastic properties of hexagonal XSi2 (X = Cr, Mo, W) from first-principles

NASA Astrophysics Data System (ADS)

Zhu, Haiyan; Shi, Liwei; Li, Shuaiqi; Zhang, Shaobo; Xia, Wangsuo

2018-02-01

Structural, electronic properties and elastic anisotropy of hexagonal C40 XSi2 (X = Cr, Mo, W) under equibiaxial in-plane strains are systematically studied using first-principle calculations. The energy gaps show significant changes with biaxial strains, whereas they are always indirect band-gap materials for -6% <ɛxx < 6%. All elastic constants, bulk modulus, shear modulus, Young's modulus increase (decrease) almost linearly with increasing compressive (tensile) strains. The evolutions of BH /GH ratio and Poisson's ratio indicate that these compounds have a better (worse) ductile behaviour under compressive (tensile) strains. A set of 3D plots show a larger directional variability in the Young's modulus E and shear modulus G at different strains for the three compounds, which is consist with the values of anisotropy factors. Moreover, the evolution of Debye temperature and anisotropy of sound velocities with biaxial strains are discussed.

A Three-dimensional Polymer Scaffolding Material Exhibiting a Zero Poisson's Ratio.

PubMed

Soman, Pranav; Fozdar, David Y; Lee, Jin Woo; Phadke, Ameya; Varghese, Shyni; Chen, Shaochen

2012-05-14

Poisson's ratio describes the degree to which a material contracts (expands) transversally when axially strained. A material with a zero Poisson's ratio does not transversally deform in response to an axial strain (stretching). In tissue engineering applications, scaffolding having a zero Poisson's ratio (ZPR) may be more suitable for emulating the behavior of native tissues and accommodating and transmitting forces to the host tissue site during wound healing (or tissue regrowth). For example, scaffolding with a zero Poisson's ratio may be beneficial in the engineering of cartilage, ligament, corneal, and brain tissues, which are known to possess Poisson's ratios of nearly zero. Here, we report a 3D biomaterial constructed from polyethylene glycol (PEG) exhibiting in-plane Poisson's ratios of zero for large values of axial strain. We use digital micro-mirror device projection printing (DMD-PP) to create single- and double-layer scaffolds composed of semi re-entrant pores whose arrangement and deformation mechanisms contribute the zero Poisson's ratio. Strain experiments prove the zero Poisson's behavior of the scaffolds and that the addition of layers does not change the Poisson's ratio. Human mesenchymal stem cells (hMSCs) cultured on biomaterials with zero Poisson's ratio demonstrate the feasibility of utilizing these novel materials for biological applications which require little to no transverse deformations resulting from axial strains. Techniques used in this work allow Poisson's ratio to be both scale-independent and independent of the choice of strut material for strains in the elastic regime, and therefore ZPR behavior can be imparted to a variety of photocurable biomaterial.

Discovery of HIV Type 1 Aspartic Protease Hit Compounds through Combined Computational Approaches.

PubMed

Xanthopoulos, Dimitrios; Kritsi, Eftichia; Supuran, Claudiu T; Papadopoulos, Manthos G; Leonis, Georgios; Zoumpoulakis, Panagiotis

2016-08-05

A combination of computational techniques and inhibition assay experiments was employed to identify hit compounds from commercial libraries with enhanced inhibitory potency against HIV type 1 aspartic protease (HIV PR). Extensive virtual screening with the aid of reliable pharmacophore models yielded five candidate protease inhibitors. Subsequent molecular dynamics and molecular mechanics Poisson-Boltzmann surface area free-energy calculations for the five ligand-HIV PR complexes suggested a high stability of the systems through hydrogen-bond interactions between the ligands and the protease's flaps (Ile50/50'), as well as interactions with residues of the active site (Asp25/25'/29/29'/30/30'). Binding-energy calculations for the three most promising compounds yielded values between -5 and -10 kcal mol(-1) and suggested that van der Waals interactions contribute most favorably to the total energy. The predicted binding-energy values were verified by in vitro inhibition assays, which showed promising results in the high nanomolar range. These results provide structural considerations that may guide further hit-to-lead optimization toward improved anti-HIV drugs. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Nonlocal Poisson-Fermi model for ionic solvent.

PubMed

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.

Physical properties of biophotons and their biological functions.

PubMed

Chang, Jiin-Ju

2008-05-01

Biophotons (BPHs) are weak photons within or emitted from living organisms. The intensities of BPHs range from a few to several hundred photons s(-1) x cm(-2). BPH emission originates from a de-localized coherent electromagnetic field within the living organisms and is regulated by the field. In this paper based on the experimental results of Poisson and sub-Poisson distributions of photocount statistics, the coherent properties of BPHs and their functions in cell communication are described. Discussions are made on functions which BPHs may play in DNA and proteins functioning including the process of DNA replication, protein synthesis and cell signalling and in oxidative phosporylation and photosynthesis.

Saint-Venant end effects for materials with negative Poisson's ratios

NASA Technical Reports Server (NTRS)

Lakes, R. S.

1992-01-01

Results are presented from an analysis of Saint-Venant end effects for materials with negative Poisson's ratio. Examples are presented showing that slow decay of end stress occurs in circular cylinders of negative Poisson's ratio, whereas a sandwich panel containing rigid face sheets and a compliant core exhibits no anomalous effects for negative Poisson's ratio (but exhibits slow stress decay for core Poisson's ratios approaching 0.5). In sand panels with stiff but not perfectly rigid face sheets, a negative Poisson's ratio results in end stress decay, which is faster than it would be otherwise. It is suggested that the slow decay previously predicted for sandwich strips in plane deformation as a result of the geometry can be mitigated by the use of a negative Poisson's ratio material for the core.

Poisson's ratio of fiber-reinforced composites

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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.

Poisson Mixture Regression Models for Heart Disease Prediction.

PubMed

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.

Constructions and classifications of projective Poisson varieties.

PubMed

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.

Poisson Mixture Regression Models for Heart Disease Prediction

PubMed Central

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

Constructions and classifications of projective Poisson varieties

NASA Astrophysics Data System (ADS)

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.

Statistical distributions of earthquake numbers: consequence of branching process

NASA Astrophysics Data System (ADS)

Kagan, Yan Y.

2010-03-01

We discuss various statistical distributions of earthquake numbers. Previously, we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson, geometric, logarithmic and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three distributions above can be considered special cases of the NBD. In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/moment-frequency relation and the NBD of earthquake counts in large time/space windows, as well as the dependence of the NBD parameters on the magnitude threshold (magnitude of an earthquake catalogue completeness). We discuss applying these distributions, especially the NBD, to approximate event numbers in earthquake catalogues. There are many different representations of the NBD. Most can be traced either to the Pascal distribution or to the mixture of the Poisson distribution with the gamma law. We discuss advantages and drawbacks of both representations for statistical analysis of earthquake catalogues. We also consider applying the NBD to earthquake forecasts and describe the limits of the application for the given equations. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrence, the NBD has two parameters. The second parameter can be used to characterize clustering or overdispersion of a process. We determine the parameter values and their uncertainties for several local and global catalogues, and their subdivisions in various time intervals, magnitude thresholds, spatial windows, and tectonic categories. The theoretical model of how the clustering parameter depends on the corner (maximum) magnitude can be used to predict future earthquake number distribution in regions where very large earthquakes have not yet occurred.

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

PubMed

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.

Influence of loading and unloading velocity of confining pressure on strength and permeability characteristics of crystalline sandstone

NASA Astrophysics Data System (ADS)

Zhang, Dong-ming; Yang, Yu-shun; Chu, Ya-pei; Zhang, Xiang; Xue, Yan-guang

2018-06-01

The triaxial compression test of crystalline sandstone under different loading and unloading velocity of confining pressure is carried out by using the self-made "THM coupled with servo-controlled seepage apparatus for containing-gas coal", analyzed the strength, deformation and permeability characteristics of the sample, the results show that: with the increase of confining pressures loading-unloading velocity, Mohr's stress circle center of the specimen shift to the right, and the ultimate intensity, peak strain and residual stress of the specimens increase gradually. With the decrease of unloading velocity of confining pressure, the axial strain, the radial strain and the volumetric strain of the sample decrease first and then increases, but the radial strain decreases more greatly. The loading and unloading of confining pressure has greater influence on axial strain of specimens. The deformation modulus decreases rapidly with the increase of axial strain and the Poisson's ratio decreases gradually at the initial stage of loading. When the confining pressure is loaded, the deformation modulus decrease gradually, and the Poisson's ratio increases gradually. When the confining pressure is unloaded, the deformation modulus increase gradually, and the Poisson's ratio decreases gradually. When the specimen reaches the ultimate intensity, the deformation modulus decreases rapidly, while the Poisson's ratio increases rapidly. The fitting curve of the confining pressure and the deformation modulus and the Poisson's ratio in accordance with the distribution of quadratic polynomial function in the loading-unloading confining pressure. There is a corresponding relationship between the evolution of rock permeability and damage deformation during the process of loading and unloading. In the late stage of yielding, the permeability increases slowly, and the permeability increases sharply after the rock sample is destroyed. Fitting the permeability and confining pressure conform to the variation law of the exponential function.

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

NASA Astrophysics Data System (ADS)

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.

Photon statistics in scintillation crystals

NASA Astrophysics Data System (ADS)

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:Ce and CsI:Na. We also found an empirical relationship between the Fano factor and the covariance as a function of time between two detectors looking at the same scintillation pulse. This empirical model was used to estimate the Fano factor of LaBr3:Ce and YAP:Ce using the experimentally measured timing-covariance. The estimates of the Fano factor from the time-covariance results were consistent with the estimates of the correlation between the integral signals. We found scintillation light from some scintillators to be sub-Poisson. For the same mean number of total scintillation photons, sub-Poisson light has lower noise. We then conducted a simulation study to investigate whether this low-noise sub-Poisson light can be used to improve spatial resolution. We calculated the Cramer-Rao bound for dierent detector geometries, position of interactions and Fano factors. The Cramer-Rao calculations were veried by generating simulated data and estimating the variance of the maximum likelihood estimator. We found that the Fano factor has no impact on the spatial resolution in gamma-ray imaging systems.

Earthquake number forecasts testing

NASA Astrophysics Data System (ADS)

Kagan, Yan Y.

2017-10-01

We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness and kurtosis both tend to zero for large earthquake rates: for the Gaussian law, these values are identically zero. A calculation of the NBD skewness and kurtosis levels based on the values of the first two statistical moments of the distribution, shows rapid increase of these upper moments levels. However, the observed catalogue values of skewness and kurtosis are rising even faster. This means that for small time intervals, the earthquake number distribution is even more heavy-tailed than the NBD predicts. Therefore for small time intervals, we propose using empirical number distributions appropriately smoothed for testing forecasted earthquake numbers.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

On the statistical properties of viral misinformation in online social media

NASA Astrophysics Data System (ADS)

Bessi, Alessandro

2017-03-01

The massive diffusion of online social media allows for the rapid and uncontrolled spreading of conspiracy theories, hoaxes, unsubstantiated claims, and false news. Such an impressive amount of misinformation can influence policy preferences and encourage behaviors strongly divergent from recommended practices. In this paper, we study the statistical properties of viral misinformation in online social media. By means of methods belonging to Extreme Value Theory, we show that the number of extremely viral posts over time follows a homogeneous Poisson process, and that the interarrival times between such posts are independent and identically distributed, following an exponential distribution. Moreover, we characterize the uncertainty around the rate parameter of the Poisson process through Bayesian methods. Finally, we are able to derive the predictive posterior probability distribution of the number of posts exceeding a certain threshold of shares over a finite interval of time.

Poisson Noise Removal in Spherical Multichannel Images: Application to Fermi data

NASA Astrophysics Data System (ADS)

Schmitt, Jérémy; Starck, Jean-Luc; Fadili, Jalal; Digel, Seth

2012-03-01

The Fermi Gamma-ray Space Telescope, which was launched by NASA in June 2008, is a powerful space observatory which studies the high-energy gamma-ray sky [5]. Fermi's main instrument, the Large Area Telescope (LAT), detects photons in an energy range between 20MeV and >300 GeV. The LAT is much more sensitive than its predecessor, the energetic gamma ray experiment telescope (EGRET) telescope on the Compton Gamma-ray Observatory, and is expected to find several thousand gamma-ray point sources, which is an order of magnitude more than its predecessor EGRET [13]. Even with its relatively large acceptance (∼2m2 sr), the number of photons detected by the LAT outside the Galactic plane and away from intense sources is relatively low and the sky overall has a diffuse glow from cosmic-ray interactions with interstellar gas and low energy photons that makes a background against which point sources need to be detected. In addition, the per-photon angular resolution of the LAT is relatively poor and strongly energy dependent, ranging from>10° at 20MeV to ∼0.1° above 100 GeV. Consequently, the spherical photon count images obtained by Fermi are degraded by the fluctuations on the number of detected photons. This kind of noise is strongly signal dependent : on the brightest parts of the image like the galactic plane or the brightest sources, we have a lot of photons per pixel, and so the photon noise is low. Outside the galactic plane, the number of photons per pixel is low, which means that the photon noise is high. Such a signal-dependent noise cannot be accurately modeled by a Gaussian distribution. The basic photon-imaging model assumes that the number of detected photons at each pixel location is Poisson distributed. More specifically, the image is considered as a realization of an inhomogeneous Poisson process. This statistical noise makes the source detection more difficult, consequently it is highly desirable to have an efficient denoising method for spherical Poisson data. Several techniques have been proposed in the literature to estimate Poisson intensity in 2-dimensional (2D). A major class of methods adopt a multiscale Bayesian framework specifically tailored for Poisson data [18], independently initiated by Timmerman and Nowak [23] and Kolaczyk [14]. Lefkimmiaits et al. [15] proposed an improved Bayesian framework for analyzing Poisson processes, based on a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities in adjacent scales are modeled as mixtures of conjugate parametric distributions. Another approach includes preprocessing the count data by a variance stabilizing transform(VST) such as theAnscombe [4] and the Fisz [10] transforms, applied respectively in the spatial [8] or in the wavelet domain [11]. The transform reforms the data so that the noise approximately becomes Gaussian with a constant variance. Standard techniques for independent identically distributed Gaussian noise are then used for denoising. Zhang et al. [25] proposed a powerful method called multiscale (MS-VST). It consists in combining a VST with a multiscale transform (wavelets, ridgelets, or curvelets), yielding asymptotically normally distributed coefficients with known variances. The interest of using a multiscale method is to exploit the sparsity properties of the data : the data are transformed into a domain in which it is sparse, and, as the noise is not sparse in any transform domain, it is easy to separate it from the signal. When the noise is Gaussian of known variance, it is easy to remove it with a high thresholding in the wavelet domain. The choice of the multiscale transform depends on the morphology of the data. Wavelets represent more efficiently regular structures and isotropic singularities, whereas ridgelets are designed to represent global lines in an image, and curvelets represent efficiently curvilinear contours. Significant coefficients are then detected with binary hypothesis testing, and the final estimate is reconstructed with an iterative scheme. In Ref

Unimodularity criteria for Poisson structures on foliated manifolds

NASA Astrophysics Data System (ADS)

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.

Ensemble docking to difficult targets in early-stage drug discovery: Methodology and application to fibroblast growth factor 23.

PubMed

Velazquez, Hector A; Riccardi, Demian; Xiao, Zhousheng; Quarles, Leigh Darryl; Yates, Charless Ryan; Baudry, Jerome; Smith, Jeremy C

2018-02-01

Ensemble docking is now commonly used in early-stage in silico drug discovery and can be used to attack difficult problems such as finding lead compounds which can disrupt protein-protein interactions. We give an example of this methodology here, as applied to fibroblast growth factor 23 (FGF23), a protein hormone that is responsible for regulating phosphate homeostasis. The first small-molecule antagonists of FGF23 were recently discovered by combining ensemble docking with extensive experimental target validation data (Science Signaling, 9, 2016, ra113). Here, we provide a detailed account of how ensemble-based high-throughput virtual screening was used to identify the antagonist compounds discovered in reference (Science Signaling, 9, 2016, ra113). Moreover, we perform further calculations, redocking those antagonist compounds identified in reference (Science Signaling, 9, 2016, ra113) that performed well on drug-likeness filters, to predict possible binding regions. These predicted binding modes are rescored with the molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) approach to calculate the most likely binding site. Our findings suggest that the antagonist compounds antagonize FGF23 through the disruption of protein-protein interactions between FGF23 and fibroblast growth factor receptor (FGFR). © 2017 John Wiley & Sons A/S.

Cyclocurcumin, a curcumin derivative, exhibits immune-modulating ability and is a potential compound for the treatment of rheumatoid arthritis as predicted by the MM-PBSA method.

PubMed

Fu, Min; Chen, Lihui; Zhang, Limin; Yu, Xiao; Yang, Qingrui

2017-05-01

The control and treatment of rheumatoid arthritis is a challenge in today's world. Therefore, the pursuit of natural disease-modifying antirheumatic drugs (DMRDs) remains a top priority in rheumatology. The present study focused on curcumin and its derivatives in the search for new DMRDs. We focused on prominent p38 mitogen-activated protein (MAP) kinase p38α which is a prime regulator of tumor necrosis factor-α (TNF-α), a key mediator of rheumatoid arthritis. In the present study, we used the X-ray crystallographic structure of p38α for molecular docking simulations and molecular dynamic simulations to study the binding modes of curcumin and its derivatives with the active site of p38α. The ATP-binding domain was used for evaluating curcumin and its derivatives. Molecular docking simulation results were used to select 4 out of 8 compounds. These 4 compounds were simulated using GROMACS molecular simulation platform; the results generated were subjected to molecular mechanics-Poisson Boltzmann surface area (MM-PBSA) calculations. The results showed cyclocurcumin as a potential natural compound for development of a potent DMRD. These data were further supported by inhibition of TNF-α release from lipopolysaccharide (LPS)-stimulated human macrophages following cyclocurcumin treatment.

Structural, electronic, mechanical, and thermoelectric properties of a novel half Heusler compound HfPtPb

NASA Astrophysics Data System (ADS)

Kaur, Kulwinder; Rai, D. P.; Thapa, R. K.; Srivastava, Sunita

2017-07-01

We explore the structural, electronic, mechanical, and thermoelectric properties of a new half Heusler compound HfPtPb, an all metallic heavy element, recently proposed to be stable [Gautier et al., Nat. Chem. 7, 308 (2015)]. In this work, we employ density functional theory and semi-classical Boltzmann transport equations with constant relaxation time approximation. The mechanical properties, such as shear modulus, Young's modulus, elastic constants, Poisson's ratio, and shear anisotropy factor, have been investigated. The elastic and phonon properties reveal that this compound is mechanically and dynamically stable. Pugh's ratio and Frantsevich's ratio demonstrate its ductile behavior, and the shear anisotropic factor reveals the anisotropic nature of HfPtPb. The band structure predicts this compound to be a semiconductor with a band gap of 0.86 eV. The thermoelectric transport parameters, such as Seebeck coefficient, electrical conductivity, electronic thermal conductivity, and lattice thermal conductivity, have been calculated as a function of temperature. The highest value of Seebeck coefficient is obtained for n-type doping at an optimal carrier concentration of 1.0 × 1020 e/cm3. We predict the maximum value of figure of merit (0.25) at 1000 K. Our investigation suggests that this material is an n-type semiconductor.

A test of inflated zeros for Poisson regression models.

PubMed

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.

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

PubMed

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)

Double-observer line transect surveys with Markov-modulated Poisson process models for animal availability.

PubMed

Borchers, D L; Langrock, R

2015-12-01

We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markov-modulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a mark-recapture component arising from the independent-observer survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multiple-detection estimators with estimators that use only initial detections of individuals, and with a single-observer estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and double-observer data but not with single-observer data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a double-observer survey of North Atlantic minke whales, and find that double-observer data greatly improve estimator precision here too. © 2015 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Protein-ion binding process on finite macromolecular concentration. A Poisson-Boltzmann and Monte Carlo study.

PubMed

de Carvalho, Sidney Jurado; Fenley, Márcia O; da Silva, Fernando Luís Barroso

2008-12-25

Electrostatic interactions are one of the key driving forces for protein-ligands complexation. Different levels for the theoretical modeling of such processes are available on the literature. Most of the studies on the Molecular Biology field are performed within numerical solutions of the Poisson-Boltzmann Equation and the dielectric continuum models framework. In such dielectric continuum models, there are two pivotal questions: (a) how the protein dielectric medium should be modeled, and (b) what protocol should be used when solving this effective Hamiltonian. By means of Monte Carlo (MC) and Poisson-Boltzmann (PB) calculations, we define the applicability of the PB approach with linear and nonlinear responses for macromolecular electrostatic interactions in electrolyte solution, revealing some physical mechanisms and limitations behind it especially due the raise of both macromolecular charge and concentration out of the strong coupling regime. A discrepancy between PB and MC for binding constant shifts is shown and explained in terms of the manner PB approximates the excess chemical potentials of the ligand, and not as a consequence of the nonlinear thermal treatment and/or explicit ion-ion interactions as it could be argued. Our findings also show that the nonlinear PB predictions with a low dielectric response well reproduce the pK shifts calculations carried out with an uniform dielectric model. This confirms and completes previous results obtained by both MC and linear PB calculations.

Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading

DOE PAGES

Sanborn, Brett; Song, Bo

2018-06-03

Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratiomore » of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.« less

Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanborn, Brett; Song, Bo

Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratiomore » of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.« less

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

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

PubMed

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.

MODEL FOR INSTANTANEOUS RESIDENTIAL WATER DEMANDS

EPA Science Inventory

Residential wateer use is visualized as a customer-server interaction often encountered in queueing theory. Individual customers are assumed to arrive according to a nonhomogeneous Poisson process, then engage water servers for random lengths of time. Busy servers are assumed t...

Tailpulse signal generator

DOEpatents

Baker, John [Walnut Creek, CA; Archer, Daniel E [Knoxville, TN; Luke, Stanley John [Pleasanton, CA; Decman, Daniel J [Livermore, CA; White, Gregory K [Livermore, CA

2009-06-23

A tailpulse signal generating/simulating apparatus, system, and method designed to produce electronic pulses which simulate tailpulses produced by a gamma radiation detector, including the pileup effect caused by the characteristic exponential decay of the detector pulses, and the random Poisson distribution pulse timing for radioactive materials. A digital signal process (DSP) is programmed and configured to produce digital values corresponding to pseudo-randomly selected pulse amplitudes and pseudo-randomly selected Poisson timing intervals of the tailpulses. Pulse amplitude values are exponentially decayed while outputting the digital value to a digital to analog converter (DAC). And pulse amplitudes of new pulses are added to decaying pulses to simulate the pileup effect for enhanced realism in the simulation.

Deformation mechanisms in negative Poisson's ratio materials - Structural aspects

NASA Technical Reports Server (NTRS)

Lakes, R.

1991-01-01

Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with non-central force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.

Theoretical investigations on structural, elastic and electronic properties of thallium halides

NASA Astrophysics Data System (ADS)

Singh, Rishi Pal; Singh, Rajendra Kumar; Rajagopalan, Mathrubutham

2011-04-01

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

Slow diffusion by Markov random flights

NASA Astrophysics Data System (ADS)

Kolesnik, Alexander D.

2018-06-01

We present a conception of the slow diffusion processes in the Euclidean spaces Rm , m ≥ 1, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow diffusion condition that, on long time intervals, leads to the stationary distributions, is given. The stationary distributions of slow diffusion processes in some Euclidean spaces of low dimensions, are presented.

Fuzzy classifier based support vector regression framework for Poisson ratio determination

NASA Astrophysics Data System (ADS)

Asoodeh, Mojtaba; Bagheripour, Parisa

2013-09-01

Poisson ratio is considered as one of the most important rock mechanical properties of hydrocarbon reservoirs. Determination of this parameter through laboratory measurement is time, cost, and labor intensive. Furthermore, laboratory measurements do not provide continuous data along the reservoir intervals. Hence, a fast, accurate, and inexpensive way of determining Poisson ratio which produces continuous data over the whole reservoir interval is desirable. For this purpose, support vector regression (SVR) method based on statistical learning theory (SLT) was employed as a supervised learning algorithm to estimate Poisson ratio from conventional well log data. SVR is capable of accurately extracting the implicit knowledge contained in conventional well logs and converting the gained knowledge into Poisson ratio data. Structural risk minimization (SRM) principle which is embedded in the SVR structure in addition to empirical risk minimization (EMR) principle provides a robust model for finding quantitative formulation between conventional well log data and Poisson ratio. Although satisfying results were obtained from an individual SVR model, it had flaws of overestimation in low Poisson ratios and underestimation in high Poisson ratios. These errors were eliminated through implementation of fuzzy classifier based SVR (FCBSVR). The FCBSVR significantly improved accuracy of the final prediction. This strategy was successfully applied to data from carbonate reservoir rocks of an Iranian Oil Field. Results indicated that SVR predicted Poisson ratio values are in good agreement with measured values.

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

PubMed

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.

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

PubMed

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

PubMed

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.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S.; Genovese, L.

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 themore » 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.« less

Inhomogeneity of the density of Parascaris spp. eggs in faeces of individual foals and the use of hypothesis testing for treatment decision making.

PubMed

Wilkes, E J A; Cowling, A; Woodgate, R G; Hughes, K J

2016-10-15

Faecal egg counts (FEC) are used widely for monitoring of parasite infection in animals, treatment decision-making and estimation of anthelmintic efficacy. When a single count or sample mean is used as a point estimate of the expectation of the egg distribution over some time interval, the variability in the egg density is not accounted for. Although variability, including quantifying sources, of egg count data has been described, the spatiotemporal distribution of nematode eggs in faeces is not well understood. We believe that statistical inference about the mean egg count for treatment decision-making has not been used previously. The aim of this study was to examine the density of Parascaris eggs in solution and faeces and to describe the use of hypothesis testing for decision-making. Faeces from two foals with Parascaris burdens were mixed with magnesium sulphate solution and 30 McMaster chambers were examined to determine the egg distribution in a well-mixed solution. To examine the distribution of eggs in faeces from an individual animal, three faecal piles from a foal with a known Parascaris burden were obtained, from which 81 counts were performed. A single faecal sample was also collected daily from 20 foals on three consecutive days and a FEC was performed on three separate portions of each sample. As appropriate, Poisson or negative binomial confidence intervals for the distribution mean were calculated. Parascaris eggs in a well-mixed solution conformed to a homogeneous Poisson process, while the egg density in faeces was not homogeneous, but aggregated. This study provides an extension from homogeneous to inhomogeneous Poisson processes, leading to an understanding of why Poisson and negative binomial distributions correspondingly provide a good fit for egg count data. The application of one-sided hypothesis tests for decision-making is presented. Copyright © 2016 Elsevier B.V. All rights reserved.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution.

PubMed

Lu, Benzhuo; Zhou, Y C; Huber, Gary A; Bond, Stephen D; Holst, Michael J; McCammon, J Andrew

2007-10-07

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

A fourth order PDE based fuzzy c- means approach for segmentation of microscopic biopsy images in presence of Poisson noise for cancer detection.

PubMed

Kumar, Rajesh; Srivastava, Subodh; Srivastava, Rajeev

2017-07-01

For cancer detection from microscopic biopsy images, image segmentation step used for segmentation of cells and nuclei play an important role. Accuracy of segmentation approach dominate the final results. Also the microscopic biopsy images have intrinsic Poisson noise and if it is present in the image the segmentation results may not be accurate. The objective is to propose an efficient fuzzy c-means based segmentation approach which can also handle the noise present in the image during the segmentation process itself i.e. noise removal and segmentation is combined in one step. To address the above issues, in this paper a fourth order partial differential equation (FPDE) based nonlinear filter adapted to Poisson noise with fuzzy c-means segmentation method is proposed. This approach is capable of effectively handling the segmentation problem of blocky artifacts while achieving good tradeoff between Poisson noise removals and edge preservation of the microscopic biopsy images during segmentation process for cancer detection from cells. The proposed approach is tested on breast cancer microscopic biopsy data set with region of interest (ROI) segmented ground truth images. The microscopic biopsy data set contains 31 benign and 27 malignant images of size 896 × 768. The region of interest selected ground truth of all 58 images are also available for this data set. Finally, the result obtained from proposed approach is compared with the results of popular segmentation algorithms; fuzzy c-means, color k-means, texture based segmentation, and total variation fuzzy c-means approaches. The experimental results shows that proposed approach is providing better results in terms of various performance measures such as Jaccard coefficient, dice index, Tanimoto coefficient, area under curve, accuracy, true positive rate, true negative rate, false positive rate, false negative rate, random index, global consistency error, and variance of information as compared to other segmentation approaches used for cancer detection. Copyright © 2017 Elsevier B.V. All rights reserved.

On the Overdispersed Molecular Clock

PubMed Central

Takahata, Naoyuki

1987-01-01

Rates of molecular evolution at some loci are more irregular than described by simple Poisson processes. Three situations under which molecular evolution would not follow simple Poisson processes are reevaluated from the viewpoint of the neutrality hypothesis: (i) concomitant or multiple substitutions in a gene, (ii) fluctuating substitution rates in time caused by coupled effects of deleterious mutations and bottlenecks, and (iii) changes in the degree of selective constraints against a gene (neutral space) caused by successive substitutions. The common underlying assumption that these causes are lineage nonspecific excludes the case where mutation rates themselves change systematically among lineages or taxonomic groups, and severely limits the extent of variation in the number of substitutions among lineages. Even under this stringent condition, however, the third hypothesis, the fluctuating neutral space model, can generate fairly large variation. This is described by a time-dependent renewal process, which does not exhibit any episodic nature of molecular evolution. It is argued that the observed elevated variances in the number of nucleotide or amino acid substitutions do not immediately call for positive Darwinian selection in molecular evolution. PMID:3596230

A two-phase Poisson process model and its application to analysis of cancer mortality among A-bomb survivors.

PubMed

Ohtaki, Megu; Tonda, Tetsuji; Aihara, Kazuyuki

2015-10-01

We consider a two-phase Poisson process model where only early successive transitions are assumed to be sensitive to exposure. In the case where intensity transitions are low, we derive analytically an approximate formula for the distribution of time to event for the excess hazard ratio (EHR) due to a single point exposure. The formula for EHR is a polynomial in exposure dose. Since the formula for EHR contains no unknown parameters except for the number of total stages, number of exposure-sensitive stages, and a coefficient of exposure effect, it is applicable easily under a variety of situations where there exists a possible latency time from a single point exposure to occurrence of event. Based on the multistage hypothesis of cancer, we formulate a radiation carcinogenesis model in which only some early consecutive stages of the process are sensitive to exposure, whereas later stages are not affected. An illustrative analysis using the proposed model is given for cancer mortality among A-bomb survivors. Copyright © 2015 Elsevier Inc. All rights reserved.

Fedosov’s formal symplectic groupoids and contravariant connections

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2006-10-01

Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kähler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections.

DFT investigation on electronic, magnetic, mechanical and thermodynamic properties under pressure of some EuMO3 (M  =  Ga, In) perovskites

NASA Astrophysics Data System (ADS)

Dar, Sajad Ahmad; Srivastava, Vipul; Sakalle, Umesh Kumar; Parey, Vanshree; Pagare, Gitanjali

2017-10-01

The structural, electronic, magnetic and elastic properties of cubic EuMO3 (M  =  Ga, In) perovskites has been successfully predicted within well accepted density functional theory using full potential linearized augmented plane wave (FP-LAPW). The structural study reveals ferromagnetic stability for both the compounds. The Hubbard correlation (GGA+U) calculated spin polarized electronic band and density of states presents half-metallic nature for both the compounds. The magnetic moments calculated with different approximations were found to be approximately 6 µ B for EuGaO3 and approximately 7 µ B for EuInO3. The three independent elastic constants (C 11, C 12, C 44) have been used for the prediction of mechanical properties like Young modulus (Y), Shear modulus (G), Poisson ratio (ν), Anisotropic factor (A) under pressure. The B/G ratio presents the ductile nature for both compounds. The thermodynamic parameters like specific heat capacity, thermal expansion, Grüneisen parameter and Debye temperature etc have also been analyzed in the temperature range 0-900 K and pressure range from 0 to 30 GPa.

Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes.

PubMed

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

2008-05-01

This paper documents the application of the Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM) for modeling motor vehicle crashes. The COM-Poisson distribution, originally developed in 1962, has recently been re-introduced by statisticians for analyzing count data subjected to over- and under-dispersion. This innovative distribution is an extension of the Poisson distribution. The objectives of this study were to evaluate the application of the COM-Poisson GLM for analyzing motor vehicle crashes and compare the results with the traditional negative binomial (NB) model. The comparison analysis was carried out using the most common functional forms employed by transportation safety analysts, which link crashes to the entering flows at intersections or on segments. To accomplish the objectives of the study, several NB and COM-Poisson GLMs were developed and compared using two datasets. The first dataset contained crash data collected at signalized four-legged intersections in Toronto, Ont. The second dataset included data collected for rural four-lane divided and undivided highways in Texas. Several methods were used to assess the statistical fit and predictive performance of the models. The results of this study show that COM-Poisson GLMs perform as well as NB models in terms of GOF statistics and predictive performance. Given the fact the COM-Poisson distribution can also handle under-dispersed data (while the NB distribution cannot or has difficulties converging), which have sometimes been observed in crash databases, the COM-Poisson GLM offers a better alternative over the NB model for modeling motor vehicle crashes, especially given the important limitations recently documented in the safety literature about the latter type of model.

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

PubMed

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 stratification.

Frequency-Rank Distributions

ERIC Educational Resources Information Center

Brookes, Bertram C.; Griffiths, Jose M.

1978-01-01

Frequency, rank, and frequency rank distributions are defined. Extensive discussion on several aspects of frequency rank distributions includes the Poisson process as a means of exploring the stability of ranks; the correlation of frequency rank distributions; and the transfer coefficient, a new measure in frequency rank distribution. (MBR)

A New Model that Generates Lotka's Law.

ERIC Educational Resources Information Center

Huber, John C.

2002-01-01

Develops a new model for a process that generates Lotka's Law. Topics include measuring scientific productivity through the number of publications; rate of production; career duration; randomness; Poisson distribution; computer simulations; goodness-of-fit; theoretical support for the model; and future research. (Author/LRW)

A Behavioral Theory of Timing.

ERIC Educational Resources Information Center

Killeen, Peter R.; Fetterman, J. Gregor

1988-01-01

A theory of timing is proposed, based on the observation that signals of reinforcement elicit adjunctive behaviors. Transitions between these behaviors are described as a Poisson process. These behaviors may come to serve as the basis for conditional discriminations of the passage of time. (SLD)

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

PubMed

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.

Identification of Novel Compounds against an R294K Substitution of Influenza A (H7N9) Virus Using Ensemble Based Drug Virtual Screening

PubMed Central

Tran, Nhut; Van, Thanh; Nguyen, Hieu; Le, Ly

2015-01-01

Influenza virus H7N9 foremost emerged in China in 2013 and killed hundreds of people in Asia since they possessed all mutations that enable them to resist to all existing influenza drugs, resulting in high mortality to human. In the effort to identify novel inhibitors combat resistant strains of influenza virus H7N9; we performed virtual screening targeting the Neuraminidase (NA) protein against natural compounds of traditional Chinese medicine database (TCM) and ZINC natural products. Compounds expressed high binding affinity to the target protein was then evaluated for molecular properties to determine drug-like molecules. 4 compounds showed their binding energy less than -11Kcal/mol were selected for molecular dynamics (MD) simulation to capture intermolecular interactions of ligand-protein complexes. The molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) method was utilized to estimate binding free energy of the complex. In term of stability, NA-7181 (IUPAC namely {9-Hydroxy-10-[3-(trifluoromrthyl) cyclohexyl]-4.8-diazatricyclo [6.4.0.02,6]dodec-4-yl}(perhydro-1H-inden-5-yl)formaldehyde) achieved stable conformation after 20ns and 27ns for ligand and protein root mean square deviation, respectively. In term of binding free energy, 7181 gave the negative value of -30.031 (KJ/mol) indicating the compound obtained a favourable state in the active site of the protein. PMID:25589893

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Y.; Zheng, W.T., E-mail: WTZheng@jlu.edu.cn; Guan, W.M.

The structural formation, elastic properties, hardness and electronic structure of TMB{sub 4} (TM=Cr, Re, Ru and Os) compounds are investigated using first-principles approach. The value of C{sub 22} for these compounds is almost two times bigger than the C{sub 11} and C{sub 33}. The intrinsic hardness, shear modulus and Young's modulus are calculated to be in a sequence of CrB{sub 4}>ReB{sub 4}>RuB{sub 4}>OsB{sub 4}, and the Poisson's ratio and B/G ratio of TMB{sub 4} follow the order of CrB{sub 4}ReB{sub 4}>RuB{sub 4}>OsB{sub 4}. • The trend of hardness for TMB{sub 4} is consistent with the variation of elastic modulus. •more » The C{sub 22} value of TMB{sub 4} is bigger than that of C{sub 11} and C{sub 33}. • The high hardness of TMB{sub 4} is originated from the B–B bonds cage.« less

Structural and elastic properties of AIBIIIC 2 VI semiconductors

NASA Astrophysics Data System (ADS)

Kumar, V.; Singh, Bhanu P.

2018-01-01

The plane wave pseudo-potential method within density functional theory has been used to calculate the structural and elastic properties of AIBIIIC 2 VI semiconductors. The electronic band structure, density of states, lattice constants (a and c), internal parameter (u), tetragonal distortion (η), energy gap (Eg), and bond lengths of the A-C (dAC) and B-C (dBC) bonds in AIBIIIC 2 VI semiconductors have been calculated. The values of elastic constants (Cij), bulk modulus (B), shear modulus (G), Young's modulus (Y), Poisson's ratio (υ), Zener anisotropy factor (A), Debye temperature (ϴD) and G/B ratio have also been calculated. The values of all 15 parameters of CuTlS2 and CuTlSe2 compounds, and 8 parameters of 20 compounds of AIBIIIC 2 VI family, except AgInS2 and AgInSe2, have been calculated for the first time. Reasonably good agreement has been obtained between the calculated, reported and available experimental values.

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

NASA Technical Reports Server (NTRS)

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.

Method of Poisson's ratio imaging within a material part

NASA Technical Reports Server (NTRS)

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.

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed Central

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. PMID:28983398

Non-linear properties of metallic cellular materials with a negative Poisson's ratio

NASA Technical Reports Server (NTRS)

Choi, J. B.; Lakes, R. S.

1992-01-01

Negative Poisson's ratio copper foam was prepared and characterized experimentally. The transformation into re-entrant foam was accomplished by applying sequential permanent compressions above the yield point to achieve a triaxial compression. The Poisson's ratio of the re-entrant foam depended on strain and attained a relative minimum at strains near zero. Poisson's ratio as small as -0.8 was achieved. The strain dependence of properties occurred over a narrower range of strain than in the polymer foams studied earlier. Annealing of the foam resulted in a slightly greater magnitude of negative Poisson's ratio and greater toughness at the expense of a decrease in the Young's modulus.

Relation Between Firing Statistics of Spiking Neuron with Delayed Fast Inhibitory Feedback and Without Feedback

NASA Astrophysics Data System (ADS)

Vidybida, Alexander; Shchur, Olha

We consider a class of spiking neuronal models, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed with a Poisson process. Each output impulse is applied to the neuron itself after a finite delay Δ. This impulse acts as being delivered through a fast Cl-type inhibitory synapse. We derive a general relation which allows calculating exactly the probability density function (pdf) p(t) of output interspike intervals of a neuron with feedback based on known pdf p0(t) for the same neuron without feedback and on the properties of the feedback line (the Δ value). Similar relations between corresponding moments are derived. Furthermore, we prove that the initial segment of pdf p0(t) for a neuron with a fixed threshold level is the same for any neuron satisfying the imposed conditions and is completely determined by the input stream. For the Poisson input stream, we calculate that initial segment exactly and, based on it, obtain exactly the initial segment of pdf p(t) for a neuron with feedback. That is the initial segment of p(t) is model-independent as well. The obtained expressions are checked by means of Monte Carlo simulation. The course of p(t) has a pronounced peculiarity, which makes it impossible to approximate p(t) by Poisson or another simple stochastic process.

WAITING TIME DISTRIBUTION OF SOLAR ENERGETIC PARTICLE EVENTS MODELED WITH A NON-STATIONARY POISSON PROCESS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, C.; Su, W.; Fang, C.

2014-09-10

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 {sup –γ}. The SEEs display a broken power-law WTD. The power-law index is γ{sub 1} = 0.99 for the short waiting times (<70 hr) and γ{sub 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 ∼more » 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{sup –α}exp (– βλ), the time-dependent Poisson distribution can produce a power-law tail WTD of ∼Δt {sup α} {sup –3}, where 0 ≤ α < 2.« less

Markov and semi-Markov processes as a failure rate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grabski, Franciszek

2016-06-08

In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.

A POISSON PROCESS APPROACH FOR RECURRENT EVENT DATA WITH ENVIRONMENTAL COVARIATES. (R825266)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Modeling Creep Processes in Aging Polymers

NASA Astrophysics Data System (ADS)

Olali, N. V.; Voitovich, L. V.; Zazimko, N. N.; Malezhik, M. P.

2016-03-01

The photoelastic method is generalized to creep in hereditary aging materials. Optical-creep curves and mechanical-creep or optical-relaxation curves are used to interpret fringe patterns. For materials with constant Poisson's ratio, it is sufficient to use mechanical- or optical-creep curves for this purpose

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Improvements in continuum modeling for biomolecular systems

NASA Astrophysics Data System (ADS)

Yu, Qiao; Ben-Zhuo, Lu

2016-01-01

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann (PB)/Poisson-Nernst-Planck (PNP) equations has made great contributions towards simulation of these processes. However, the model has shortcomings in its commonly used form and cannot capture (or cannot accurately capture) some important physical properties of the biological systems. Considerable efforts have been made to improve the continuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecular systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress. Project supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation.

The Nonhomogeneous Poisson Process for Fast Radio Burst Rates

DOE PAGES

Lawrence, Earl; Wiel, Scott Vander; Law, Casey; ...

2017-08-30

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model dependence of the rate on both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patternsmore » and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 587 events per sky per day above a flux of 1 Jy (95% CI: 272, 924) and a flux power-law index of 0:91 (95% CI: 0.57, 1.25).« less

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle.

PubMed

Osche, G R

2000-08-20

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.

Chemical reaction networks as a model to describe UVC- and radiolytically-induced reactions of simple compounds.

PubMed

Dondi, Daniele; Merli, Daniele; Albini, Angelo; Zeffiro, Alberto; Serpone, Nick

2012-05-01

When a chemical system is submitted to high energy sources (UV, ionizing radiation, plasma sparks, etc.), as is expected to be the case of prebiotic chemistry studies, a plethora of reactive intermediates could form. If oxygen is present in excess, carbon dioxide and water are the major products. More interesting is the case of reducing conditions where synthetic pathways are also possible. This article examines the theoretical modeling of such systems with random-generated chemical networks. Four types of random-generated chemical networks were considered that originated from a combination of two connection topologies (viz., Poisson and scale-free) with reversible and irreversible chemical reactions. The results were analyzed taking into account the number of the most abundant products required for reaching 50% of the total number of moles of compounds at equilibrium, as this may be related to an actual problem of complex mixture analysis. The model accounts for multi-component reaction systems with no a priori knowledge of reacting species and the intermediates involved if system components are sufficiently interconnected. The approach taken is relevant to an earlier study on reactions that may have occurred in prebiotic systems where only a few compounds were detected. A validation of the model was attained on the basis of results of UVC and radiolytic reactions of prebiotic mixtures of low molecular weight compounds likely present on the primeval Earth.

Pumped shot noise in adiabatically modulated graphene-based double-barrier structures.

PubMed

Zhu, Rui; Lai, Maoli

2011-11-16

Quantum pumping processes are accompanied by considerable quantum noise. Based on the scattering approach, we investigated the pumped shot noise properties in adiabatically modulated graphene-based double-barrier structures. It is found that compared with the Poisson processes, the pumped shot noise is dramatically enhanced where the dc pumped current changes flow direction, which demonstrates the effect of the Klein paradox.

Pumped shot noise in adiabatically modulated graphene-based double-barrier structures

NASA Astrophysics Data System (ADS)

Zhu, Rui; Lai, Maoli

2011-11-01

Quantum pumping processes are accompanied by considerable quantum noise. Based on the scattering approach, we investigated the pumped shot noise properties in adiabatically modulated graphene-based double-barrier structures. It is found that compared with the Poisson processes, the pumped shot noise is dramatically enhanced where the dc pumped current changes flow direction, which demonstrates the effect of the Klein paradox.

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

PubMed

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.

PubMed

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.

Prescription-induced jump distributions in multiplicative Poisson processes.

PubMed

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Prescription-induced jump distributions in multiplicative Poisson processes

NASA Astrophysics Data System (ADS)

Suweis, Samir; Porporato, Amilcare; Rinaldo, Andrea; Maritan, Amos

2011-06-01

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative Gaussian white noise, the Stratonovich prescription does not correspond to the well-known midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, one induced by the inertial term and the other determined by the jump event. We also show that, when the multiplicative noise is linear in the random variable, one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Effect of Fiber Poisson Contraction on Matrix Multicracking Evolution of Fiber-Reinforced Ceramic-Matrix Composites

NASA Astrophysics Data System (ADS)

Longbiao, Li

2015-12-01

An analytical methodology has been developed to investigate the effect of fiber Poisson contraction on matrix multicracking evolution of fiber-reinforced ceramic-matrix composites (CMCs). The modified shear-lag model incorporated with the Coulomb friction law is adopted to solve the stress distribution in the interface slip region and intact region of the damaged composite. The critical matrix strain energy criterion which presupposes the existence of an ultimate or critical strain energy limit beyond which the matrix fails has been adopted to describe matrix multicracking of CMCs. As more energy is placed into the composite, matrix fractures and the interface debonding occurs to dissipate the extra energy. The interface debonded length under the process of matrix multicracking is obtained by treating the interface debonding as a particular crack propagation problem along the fiber/matrix interface. The effects of the interfacial frictional coefficient, fiber Poisson ratio, fiber volume fraction, interface debonded energy and cycle number on the interface debonding and matrix multicracking evolution have been analyzed. The theoretical results are compared with experimental data of unidirectional SiC/CAS, SiC/CAS-II and SiC/Borosilicate composites.

The solution of large multi-dimensional Poisson problems

NASA Technical Reports Server (NTRS)

Stone, H. S.

1974-01-01

The Buneman algorithm for solving Poisson problems can be adapted to solve large Poisson problems on computers with a rotating drum memory so that the computation is done with very little time lost due to rotational latency of the drum.

Accelerated iteration schemes for transonic flow calculations using fast poisson solvers. [aerodynamics

NASA Technical Reports Server (NTRS)

Jameson, A.

1975-01-01

The use of a fast elliptic solver in combination with relaxation is presented as an effective way to accelerate the convergence of transonic flow calculations, particularly when a marching scheme can be used to treat the supersonic zone in the relaxation process.

On the Determination of Poisson Statistics for Haystack Radar Observations of Orbital Debris

NASA Technical Reports Server (NTRS)

Stokely, Christopher L.; Benbrook, James R.; Horstman, Matt

2007-01-01

A convenient and powerful method is used to determine if radar detections of orbital debris are observed according to Poisson statistics. This is done by analyzing the time interval between detection events. For Poisson statistics, the probability distribution of the time interval between events is shown to be an exponential distribution. This distribution is a special case of the Erlang distribution that is used in estimating traffic loads on telecommunication networks. Poisson statistics form the basis of many orbital debris models but the statistical basis of these models has not been clearly demonstrated empirically until now. Interestingly, during the fiscal year 2003 observations with the Haystack radar in a fixed staring mode, there are no statistically significant deviations observed from that expected with Poisson statistics, either independent or dependent of altitude or inclination. One would potentially expect some significant clustering of events in time as a result of satellite breakups, but the presence of Poisson statistics indicates that such debris disperse rapidly with respect to Haystack's very narrow radar beam. An exception to Poisson statistics is observed in the months following the intentional breakup of the Fengyun satellite in January 2007.

Poisson geometry from a Dirac perspective

NASA Astrophysics Data System (ADS)

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.

Interactive Graphic Simulation of Rolling Element Bearings. Phase I. Low Frequency Phenomenon and RAPIDREB Development.

DTIC Science & Technology

1981-11-01

RDRER413 C EH 11-22 HOUSING ELASTIC MODUJLUS (F/L**2). RDRE8415 C PO4 ?3-34 HOUSING POISSON-S PATTO . PDPR416 C DENH 35-46 HOUSING MATERIAL DFNSITY (MA/L...23-34 CAGE POISSON-S PATTO . RDPRE427 C DENC 35-46 CAC7E MATFRIAL DENSITY (MA/L-03), PDPEP4?8 C RDRER4?9 C CARD 11 RDRE9430 C ---- ROPER431 C JF 11-16

Cumulative Poisson Distribution Program

NASA Technical Reports Server (NTRS)

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.

Poly-symplectic Groupoids and Poly-Poisson Structures

NASA Astrophysics Data System (ADS)

Martinez, Nicolas

2015-05-01

We introduce poly-symplectic groupoids, which are natural extensions of symplectic groupoids to the context of poly-symplectic geometry, and define poly-Poisson structures as their infinitesimal counterparts. We present equivalent descriptions of poly-Poisson structures, including one related with AV-Dirac structures. We also discuss symmetries and reduction in the setting of poly-symplectic groupoids and poly-Poisson structures, and use our viewpoint to revisit results and develop new aspects of the theory initiated in Iglesias et al. (Lett Math Phys 103:1103-1133, 2013).

Combined analysis of magnetic and gravity anomalies using normalized source strength (NSS)

NASA Astrophysics Data System (ADS)

Li, L.; Wu, Y.

2017-12-01

Gravity field and magnetic field belong to potential fields which lead inherent multi-solution. Combined analysis of magnetic and gravity anomalies based on Poisson's relation is used to determinate homology gravity and magnetic anomalies and decrease the ambiguity. The traditional combined analysis uses the linear regression of the reduction to pole (RTP) magnetic anomaly to the first order vertical derivative of the gravity anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope and intercept. In the calculation process, due to the effect of remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization. In this case the homology gravity and magnetic anomalies display irrelevant results in the linear regression calculation. The normalized source strength (NSS) can be transformed from the magnetic tensor matrix, which is insensitive to the remanence. Here we present a new combined analysis using NSS. Based on the Poisson's relation, the gravity tensor matrix can be transformed into the pseudomagnetic tensor matrix of the direction of geomagnetic field magnetization under the homologous condition. The NSS of pseudomagnetic tensor matrix and original magnetic tensor matrix are calculated and linear regression analysis is carried out. The calculated correlation coefficient, slope and intercept indicate the homology level, Poisson's ratio and the distribution of remanent respectively. We test the approach using synthetic model under complex magnetization, the results show that it can still distinguish the same source under the condition of strong remanence, and establish the Poisson's ratio. Finally, this approach is applied in China. The results demonstrated that our approach is feasible.

Estimating random errors due to shot noise in backscatter lidar observations.

PubMed

Liu, Zhaoyan; Hunt, William; Vaughan, Mark; Hostetler, Chris; McGill, Matthew; Powell, Kathleen; Winker, David; Hu, Yongxiang

2006-06-20

We discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson- distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root mean square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF, uncertainties can be reliably calculated from or for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations lidar and tested using data from the Lidar In-space Technology Experiment.

Examining the spatially non-stationary associations between the second demographic transition and infant mortality: A Poisson GWR approach.

PubMed

Yang, Tse-Chuan; Shoff, Carla; Matthews, Stephen A

2013-01-01

Based on ecological studies, second demographic transition (SDT) theorists concluded that some areas in the US were in vanguard of the SDT compared to others, implying spatial nonstationarity may be inherent in the SDT process. Linking the SDT to the infant mortality literature, we sought out to answer two related questions: Are the main components of the SDT, specifically marriage postponement, cohabitation, and divorce, associated with infant mortality? If yes, do these associations vary across the US? We applied global Poisson and geographically weighted Poisson regression (GWPR) models, a place-specific analytic approach, to county-level data in the contiguous US. After accounting for the racial/ethnic and socioeconomic compositions of counties and prenatal care utilization, we found (1) marriage postponement was negatively related to infant mortality in the southwestern states, but positively associated with infant mortality in parts of Indiana, Kentucky, and Tennessee, (2) cohabitation rates were positively related to infant mortality, and this relationship was stronger in California, coastal Virginia, and the Carolinas than other areas, and (3) a positive association between divorce rates and infant mortality in southwestern and northeastern areas of the US. These spatial patterns suggested that the associations between the SDT and infant mortality were stronger in the areas in vanguard of the SDT than in others. The comparison between global Poisson and GWPR results indicated that a place-specific spatial analysis not only fit the data better, but also provided insights into understanding the non-stationarity of the associations between the SDT and infant mortality.

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

NASA Technical Reports Server (NTRS)

Liu, Zhaoyan; Hunt, William; Vaughan, Mark A.; Hostetler, Chris A.; McGill, Matthew J.; Powell, Kathy; Winker, David M.; Hu, Yongxiang

2006-01-01

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Dual Roles for Spike Signaling in Cortical Neural Populations

PubMed Central

Ballard, Dana H.; Jehee, Janneke F. M.

2011-01-01

A prominent feature of signaling in cortical neurons is that of randomness in the action potential. The output of a typical pyramidal cell can be well fit with a Poisson model, and variations in the Poisson rate repeatedly have been shown to be correlated with stimuli. However while the rate provides a very useful characterization of neural spike data, it may not be the most fundamental description of the signaling code. Recent data showing γ frequency range multi-cell action potential correlations, together with spike timing dependent plasticity, are spurring a re-examination of the classical model, since precise timing codes imply that the generation of spikes is essentially deterministic. Could the observed Poisson randomness and timing determinism reflect two separate modes of communication, or do they somehow derive from a single process? We investigate in a timing-based model whether the apparent incompatibility between these probabilistic and deterministic observations may be resolved by examining how spikes could be used in the underlying neural circuits. The crucial component of this model draws on dual roles for spike signaling. In learning receptive fields from ensembles of inputs, spikes need to behave probabilistically, whereas for fast signaling of individual stimuli, the spikes need to behave deterministically. Our simulations show that this combination is possible if deterministic signals using γ latency coding are probabilistically routed through different members of a cortical cell population at different times. This model exhibits standard features characteristic of Poisson models such as orientation tuning and exponential interval histograms. In addition, it makes testable predictions that follow from the γ latency coding. PMID:21687798

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

PubMed

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 (<100), estimation error is small for the fractional 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.

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

NASA Astrophysics Data System (ADS)

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.

Football goal distributions and extremal statistics

NASA Astrophysics Data System (ADS)

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.

NHPP for FRBs, Version 1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lawrence, Earl; Wiel, Scott Vander

This code implements the non-homogeneous poisson process model for estimating the rate of fast radio bursts. It includes modeling terms for the distribution of events in the Universe and the detection sensitivity of the radio telescopes and arrays used in observation. The model is described in LA-UR-16-26261.

Exploring Term Dependences in Probabilistic Information Retrieval Model.

ERIC Educational Resources Information Center

Cho, Bong-Hyun; Lee, Changki; Lee, Gary Geunbae

2003-01-01

Describes a theoretic process to apply Bahadur-Lazarsfeld expansion (BLE) to general probabilistic models and the state-of-the-art 2-Poisson model. Through experiments on two standard document collections, one in Korean and one in English, it is demonstrated that incorporation of term dependences using BLE significantly contributes to performance…

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

How does variance in fertility change over the demographic transition?

PubMed Central

Hruschka, Daniel J.; Burger, Oskar

2016-01-01

Most work on the human fertility transition has focused on declines in mean fertility. However, understanding changes in the variance of reproductive outcomes can be equally important for evolutionary questions about the heritability of fertility, individual determinants of fertility and changing patterns of reproductive skew. Here, we document how variance in completed fertility among women (45–49 years) differs across 200 surveys in 72 low- to middle-income countries where fertility transitions are currently in progress at various stages. Nearly all (91%) of samples exhibit variance consistent with a Poisson process of fertility, which places systematic, and often severe, theoretical upper bounds on the proportion of variance that can be attributed to individual differences. In contrast to the pattern of total variance, these upper bounds increase from high- to mid-fertility samples, then decline again as samples move from mid to low fertility. Notably, the lowest fertility samples often deviate from a Poisson process. This suggests that as populations move to low fertility their reproduction shifts from a rate-based process to a focus on an ideal number of children. We discuss the implications of these findings for predicting completed fertility from individual-level variables. PMID:27022082

Supervised Gamma Process Poisson Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, Dylan Zachary

This thesis develops the supervised gamma process Poisson factorization (S- GPPF) framework, a novel supervised topic model for joint modeling of count matrices and document labels. S-GPPF is fully generative and nonparametric: document labels and count matrices are modeled under a uni ed probabilistic framework and the number of latent topics is controlled automatically via a gamma process prior. The framework provides for multi-class classification of documents using a generative max-margin classifier. Several recent data augmentation techniques are leveraged to provide for exact inference using a Gibbs sampling scheme. The first portion of this thesis reviews supervised topic modeling andmore » several key mathematical devices used in the formulation of S-GPPF. The thesis then introduces the S-GPPF generative model and derives the conditional posterior distributions of the latent variables for posterior inference via Gibbs sampling. The S-GPPF is shown to exhibit state-of-the-art performance for joint topic modeling and document classification on a dataset of conference abstracts, beating out competing supervised topic models. The unique properties of S-GPPF along with its competitive performance make it a novel contribution to supervised topic modeling.« less

Models for Serially Correlated Over or Underdispersed Unequally Spaced Longitudinal Count Data with Applications to Asthma Inhaler Use

DTIC Science & Technology

2007-08-01

the gamma prior and Poisson counts are conditioned on an unobserved AR( 1 ) process that accounts for the time since the last observation . This model did...to the observation equation. For unequally spaced observations the AR( 1 ) errors are replaced by a continuous time AR( 1 ) process , and the distance...unequal spaced observations are handled in the XJG model by assuming an underlying continuous time AR( 1 ) (CAR(l)) process . It is implemented by

Efficient exact motif discovery.

PubMed

Marschall, Tobias; Rahmann, Sven

2009-06-15

The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. The method has been implemented in Java. It can be obtained from http://ls11-www.cs.tu-dortmund.de/people/marschal/paa_md/.

The non-equilibrium allele frequency spectrum in a Poisson random field framework.

PubMed

Kaj, Ingemar; Mugal, Carina F

2016-10-01

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics. Copyright © 2016 Elsevier Inc. All rights reserved.

Method for resonant measurement

DOEpatents

Rhodes, George W.; Migliori, Albert; Dixon, Raymond D.

1996-01-01

A method of measurement of objects to determine object flaws, Poisson's ratio (.sigma.) and shear modulus (.mu.) is shown and described. First, the frequency for expected degenerate responses is determined for one or more input frequencies and then splitting of degenerate resonant modes are observed to identify the presence of flaws in the object. Poisson's ratio and the shear modulus can be determined by identification of resonances dependent only on the shear modulus, and then using that shear modulus to find Poisson's ratio using other modes dependent on both the shear modulus and Poisson's ratio.

Elasticity of α-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio

NASA Astrophysics Data System (ADS)

Yeganeh-Haeri, Amir; Weidner, Donald J.; Parise, John B.

1992-07-01

Laser Brillouin spectroscopy was used to determine the adiabatic single-crystal elastic stiffness coefficients of silicon dioxide (SiO_2) in the α-cristobalite structure. This SiO_2 polymorph, unlike other silicas and silicates, exhibits a negative Poisson's ratio; α-cristobalite contracts laterally when compressed and expands laterally when stretched. Tensorial analysis of the elastic coefficients shows that Poisson's ratio reaches a maximum value of -0.5 in some directions, whereas averaged values for the single-phased aggregate yield a Poisson's ratio of -0.16.

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

PubMed

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.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

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.

Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels.

PubMed

Park, H M; Lee, J S; Kim, T W

2007-11-15

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.

Efficiency optimization of a fast Poisson solver in beam dynamics simulation

NASA Astrophysics Data System (ADS)

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.

Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.

PubMed

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.

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

PubMed

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.

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

PubMed Central

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. PMID:28586344

Complex wet-environments in electronic-structure calculations

NASA Astrophysics Data System (ADS)

Fisicaro, Giuseppe; Genovese, Luigi; Andreussi, Oliviero; Marzari, Nicola; Goedecker, Stefan

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 an applied electrochemical potentials, including complex electrostatic screening coming from the solvent. In the present work we present a solver to handle both the Generalized Poisson and the Poisson-Boltzmann equation. A preconditioned conjugate gradient (PCG) method has been implemented for the Generalized Poisson and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations. On the other hand, a self-consistent procedure enables us to solve the Poisson-Boltzmann problem. The algorithms take advantage of a preconditioning procedure based on the BigDFT Poisson solver for the standard Poisson equation. They exhibit very high accuracy and parallel efficiency, and allow different boundary conditions, including surfaces. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and it will be released as a independent program, suitable for integration in other codes. We present test calculations for large proteins to demonstrate efficiency and performances. This work was done within the PASC and NCCR MARVEL projects. Computer resources were provided by the Swiss National Supercomputing Centre (CSCS) under Project ID s499. LG acknowledges also support from the EXTMOS EU project.

Persistently Auxetic Materials: Engineering the Poisson Ratio of 2D Self-Avoiding Membranes under Conditions of Non-Zero Anisotropic Strain.

PubMed

Ulissi, Zachary W; Govind Rajan, Ananth; Strano, Michael S

2016-08-23

Entropic surfaces represented by fluctuating two-dimensional (2D) membranes are predicted to have desirable mechanical properties when unstressed, including a negative Poisson's ratio ("auxetic" behavior). Herein, we present calculations of the strain-dependent Poisson ratio of self-avoiding 2D membranes demonstrating desirable auxetic properties over a range of mechanical strain. Finite-size membranes with unclamped boundary conditions have positive Poisson's ratio due to spontaneous non-zero mean curvature, which can be suppressed with an explicit bending rigidity in agreement with prior findings. Applying longitudinal strain along a singular axis to this system suppresses this mean curvature and the entropic out-of-plane fluctuations, resulting in a molecular-scale mechanism for realizing a negative Poisson's ratio above a critical strain, with values significantly more negative than the previously observed zero-strain limit for infinite sheets. We find that auxetic behavior persists over surprisingly high strains of more than 20% for the smallest surfaces, with desirable finite-size scaling producing surfaces with negative Poisson's ratio over a wide range of strains. These results promise the design of surfaces and composite materials with tunable Poisson's ratio by prestressing platelet inclusions or controlling the surface rigidity of a matrix of 2D materials.

Studying the time trend of Methicillin-resistant Staphylococcus aureus (MRSA) in Norway by use of non-stationary γ-Poisson distributions.

PubMed

Moxnes, John F; Moen, Aina E Fossum; Leegaard, Truls Michael

2015-10-05

Study the time development of methicillin-resistant Staphylococcus aureus (MRSA) and forecast future behaviour. The major question: Is the number of MRSA isolates in Norway increasing and will it continue to increase? Time trend analysis using non-stationary γ-Poisson distributions. Two data sets were analysed. The first data set (data set I) consists of all MRSA isolates collected in Oslo County from 1997 to 2010; the study area includes the Norwegian capital of Oslo and nearby surrounding areas, covering approximately 11% of the Norwegian population. The second data set (data set II) consists of all MRSA isolates collected in Health Region East from 2002 to 2011. Health Region East consists of Oslo County and four neighbouring counties, and is the most populated area of Norway. Both data sets I and II consist of all persons in the area and time period described in the Settings, from whom MRSA have been isolated. MRSA infections have been mandatory notifiable in Norway since 1995, and MRSA colonisation since 2004. In the time period studied, all bacterial samples in Norway have been sent to a medical microbiological laboratory at the regional hospital for testing. In collaboration with the regional hospitals in five counties, we have collected all MRSA findings in the South-Eastern part of Norway over long time periods. On an average, a linear or exponential increase in MRSA numbers was observed in the data sets. A Poisson process with increasing intensity did not capture the dispersion of the time series, but a γ-Poisson process showed good agreement and captured the overdispersion. The numerical model showed numerical internal consistency. In the present study, we find that the number of MRSA isolates is increasing in the most populated area of Norway during the time period studied. We also forecast a continuous increase until the year 2017. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Poisson Spot with Magnetic Levitation

ERIC Educational Resources Information Center

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.

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

NASA Astrophysics Data System (ADS)

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).

Modeling health survey data with excessive zero and K responses.

PubMed

Lin, Ting Hsiang; Tsai, Min-Hsiao

2013-04-30

Zero-inflated Poisson regression is a popular tool used to analyze data with excessive zeros. Although much work has already been performed to fit zero-inflated data, most models heavily depend on special features of the individual data. To be specific, this means that there is a sizable group of respondents who endorse the same answers making the data have peaks. In this paper, we propose a new model with the flexibility to model excessive counts other than zero, and the model is a mixture of multinomial logistic and Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts, including zeros, K (where K is a positive integer) and all other values. The Poisson regression component models the counts that are assumed to follow a Poisson distribution. Two examples are provided to illustrate our models when the data have counts containing many ones and sixes. As a result, the zero-inflated and K-inflated models exhibit a better fit than the zero-inflated Poisson and standard Poisson regressions. Copyright © 2012 John Wiley & Sons, Ltd.

Final Scientific Report,

DTIC Science & Technology

1980-11-26

and J.B. Thomas, "The Effect of a Memoryless Nonlinearity on the Spectrum of a Random Process," IEEE Transactions on Information Theory, Vol. IT-23, pp...Density Function from Measurements Corrupted by Poisson Noise," IEEE Transactions on Information Theory, Vol. IT-23, pp. 764-766, November 1977. H. Derin...pp. 243-249, December 1977. G.L. Wise and N.C. Gallagher, "On Spherically Invariant Random Processes," IEEE Transactions on Information Theory, Vol. IT

First-principles prediction of Si-doped Fe carbide as one of the possible constituents of Earth's inner core

NASA Astrophysics Data System (ADS)

Das, Tilak; Chatterjee, Swastika; Ghosh, Sujoy; Saha-Dasgupta, Tanusri

2017-09-01

We perform a computational study based on first-principles calculations to investigate the relative stability and elastic properties of the doped and undoped Fe carbide compounds at 200-364 GPa. We find that upon doping a few weight percent of Si impurities at the carbon sites in Fe7C3 carbide phases, the values of Poisson's ratio and density increase while VP, and VS decrease compared to their undoped counterparts. This leads to marked improvement in the agreement of seismic parameters such as P wave and S wave velocity, Poisson's ratio, and density with the Preliminary Reference Earth Model (PREM) data. The agreement with PREM data is found to be better for the orthorhombic phase of iron carbide (o-Fe7C3) compared to hexagonal phase (h-Fe7C3). Our theoretical analysis indicates that Fe carbide containing Si impurities can be a possible constituent of the Earth's inner core. Since the density of undoped Fe7C3 is low compared to that of inner core, as discussed in a recent theoretical study, our proposal of Si-doped Fe7C3 can provide an alternative solution as an important component of the Earth's inner core.

Poisson-process generalization for the trading waiting-time distribution in a double-auction mechanism

NASA Astrophysics Data System (ADS)

Cincotti, Silvano; Ponta, Linda; Raberto, Marco; Scalas, Enrico

2005-05-01

In this paper, empirical analyses and computational experiments are presented on high-frequency data for a double-auction (book) market. Main objective of the paper is to generalize the order waiting time process in order to properly model such empirical evidences. The empirical study is performed on the best bid and best ask data of 7 U.S. financial markets, for 30-stock time series. In particular, statistical properties of trading waiting times have been analyzed and quality of fits is evaluated by suitable statistical tests, i.e., comparing empirical distributions with theoretical models. Starting from the statistical studies on real data, attention has been focused on the reproducibility of such results in an artificial market. The computational experiments have been performed within the Genoa Artificial Stock Market. In the market model, heterogeneous agents trade one risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market orders depending on their budget constraints. The price is cleared by means of a limit order book. The order generation is modelled with a renewal process. Based on empirical trading estimation, the distribution of waiting times between two consecutive orders is modelled by a mixture of exponential processes. Results show that the empirical waiting-time distribution can be considered as a generalization of a Poisson process. Moreover, the renewal process can approximate real data and implementation on the artificial stocks market can reproduce the trading activity in a realistic way.

The blocking probability of Geiger-mode avalanche photo-diodes

NASA Technical Reports Server (NTRS)

Moision, Bruce; Srinivasan, Meera; Hamkins, Jon

2005-01-01

When a photo is detected by a Geiger-mode avalanche photo-diode (GMAPD), the detector is rendered inactive, or blocked, for a certain period of time. In this paper we derive the blocking probability for a GMAPD whose input is either an unmodulated, Benoulli modulated or pulse-position-modulated Poisson process.

An INAR(1) Negative Multinomial Regression Model for Longitudinal Count Data.

ERIC Educational Resources Information Center

Bockenholt, Ulf

1999-01-01

Discusses a regression model for the analysis of longitudinal count data in a panel study by adapting an integer-valued first-order autoregressive (INAR(1)) Poisson process to represent time-dependent correlation between counts. Derives a new negative multinomial distribution by combining INAR(1) representation with a random effects approach.…

Improving Multiple Surface Range Estimation of a 3-Dimensional FLASH LADAR in the Presence of Atmospheric Turbulence

DTIC Science & Technology

2013-06-01

during the design process. For instance, the detector could be calibrated with incoherent il- lumination and a separate calibration could be performed...Poisson dis- tribution is often employed as a statistical distribution for the detected images. How- ever, due to the highly coherent nature of laser

IRT-ZIP Modeling for Multivariate Zero-Inflated Count Data

ERIC Educational Resources Information Center

Wang, Lijuan

2010-01-01

This study introduces an item response theory-zero-inflated Poisson (IRT-ZIP) model to investigate psychometric properties of multiple items and predict individuals' latent trait scores for multivariate zero-inflated count data. In the model, two link functions are used to capture two processes of the zero-inflated count data. Item parameters are…

Holographic study of conventional and negative Poisson's ratio metallic foams - Elasticity, yield and micro-deformation

NASA Technical Reports Server (NTRS)

Chen, C. P.; Lakes, R. S.

1991-01-01

An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modeling on the basis of cellular rib bending. The reentrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.

Assessing historical rate changes in global tsunami occurrence

USGS Publications Warehouse

Geist, E.L.; Parsons, T.

2011-01-01

The global catalogue of tsunami events is examined to determine if transient variations in tsunami rates are consistent with a Poisson process commonly assumed for tsunami hazard assessments. The primary data analyzed are tsunamis with maximum sizes >1m. The record of these tsunamis appears to be complete since approximately 1890. A secondary data set of tsunamis >0.1m is also analyzed that appears to be complete since approximately 1960. Various kernel density estimates used to determine the rate distribution with time indicate a prominent rate change in global tsunamis during the mid-1990s. Less prominent rate changes occur in the early- and mid-20th century. To determine whether these rate fluctuations are anomalous, the distribution of annual event numbers for the tsunami catalogue is compared to Poisson and negative binomial distributions, the latter of which includes the effects of temporal clustering. Compared to a Poisson distribution, the negative binomial distribution model provides a consistent fit to tsunami event numbers for the >1m data set, but the Poisson null hypothesis cannot be falsified for the shorter duration >0.1m data set. Temporal clustering of tsunami sources is also indicated by the distribution of interevent times for both data sets. Tsunami event clusters consist only of two to four events, in contrast to protracted sequences of earthquakes that make up foreshock-main shock-aftershock sequences. From past studies of seismicity, it is likely that there is a physical triggering mechanism responsible for events within the tsunami source 'mini-clusters'. In conclusion, prominent transient rate increases in the occurrence of global tsunamis appear to be caused by temporal grouping of geographically distinct mini-clusters, in addition to the random preferential location of global M >7 earthquakes along offshore fault zones.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

PubMed

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

NASA Astrophysics Data System (ADS)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

The origin of bursts and heavy tails in human dynamics.

PubMed

Barabási, Albert-László

2005-05-12

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behaviour into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.

Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands

NASA Astrophysics Data System (ADS)

Korobov, A.

2011-08-01

Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands.

PubMed

Korobov, A

2011-08-01

Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

Efficient statistical mapping of avian count data

USGS Publications Warehouse

Royle, J. Andrew; Wikle, C.K.

2005-01-01

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.

Detecting fission from special nuclear material sources

DOEpatents

Rowland, Mark S [Alamo, CA; Snyderman, Neal J [Berkeley, CA

2012-06-05

A neutron detector system for discriminating fissile material from non-fissile material wherein a digital data acquisition unit collects data at high rate, and in real-time processes large volumes of data directly into information that a first responder can use to discriminate materials. The system comprises counting neutrons from the unknown source and detecting excess grouped neutrons to identify fission in the unknown source. The system includes a graphing component that displays the plot of the neutron distribution from the unknown source over a Poisson distribution and a plot of neutrons due to background or environmental sources. The system further includes a known neutron source placed in proximity to the unknown source to actively interrogate the unknown source in order to accentuate differences in neutron emission from the unknown source from Poisson distributions and/or environmental sources.

Gaussian process-based Bayesian nonparametric inference of population size trajectories from gene genealogies.

PubMed

Palacios, Julia A; Minin, Vladimir N

2013-03-01

Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.

Background stratified Poisson regression analysis of cohort data.

PubMed

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.

[Application of negative binomial regression and modified Poisson regression in the research of risk factors for injury frequency].

PubMed

Cao, Qingqing; Wu, Zhenqiang; Sun, Ying; Wang, Tiezhu; Han, Tengwei; Gu, Chaomei; Sun, Yehuan

2011-11-01

To Eexplore the application of negative binomial regression and modified Poisson regression analysis in analyzing the influential factors for injury frequency and the risk factors leading to the increase of injury frequency. 2917 primary and secondary school students were selected from Hefei by cluster random sampling method and surveyed by questionnaire. The data on the count event-based injuries used to fitted modified Poisson regression and negative binomial regression model. The risk factors incurring the increase of unintentional injury frequency for juvenile students was explored, so as to probe the efficiency of these two models in studying the influential factors for injury frequency. The Poisson model existed over-dispersion (P < 0.0001) based on testing by the Lagrangemultiplier. Therefore, the over-dispersion dispersed data using a modified Poisson regression and negative binomial regression model, was fitted better. respectively. Both showed that male gender, younger age, father working outside of the hometown, the level of the guardian being above junior high school and smoking might be the results of higher injury frequencies. On a tendency of clustered frequency data on injury event, both the modified Poisson regression analysis and negative binomial regression analysis can be used. However, based on our data, the modified Poisson regression fitted better and this model could give a more accurate interpretation of relevant factors affecting the frequency of injury.

High order solution of Poisson problems with piecewise constant coefficients and interface jumps

NASA Astrophysics Data System (ADS)

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

2017-04-01

We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains-which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity.

Continuum simulations of acetylcholine consumption by acetylcholinesterase: a Poisson-Nernst-Planck approach.

PubMed

Zhou, Y C; Lu, Benzhuo; Huber, Gary A; Holst, Michael J; McCammon, J Andrew

2008-01-17

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes.

Application of an Elongated Kelvin Model to Space Shuttle Foams

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.; Ghosn, Louis J.; Lerch, Bradley A.

2009-01-01

The space shuttle foams are rigid closed-cell polyurethane foams. The two foams used most-extensively oil space shuttle external tank are BX-265 and NCFL4-124. Because of the foaming and rising process, the foam microstructures are elongated in the rise direction. As a result, these two foams exhibit a nonisotropic mechanical behavior. A detailed microstructural characterization of the two foams is presented. Key features of the foam cells are described and the average cell dimensions in the two foams are summarized. Experimental studies are also conducted to measure the room temperature mechanical response of the two foams in the two principal material directions (parallel to the rise and perpendicular to the rise). The measured elastic modulus, proportional limit stress, ultimate tensile strength, and Poisson's ratios are reported. The generalized elongated Kelvin foam model previously developed by the authors is reviewed and the equations which result from this model are summarized. Using the measured microstructural dimensions and the measured stiffness ratio, the foam tensile strength ratio and Poisson's ratios are predicted for both foams and are compared with the experimental data. The predicted tensile strength ratio is in close agreement with the measured strength ratio for both BX-265 and NCFI24-124. The comparison between the predicted Poisson's ratios and the measured values is not as favorable.

Modeling Zero-Inflated and Overdispersed Count Data: An Empirical Study of School Suspensions

ERIC Educational Resources Information Center

Desjardins, Christopher David

2016-01-01

The purpose of this article is to develop a statistical model that best explains variability in the number of school days suspended. Number of school days suspended is a count variable that may be zero-inflated and overdispersed relative to a Poisson model. Four models were examined: Poisson, negative binomial, Poisson hurdle, and negative…

Alternative Derivations for the Poisson Integral Formula

ERIC Educational Resources Information Center

Chen, J. T.; Wu, C. S.

2006-01-01

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

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

PubMed

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.

Understanding poisson regression.

PubMed

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.

Modified Regression Correlation Coefficient for Poisson Regression Model

NASA Astrophysics Data System (ADS)

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).

Noncommutative gauge theory for Poisson manifolds

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Wess, Julius

2000-09-01

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.

Nearly associative deformation quantization

NASA Astrophysics Data System (ADS)

Vassilevich, Dmitri; Oliveira, Fernando Martins Costa

2018-04-01

We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.

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

PubMed

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.

Poisson image reconstruction with Hessian Schatten-norm regularization.

PubMed

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.

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

2010-06-01

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

A Fock space representation for the quantum Lorentz gas

NASA Astrophysics Data System (ADS)

Maassen, H.; Tip, A.

1995-02-01

A Fock space representation is given for the quantum Lorentz gas, i.e., for random Schrödinger operators of the form H(ω)=p2+Vω=p2+∑ φ(x-xj(ω)), acting in H=L2(Rd), with Poisson distributed xjs. An operator H is defined in K=H⊗P=H⊗L2(Ω,P(dω))=L2(Ω,P(dω);H) by the action of H(ω) on its fibers in a direct integral decomposition. The stationarity of the Poisson process allows a unitarily equivalent description in terms of a new family {H(k)||k∈Rd}, where each H(k) acts in P [A. Tip, J. Math. Phys. 35, 113 (1994)]. The space P is then unitarily mapped upon the symmetric Fock space over L2(Rd,ρdx), with ρ the intensity of the Poisson process (the average number of points xj per unit volume; the scatterer density), and the equivalent of H(k) is determined. Averages now become vacuum expectation values and a further unitary transformation (removing ρ in ρdx) is made which leaves the former invariant. The resulting operator HF(k) has an interesting structure: On the nth Fock layer we encounter a single particle moving in the field of n scatterers and the randomness now appears in the coefficient √ρ in a coupling term connecting neighboring Fock layers. We also give a simple direct self-adjointness proof for HF(k), based upon Nelson's commutator theorem. Restriction to a finite number of layers (a kind of low scatterer density approximation) still gives nontrivial results, as is demonstrated by considering an example.

Human dynamics scaling characteristics for aerial inbound logistics operation

NASA Astrophysics Data System (ADS)

Wang, Qing; Guo, Jin-Li

2010-05-01

In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions - that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models.

Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes.

PubMed

Xu, Jingjie; Xie, Yan; Lu, Benzhuo; Zhang, Linbo

2016-08-25

The Debye-Hückel limiting law is used to study the binding kinetics of substrate-enzyme system as well as to estimate the reaction rate of a electrostatically steered diffusion-controlled reaction process. It is based on a linearized Poisson-Boltzmann model and known for its accurate predictions in dilute solutions. However, the substrate and product particles are in nonequilibrium states and are possibly charged, and their contributions to the total electrostatic field cannot be explicitly studied in the Poisson-Boltzmann model. Hence the influences of substrate and product on reaction rate coefficient were not known. In this work, we consider all the charged species, including the charged substrate, product, and mobile salt ions in a Poisson-Nernst-Planck model, and then compare the results with previous work. The results indicate that both the charged substrate and product can significantly influence the reaction rate coefficient with different behaviors under different setups of computational conditions. It is interesting to find that when substrate and product are both considered, under an overall neutral boundary condition for all the bulk charged species, the computed reaction rate kinetics recovers a similar Debye-Hückel limiting law again. This phenomenon implies that the charged product counteracts the influence of charged substrate on reaction rate coefficient. Our analysis discloses the fact that the total charge concentration of substrate and product, though in a nonequilibrium state individually, obeys an equilibrium Boltzmann distribution, and therefore contributes as a normal charged ion species to ionic strength. This explains why the Debye-Hückel limiting law still works in a considerable range of conditions even though the effects of charged substrate and product particles are not specifically and explicitly considered in the theory.

A stochastic automata network for earthquake simulation and hazard estimation

NASA Astrophysics Data System (ADS)

Belubekian, Maya Ernest

1998-11-01

This research develops a model for simulation of earthquakes on seismic faults with available earthquake catalog data. The model allows estimation of the seismic hazard at a site of interest and assessment of the potential damage and loss in a region. There are two approaches for studying the earthquakes: mechanistic and stochastic. In the mechanistic approach, seismic processes, such as changes in stress or slip on faults, are studied in detail. In the stochastic approach, earthquake occurrences are simulated as realizations of a certain stochastic process. In this dissertation, a stochastic earthquake occurrence model is developed that uses the results from dislocation theory for the estimation of slip released in earthquakes. The slip accumulation and release laws and the event scheduling mechanism adopted in the model result in a memoryless Poisson process for the small and moderate events and in a time- and space-dependent process for large events. The minimum and maximum of the hazard are estimated by the model when the initial conditions along the faults correspond to a situation right after a largest event and after a long seismic gap, respectively. These estimates are compared with the ones obtained from a Poisson model. The Poisson model overestimates the hazard after the maximum event and underestimates it in the period of a long seismic quiescence. The earthquake occurrence model is formulated as a stochastic automata network. Each fault is divided into cells, or automata, that interact by means of information exchange. The model uses a statistical method called bootstrap for the evaluation of the confidence bounds on its results. The parameters of the model are adjusted to the target magnitude patterns obtained from the catalog. A case study is presented for the city of Palo Alto, where the hazard is controlled by the San Andreas, Hayward and Calaveras faults. The results of the model are used to evaluate the damage and loss distribution in Palo Alto. The sensitivity analysis of the model results to the variation in basic parameters shows that the maximum magnitude has the most significant impact on the hazard, especially for long forecast periods.

Evaluating the double Poisson generalized linear model.

PubMed

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.

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

PubMed

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.

Schrödinger-Poisson-Vlasov-Poisson correspondence

NASA Astrophysics Data System (ADS)

Mocz, Philip; Lancaster, Lachlan; Fialkov, Anastasia; Becerra, Fernando; Chavanis, Pierre-Henri

2018-04-01

The Schrödinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As ℏ/m →0 , m being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as ℏ/m →0 due to interference and the uncertainty principle, the potential field converges to the classical answer as (ℏ/m )2. Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as ℏ/m →0 . The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schrödinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultralight axions, which in the classical limit (ℏ/m →0 ) is expected to manifest itself as collisionless cold dark matter.

Limitations of Poisson statistics in describing radioactive decay.

PubMed

Sitek, Arkadiusz; Celler, Anna M

2015-12-01

The assumption that nuclear decays are governed by Poisson statistics is an approximation. This approximation becomes unjustified when data acquisition times longer than or even comparable with the half-lives of the radioisotope in the sample are considered. In this work, the limits of the Poisson-statistics approximation are investigated. The formalism for the statistics of radioactive decay based on binomial distribution is derived. The theoretical factor describing the deviation of variance of the number of decays predicated by the Poisson distribution from the true variance is defined and investigated for several commonly used radiotracers such as (18)F, (15)O, (82)Rb, (13)N, (99m)Tc, (123)I, and (201)Tl. The variance of the number of decays estimated using the Poisson distribution is significantly different than the true variance for a 5-minute observation time of (11)C, (15)O, (13)N, and (82)Rb. Durations of nuclear medicine studies often are relatively long; they may be even a few times longer than the half-lives of some short-lived radiotracers. Our study shows that in such situations the Poisson statistics is unsuitable and should not be applied to describe the statistics of the number of decays in radioactive samples. However, the above statement does not directly apply to counting statistics at the level of event detection. Low sensitivities of detectors which are used in imaging studies make the Poisson approximation near perfect. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

NASA Astrophysics Data System (ADS)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

Spotlight SAR interferometry for terrain elevation mapping and interferometric change detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eichel, P.H.; Ghiglia, D.C.; Jakowatz, C.V. Jr.

1996-02-01

In this report, we employ an approach quite different from any previous work; we show that a new methodology leads to a simpler and clearer understanding of the fundamental principles of SAR interferometry. This methodology also allows implementation of an important collection mode that has not been demonstrated to date. Specifically, we introduce the following six new concepts for the processing of interferometric SAR (INSAR) data: (1) processing using spotlight mode SAR imaging (allowing ultra-high resolution), as opposed to conventional strip-mapping techniques; (2) derivation of the collection geometry constraints required to avoid decorrelation effects in two-pass INSAR; (3) derivation ofmore » maximum likelihood estimators for phase difference and the change parameter employed in interferometric change detection (ICD); (4) processing for the two-pass case wherein the platform ground tracks make a large crossing angle; (5) a robust least-squares method for two-dimensional phase unwrapping formulated as a solution to Poisson`s equation, instead of using traditional path-following techniques; and (6) the existence of a simple linear scale factor that relates phase differences between two SAR images to terrain height. We show both theoretical analysis, as well as numerous examples that employ real SAR collections to demonstrate the innovations listed above.« less

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

PubMed

Kendal, W S

2000-04-01

To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

A cascade model of information processing and encoding for retinal prosthesis.

PubMed

Pei, Zhi-Jun; Gao, Guan-Xin; Hao, Bo; Qiao, Qing-Li; Ai, Hui-Jian

2016-04-01

Retinal prosthesis offers a potential treatment for individuals suffering from photoreceptor degeneration diseases. Establishing biological retinal models and simulating how the biological retina convert incoming light signal into spike trains that can be properly decoded by the brain is a key issue. Some retinal models have been presented, ranking from structural models inspired by the layered architecture to functional models originated from a set of specific physiological phenomena. However, Most of these focus on stimulus image compression, edge detection and reconstruction, but do not generate spike trains corresponding to visual image. In this study, based on state-of-the-art retinal physiological mechanism, including effective visual information extraction, static nonlinear rectification of biological systems and neurons Poisson coding, a cascade model of the retina including the out plexiform layer for information processing and the inner plexiform layer for information encoding was brought forward, which integrates both anatomic connections and functional computations of retina. Using MATLAB software, spike trains corresponding to stimulus image were numerically computed by four steps: linear spatiotemporal filtering, static nonlinear rectification, radial sampling and then Poisson spike generation. The simulated results suggested that such a cascade model could recreate visual information processing and encoding functionalities of the retina, which is helpful in developing artificial retina for the retinally blind.

Hierarchy of temporal responses of multivariate self-excited epidemic processes

NASA Astrophysics Data System (ADS)

Saichev, Alexander; Maillart, Thomas; Sornette, Didier

2013-04-01

Many natural and social systems are characterized by bursty dynamics, for which past events trigger future activity. These systems can be modelled by so-called self-excited Hawkes conditional Poisson processes. It is generally assumed that all events have similar triggering abilities. However, some systems exhibit heterogeneity and clusters with possibly different intra- and inter-triggering, which can be accounted for by generalization into the "multivariate" self-excited Hawkes conditional Poisson processes. We develop the general formalism of the multivariate moment generating function for the cumulative number of first-generation and of all generation events triggered by a given mother event (the "shock") as a function of the current time t. This corresponds to studying the response function of the process. A variety of different systems have been analyzed. In particular, for systems in which triggering between events of different types proceeds through a one-dimension directed or symmetric chain of influence in type space, we report a novel hierarchy of intermediate asymptotic power law decays ˜ 1/ t 1-( m+1) θ of the rate of triggered events as a function of the distance m of the events to the initial shock in the type space, where 0 < θ < 1 for the relevant long-memory processes characterizing many natural and social systems. The richness of the generated time dynamics comes from the cascades of intermediate events of possibly different kinds, unfolding via random changes of types genealogy.

A superstatistical model of metastasis and cancer survival

NASA Astrophysics Data System (ADS)

Leon Chen, L.; Beck, Christian

2008-05-01

We introduce a superstatistical model for the progression statistics of malignant cancer cells. The metastatic cascade is modeled as a complex nonequilibrium system with several macroscopic pathways and inverse-chi-square distributed parameters of the underlying Poisson processes. The predictions of the model are in excellent agreement with observed survival-time probability distributions of breast cancer patients.

Simulating Osmotic Equilibria: A New Tool for Calculating Activity Coefficients in Concentrated Aqueous Salt Solutions.

PubMed

Bley, Michael; Duvail, Magali; Guilbaud, Philippe; Dufrêche, Jean-François

2017-10-19

Herein, a new theoretical method is presented for predicting osmotic equilibria and activities, where a bulk liquid and its corresponding vapor phase are simulated by means of molecular dynamics using explicit polarization. Calculated time-averaged number density profiles provide the amount of evaporated molecules present in the vapor phase and consequently the vapor-phase density. The activity of the solvent and the corresponding osmotic coefficient are determined by the vapor density at different solute concentrations with respect to the reference vapor density of the pure solvent. With the extended Debye-Hückel equation for the activity coefficient along with the corresponding Gibbs-Duhem relation, the activity coefficients of the solutes are calculated by fitting the osmotic coefficients. A simple model based on the combination of Poisson processes and Maxwell-Boltzmann velocity distributions is introduced to interpret statistical phenomena observed during the simulations, which are related to evaporation and recondensation. This method is applied to aqueous dysprosium nitrate [Dy(NO 3 ) 3 ] solutions at different concentrations. The obtained densities of the liquid bulk and the osmotic and activity coefficients are in good agreement with the experimental results for concentrated and saturated solutions. Density profiles of the liquid-vapor interface at different concentrations provide detailed insight into the spatial distributions of all compounds.

On the Dequantization of Fedosov's Deformation Quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2003-08-01

To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to the formal neighborhood of the diagonal of the product M x M~, where M~ is a copy of M with the opposite Poisson structure. We call it dequantization of the natural deformation quantization. Then we "dequantize" Fedosov's quantization.

A discrimination-association model for decomposing component processes of the implicit association test.

PubMed

Stefanutti, Luca; Robusto, Egidio; Vianello, Michelangelo; Anselmi, Pasquale

2013-06-01

A formal model is proposed that decomposes the implicit association test (IAT) effect into three process components: stimuli discrimination, automatic association, and termination criterion. Both response accuracy and reaction time are considered. Four independent and parallel Poisson processes, one for each of the four label categories of the IAT, are assumed. The model parameters are the rate at which information accrues on the counter of each process and the amount of information that is needed before a response is given. The aim of this study is to present the model and an illustrative application in which the process components of a Coca-Pepsi IAT are decomposed.

Pervasive randomness in physics: an introduction to its modelling and spectral characterisation

NASA Astrophysics Data System (ADS)

Howard, Roy

2017-10-01

An introduction to the modelling and spectral characterisation of random phenomena is detailed at a level consistent with a first exposure to the subject at an undergraduate level. A signal framework for defining a random process is provided and this underpins an introduction to common random processes including the Poisson point process, the random walk, the random telegraph signal, shot noise, information signalling random processes, jittered pulse trains, birth-death random processes and Markov chains. An introduction to the spectral characterisation of signals and random processes, via either an energy spectral density or a power spectral density, is detailed. The important case of defining a white noise random process concludes the paper.

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

NASA Astrophysics Data System (ADS)

Nutku, Yavuz

2003-07-01

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.

A note on Poisson goodness-of-fit tests for ionizing radiation induced chromosomal aberration samples.

PubMed

Higueras, Manuel; González, J E; Di Giorgio, Marina; Barquinero, J F

2018-06-13

To present Poisson exact goodness-of-fit tests as alternatives and complements to the asymptotic u-test, which is the most widely used in cytogenetic biodosimetry, to decide whether a sample of chromosomal aberrations in blood cells comes from an homogeneous or inhomogeneous exposure. Three Poisson exact goodness-of-fit test from the literature are introduced and implemented in the R environment. A Shiny R Studio application, named GOF Poisson, has been updated for the purpose of giving support to this work. The three exact tests and the u-test are applied in chromosomal aberration data from clinical and accidental radiation exposure patients. It is observed how the u-test is not an appropriate approximation in small samples with small yield of chromosomal aberrations. Tools are provided to compute the three exact tests, which is not as trivial as the implementation of the u-test. Poisson exact goodness-of-fit tests should be considered jointly to the u-test for detecting inhomogeneous exposures in the cytogenetic biodosimetry practice.

On covariant Poisson brackets in classical field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Forger, Michael; Salles, Mário O.; Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN

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,more » 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.« less

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

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.

Adaptive Sensing and Fusion of Multi-Sensor Data and Historical Information

DTIC Science & Technology

2009-11-06

integrate MTL and semi-supervised learning into a single framework , thereby exploiting two forms of contextual information. A key new objective of the...this report we integrate MTL and semi-supervised learning into a single framework , thereby exploiting two forms of contextual information. A key new...process [8], denoted as X ∼ BeP (B), where B is a measure on Ω. If B is continuous, X is a Poisson process with intensity B and can be constructed as X = N

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Yang; Xiao, Jianyuan; Zhang, Ruili

Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.

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

PubMed

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.

PubMed

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.

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

PubMed Central

Mohammadi, Tayeb; 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. PMID:27703493

Species abundance in a forest community in South China: A case of poisson lognormal distribution

USGS Publications Warehouse

Yin, Z.-Y.; Ren, H.; Zhang, Q.-M.; Peng, S.-L.; Guo, Q.-F.; Zhou, G.-Y.

2005-01-01

Case studies on Poisson lognormal distribution of species abundance have been rare, especially in forest communities. We propose a numerical method to fit the Poisson lognormal to the species abundance data at an evergreen mixed forest in the Dinghushan Biosphere Reserve, South China. Plants in the tree, shrub and herb layers in 25 quadrats of 20 m??20 m, 5 m??5 m, and 1 m??1 m were surveyed. Results indicated that: (i) for each layer, the observed species abundance with a similarly small median, mode, and a variance larger than the mean was reverse J-shaped and followed well the zero-truncated Poisson lognormal; (ii) the coefficient of variation, skewness and kurtosis of abundance, and two Poisson lognormal parameters (?? and ??) for shrub layer were closer to those for the herb layer than those for the tree layer; and (iii) from the tree to the shrub to the herb layer, the ?? and the coefficient of variation decreased, whereas diversity increased. We suggest that: (i) the species abundance distributions in the three layers reflects the overall community characteristics; (ii) the Poisson lognormal can describe the species abundance distribution in diverse communities with a few abundant species but many rare species; and (iii) 1/?? should be an alternative measure of diversity.

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first-order Fuzzy-Border continuum solvation model

PubMed Central

Sharma, Ity; Kaminski, George A.

2012-01-01

We have computed pKa values for eleven substituted phenol compounds using the continuum Fuzzy-Border (FB) solvation model. Hydration energies for 40 other compounds, including alkanes, alkenes, alkynes, ketones, amines, alcohols, ethers, aromatics, amides, heterocycles, thiols, sulfides and acids have been calculated. The overall average unsigned error in the calculated acidity constant values was equal to 0.41 pH units and the average error in the solvation energies was 0.076 kcal/mol. We have also reproduced pKa values of propanoic and butanoic acids within ca. 0.1 pH units from the experimental values by fitting the solvation parameters for carboxylate ion carbon and oxygen atoms. The FB model combines two distinguishing features. First, it limits the amount of noise which is common in numerical treatment of continuum solvation models by using fixed-position grid points. Second, it employs either second- or first-order approximation for the solvent polarization, depending on a particular implementation. These approximations are similar to those used for solute and explicit solvent fast polarization treatment which we developed previously. This article describes results of employing the first-order technique. This approximation places the presented methodology between the Generalized Born and Poisson-Boltzmann continuum solvation models with respect to their accuracy of reproducing the many-body effects in modeling a continuum solvent. PMID:22815192

Hydrogen storage in lithium hydride: A theoretical approach

NASA Astrophysics Data System (ADS)

Banger, Suman; Nayak, Vikas; Verma, U. P.

2018-04-01

First principles calculations have been carried out to analyze structural stability of lithium hydride (LiH) in NaCl phase using the full potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). Calculations have been extended to physiosorbed H-atom compounds LiH·H2, LiH·3H2 and LiH·4H2. The obtained results are discussed in the paper. The results for LiH are in excellent agreement with earlier reported data. The obtained direct energy band gap of LiH is 3.0 eV which is in excellent agreement with earlier reported theoretical band gap. The electronic band structure plots of the hydrogen adsorbed compounds show metallic behavior. The elastic constants, anisotropy factor, shear modulus, Young's modulus, Poisson's ratio and cohesive energies of all the compounds are calculated. Calculation of the optical spectra such as the real and imaginary parts of dielectric function, optical reflectivity, absorption coefficient, optical conductivity, refractive index, extinction coefficient and electron energy loss are performed for the energy range 0-15 eV. The obtained results for LiH·H2, LiH·3H2 and LiH·4H2, are reported for the first time. This study has been made in search of materials for hydrogen storage. It is concluded that LiH is a promising material for hydrogen storage.

NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM

NASA Technical Reports Server (NTRS)

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.

Anomaly Detection in Dynamic Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turcotte, Melissa

2014-10-14

Anomaly detection in dynamic communication networks has many important security applications. These networks can be extremely large and so detecting any changes in their structure can be computationally challenging; hence, computationally fast, parallelisable methods for monitoring the network are paramount. For this reason the methods presented here use independent node and edge based models to detect locally anomalous substructures within communication networks. As a first stage, the aim is to detect changes in the data streams arising from node or edge communications. Throughout the thesis simple, conjugate Bayesian models for counting processes are used to model these data streams. Amore » second stage of analysis can then be performed on a much reduced subset of the network comprising nodes and edges which have been identified as potentially anomalous in the first stage. The first method assumes communications in a network arise from an inhomogeneous Poisson process with piecewise constant intensity. Anomaly detection is then treated as a changepoint problem on the intensities. The changepoint model is extended to incorporate seasonal behavior inherent in communication networks. This seasonal behavior is also viewed as a changepoint problem acting on a piecewise constant Poisson process. In a static time frame, inference is made on this extended model via a Gibbs sampling strategy. In a sequential time frame, where the data arrive as a stream, a novel, fast Sequential Monte Carlo (SMC) algorithm is introduced to sample from the sequence of posterior distributions of the change points over time. A second method is considered for monitoring communications in a large scale computer network. The usage patterns in these types of networks are very bursty in nature and don’t fit a Poisson process model. For tractable inference, discrete time models are considered, where the data are aggregated into discrete time periods and probability models are fitted to the communication counts. In a sequential analysis, anomalous behavior is then identified from outlying behavior with respect to the fitted predictive probability models. Seasonality is again incorporated into the model and is treated as a changepoint model on the transition probabilities of a discrete time Markov process. Second stage analytics are then developed which combine anomalous edges to identify anomalous substructures in the network.« less

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

PubMed

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.

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

PubMed

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

The exponential-Poisson model for recurrent event data: an application to a set of data on malaria in Brazil.

PubMed

Macera, Márcia A C; Louzada, Francisco; Cancho, Vicente G; Fontes, Cor J F

2015-03-01

In this paper, we introduce a new model for recurrent event data characterized by a baseline rate function fully parametric, which is based on the exponential-Poisson distribution. The model arises from a latent competing risk scenario, in the sense that there is no information about which cause was responsible for the event occurrence. Then, the time of each recurrence is given by the minimum lifetime value among all latent causes. The new model has a particular case, which is the classical homogeneous Poisson process. The properties of the proposed model are discussed, including its hazard rate function, survival function, and ordinary moments. The inferential procedure is based on the maximum likelihood approach. We consider an important issue of model selection between the proposed model and its particular case by the likelihood ratio test and score test. Goodness of fit of the recurrent event models is assessed using Cox-Snell residuals. A simulation study evaluates the performance of the estimation procedure in the presence of a small and moderate sample sizes. Applications on two real data sets are provided to illustrate the proposed methodology. One of them, first analyzed by our team of researchers, considers the data concerning the recurrence of malaria, which is an infectious disease caused by a protozoan parasite that infects red blood cells. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu Benzhuo; Holst, Michael J.; Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA 92093

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised formore » time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.« less

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions

PubMed Central

Lu, Benzhuo; Holst, Michael J.; McCammon, J. Andrew; Zhou, Y. C.

2010-01-01

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. PMID:21709855

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

PubMed

Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

Smart materials systems through mesoscale patterning

NASA Astrophysics Data System (ADS)

Aksay, Ilhan A.; Groves, John T.; Gruner, Sol M.; Lee, P. C. Y.; Prud'homme, Robert K.; Shih, Wei-Heng; Torquato, Salvatore; Whitesides, George M.

1996-02-01

We report work on the fabrication of smart materials with two unique strategies: (1) self- assembly and (2) laser stereolithography. Both methods are akin to the processes used by biological systems. The first one is ideal for pattern development and the fabrication of miniaturized units in the submicron range and the second one in the 10 micrometer to 1 mm size range. By using these miniaturized units as building blocks, one can also produce smart material systems that can be used at larger length scales such as smart structural components. We have chosen to focus on two novel piezoceramic systems: (1) high-displacement piezoelectric actuators, and (2) piezoceramic hydrophone composites possessing negative Poisson ratio matrices. High-displacement actuators are essential in such applications as linear motors, pumps, switches, loud speakers, variable-focus mirrors, and laser deflectors. Arrays of such units can potentially be used for active vibration control of helicopter rotors as well as the fabrication of adaptive rotors. In the case of piezoceramic hydrophone composites, we utilize matrices having a negative Poisson's ratio in order to produce highly sensitive, miniaturized sensors. We envision such devices having promising new application areas such as the implantation of hydrophones in small blood vessels to monitor blood pressure. Negative Poisson ratio materials have promise as robust shock absorbers, air filters, and fasteners, and hence, can be used in aircraft and land vehicles.

Theoretical simulations of the structural stabilities, elastic, thermodynamic and electronic properties of Pt3Sc and Pt3Y compounds

NASA Astrophysics Data System (ADS)

Boulechfar, R.; Khenioui, Y.; Drablia, S.; Meradji, H.; Abu-Jafar, M.; Omran, S. Bin; Khenata, R.; Ghemid, S.

2018-05-01

Ab-initio calculations based on density functional theory have been performed to study the structural, electronic, thermodynamic and mechanical properties of intermetallic compounds Pt3Sc and Pt3Y using the full-potential linearized augmented plane wave(FP-LAPW) method. The total energy calculations performed for L12, D022 and D024 structures confirm the experimental phase stability. Using the generalized gradient approximation (GGA), the values of enthalpies formation are -1.23 eV/atom and -1.18 eV/atom for Pt3Sc and Pt3Y, respectively. The densities of states (DOS) spectra show the existence of a pseudo-gap at the Fermi level for both compounds which indicate the strong spd hybridization and directing covalent bonding. Furthermore, the density of states at the Fermi level N(EF), the electronic specific heat coefficient (γele) and the number of bonding electrons per atom are predicted in addition to the elastic constants (C11, C12 and C44). The shear modulus (GH), Young's modulus (E), Poisson's ratio (ν), anisotropy factor (A), ratio of B/GH and Cauchy pressure (C12-C44) are also estimated. These parameters show that the Pt3Sc and Pt3Y are ductile compounds. The thermodynamic properties were calculated using the quasi-harmonic Debye model to account for their lattice vibrations. In addition, the influence of the temperature and pressure was analyzed on the heat capacities (Cp and Cv), thermal expansion coefficient (α), Debye temperature (θD) and Grüneisen parameter (γ).

Finite element solution of torsion and other 2-D Poisson equations

NASA Technical Reports Server (NTRS)

Everstine, G. C.

1982-01-01

The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

Mechanical properties investigation on single-wall ZrO2 nanotubes: A finite element method with equivalent Poisson's ratio for chemical bonds

NASA Astrophysics Data System (ADS)

Yang, Xiao; Li, Huijian; Hu, Minzheng; Liu, Zeliang; Wärnå, John; Cao, Yuying; Ahuja, Rajeev; Luo, Wei

2018-04-01

A method to obtain the equivalent Poisson's ratio in chemical bonds as classical beams with finite element method was proposed from experimental data. The UFF (Universal Force Field) method was employed to calculate the elastic force constants of Zrsbnd O bonds. By applying the equivalent Poisson's ratio, the mechanical properties of single-wall ZrNTs (ZrO2 nanotubes) were investigated by finite element analysis. The nanotubes' Young's modulus (Y), Poisson's ratio (ν) of ZrNTs as function of diameters, length and chirality have been discussed, respectively. We found that the Young's modulus of single-wall ZrNTs is calculated to be between 350 and 420 GPa.

Poisson's spot and Gouy phase

NASA Astrophysics Data System (ADS)

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.

Multimedia Network Design Study

DTIC Science & Technology

1989-09-30

manipulation and analysis of the equations involved, thereby providing the application of the great range of powerful mathematical optimization...be treated by this analysis. First, all arrivals to the network have the Poisson distribution, and separate traffic classes may have separate qrrival...different for open and closed networks, so these two situations will be treated separately in the following subsections. 2.3.1 The Computational Process in

Modeling Rare Baseball Events--Are They Memoryless?

ERIC Educational Resources Information Center

Huber, Michael; Glen, Andrew

2007-01-01

Three sets of rare baseball events--pitching a no-hit game, hitting for the cycle, and turning a triple play--offer excellent examples of events whose occurrence may be modeled as Poisson processes. That is, the time of occurrence of one of these events doesn't affect when we see the next occurrence of such. We modeled occurrences of these three…

Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise, and multifractality.

PubMed

Kendal, Wayne S; Jørgensen, Bent

2011-12-01

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality.

Markov model of fatigue of a composite material with the poisson process of defect initiation

NASA Astrophysics Data System (ADS)

Paramonov, Yu.; Chatys, R.; Andersons, J.; Kleinhofs, M.

2012-05-01

As a development of the model where only one weak microvolume (WMV) and only a pulsating cyclic loading are considered, in the current version of the model, we take into account the presence of several weak sites where fatigue damage can accumulate and a loading with an arbitrary (but positive) stress ratio. The Poisson process of initiation of WMVs is considered, whose rate depends on the size of a specimen. The cumulative distribution function (cdf) of the fatigue life of every individual WMV is calculated using the Markov model of fatigue. For the case where this function is approximated by a lognormal distribution, a formula for calculating the cdf of fatigue life of the specimen (modeled as a chain of WMVs) is obtained. Only a pulsating cyclic loading was considered in the previous version of the model. Now, using the modified energy method, a loading cycle with an arbitrary stress ratio is "transformed" into an equivalent cycle with some other stress ratio. In such a way, the entire probabilistic fatigue diagram for any stress ratio with a positive cycle stress can be obtained. Numerical examples are presented.

Semiparametric bivariate zero-inflated Poisson models with application to studies of abundance for multiple species

USGS Publications Warehouse

Arab, Ali; Holan, Scott H.; Wikle, Christopher K.; Wildhaber, Mark L.

2012-01-01

Ecological studies involving counts of abundance, presence–absence or occupancy rates often produce data having a substantial proportion of zeros. Furthermore, these types of processes are typically multivariate and only adequately described by complex nonlinear relationships involving externally measured covariates. Ignoring these aspects of the data and implementing standard approaches can lead to models that fail to provide adequate scientific understanding of the underlying ecological processes, possibly resulting in a loss of inferential power. One method of dealing with data having excess zeros is to consider the class of univariate zero-inflated generalized linear models. However, this class of models fails to address the multivariate and nonlinear aspects associated with the data usually encountered in practice. Therefore, we propose a semiparametric bivariate zero-inflated Poisson model that takes into account both of these data attributes. The general modeling framework is hierarchical Bayes and is suitable for a broad range of applications. We demonstrate the effectiveness of our model through a motivating example on modeling catch per unit area for multiple species using data from the Missouri River Benthic Fishes Study, implemented by the United States Geological Survey.

Speech parts as Poisson processes.

PubMed

Badalamenti, A F

2001-09-01

This paper presents evidence that six of the seven parts of speech occur in written text as Poisson processes, simple or recurring. The six major parts are nouns, verbs, adjectives, adverbs, prepositions, and conjunctions, with the interjection occurring too infrequently to support a model. The data consist of more than the first 5000 words of works by four major authors coded to label the parts of speech, as well as periods (sentence terminators). Sentence length is measured via the period and found to be normally distributed with no stochastic model identified for its occurrence. The models for all six speech parts but the noun significantly distinguish some pairs of authors and likewise for the joint use of all words types. Any one author is significantly distinguished from any other by at least one word type and sentence length very significantly distinguishes each from all others. The variety of word type use, measured by Shannon entropy, builds to about 90% of its maximum possible value. The rate constants for nouns are close to the fractions of maximum entropy achieved. This finding together with the stochastic models and the relations among them suggest that the noun may be a primitive organizer of written text.

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties.

PubMed

Burkitt, A N

2006-08-01

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker-Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).

Comparing neuronal spike trains with inhomogeneous Poisson distribution: evaluation procedure and experimental application in cases of cyclic activity.

PubMed

Fiore, Lorenzo; Lorenzetti, Walter; Ratti, Giovannino

2005-11-30

A procedure is proposed to compare single-unit spiking activity elicited in repetitive cycles with an inhomogeneous Poisson process (IPP). Each spike sequence in a cycle is discretized and represented as a point process on a circle. The interspike interval probability density predicted for an IPP is computed on the basis of the experimental firing probability density; differences from the experimental interval distribution are assessed. This procedure was applied to spike trains which were repetitively induced by opening-closing movements of the distal article of a lobster leg. As expected, the density of short interspike intervals, less than 20-40 ms in length, was found to lie greatly below the level predicted for an IPP, reflecting the occurrence of the refractory period. Conversely, longer intervals, ranging from 20-40 to 100-120 ms, were markedly more abundant than expected; this provided evidence for a time window of increased tendency to fire again after a spike. Less consistently, a weak depression of spike generation was observed for longer intervals. A Monte Carlo procedure, implemented for comparison, produced quite similar results, but was slightly less precise and more demanding as concerns computation time.