The Fractional Poisson Process and the Inverse Stable Subordinator
Meerschaert, Mark; Nane, Erkan; Vellaisamy, P.
2011-01-01
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extend...
Poisson-type inequalities for growth properties of positive superharmonic functions.
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.
On the Fractional Poisson Process and the Discretized Stable Subordinator
Directory of Open Access Journals (Sweden)
Rudolf Gorenflo
2015-08-01
Full Text Available We consider the renewal counting number process N = N(t as a forward march over the non-negative integers with independent identically distributed waiting times. We embed the values of the counting numbers N in a “pseudo-spatial” non-negative half-line x ≥ 0 and observe that for physical time likewise we have t ≥ 0. Thus we apply the Laplace transform with respect to both variables x and t. Applying then a modification of the Montroll-Weiss-Cox formalism of continuous time random walk we obtain the essential characteristics of a renewal process in the transform domain and, if we are lucky, also in the physical domain. The process t = t(N of accumulation of waiting times is inverse to the counting number process, in honour of the Danish mathematician and telecommunication engineer A.K. Erlang we call it the Erlang process. It yields the probability of exactly n renewal events in the interval (0; t]. We apply our Laplace-Laplace formalism to the fractional Poisson process whose waiting times are of Mittag-Leffler type and to a renewal process whose waiting times are of Wright type. The process of Mittag-Leffler type includes as a limiting case the classical Poisson process, the process of Wright type represents the discretized stable subordinator and a re-scaled version of it was used in our method of parametric subordination of time-space fractional diffusion processes. Properly rescaling the counting number process N(t and the Erlang process t(N yields as diffusion limits the inverse stable and the stable subordinator, respectively.
Super-stable Poissonian structures
International Nuclear Information System (INIS)
Eliazar, Iddo
2012-01-01
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. (paper)
Super-stable Poissonian structures
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.
International Nuclear Information System (INIS)
Kocer, C.; McKenzie, D.R.; Bilek, M.M.
2009-01-01
The theory of elasticity predicts a variety of phenomena associated with solids that possess a negative Poisson's ratio. The fabrication of metamaterials with a 'designed' microstructure that exhibit a Poisson's ratio approaching the thermodynamic limits of 1/2 and -1 increases the likelihood of realising these phenomena for applications. In this work, we investigate the properties of a layered composite, with alternating layers of materials with negative and positive Poisson's ratio approaching the thermodynamic limits. Using the finite element method to simulate uniaxial loading and indentation of a free standing composite, we observed an increase in the resistance to mechanical deformation above the average value of the two materials. Even though the greatest increase in stiffness is gained as the thermodynamic limits are approached, a significant amount of added stiffness can be attained, provided that the Young's modulus of the negative Poisson's ratio material is not less than that of the positive Poisson's ratio material
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.
Laplace-Laplace analysis of the fractional Poisson process
Gorenflo, Rudolf; Mainardi, Francesco
2013-01-01
We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.
Coordination of Conditional Poisson Samples
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Grafström Anton
2015-12-01
Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.
Alternative Forms of Compound Fractional Poisson Processes
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Luisa Beghin
2012-01-01
Full Text Available We study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves. The corresponding distributions are obtained explicitly and proved to be solution of fractional equations of order less than one. Only in the final case treated in this paper, where the number of jumps is given by the fractional-difference Poisson process defined in Orsingher and Polito (2012, we have a fractional driving equation, with respect to the time argument, with order greater than one. Moreover, in this case, the compound Poisson process is Markovian and this is also true for the corresponding limiting process. All the processes considered here are proved to be compositions of continuous time random walks with stable processes (or inverse stable subordinators. These subordinating relationships hold, not only in the limit, but also in the finite domain. In some cases the densities satisfy master equations which are the fractional analogues of the well-known Kolmogorov one.
On the fractal characterization of Paretian Poisson processes
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.
On poisson-stopped-sums that are mixed poisson
Valero Baya, Jordi; Pérez Casany, Marta; Ginebra Molins, Josep
2013-01-01
Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it. Peer Reviewed
Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
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.
? filtering for stochastic systems driven by Poisson processes
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.
Polynomial Poisson algebras: Gel'fand-Kirillov problem and Poisson spectra
Lecoutre, César
2014-01-01
We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras.\\ud \\ud First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to...
Coherent transform, quantization, and Poisson geometry
Novikova, E; Itskov, V; Karasev, M V
1998-01-01
This volume contains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.
The BRST complex of homological Poisson reduction
Müller-Lennert, Martin
2017-02-01
BRST complexes are differential graded Poisson algebras. They are associated with a coisotropic ideal J of a Poisson algebra P and provide a description of the Poisson algebra (P/J)^J as their cohomology in degree zero. Using the notion of stable equivalence introduced in Felder and Kazhdan (Contemporary Mathematics 610, Perspectives in representation theory, 2014), we prove that any two BRST complexes associated with the same coisotropic ideal are quasi-isomorphic in the case P = R[V] where V is a finite-dimensional symplectic vector space and the bracket on P is induced by the symplectic structure on V. As a corollary, the cohomology of the BRST complexes is canonically associated with the coisotropic ideal J in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal J. We finally quantize the BRST complex rigorously in the presence of infinitely many ghost variables and discuss the uniqueness of the quantization procedure.
Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.
Frejlich, Pedro; Mărcuț, Ioan
2018-01-01
Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.
Comparison of Poisson structures and Poisson-Lie dynamical r-matrices
Enriquez, B.; Etingof, P.; Marshall, I.
2004-01-01
We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.
Terashima, Yuji
2008-01-01
In this paper, defining Poisson functions on super manifolds, we show that the graphs of Poisson functions are Dirac structures, and find Poisson functions which include as special cases both quasi-Poisson structures and twisted Poisson structures.
A relation between Liapunov stability, non-wanderingness and Poisson stability
International Nuclear Information System (INIS)
Ahmad, K.H.
1985-07-01
In this work, some of the relations among Liapunov stability, non-wanderingness and Poisson stability are considered. In particular it is shown that for a non-wandering point in a set, positive (resp. negative) Liapunov stability in that set implies positive (resp. negative) Poisson stability in the same set. (author)
Positive ground state solutions to Schrodinger-Poisson systems with a negative non-local term
Directory of Open Access Journals (Sweden)
Yan-Ping Gao
2015-04-01
Full Text Available In this article, we study the Schrodinger-Poisson system $$\\displaylines{ -\\Delta u+u-\\lambda K(x\\phi(xu=a(x|u|^{p-1}u, \\quad x\\in\\mathbb{R}^3, \\cr -\\Delta\\phi=K(xu^{2},\\quad x\\in\\mathbb{R}^3, }$$ with $p\\in(1,5$. Assume that $a:\\mathbb{R}^3\\to \\mathbb{R^{+}}$ and $K:\\mathbb{R}^3\\to \\mathbb{R^{+}}$ are nonnegative functions and satisfy suitable assumptions, but not requiring any symmetry property on them, we prove the existence of a positive ground state solution resolved by the variational methods.
Formal equivalence of Poisson structures around Poisson submanifolds
Marcut, I.T.
2012-01-01
Let (M,π) be a Poisson manifold. A Poisson submanifold P ⊂ M gives rise to a Lie algebroid AP → P. Formal deformations of π around P are controlled by certain cohomology groups associated to AP. Assuming that these groups vanish, we prove that π is formally rigid around P; that is, any other Poisson
Study on two-dimensional POISSON design of large-scale FFAG magnet
International Nuclear Information System (INIS)
Ouyang Huafu
2006-01-01
In order to decrease the edge effect of the field, the designed magnetic field distribution in a large-scale FFAG magnet is realized by both the trim coil and the shape of the magnet pole-face. Through two-dimensional POISSON simulations, the distribution about the current and the position of the trim coil and the shape of the magnet pole are determined. In order to facilitate the POISSON design, two codes are writteen to automatically adjust the current and the position of the trim coil and the shape of magnet pole-face appeared in the POISSON input file. With the two codes, the efficiency of POISSON simulations is improved and the mistakes which might occur in writing and adjusting the POISSON input file manually could be avoided. (authors)
(Quasi-)Poisson enveloping algebras
Yang, Yan-Hong; Yao, Yuan; Ye, Yu
2010-01-01
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...
NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM
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.
Zaitsev, Vladimir Y.; Radostin, Andrey V.; Dyskin, Arcady V.; Pasternak, Elena
2017-04-01
We report results of analysis of literature data on P- and S-wave velocities of rocks subjected to variable hydrostatic pressure. Out of about 90 examined samples, in more than 40% of the samples the reconstructed Poisson's ratios are negative for lowest confining pressure with gradual transition to the conventional positive values at higher pressure. The portion of rocks exhibiting negative Poisson's ratio appeared to be unexpectedly high. To understand the mechanism of negative Poisson's ratio, pressure dependences of P- and S-wave velocities were analyzed using the effective medium model in which the reduction in the elastic moduli due to cracks is described in terms of compliances with respect to shear and normal loading that are imparted to the rock by the presence of cracks. This is in contrast to widely used descriptions of effective cracked medium based on a specific crack model (e.g., penny-shape crack) in which the ratio between normal and shear compliances of such a crack is strictly predetermined. The analysis of pressure-dependences of the elastic wave velocities makes it possible to reveal the ratio between pure normal and shear compliances (called q-ratio below) for real defects and quantify their integral content in the rock. The examination performed demonstrates that a significant portion (over 50%) of cracks exhibit q-ratio several times higher than that assumed for the conventional penny-shape cracks. This leads to faster reduction of the Poisson's ratio with increasing the crack concentration. Samples with negative Poisson's ratio are characterized by elevated q-ratio and simultaneously crack concentration. Our results clearly indicate that the traditional crack model is not adequate for a significant portion of rocks and that the interaction between the opposite crack faces leading to domination of the normal compliance and reduced shear displacement discontinuity can play an important role in the mechanical behavior of rocks.
Topological Poisson Sigma models on Poisson-Lie groups
International Nuclear Information System (INIS)
Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David
2003-01-01
We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)
Hallin, M.; Piegorsch, W.; El Shaarawi, A.
2012-01-01
The random variable X taking values 0,1,2,…,x,… with probabilities pλ(x) = e−λλx/x!, where λ∈R0+ is called a Poisson variable, and its distribution a Poisson distribution, with parameter λ. The Poisson distribution with parameter λ can be obtained as the limit, as n → ∞ and p → 0 in such a way that
POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity
International Nuclear Information System (INIS)
Colman, J.
2001-01-01
1 - Description of program or function: POISSON, SUPERFISH is a group of (1) codes that solve Poisson's equation and are used to compute field quality for both magnets and fixed electric potentials and (2) RF cavity codes that calculate resonant frequencies and field distributions of the fundamental and higher modes. The group includes: POISSON, PANDIRA, SUPERFISH, AUTOMESH, LATTICE, FORCE, MIRT, PAN-T, TEKPLOT, SF01, and SHY. POISSON solves Poisson's (or Laplace's) equation for the vector (scalar) potential with nonlinear isotropic iron (dielectric) and electric current (charge) distributions for two-dimensional Cartesian or three-dimensional cylindrical symmetry. It calculates the derivatives of the potential, the stored energy, and performs harmonic (multipole) analysis of the potential. PANDIRA is similar to POISSON except it allows anisotropic and permanent magnet materials and uses a different numerical method to obtain the potential. SUPERFISH solves for the accelerating (TM) and deflecting (TE) resonant frequencies and field distributions in an RF cavity with two-dimensional Cartesian or three-dimensional cylindrical symmetry. Only the azimuthally symmetric modes are found for cylindrically symmetric cavities. AUTOMESH prepares input for LATTICE from geometrical data describing the problem, (i.e., it constructs the 'logical' mesh and generates (x,y) coordinate data for straight lines, arcs of circles, and segments of hyperbolas). LATTICE generates an irregular triangular (physical) mesh from the input data, calculates the 'point current' terms at each mesh point in regions with distributed current density, and sets up the mesh point relaxation order needed to write the binary problem file for the equation-solving POISSON, PANDIRA, or SUPERFISH. FORCE calculates forces and torques on coils and iron regions from POISSON or PANDIRA solutions for the potential. MIRT optimizes magnet profiles, coil shapes, and current densities from POISSON output based on a
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
2009-01-01
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
International Nuclear Information System (INIS)
Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-01
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.
Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Boxma, O.J.; Yechiali, U.; Ruggeri, F.; Kenett, R.S.; Faltin, F.W.
2007-01-01
The Poisson process is a stochastic counting process that arises naturally in a large variety of daily life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
Poisson Processes in Free Probability
An, Guimei; Gao, Mingchu
2015-01-01
We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...
Energy Technology Data Exchange (ETDEWEB)
Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague 186 75 (Czech Republic); Schupp, Peter, E-mail: p.schupp@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany); Vysoký, Jan, E-mail: vysokjan@fjfi.cvut.cz [Jacobs University Bremen, 28759 Bremen (Germany); Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Prague 115 19 (Czech Republic)
2014-06-02
We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.
International Nuclear Information System (INIS)
Jurčo, Branislav; Schupp, Peter; Vysoký, Jan
2014-01-01
We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.
Directory of Open Access Journals (Sweden)
Lusi Eka Afri
2017-03-01
Full Text Available Regresi Binomial Negatif dan regresi Conway-Maxwell-Poisson merupakan solusi untuk mengatasi overdispersi pada regresi Poisson. Kedua model tersebut merupakan perluasan dari model regresi Poisson. Menurut Hinde dan Demetrio (2007, terdapat beberapa kemungkinan terjadi overdispersi pada regresi Poisson yaitu keragaman hasil pengamatan keragaman individu sebagai komponen yang tidak dijelaskan oleh model, korelasi antar respon individu, terjadinya pengelompokan dalam populasi dan peubah teramati yang dihilangkan. Akibatnya dapat menyebabkan pendugaan galat baku yang terlalu rendah dan akan menghasilkan pendugaan parameter yang bias ke bawah (underestimate. Penelitian ini bertujuan untuk membandingan model Regresi Binomial Negatif dan model regresi Conway-Maxwell-Poisson (COM-Poisson dalam mengatasi overdispersi pada data distribusi Poisson berdasarkan statistik uji devians. Data yang digunakan dalam penelitian ini terdiri dari dua sumber data yaitu data simulasi dan data kasus terapan. Data simulasi yang digunakan diperoleh dengan membangkitkan data berdistribusi Poisson yang mengandung overdispersi dengan menggunakan bahasa pemrograman R berdasarkan karakteristik data berupa , peluang munculnya nilai nol (p serta ukuran sampel (n. Data dibangkitkan berguna untuk mendapatkan estimasi koefisien parameter pada regresi binomial negatif dan COM-Poisson. Kata Kunci: overdispersi, regresi binomial negatif, regresi Conway-Maxwell-Poisson Negative binomial regression and Conway-Maxwell-Poisson regression could be used to overcome over dispersion on Poisson regression. Both models are the extension of Poisson regression model. According to Hinde and Demetrio (2007, there will be some over dispersion on Poisson regression: observed variance in individual variance cannot be described by a model, correlation among individual response, and the population group and the observed variables are eliminated. Consequently, this can lead to low standard error
Comparison between two bivariate Poisson distributions through the ...
African Journals Online (AJOL)
These two models express themselves by their probability mass function. ... To remedy this problem, Berkhout and Plug proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive.
On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action
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.
Optimized thick-wall cylinders by virtue of Poisson's ratio selection
International Nuclear Information System (INIS)
Whitty, J.P.M.; Henderson, B.; Francis, J.; Lloyd, N.
2011-01-01
The principal stress distributions in thick-wall cylinders due to variation in the Poisson's ratio are predicted using analytical and finite element methods. Analyses of appropriate brittle and ductile failure criteria show that under the isochoric pressure conditions investigated that auextic (i.e. those possessing a negative Poisson's ratio) materials act as stress concentrators; hence they are predicted to fail before their conventional (i.e. possessing a positive Poisson's ratio) material counterparts. The key finding of the work presented shows that for constrained thick-wall cylinders the maximum tensile principal stress can vanish at a particular Poisson's ratio and aspect ratio. This phenomenon is exploited in order to present an optimized design criterion for thick-wall cylinders. Moreover, via the use of a cogent finite element model, this criterion is also shown to be applicable for the design of micro-porous materials.
Homogeneous Poisson structures
International Nuclear Information System (INIS)
Shafei Deh Abad, A.; Malek, F.
1993-09-01
We provide an algebraic definition for Schouten product and give a decomposition for any homogenenous Poisson structure in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in R k is also characterized. (author). 4 refs
Understanding poisson regression.
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.
International Nuclear Information System (INIS)
Harwood, L.H.
1981-01-01
At MSU we have used the POISSON family of programs extensively for magnetic field calculations. In the presently super-saturated computer situation, reducing the run time for the program is imperative. Thus, a series of modifications have been made to POISSON to speed up convergence. Two of the modifications aim at having the first guess solution as close as possible to the final solution. The other two aim at increasing the convergence rate. In this discussion, a working knowledge of POISSON is assumed. The amount of new code and expected time saving for each modification is discussed
A new multivariate zero-adjusted Poisson model with applications to biomedicine.
Liu, Yin; Tian, Guo-Liang; Tang, Man-Lai; Yuen, Kam Chuen
2018-05-25
Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, ) cannot be used to fit multivariate count data with excess zero-vectors; (ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases; (iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Remarks on 'Poisson ratio beyond the limits of the elasticity theory'
International Nuclear Information System (INIS)
Wojciechowski, K.W.
2002-12-01
The non-chiral, elastically isotropic model exhibits Poison ratios in the range -1 ≤ σ ≤ 1 without any molecular rotation. The centres of discs-atoms are replaced in the vertices of a perfect triangle of the side length equal to σ. The positive sign of the Lame constant λ is not necessary for the stability of an isotropic system at any dimensionality. As the upper limit for the Poisson ratio in 2D isotropic systems is 1, crystalline or polycrystalline 2D systems can be obtained having the Poisson ratio exceeding 1/2. Both the traditional theory of elasticity and the Cosserat one exclude Poisson ratios exceeding 1/2 in 3D isotropic systems. Neighter anisotropy nor rotation are necessary to obtain extreme values of the Poisson ratio (author)
Non-equal-time Poisson brackets
Nikolic, H.
1998-01-01
The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.
Non-chiral, molecular model of negative Poisson ratio in two dimensions
International Nuclear Information System (INIS)
Wojciechowski, K W
2003-01-01
A two-dimensional model of tri-atomic molecules (in which 'atoms' are distributed on vertices of equilateral triangles, and which are further referred to as cyclic trimers) is solved exactly in the static (zero-temperature) limit for the nearest-neighbour site-site interactions. It is shown that the cyclic trimers form a mechanically stable and elastically isotropic non-chiral phase of negative Poisson ratio. The properties of the system are illustrated by three examples of atom-atom interaction potentials: (i) the purely repulsive (n-inverse-power) potential, (ii) the purely attractive (n-power) potential and (iii) the Lennard-Jones potential which shows both the repulsive and the attractive part. The analytic form of the dependence of the Poisson ratio on the interatomic potential is obtained. It is shown that the Poisson ratio depends, in a universal way, only on the trimer anisotropy parameter both (1) in the limit of n → ∞ for cases (i) and (ii), as well as (2) at the zero external pressure for any potential with a doubly differentiable minimum, case (iii) is an example
Branes in Poisson sigma models
International Nuclear Information System (INIS)
Falceto, Fernando
2010-01-01
In this review we discuss possible boundary conditions (branes) for the Poisson sigma model. We show how to carry out the perturbative quantization in the presence of a general pre-Poisson brane and how this is related to the deformation quantization of Poisson structures. We conclude with an open problem: the perturbative quantization of the system when the boundary has several connected components and we use a different pre-Poisson brane in every component.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios; Burganos, Vasilis N.
2013-01-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Extended Poisson Exponential Distribution
Directory of Open Access Journals (Sweden)
Anum Fatima
2015-09-01
Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
Poisson branching point processes
International Nuclear Information System (INIS)
Matsuo, K.; Teich, M.C.; Saleh, B.E.A.
1984-01-01
We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage. In addition, each initiating event independently contributes a nonstationary Poisson point process (whose rate is a specified function) located at that point. The additional contributions from all points of a given stage constitute a doubly stochastic Poisson point process (DSPP) whose rate is a filtered version of the initiating point process at that stage. The process studied is a generalization of a Poisson branching process in which random time delays are permitted in the generation of events. Particular attention is given to the limit in which the number of branching stages is infinite while the average number of added events per event of the previous stage is infinitesimal. In the special case when the branching is instantaneous this limit of continuous branching corresponds to the well-known Yule--Furry process with an initial Poisson population. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers
On (co)homology of Frobenius Poisson algebras
Zhu, Can; Van Oystaeyen, Fred; ZHANG, Yinhuo
2014-01-01
In this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisk...
A multiresolution method for solving the Poisson equation using high order regularization
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Walther, Jens Honore
2016-01-01
We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regulari......We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches...... and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poisson solver produces convergence rates...
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations
Haas, F.; Shukla, P. K.
2008-01-01
Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved p...
Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes
Orsingher, Enzo; Polito, Federico
2012-08-01
In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.
A twisted generalization of Novikov-Poisson algebras
Yau, Donald
2010-01-01
Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.
Poisson hierarchy of discrete strings
International Nuclear Information System (INIS)
Ioannidou, Theodora; Niemi, Antti J.
2016-01-01
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Poisson hierarchy of discrete strings
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere
International Nuclear Information System (INIS)
Sheu, A.J.L.
1991-01-01
We show that deformation quantizations of the Poisson structures on the Poisson Lie group SU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization of SU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure on SU(2) at the classical level is preserved under quantization. (orig.)
Cumulative Poisson Distribution Program
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.
Nonlinear Poisson equation for heterogeneous media.
Hu, Langhua; Wei, Guo-Wei
2012-08-22
The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Poisson's ratio of fiber-reinforced composites
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.
Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations
International Nuclear Information System (INIS)
Haas, F.; Shukla, P. K.
2008-01-01
Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed.
Non-holonomic dynamics and Poisson geometry
International Nuclear Information System (INIS)
Borisov, A V; Mamaev, I S; Tsiganov, A V
2014-01-01
This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie-Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles
Poisson brackets of orthogonal polynomials
Cantero, María José; Simon, Barry
2009-01-01
For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.
Constructions and classifications of projective Poisson varieties.
Pym, Brent
2018-01-01
This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.
Constructions and classifications of projective Poisson varieties
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.
Invariants and labels for Lie-Poisson Systems
International Nuclear Information System (INIS)
Thiffeault, J.L.; Morrison, P.J.
1998-04-01
Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system
Nonlocal Poisson-Fermi model for ionic solvent.
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.
Estimation in the positive stable shared frailty Cox proportional hazards model
DEFF Research Database (Denmark)
Martinussen, Torben; Pipper, Christian Bressen
2005-01-01
model in situations where the correlated survival data show a decreasing association with time. In this paper, we devise a likelihood based estimation procedure for the positive stable shared frailty Cox model, which is expected to obtain high efficiency. The proposed estimator is provided with large...
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
International Nuclear Information System (INIS)
Meusburger, C.; Schroers, B. J.
2008-01-01
Each of the local isometry groups arising in three-dimensional (3d) gravity can be viewed as a group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement and use it as a unifying framework for studying Poisson structures associated with the local isometry groups. We show that, in all cases except for the case of Euclidean signature with positive cosmological constant, the local isometry groups are equipped with the Poisson-Lie structure of a classical double. We calculate the dressing action of the factor groups on each other and find, among others, a simple and unified description of the symplectic leaves of SU(2) and SL(2,R). We also compute the Poisson structure on the dual Poisson-Lie groups of the local isometry groups and on their Heisenberg doubles; together, they determine the Poisson structure of the phase space of 3d gravity in the so-called combinatorial description
Avoiding negative populations in explicit Poisson tau-leaping.
Cao, Yang; Gillespie, Daniel T; Petzold, Linda R
2005-08-01
The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure.
Poisson Mixture Regression Models for Heart Disease Prediction.
Mufudza, Chipo; Erol, Hamza
2016-01-01
Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.
Poisson Mixture Regression Models for Heart Disease Prediction
Erol, Hamza
2016-01-01
Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611
Singularities of Poisson structures and Hamiltonian bifurcations
Meer, van der J.C.
2010-01-01
Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom
Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems
International Nuclear Information System (INIS)
Chang, Liu; Peng, Chang; Shi-Xing, Liu; Yong-Xin, Guo
2010-01-01
This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost-Poisson structure for generalised Chaplygin's systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noncanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion
Poisson Spot with Magnetic Levitation
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.
Newton/Poisson-Distribution Program
Bowerman, Paul N.; Scheuer, Ernest M.
1990-01-01
NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.
Dupé , François-Xavier; Fadili , Jalal M.; Starck , Jean-Luc
2012-01-01
International audience; In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On the other hand, as a prior, the images to restore are assumed to be positive and sparsely represented in a dictionary of waveforms such as wavelets or curvelets. Both analysis and synthesis-type spars...
A Martingale Characterization of Mixed Poisson Processes.
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
Poisson-Hopf limit of quantum algebras
International Nuclear Information System (INIS)
Ballesteros, A; Celeghini, E; Olmo, M A del
2009-01-01
The Poisson-Hopf analogue of an arbitrary quantum algebra U z (g) is constructed by introducing a one-parameter family of quantizations U z,ℎ (g) depending explicitly on ℎ and by taking the appropriate ℎ → 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su q P (3) case is introduced. The q-Serre relations are also extended to the Poisson limit. This approach opens the perspective for possible applications of higher rank q-deformed Hopf algebras in semiclassical contexts
Reduction of Nambu-Poisson Manifolds by Regular Distributions
Das, Apurba
2018-03-01
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.
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.
Bouleau, Nicolas
2015-01-01
A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calcul...
Gerla, Daan J; Mooij, Wolf M
2014-09-01
Positive and negative interactions within and between species may occur simultaneously, with the net effect depending on population densities. For instance, at low densities plants may ameliorate stress, while competition for resources dominates at higher densities. Here, we propose a simple two-species model in which con- and heterospecifics have a positive effect on per capita growth rate at low densities, while negative interactions dominate at high densities. The model thus includes both Allee effects (intraspecific positive effects) and mutualism (interspecific positive effects), as well as intra- and interspecific competition. Using graphical methods we derive conditions for alternative stable states and species coexistence. We show that mutual non-invasibility (i.e. the inability of each species to invade a population of the other) is more likely when species have a strong positive effect on the own species or a strong negative effect on the other species. Mutual non-invasibility implies alternative stable states, however, there may also be alternative stable states at which species coexist. In the case of species symmetry (i.e. when species are indistinguishable), such alternative coexistence states require that if the positive effect exerted at low densities at the own species is stronger than on the other species, the negative effect at higher densities is also stronger on the own species than on the other species, or, vice versa, if the interspecific positive effects at low densities are stronger than the intraspecific effects, the negative effects at higher densities are also stronger between species than within species. However, the reachability of alternative stable states is restricted by the frequency and density at which species are introduced during community assembly, so that alternative stable states do not always represent alternative endstates of community assembly. Copyright © 2014 Elsevier Inc. All rights reserved.
Unimodularity criteria for Poisson structures on foliated manifolds
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.
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Laurençot, P.
2007-01-01
Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007
Perturbation-induced emergence of Poisson-like behavior in non-Poisson systems
International Nuclear Information System (INIS)
Akin, Osman C; Grigolini, Paolo; Paradisi, Paolo
2009-01-01
The response of a system with ON–OFF intermittency to an external harmonic perturbation is discussed. ON–OFF intermittency is described by means of a sequence of random events, i.e., the transitions from the ON to the OFF state and vice versa. The unperturbed waiting times (WTs) between two events are assumed to satisfy a renewal condition, i.e., the WTs are statistically independent random variables. The response of a renewal model with non-Poisson ON–OFF intermittency, associated with non-exponential WT distribution, is analyzed by looking at the changes induced in the WT statistical distribution by the harmonic perturbation. The scaling properties are also studied by means of diffusion entropy analysis. It is found that, in the range of fast and relatively strong perturbation, the non-Poisson system displays a Poisson-like behavior in both WT distribution and scaling. In particular, the histogram of perturbed WTs becomes a sequence of equally spaced peaks, with intensity decaying exponentially in time. Further, the diffusion entropy detects an ordinary scaling (related to normal diffusion) instead of the expected unperturbed anomalous scaling related to the inverse power-law decay. Thus, an analysis based on the WT histogram and/or on scaling methods has to be considered with some care when dealing with perturbed intermittent systems
Principles of applying Poisson units in radiology
International Nuclear Information System (INIS)
Benyumovich, M.S.
2000-01-01
The probability that radioactive particles hit particular space patterns (e.g. cells in the squares of a count chamber net) and time intervals (e.g. radioactive particles hit a given area per time unit) follows the Poisson distribution. The mean is the only parameter from which all this distribution depends. A metrological base of counting the cells and radioactive particles is a property of the Poisson distribution assuming equality of a standard deviation to a root square of mean (property 1). The application of Poisson units in counting of blood formed elements and cultured cells was proposed by us (Russian Federation Patent No. 2126230). Poisson units relate to the means which make the property 1 valid. In a case of cells counting, the square of these units is equal to 1/10 of one of count chamber net where they count the cells. Thus one finds the means from the single cell count rate divided by 10. Finding the Poisson units when counting the radioactive particles should assume determination of a number of these particles sufficient to make equality 1 valid. To this end one should subdivide a time interval used in counting a single particle count rate into different number of equal portions (count numbers). Next one should pick out the count number ensuring the satisfaction of equality 1. Such a portion is taken as a Poisson unit in the radioactive particles count. If the flux of particles is controllable one should set up a count rate sufficient to make equality 1 valid. Operations with means obtained by with the use of Poisson units are performed on the base of approximation of the Poisson distribution by a normal one. (author)
Team behaviour analysis in sports using the poisson equation
Direkoglu, Cem; O'Connor, Noel E.
2012-01-01
We propose a novel physics-based model for analysing team play- ers’ positions and movements on a sports playing field. The goal is to detect for each frame the region with the highest population of a given team’s players and the region towards which the team is moving as they press for territorial advancement, termed the region of intent. Given the positions of team players from a plan view of the playing field at any given time, we solve a particular Poisson equation to generate a smooth di...
A Seemingly Unrelated Poisson Regression Model
King, Gary
1989-01-01
This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.
Poisson geometry from a Dirac perspective
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.
A novel method for the accurate evaluation of Poisson's ratio of soft polymer materials.
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.
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.
Bases chimiosensorielles du comportement alimentaire chez les poissons
Directory of Open Access Journals (Sweden)
SAGLIO Ph.
1981-07-01
Full Text Available Le comportement alimentaire, indispensable à la survie de l'individu et donc de l'espèce, occupe à ce titre une position de première importance dans la hiérarchie des comportements fondamentaux qui tous en dépendent très étroitement. Chez les poissons, cette prééminence se trouve illustrée par l'extrême diversité des supports sensoriels impliqués et des expressions comportementales qui leur sont liées. A la suite d'un certain nombre de mises en évidence neurophysiologiques et éthologiques de l'importance du sens chimique (olfaction, gustation dans le comportement alimentaire des poissons, de très importants secteurs d'études électrophysiologiques et d'analyses physico-chimiques visant à en déterminer la nature exacte (en termes de substances actives se sont développés ces vingt dernières années. De tous ces travaux dont les plus avancés sont présentés ici, il ressort que les acides aminés de série L plus ou moins associés à d'autres composés de poids moléculaires < 1000 constituent des composés chimiques jouant un rôle déterminant dans le comportement alimentaire de nombreuses espèces de poissons carnivores.
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.
Evaluating the double Poisson generalized linear model.
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.
International Nuclear Information System (INIS)
Sharifi, M. J.; Adibi, A.
2000-01-01
In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as poisson, Laplace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in several cases including the problem of finding electron concentration profile in the channel of a HEMT. In another section, we solve the Poisson equation by this method, choosing the problem of SBD as an example. Finally we solve the Laplace equation in two dimensions and as an example, we focus on the VED. In this paper, we have shown that, the method can get stable and precise results in solving all of these problems. Also the programs which have been written based on this method become considerably faster, more clear, and more abstract
A test of inflated zeros for Poisson regression models.
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.
Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.
Hougaard, P; Lee, M L; Whitmore, G A
1997-12-01
Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.
Relaxed Poisson cure rate models.
Rodrigues, Josemar; Cordeiro, Gauss M; Cancho, Vicente G; Balakrishnan, N
2016-03-01
The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Poisson denoising on the sphere
Schmitt, J.; Starck, J. L.; Fadili, J.; Grenier, I.; Casandjian, J. M.
2009-08-01
In the scope of the Fermi mission, Poisson noise removal should improve data quality and make source detection easier. This paper presents a method for Poisson data denoising on sphere, called Multi-Scale Variance Stabilizing Transform on Sphere (MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a transform which aims to stabilize a Poisson data set such that each stabilized sample has an (asymptotically) constant variance. In addition, for the VST used in the method, the transformed data are asymptotically Gaussian. Thus, MS-VSTS consists in decomposing the data into a sparse multi-scale dictionary (wavelets, curvelets, ridgelets...), and then applying a VST on the coefficients in order to get quasi-Gaussian stabilized coefficients. In this present article, the used multi-scale transform is the Isotropic Undecimated Wavelet Transform. Then, hypothesis tests are made to detect significant coefficients, and the denoised image is reconstructed with an iterative method based on Hybrid Steepest Descent (HST). The method is tested on simulated Fermi data.
Selective Contrast Adjustment by Poisson Equation
Directory of Open Access Journals (Sweden)
Ana-Belen Petro
2013-09-01
Full Text Available Poisson Image Editing is a new technique permitting to modify the gradient vector field of an image, and then to recover an image with a gradient approaching this modified gradient field. This amounts to solve a Poisson equation, an operation which can be efficiently performed by Fast Fourier Transform (FFT. This paper describes an algorithm applying this technique, with two different variants. The first variant enhances the contrast by increasing the gradient in the dark regions of the image. This method is well adapted to images with back light or strong shadows, and reveals details in the shadows. The second variant of the same Poisson technique enhances all small gradients in the image, thus also sometimes revealing details and texture.
PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON
Directory of Open Access Journals (Sweden)
PUTU SUSAN PRADAWATI
2013-09-01
Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.
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.
Analyzing hospitalization data: potential limitations of Poisson regression.
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.
The quantum poisson-Lie T-duality and mirror symmetry
International Nuclear Information System (INIS)
Parkhomenko, S.E.
1999-01-01
Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also
Investigation of Random Switching Driven by a Poisson Point Process
DEFF Research Database (Denmark)
Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef
2015-01-01
This paper investigates the switching mechanism of a two-dimensional switched system, when the switching events are generated by a Poisson point process. A model, in the shape of a stochastic process, for such a system is derived and the distribution of the trajectory's position is developed...... together with marginal density functions for the coordinate functions. Furthermore, the joint probability distribution is given explicitly....
Statistics of weighted Poisson events and its applications
International Nuclear Information System (INIS)
Bohm, G.; Zech, G.
2014-01-01
The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD
Noncommutative gauge theory for Poisson manifolds
Energy Technology Data Exchange (ETDEWEB)
Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de
2000-09-25
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.
Noncommutative gauge theory for Poisson manifolds
International Nuclear Information System (INIS)
Jurco, Branislav; Schupp, Peter; Wess, Julius
2000-01-01
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem
Poisson-event-based analysis of cell proliferation.
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.
Almost Poisson integration of rigid body systems
International Nuclear Information System (INIS)
Austin, M.A.; Krishnaprasad, P.S.; Li-Sheng Wang
1993-01-01
In this paper we discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by lie group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is an O(h 3 ) error estimate for the Lie-Poisson structure, where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored. 24 refs., 9 figs
Compound Poisson Approximations for Sums of Random Variables
Serfozo, Richard F.
1986-01-01
We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...
Square root approximation to the poisson channel
Tsiatmas, A.; Willems, F.M.J.; Baggen, C.P.M.J.
2013-01-01
Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding
Duality and modular class of a Nambu-Poisson structure
International Nuclear Information System (INIS)
Ibanez, R.; Leon, M. de; Lopez, B.; Marrero, J.C.; Padron, E.
2001-01-01
In this paper we introduce cohomology and homology theories for Nambu-Poisson manifolds. Also we study the relation between the existence of a duality for these theories and the vanishing of a particular Nambu-Poisson cohomology class, the modular class. The case of a regular Nambu-Poisson structure and some singular examples are discussed. (author)
Scaling the Poisson Distribution
Farnsworth, David L.
2014-01-01
We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.
Background stratified Poisson regression analysis of cohort data.
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.
International Nuclear Information System (INIS)
Unge, Rikard von
2002-01-01
We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the literature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants. (author)
Associative and Lie deformations of Poisson algebras
Remm, Elisabeth
2011-01-01
Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.
Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.
Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew
2014-12-26
Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.
A Tubular Biomaterial Construct Exhibiting a Negative Poisson's Ratio.
Directory of Open Access Journals (Sweden)
Jin Woo Lee
Full Text Available Developing functional small-diameter vascular grafts is an important objective in tissue engineering research. In this study, we address the problem of compliance mismatch by designing and developing a 3D tubular construct that has a negative Poisson's ratio νxy (NPR. NPR constructs have the unique ability to expand transversely when pulled axially, thereby resulting in a highly-compliant tubular construct. In this work, we used projection stereolithography to 3D-print a planar NPR sheet composed of photosensitive poly(ethylene glycol diacrylate biomaterial. We used a step-lithography exposure and a stitch process to scale up the projection printing process, and used the cut-missing rib unit design to develop a centimeter-scale NPR sheet, which was rolled up to form a tubular construct. The constructs had Poisson's ratios of -0.6 ≤ νxy ≤ -0.1. The NPR construct also supports higher cellular adhesion than does the construct that has positive νxy. Our NPR design offers a significant advance in the development of highly-compliant vascular grafts.
Background stratified Poisson regression analysis of cohort data
International Nuclear Information System (INIS)
Richardson, David B.; Langholz, Bryan
2012-01-01
Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models. (orig.)
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Characterization of a Compton suppression system and the applicability of Poisson statistics
International Nuclear Information System (INIS)
Nicholson, G.; Landsberger, S.; Welch, L.
2008-01-01
The Compton suppression system (CSS) has been thoroughly characterized at the University of Texas' Nuclear Engineering Teaching Laboratory (NETL). Effects of dead-time, sample displacement from primary detector, and primary energy detector position relative to the active shield detector have been measured and analyzed. Also, the applicability of Poisson counting statistics to Compton suppression spectroscopy has been evaluated. (author)
Network Traffic Monitoring Using Poisson Dynamic Linear Models
Energy Technology Data Exchange (ETDEWEB)
Merl, D. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2011-05-09
In this article, we discuss an approach for network forensics using a class of nonstationary Poisson processes with embedded dynamic linear models. As a modeling strategy, the Poisson DLM (PoDLM) provides a very flexible framework for specifying structured effects that may influence the evolution of the underlying Poisson rate parameter, including diurnal and weekly usage patterns. We develop a novel particle learning algorithm for online smoothing and prediction for the PoDLM, and demonstrate the suitability of the approach to real-time deployment settings via a new application to computer network traffic monitoring.
Test of Poisson Process for Earthquakes in and around Korea
International Nuclear Information System (INIS)
Noh, Myunghyun; Choi, Hoseon
2015-01-01
Since Cornell's work on the probabilistic seismic hazard analysis (hereafter, PSHA), majority of PSHA computer codes are assuming that the earthquake occurrence is Poissonian. To the author's knowledge, it is uncertain who first opened the issue of the Poisson process for the earthquake occurrence. The systematic PSHA in Korea, led by the nuclear industry, were carried out for more than 25 year with the assumption of the Poisson process. However, the assumption of the Poisson process has never been tested. Therefore, the test is of significance. We tested whether the Korean earthquakes follow the Poisson process or not. The Chi-square test with the significance level of 5% was applied. The test turned out that the Poisson process could not be rejected for the earthquakes of magnitude 2.9 or larger. However, it was still observed in the graphical comparison that some portion of the observed distribution significantly deviated from the Poisson distribution. We think this is due to the small earthquake data. The earthquakes of magnitude 2.9 or larger occurred only 376 times during 34 years. Therefore, the judgment on the Poisson process derived in the present study is not conclusive
Sepúlveda, Nuno
2013-02-26
Background: The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model.Results: Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates.Conclusions: In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data. 2013 Seplveda et al.; licensee BioMed Central Ltd.
Sepúlveda, Nuno; Campino, Susana G; Assefa, Samuel A; Sutherland, Colin J; Pain, Arnab; Clark, Taane G
2013-02-26
The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model. Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates. In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data.
Sepú lveda, Nuno; Campino, Susana G; Assefa, Samuel A; Sutherland, Colin J; Pain, Arnab; Clark, Taane G
2013-01-01
Background: The advent of next generation sequencing technology has accelerated efforts to map and catalogue copy number variation (CNV) in genomes of important micro-organisms for public health. A typical analysis of the sequence data involves mapping reads onto a reference genome, calculating the respective coverage, and detecting regions with too-low or too-high coverage (deletions and amplifications, respectively). Current CNV detection methods rely on statistical assumptions (e.g., a Poisson model) that may not hold in general, or require fine-tuning the underlying algorithms to detect known hits. We propose a new CNV detection methodology based on two Poisson hierarchical models, the Poisson-Gamma and Poisson-Lognormal, with the advantage of being sufficiently flexible to describe different data patterns, whilst robust against deviations from the often assumed Poisson model.Results: Using sequence coverage data of 7 Plasmodium falciparum malaria genomes (3D7 reference strain, HB3, DD2, 7G8, GB4, OX005, and OX006), we showed that empirical coverage distributions are intrinsically asymmetric and overdispersed in relation to the Poisson model. We also demonstrated a low baseline false positive rate for the proposed methodology using 3D7 resequencing data and simulation. When applied to the non-reference isolate data, our approach detected known CNV hits, including an amplification of the PfMDR1 locus in DD2 and a large deletion in the CLAG3.2 gene in GB4, and putative novel CNV regions. When compared to the recently available FREEC and cn.MOPS approaches, our findings were more concordant with putative hits from the highest quality array data for the 7G8 and GB4 isolates.Conclusions: In summary, the proposed methodology brings an increase in flexibility, robustness, accuracy and statistical rigour to CNV detection using sequence coverage data. 2013 Seplveda et al.; licensee BioMed Central Ltd.
Poisson sigma model with branes and hyperelliptic Riemann surfaces
International Nuclear Information System (INIS)
Ferrario, Andrea
2008-01-01
We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions
Method of Poisson's ratio imaging within a material part
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.
The applicability of the Poisson distribution in radiochemical measurements
International Nuclear Information System (INIS)
Luthardt, M.; Proesch, U.
1980-01-01
The fact that, on principle, the Poisson distribution describes the statistics of nuclear decay is generally accepted. The applicability of this distribution to nuclear radiation measurements has recently been questioned. Applying the chi-squared test for goodness of fit on the analogy of the moving average, at least 3 cases may be distinguished, which lead to an incorrect rejection of the Poisson distribution for measurements. Examples are given. Distributions, which make allowance for special parameters, should only be used after careful examination of the data with regard to other interfering effects. The Poisson distribution will further on be applicable to many simple measuring operations. Some basic equations for the analysis of poisson-distributed data are given. (author)
Multivariate fractional Poisson processes and compound sums
Beghin, Luisa; Macci, Claudio
2015-01-01
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.
Contravariant gravity on Poisson manifolds and Einstein gravity
International Nuclear Information System (INIS)
Kaneko, Yukio; Watamura, Satoshi; Muraki, Hisayoshi
2017-01-01
A relation between gravity on Poisson manifolds proposed in Asakawa et al (2015 Fortschr. Phys . 63 683–704) and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein–Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner. (paper)
Modified Regression Correlation Coefficient for Poisson Regression Model
Kaengthong, Nattacha; Domthong, Uthumporn
2017-09-01
This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).
A comparison of Poisson-one-inflated power series distributions for ...
African Journals Online (AJOL)
A class of Poisson-one-inflated power series distributions (the binomial, the Poisson, the negative binomial, the geometric, the log-series and the misrecorded Poisson) are proposed for modeling rural out-migration at the household level. The probability mass functions of the mixture distributions are derived and fitted to the ...
Monitoring Poisson observations using combined applications of Shewhart and EWMA charts
Abujiya, Mu'azu Ramat
2017-11-01
The Shewhart and exponentially weighted moving average (EWMA) charts for nonconformities are the most widely used procedures of choice for monitoring Poisson observations in modern industries. Individually, the Shewhart EWMA charts are only sensitive to large and small shifts, respectively. To enhance the detection abilities of the two schemes in monitoring all kinds of shifts in Poisson count data, this study examines the performance of combined applications of the Shewhart, and EWMA Poisson control charts. Furthermore, the study proposes modifications based on well-structured statistical data collection technique, ranked set sampling (RSS), to detect shifts in the mean of a Poisson process more quickly. The relative performance of the proposed Shewhart-EWMA Poisson location charts is evaluated in terms of the average run length (ARL), standard deviation of the run length (SDRL), median run length (MRL), average ratio ARL (ARARL), average extra quadratic loss (AEQL) and performance comparison index (PCI). Consequently, all the new Poisson control charts based on RSS method are generally more superior than most of the existing schemes for monitoring Poisson processes. The use of these combined Shewhart-EWMA Poisson charts is illustrated with an example to demonstrate the practical implementation of the design procedure.
Poisson-Jacobi reduction of homogeneous tensors
International Nuclear Information System (INIS)
Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P
2004-01-01
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N
Limitations of Poisson statistics in describing radioactive decay.
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.
Bases chimiosensorielles du comportement alimentaire chez les poissons
Saglio, P.
1981-01-01
Le comportement alimentaire, indispensable à la survie de l'individu et donc de l'espèce, occupe à ce titre une position de première importance dans la hiérarchie des comportements fondamentaux qui tous en dépendent très étroitement. Chez les poissons, cette prééminence se trouve illustrée par l'extrême diversité des supports sensoriels impliqués et des expressions comportementales qui leur sont liées. A la suite d'un certain nombre de mises en évidence neurophysiologiques et éthologiques de ...
Poisson solvers for self-consistent multi-particle simulations
International Nuclear Information System (INIS)
Qiang, J; Paret, S
2014-01-01
Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density distribution in the multi-particle simulation. In this paper, we review a number of numerical methods that can be used to solve the Poisson equation efficiently. The computational complexity of those numerical methods will be O(N log(N)) or O(N) instead of O(N2), where N is the total number of grid points used to solve the Poisson equation
Poisson image reconstruction with Hessian Schatten-norm regularization.
Lefkimmiatis, Stamatios; Unser, Michael
2013-11-01
Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupted by Poisson noise. In this paper, we propose an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators. In particular, the employed regularizers involve the Hessian as the regularization operator and Schatten matrix norms as the potential functions. For the solution of the problem, we propose two optimization algorithms that are specifically tailored to the Poisson nature of the noise. These algorithms are based on an augmented-Lagrangian formulation of the problem and correspond to two variants of the alternating direction method of multipliers. Further, we derive a link that relates the proximal map of an l(p) norm with the proximal map of a Schatten matrix norm of order p. This link plays a key role in the development of one of the proposed algorithms. Finally, we provide experimental results on natural and biological images for the task of Poisson image deblurring and demonstrate the practical relevance and effectiveness of the proposed framework.
Seasonally adjusted birth frequencies follow the Poisson distribution.
Barra, Mathias; Lindstrøm, Jonas C; Adams, Samantha S; Augestad, Liv A
2015-12-15
Variations in birth frequencies have an impact on activity planning in maternity wards. Previous studies of this phenomenon have commonly included elective births. A Danish study of spontaneous births found that birth frequencies were well modelled by a Poisson process. Somewhat unexpectedly, there were also weekly variations in the frequency of spontaneous births. Another study claimed that birth frequencies follow the Benford distribution. Our objective was to test these results. We analysed 50,017 spontaneous births at Akershus University Hospital in the period 1999-2014. To investigate the Poisson distribution of these births, we plotted their variance over a sliding average. We specified various Poisson regression models, with the number of births on a given day as the outcome variable. The explanatory variables included various combinations of years, months, days of the week and the digit sum of the date. The relationship between the variance and the average fits well with an underlying Poisson process. A Benford distribution was disproved by a goodness-of-fit test (p Poisson process when monthly and day-of-the-week variation is included. The frequency is highest in summer towards June and July, Friday and Tuesday stand out as particularly busy days, and the activity level is at its lowest during weekends.
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.
Modeling laser velocimeter signals as triply stochastic Poisson processes
Mayo, W. T., Jr.
1976-01-01
Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2013-01-01
. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied......A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field...... and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain....
Some applications of the fractional Poisson probability distribution
International Nuclear Information System (INIS)
Laskin, Nick
2009-01-01
Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.
Directory of Open Access Journals (Sweden)
Rodrigues-Motta Mariana
2008-07-01
Full Text Available Abstract Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep.
International Nuclear Information System (INIS)
Whitty, J.P.M.; Henderson, B.; Francis, J.
2011-01-01
Highlights: → Incontrovertible evidence is presented that thermal stresses in cylindrical components which include nuclear reactors and containment vessels are shown to be highly dependent on the Poisson's ratio of the materials. → The key novelty is concerned with the identification of a new potential thermal applications for negative Poisson's ratio (auxetic) materials; i.e. those that get fatter when they are stretched. → Negative Poisson's ratio (auxetic) materials exhibit lower thermal stress build-up than conventional positive Poisson's ratio materials, this conjecture being proven using thermal surface plots. - Abstract: Analytical and numerical modelling have been employed to show that the choice of Poisson's ratio is one of the principal design criteria in order to reduce thermal stress build-up in isotropic materials. The modelling procedures are all twofold; consisting of a solution to a steady-state heat conduction problem followed by a linear static solution. The models developed take the form of simplistic thick-wall cylinders such model systems are applicable at macro-structural and micro-structural levels as the underlining formulations are based on the classical theory of elasticity. Generally, the results show that the Poisson's ratio of the material has a greater effect on the magnitude of the principal stresses than the aspect ratio of the cylinders investigated. Constraining the outside of these models significantly increases the thermal stresses induced. The most significant and original finding presented is that the for both freely expanding and constrained thick-wall cylinders the optimum Poisson's ratio is minus unity.
Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.
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.
Universal Poisson Statistics of mRNAs with Complex Decay Pathways.
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.
Intertime jump statistics of state-dependent Poisson processes.
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.
Cluster X-varieties, amalgamation, and Poisson-Lie groups
DEFF Research Database (Denmark)
Fock, V. V.; Goncharov, A. B.
2006-01-01
In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as cluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varie...
Poisson traces, D-modules, and symplectic resolutions.
Etingof, Pavel; Schedler, Travis
2018-01-01
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.
Poisson traces, D-modules, and symplectic resolutions
Etingof, Pavel; Schedler, Travis
2018-03-01
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.
DEFF Research Database (Denmark)
Gardsjord, Erlend Strand; Romm, Kristin Lie; Røssberg, Jan Ivar
2017-01-01
BACKGROUND: Quality of life is an important outcome measure for patients with psychosis. We investigated whether going into stable symptomatic remission is associated with a more positive development of subjective quality of life (S-QoL) and if different patient characteristics are associated wit...
Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.
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.
Evolutionary inference via the Poisson Indel Process.
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.
Particle-wave discrimination in Poisson spot experiments
International Nuclear Information System (INIS)
Reisinger, T; Bracco, G; Holst, B
2011-01-01
Matter-wave interferometry has been used extensively over the last few years to demonstrate the quantum-mechanical wave nature of increasingly larger and more massive particles. We have recently suggested the use of the historical Poisson spot setup to test the diffraction properties of larger objects. In this paper, we present the results of a classical particle van der Waals (vdW) force model for a Poisson spot experimental setup and compare these to Fresnel diffraction calculations with a vdW phase term. We include the effect of disc-edge roughness in both models. Calculations are performed with D 2 and with C 70 using realistic parameters. We find that the sensitivity of the on-axis interference/focus spot to disc-edge roughness is very different in the two cases. We conclude that by measuring the intensity on the optical axis as a function of disc-edge roughness, it can be determined whether the objects behave as de Broglie waves or classical particles. The scaling of the Poisson spot experiment to larger molecular masses is, however, not as favorable as in the case of near-field light-grating-based interferometers. Instead, we discuss the possibility of studying the Casimir-Polder potential using the Poisson spot setup.
Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
Carlet, Guido; Casati, Matteo; Shadrin, Sergey
2017-04-01
We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D > 1. Hence, in contrast with the D = 1 case, the deformation theory in the multivariable case is non-trivial.
Quantum algebras and Poisson geometry in mathematical physics
Karasev, M V
2005-01-01
This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.
Poisson's ratio and Young's modulus of lipid bilayers in different phases
Directory of Open Access Journals (Sweden)
Tayebeh eJadidi
2014-04-01
Full Text Available A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness.In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distancesin one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in orderto predict the temperature dependence of its Poisson's ratio and Young's modulus.
Estimating Bird / Aircraft Collision Probabilities and Risk Utilizing Spatial Poisson Processes
2012-06-10
ESTIMATING BIRD/AIRCRAFT COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE...AND RISK UTILIZING SPATIAL POISSON PROCESSES GRADUATE RESEARCH PAPER Presented to the Faculty Department of Operational Sciences...COLLISION PROBABILITIES AND RISK UTILIZING SPATIAL POISSON PROCESSES Brady J. Vaira, BS, MS Major, USAF Approved
Poisson structures for reduced non-holonomic systems
International Nuclear Information System (INIS)
Ramos, Arturo
2004-01-01
Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank 2 and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of the Poisson structures and extend their domain of definition. We apply the theory to the rolling disc, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder
High order Poisson Solver for unbounded flows
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2015-01-01
This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing...
Estimation of Poisson noise in spatial domain
Švihlík, Jan; Fliegel, Karel; Vítek, Stanislav; Kukal, Jaromír.; Krbcová, Zuzana
2017-09-01
This paper deals with modeling of astronomical images in the spatial domain. We consider astronomical light images contaminated by the dark current which is modeled by Poisson random process. Dark frame image maps the thermally generated charge of the CCD sensor. In this paper, we solve the problem of an addition of two Poisson random variables. At first, the noise analysis of images obtained from the astronomical camera is performed. It allows estimating parameters of the Poisson probability mass functions in every pixel of the acquired dark frame. Then the resulting distributions of the light image can be found. If the distributions of the light image pixels are identified, then the denoising algorithm can be applied. The performance of the Bayesian approach in the spatial domain is compared with the direct approach based on the method of moments and the dark frame subtraction.
Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.
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.
Holdener, Fred R.; Boyd, Robert D.
2000-01-01
The present invention is a bi-stable optical actuator device that is depowered in both stable positions. A bearing is used to transfer motion and smoothly transition from one state to another. The optical actuator device may be maintained in a stable position either by gravity or a restraining device.
On covariant Poisson brackets in classical field theory
International Nuclear Information System (INIS)
Forger, Michael; Salles, Mário O.
2015-01-01
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra
On covariant Poisson brackets in classical field theory
Energy Technology Data Exchange (ETDEWEB)
Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)
2015-10-15
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.
Hoen, Petra W.; Denollet, Johan; de Jonge, Peter; Whooley, Mary A.
Objective: Positive affect can improve survival, but the mechanisms responsible for this association are unknown. We sought to evaluate the association between positive affect and mortality in patients with stable coronary heart disease and to determine biological and behavioral factors that might
Hoen, P.W.; Denollet, J.; de Jonge, P.; Whooley, M.A.
2013-01-01
Objective: Positive affect can improve survival, but the mechanisms responsible for this association are unknown. We sought to evaluate the association between positive affect and mortality in patients with stable coronary heart disease and to determine biological and behavioral factors that might
Exact solution for the Poisson field in a semi-infinite strip.
Cohen, Yossi; Rothman, Daniel H
2017-04-01
The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.
A Method of Poisson's Ration Imaging Within a Material Part
Roth, Don J. (Inventor)
1994-01-01
The present invention is directed to a method of displaying the Poisson's ratio image of a material part. In the present invention, longitudinal data is produced using a longitudinal wave transducer and shear wave data is produced using a shear wave transducer. The respective data is then used to calculate the Poisson's ratio for the entire material part. The Poisson's ratio approximations are then used to display the data.
Fractional poisson--a simple dose-response model for human norovirus.
Messner, Michael J; Berger, Philip; Nappier, Sharon P
2014-10-01
This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.
Characterizing the performance of the Conway-Maxwell Poisson generalized linear model.
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.
Action-angle variables and a KAM theorem for b-Poisson manifolds
Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey
2015-01-01
In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.
Non-Poisson Processes: Regression to Equilibrium Versus Equilibrium Correlation Functions
2004-07-07
ARTICLE IN PRESSPhysica A 347 (2005) 268–2880378-4371/$ - doi:10.1016/j Correspo E-mail adwww.elsevier.com/locate/physaNon- Poisson processes : regression...05.40.a; 89.75.k; 02.50.Ey Keywords: Stochastic processes; Non- Poisson processes ; Liouville and Liouville-like equations; Correlation function...which is not legitimate with renewal non- Poisson processes , is a correct property if the deviation from the exponential relaxation is obtained by time
Multi-parameter full waveform inversion using Poisson
Oh, Juwon
2016-07-21
In multi-parameter full waveform inversion (FWI), the success of recovering each parameter is dependent on characteristics of the partial derivative wavefields (or virtual sources), which differ according to parameterisation. Elastic FWIs based on the two conventional parameterisations (one uses Lame constants and density; the other employs P- and S-wave velocities and density) have low resolution of gradients for P-wave velocities (or ). Limitations occur because the virtual sources for P-wave velocity or (one of the Lame constants) are related only to P-P diffracted waves, and generate isotropic explosions, which reduce the spatial resolution of the FWI for these parameters. To increase the spatial resolution, we propose a new parameterisation using P-wave velocity, Poisson\\'s ratio, and density for frequency-domain multi-parameter FWI for isotropic elastic media. By introducing Poisson\\'s ratio instead of S-wave velocity, the virtual source for the P-wave velocity generates P-S and S-S diffracted waves as well as P-P diffracted waves in the partial derivative wavefields for the P-wave velocity. Numerical examples of the cross-triangle-square (CTS) model indicate that the new parameterisation provides highly resolved descent directions for the P-wave velocity. Numerical examples of noise-free and noisy data synthesised for the elastic Marmousi-II model support the fact that the new parameterisation is more robust for noise than the two conventional parameterisations.
Construction of Nodal Bubbling Solutions for the Weighted Sinh-Poisson Equation
Directory of Open Access Journals (Sweden)
Yibin Zhang
2013-01-01
Full Text Available We consider the weighted sinh-Poisson equation in , on , where is a small parameter, , and is a unit ball in . By a constructive way, we prove that for any positive integer , there exists a nodal bubbling solution which concentrates at the origin and the other -points , , such that as , , where and is an odd integer with , or is an even integer. The same techniques lead also to a more general result on general domains.
Boundary Lax pairs from non-ultra-local Poisson algebras
International Nuclear Information System (INIS)
Avan, Jean; Doikou, Anastasia
2009-01-01
We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.
Gavish, Nir
2018-04-01
We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.
Stability of periodic steady-state solutions to a non-isentropic Euler-Poisson system
Liu, Cunming; Peng, Yue-Jun
2017-06-01
We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler-Poisson system without temperature damping term. The system arises in the theory of semiconductors for which the doping profile is a given smooth function. In this stability problem, there are no special restrictions on the size of the doping profile, but only on the size of the perturbation. We prove that small perturbations of periodic steady-states are exponentially stable for large time. For this purpose, we introduce new variables and choose a non-diagonal symmetrizer of the full Euler equations to recover dissipation estimates. This also allows to make the proof of the stability result very simple and concise.
Poisson's Ratio and Auxetic Properties of Natural Rocks
Ji, Shaocheng; Li, Le; Motra, Hem Bahadur; Wuttke, Frank; Sun, Shengsi; Michibayashi, Katsuyoshi; Salisbury, Matthew H.
2018-02-01
Here we provide an appraisal of the Poisson's ratios (υ) for natural elements, common oxides, silicate minerals, and rocks with the purpose of searching for naturally auxetic materials. The Poisson's ratios of equivalently isotropic polycrystalline aggregates were calculated from dynamically measured elastic properties. Alpha-cristobalite is currently the only known naturally occurring mineral that has exclusively negative υ values at 20-1,500°C. Quartz and potentially berlinite (AlPO4) display auxetic behavior in the vicinity of their α-β structure transition. None of the crystalline igneous and metamorphic rocks (e.g., amphibolite, gabbro, granite, peridotite, and schist) display auxetic behavior at pressures of >5 MPa and room temperature. Our experimental measurements showed that quartz-rich sedimentary rocks (i.e., sandstone and siltstone) are most likely to be the only rocks with negative Poisson's ratios at low confining pressures (≤200 MPa) because their main constituent mineral, α-quartz, already has extremely low Poisson's ratio (υ = 0.08) and they contain microcracks, micropores, and secondary minerals. This finding may provide a new explanation for formation of dome-and-basin structures in quartz-rich sedimentary rocks in response to a horizontal compressional stress in the upper crust.
Estimation of a Non-homogeneous Poisson Model: An Empirical ...
African Journals Online (AJOL)
This article aims at applying the Nonhomogeneous Poisson process to trends of economic development. For this purpose, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean ...
NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes
Directory of Open Access Journals (Sweden)
Ana C. Cebrián
2015-03-01
Full Text Available NHPoisson is an R package for the modeling of nonhomogeneous Poisson processes in one dimension. It includes functions for data preparation, maximum likelihood estimation, covariate selection and inference based on asymptotic distributions and simulation methods. It also provides specific methods for the estimation of Poisson processes resulting from a peak over threshold approach. In addition, the package supports a wide range of model validation tools and functions for generating nonhomogenous Poisson process trajectories. This paper is a description of the package and aims to help those interested in modeling data using nonhomogeneous Poisson processes.
Multivariate max-stable spatial processes
Genton, Marc G.; Padoan, S. A.; Sang, H.
2015-01-01
Max-stable processes allow the spatial dependence of extremes to be modelled and quantified, so they are widely adopted in applications. For a better understanding of extremes, it may be useful to study several variables simultaneously. To this end, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. We define a Poisson process construction and introduce multivariate versions of the Smith Gaussian extreme-value, the Schlather extremal-Gaussian and extremal-t, and the Brown–Resnick models. We develop inference for the models based on composite likelihoods. We present results of Monte Carlo simulations and an application to daily maximum wind speed and wind gust.
Multivariate max-stable spatial processes
Genton, Marc G.
2015-02-11
Max-stable processes allow the spatial dependence of extremes to be modelled and quantified, so they are widely adopted in applications. For a better understanding of extremes, it may be useful to study several variables simultaneously. To this end, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. We define a Poisson process construction and introduce multivariate versions of the Smith Gaussian extreme-value, the Schlather extremal-Gaussian and extremal-t, and the Brown–Resnick models. We develop inference for the models based on composite likelihoods. We present results of Monte Carlo simulations and an application to daily maximum wind speed and wind gust.
Adaptive maximal poisson-disk sampling on surfaces
Yan, Dongming
2012-01-01
In this paper, we study the generation of maximal Poisson-disk sets with varying radii on surfaces. Based on the concepts of power diagram and regular triangulation, we present a geometric analysis of gaps in such disk sets on surfaces, which is the key ingredient of the adaptive maximal Poisson-disk sampling framework. Moreover, we adapt the presented sampling framework for remeshing applications. Several novel and efficient operators are developed for improving the sampling/meshing quality over the state-of-theart. © 2012 ACM.
Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes
Belitser, E.N.; Serra, P.; van Zanten, H.
2015-01-01
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. To motivate our results we start by analyzing count data coming from a call center which we model as a Poisson process. This analysis is carried out using a certain
Fractional Poisson process (II)
International Nuclear Information System (INIS)
Wang Xiaotian; Wen Zhixiong; Zhang Shiying
2006-01-01
In this paper, we propose a stochastic process W H (t)(H-bar (12,1)) which we call fractional Poisson process. The process W H (t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution
Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.
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.
Bayesian regression of piecewise homogeneous Poisson processes
Directory of Open Access Journals (Sweden)
Diego Sevilla
2015-12-01
Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015
Gyrokinetic energy conservation and Poisson-bracket formulation
International Nuclear Information System (INIS)
Brizard, A.
1989-01-01
An integral expression for the gyrokinetic total energy of a magnetized plasma, with general magnetic field configuration perturbed by fully electromagnetic fields, was recently derived through the use of a gyrocenter Lie transformation. It is shown that the gyrokinetic energy is conserved by the gyrokinetic Hamiltonian flow to all orders in perturbed fields. An explicit demonstration that a gyrokinetic Hamiltonian containing quadratic nonlinearities preserves the gyrokinetic energy up to third order is given. The Poisson-bracket formulation greatly facilitates this demonstration with the help of the Jacobi identity and other properties of the Poisson brackets
Hamiltonian field description of the one-dimensional Poisson-Vlasov equations
International Nuclear Information System (INIS)
Morrison, P.J.
1981-07-01
The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained
Soft network materials with isotropic negative Poisson's ratios over large strains.
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.
Lambert, A.; Simatos, F.
2015-01-01
Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive Lévy process with nonzero Lévy measure. In this paper, we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two
Lambert, A.; Simatos, F.
2012-01-01
Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\\'evy process with non-zero L\\'evy measure. In this paper we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two
The Lie-Poisson structure of integrable classical non-linear sigma models
International Nuclear Information System (INIS)
Bordemann, M.; Forger, M.; Schaeper, U.; Laartz, J.
1993-01-01
The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into the r-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matrices r and s are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrix c. It is proposed that all these Poisson brackets taken together are representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed. (orig.)
Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data.
Sim, Shin Zhu; Gupta, Ramesh C; Ong, Seng Huat
2018-01-09
In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.
Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers
Neshveyev, Sergey; Tuset, Lars
2012-05-01
Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0 topology on the spectrum of C( G q / K q ). Next we show that the family of C*-algebras C( G q / K q ), 0 < q ≤ 1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra {{C}[G/K]} . Finally, extending a result of Nagy, we show that C( G q / K q ) is canonically KK-equivalent to C( G/ K).
Poisson-Lie T-duality open strings and D-branes
Klimcik, C.
1996-01-01
Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold G are dual to D-brane - anti-D-brane pairs propagating on the dual group manifold \\ti G. The D-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group \\ti G by the dressing action of the group G. T-duality maps the momentum of the open string into the mutual distance of the D-branes in the pair. The whole picture is then extended to the full modular space M(D) of the Poisson-Lie equivalent \\si-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of D-branes living on targets belonging to M(D). In this more general case the D-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.
Exterior differentials in superspace and Poisson brackets
International Nuclear Information System (INIS)
Soroka, Dmitrij V.; Soroka, Vyacheslav A.
2003-01-01
It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity to another bracket is introduced. It is also indicated that the resulting bracket leads to generalization of the Schouten-Nijenhuis bracket for the cases of superspace and brackets of diverse Grassmann parities. It is shown that in the case of the Grassmann-odd exterior differential the resulting bracket is the bracket given on exterior forms. The above-mentioned transition with the use of the odd exterior differential applied to the linear even/odd Poisson brackets, that correspond to semi-simple Lie groups, results, respectively, in also linear odd/even brackets which are naturally connected with the Lie superalgebra. The latter contains the BRST and anti-BRST charges and can be used for calculation of the BRST operator cogomology. (author)
Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!
International Nuclear Information System (INIS)
Nutku, Yavuz
2003-01-01
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems
DEFF Research Database (Denmark)
Harrod, Steven; Kelton, W. David
2006-01-01
Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. The authors review the risks of ignoring nonstationarity in Poisson processes and demonstrate three algorithms for generation of Poisson processes...
Poisson Regression Analysis of Illness and Injury Surveillance Data
Energy Technology Data Exchange (ETDEWEB)
Frome E.L., Watkins J.P., Ellis E.D.
2012-12-12
The Department of Energy (DOE) uses illness and injury surveillance to monitor morbidity and assess the overall health of the work force. Data collected from each participating site include health events and a roster file with demographic information. The source data files are maintained in a relational data base, and are used to obtain stratified tables of health event counts and person time at risk that serve as the starting point for Poisson regression analysis. The explanatory variables that define these tables are age, gender, occupational group, and time. Typical response variables of interest are the number of absences due to illness or injury, i.e., the response variable is a count. Poisson regression methods are used to describe the effect of the explanatory variables on the health event rates using a log-linear main effects model. Results of fitting the main effects model are summarized in a tabular and graphical form and interpretation of model parameters is provided. An analysis of deviance table is used to evaluate the importance of each of the explanatory variables on the event rate of interest and to determine if interaction terms should be considered in the analysis. Although Poisson regression methods are widely used in the analysis of count data, there are situations in which over-dispersion occurs. This could be due to lack-of-fit of the regression model, extra-Poisson variation, or both. A score test statistic and regression diagnostics are used to identify over-dispersion. A quasi-likelihood method of moments procedure is used to evaluate and adjust for extra-Poisson variation when necessary. Two examples are presented using respiratory disease absence rates at two DOE sites to illustrate the methods and interpretation of the results. In the first example the Poisson main effects model is adequate. In the second example the score test indicates considerable over-dispersion and a more detailed analysis attributes the over-dispersion to extra-Poisson
[Application of detecting and taking overdispersion into account in Poisson regression model].
Bouche, G; Lepage, B; Migeot, V; Ingrand, P
2009-08-01
Researchers often use the Poisson regression model to analyze count data. Overdispersion can occur when a Poisson regression model is used, resulting in an underestimation of variance of the regression model parameters. Our objective was to take overdispersion into account and assess its impact with an illustration based on the data of a study investigating the relationship between use of the Internet to seek health information and number of primary care consultations. Three methods, overdispersed Poisson, a robust estimator, and negative binomial regression, were performed to take overdispersion into account in explaining variation in the number (Y) of primary care consultations. We tested overdispersion in the Poisson regression model using the ratio of the sum of Pearson residuals over the number of degrees of freedom (chi(2)/df). We then fitted the three models and compared parameter estimation to the estimations given by Poisson regression model. Variance of the number of primary care consultations (Var[Y]=21.03) was greater than the mean (E[Y]=5.93) and the chi(2)/df ratio was 3.26, which confirmed overdispersion. Standard errors of the parameters varied greatly between the Poisson regression model and the three other regression models. Interpretation of estimates from two variables (using the Internet to seek health information and single parent family) would have changed according to the model retained, with significant levels of 0.06 and 0.002 (Poisson), 0.29 and 0.09 (overdispersed Poisson), 0.29 and 0.13 (use of a robust estimator) and 0.45 and 0.13 (negative binomial) respectively. Different methods exist to solve the problem of underestimating variance in the Poisson regression model when overdispersion is present. The negative binomial regression model seems to be particularly accurate because of its theorical distribution ; in addition this regression is easy to perform with ordinary statistical software packages.
Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.
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.
Quadratic Hamiltonians on non-symmetric Poisson structures
International Nuclear Information System (INIS)
Arribas, M.; Blesa, F.; Elipe, A.
2007-01-01
Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases
Formality theory from Poisson structures to deformation quantization
Esposito, Chiara
2015-01-01
This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.
GEPOIS: a two dimensional nonuniform mesh Poisson solver
International Nuclear Information System (INIS)
Quintenz, J.P.; Freeman, J.R.
1979-06-01
A computer code is described which solves Poisson's equation for the electric potential over a two dimensional cylindrical (r,z) nonuniform mesh which can contain internal electrodes. Poisson's equation is solved over a given region subject to a specified charge distribution with either Neumann or Dirichlet perimeter boundary conditions and with Dirichlet boundary conditions on internal surfaces. The static electric field is also computed over the region with special care given to normal electric field components at boundary surfaces
The cylindrical K-function and Poisson line cluster point processes
DEFF Research Database (Denmark)
Møller, Jesper; Safavimanesh, Farzaneh; Rasmussen, Jakob G.
Poisson line cluster point processes, is also introduced. Parameter estimation based on moment methods or Bayesian inference for this model is discussed when the underlying Poisson line process and the cluster memberships are treated as hidden processes. To illustrate the methodologies, we analyze two...
Estimating the period of a cyclic non-homogeneous Poisson process
Belitser, E.; Andrade Serra, De P.J.; Zanten, van J.H.
2013-01-01
Motivated by applications of Poisson processes for modelling periodic time-varying phenomena, we study a semi-parametric estimator of the period of cyclic intensity function of a non-homogeneous Poisson process. There are no parametric assumptions on the intensity function which is treated as an
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Efficiency optimization of a fast Poisson solver in beam dynamics simulation
Zheng, Dawei; Pöplau, Gisela; van Rienen, Ursula
2016-01-01
Calculating the solution of Poisson's equation relating to space charge force is still the major time consumption in beam dynamics simulations and calls for further improvement. In this paper, we summarize a classical fast Poisson solver in beam dynamics simulations: the integrated Green's function method. We introduce three optimization steps of the classical Poisson solver routine: using the reduced integrated Green's function instead of the integrated Green's function; using the discrete cosine transform instead of discrete Fourier transform for the Green's function; using a novel fast convolution routine instead of an explicitly zero-padded convolution. The new Poisson solver routine preserves the advantages of fast computation and high accuracy. This provides a fast routine for high performance calculation of the space charge effect in accelerators.
Control Multivariante Estadístico de Variables Discretas tipo Poisson
GARCIA BUSTOS, SANDRA LORENA
2016-01-01
En algunos casos, cuando el número de defectos de un proceso de producción tiene que ser controlada, la distribución de Poisson se emplea para modelar la frecuencia de estos defectos y para desarrollar un gráfico de control. En este trabajo se analiza el control de características de calidad p> 1 de Poisson . Cuando este control se necesita, hay dos enfoques principales: 1 - Un gráfico para cada variable de Poisson, el esquema múltiple.. 2 -. Sólo una gráfico para todas las variables, el sist...
Pêche thonière et dispositifs de concentration de poissons
Le Gall, Jean-yves; Cayre, Patrice; Taquet, Marc
2000-01-01
Le colloque international « Pêche thonière et dispositifs de concentration de poissons» organisé en octobre 1999, en Martinique, permet de dresser un bilan, sous forme de synthèses régionales, de l'exploitation des grands poissons pélagiques à l'aide de DCP dans les trois océans et en Méditerranée. La technologie, les méthodes de pêche, l'impact sur les ressources, le comportement agrégatif des poissons et les aspects socio-économiques de l'utilisation des DCP sont les principaux thèmes dével...
The coupling of Poisson sigma models to topological backgrounds
Energy Technology Data Exchange (ETDEWEB)
Rosa, Dario [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)
2016-12-13
We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.
An intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces.
Ying, Xiang; Xin, Shi-Qing; Sun, Qian; He, Ying
2013-09-01
Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in IR(n). To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.
Complete synchronization of the global coupled dynamical network induced by Poisson noises.
Guo, Qing; Wan, Fangyi
2017-01-01
The different Poisson noise-induced complete synchronization of the global coupled dynamical network is investigated. Based on the stability theory of stochastic differential equations driven by Poisson process, we can prove that Poisson noises can induce synchronization and sufficient conditions are established to achieve complete synchronization with probability 1. Furthermore, numerical examples are provided to show the agreement between theoretical and numerical analysis.
Transforming spatial point processes into Poisson processes using random superposition
DEFF Research Database (Denmark)
Møller, Jesper; Berthelsen, Kasper Klitgaaard
with a complementary spatial point process Y to obtain a Poisson process X∪Y with intensity function β. Underlying this is a bivariate spatial birth-death process (Xt,Yt) which converges towards the distribution of (X,Y). We study the joint distribution of X and Y, and their marginal and conditional distributions....... In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson...... process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking...
Application of zero-inflated poisson mixed models in prognostic factors of hepatitis C.
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.
Four-dimensional gravity as an almost-Poisson system
Ita, Eyo Eyo
2015-04-01
In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.
Poisson-Like Spiking in Circuits with Probabilistic Synapses
Moreno-Bote, Rubén
2014-01-01
Neuronal activity in cortex is variable both spontaneously and during stimulation, and it has the remarkable property that it is Poisson-like over broad ranges of firing rates covering from virtually zero to hundreds of spikes per second. The mechanisms underlying cortical-like spiking variability over such a broad continuum of rates are currently unknown. We show that neuronal networks endowed with probabilistic synaptic transmission, a well-documented source of variability in cortex, robustly generate Poisson-like variability over several orders of magnitude in their firing rate without fine-tuning of the network parameters. Other sources of variability, such as random synaptic delays or spike generation jittering, do not lead to Poisson-like variability at high rates because they cannot be sufficiently amplified by recurrent neuronal networks. We also show that probabilistic synapses predict Fano factor constancy of synaptic conductances. Our results suggest that synaptic noise is a robust and sufficient mechanism for the type of variability found in cortex. PMID:25032705
2D Poisson sigma models with gauged vectorial supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Bonezzi, Roberto [Dipartimento di Fisica ed Astronomia, Università di Bologna and INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-12
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
Computation of solar perturbations with Poisson series
Broucke, R.
1974-01-01
Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.
Blind beam-hardening correction from Poisson measurements
Gu, Renliang; Dogandžić, Aleksandar
2016-02-01
We develop a sparse image reconstruction method for Poisson-distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements and express the mass- attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate-descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov's proximal-gradient (NPG) step for estimating the density map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) step for estimating the incident-spectrum parameters. To accelerate convergence of the density- map NPG steps, we apply function restart and a step-size selection scheme that accounts for varying local Lipschitz constants of the Poisson NLL. Real X-ray CT reconstruction examples demonstrate the performance of the proposed scheme.
The Poisson equation on Klein surfaces
Directory of Open Access Journals (Sweden)
Monica Rosiu
2016-04-01
Full Text Available We obtain a formula for the solution of the Poisson equation with Dirichlet boundary condition on a region of a Klein surface. This formula reveals the symmetric character of the solution.
Comment on: 'A Poisson resampling method for simulating reduced counts in nuclear medicine images'.
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.
Linear odd Poisson bracket on Grassmann variables
International Nuclear Information System (INIS)
Soroka, V.A.
1999-01-01
A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson bracket having the only Grassmann-odd nilpotent differential Δ-operator of the second order. It is shown that these Δ-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Fiber-wise linear Poisson structures related to W∗-algebras
Odzijewicz, Anatol; Jakimowicz, Grzegorz; Sliżewska, Aneta
2018-01-01
In the framework of Banach differential geometry we investigate the fiber-wise linear Poisson structures as well as the Lie groupoid and Lie algebroid structures which are defined in the canonical way by the structure of a W∗-algebra (von Neumann algebra) M. The main role in this theory is played by the complex Banach-Lie groupoid G(M) ⇉ L(M) of partially invertible elements of M over the lattice L(M) of orthogonal projections of M. The Atiyah sequence and the predual Atiyah sequence corresponding to this groupoid are investigated from the point of view of Banach Poisson geometry. In particular we show that the predual Atiyah sequence fits in a short exact sequence of complex Banach sub-Poisson V B-groupoids with G(M) ⇉ L(M) as the side groupoid.
Wick calculus on spaces of generalized functions of compound poisson white noise
Lytvynov, Eugene W.; Rebenko, Alexei L.; Shchepan'ur, Gennadi V.
1997-04-01
We derive white noise calculus for a compound Poisson process. Namely, we consider, on the Schwartz space of tempered distributions, S', a measure of compound Poisson white noise, μcp, and construct a whole scale of standard nuclear triples ( Scp) - x ⊃ L2cp) ≡ L2( S', dμcp) ⊃( Scpx, x≥ 0, which are obtained as images under some isomorphism of the corresponding triples centred at a Fock space. It turns out that the most interesting case is x = 1, when our triple coincides with the triple that is constructed by using a system of Appell polynomials in the framework of non-Gaussian biorthogonal analysis. Our special attention is paid to the Wick calculus of the Poisson field, or the quantum compound Poisson white noise process in other terms, which is the family of operators acting from ( Scp) 1 into ( Scp) 1 as multiplication by the compound Poisson white noise ω( t).
An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces.
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.
Trophic position of coexisting krill species: a stable isotope approach
DEFF Research Database (Denmark)
Agersted, Mette Dalgaard; Bode, Antonio; Nielsen, Torkel Gissel
2014-01-01
Four krill species with overlapping functional biology coexist in Greenland waters. Here, we used stable isotopes to investigate and discuss their trophic role and mode of coexistence. Bulk carbon (δ13C) and nitrogen (δ15N) stable isotope analyses of Thysanoessa longicaudata, T. inermis, T. raschii...
A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.
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.
Poisson's theorem and integrals of KdV equation
International Nuclear Information System (INIS)
Tasso, H.
1978-01-01
Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)
Multivariate Max-Stable Spatial Processes
Genton, Marc G.
2014-01-06
Analysis of spatial extremes is currently based on univariate processes. Max-stable processes allow the spatial dependence of extremes to be modelled and explicitly quantified, they are therefore widely adopted in applications. For a better understanding of extreme events of real processes, such as environmental phenomena, it may be useful to study several spatial variables simultaneously. To this end, we extend some theoretical results and applications of max-stable processes to the multivariate setting to analyze extreme events of several variables observed across space. In particular, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. Then, we define a Poisson process construction in the multivariate setting and introduce multivariate versions of the Smith Gaussian extremevalue, the Schlather extremal-Gaussian and extremal-t, and the BrownResnick models. Inferential aspects of those models based on composite likelihoods are developed. We present results of various Monte Carlo simulations and of an application to a dataset of summer daily temperature maxima and minima in Oklahoma, U.S.A., highlighting the utility of working with multivariate models in contrast to the univariate case. Based on joint work with Simone Padoan and Huiyan Sang.
Multivariate Max-Stable Spatial Processes
Genton, Marc G.
2014-01-01
Analysis of spatial extremes is currently based on univariate processes. Max-stable processes allow the spatial dependence of extremes to be modelled and explicitly quantified, they are therefore widely adopted in applications. For a better understanding of extreme events of real processes, such as environmental phenomena, it may be useful to study several spatial variables simultaneously. To this end, we extend some theoretical results and applications of max-stable processes to the multivariate setting to analyze extreme events of several variables observed across space. In particular, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. Then, we define a Poisson process construction in the multivariate setting and introduce multivariate versions of the Smith Gaussian extremevalue, the Schlather extremal-Gaussian and extremal-t, and the BrownResnick models. Inferential aspects of those models based on composite likelihoods are developed. We present results of various Monte Carlo simulations and of an application to a dataset of summer daily temperature maxima and minima in Oklahoma, U.S.A., highlighting the utility of working with multivariate models in contrast to the univariate case. Based on joint work with Simone Padoan and Huiyan Sang.
Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis.
Armstrong, Ben G; Gasparrini, Antonio; Tobias, Aurelio
2014-11-24
The time stratified case cross-over approach is a popular alternative to conventional time series regression for analysing associations between time series of environmental exposures (air pollution, weather) and counts of health outcomes. These are almost always analyzed using conditional logistic regression on data expanded to case-control (case crossover) format, but this has some limitations. In particular adjusting for overdispersion and auto-correlation in the counts is not possible. It has been established that a Poisson model for counts with stratum indicators gives identical estimates to those from conditional logistic regression and does not have these limitations, but it is little used, probably because of the overheads in estimating many stratum parameters. The conditional Poisson model avoids estimating stratum parameters by conditioning on the total event count in each stratum, thus simplifying the computing and increasing the number of strata for which fitting is feasible compared with the standard unconditional Poisson model. Unlike the conditional logistic model, the conditional Poisson model does not require expanding the data, and can adjust for overdispersion and auto-correlation. It is available in Stata, R, and other packages. By applying to some real data and using simulations, we demonstrate that conditional Poisson models were simpler to code and shorter to run than are conditional logistic analyses and can be fitted to larger data sets than possible with standard Poisson models. Allowing for overdispersion or autocorrelation was possible with the conditional Poisson model but when not required this model gave identical estimates to those from conditional logistic regression. Conditional Poisson regression models provide an alternative to case crossover analysis of stratified time series data with some advantages. The conditional Poisson model can also be used in other contexts in which primary control for confounding is by fine
Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria
International Nuclear Information System (INIS)
Ling, K.; Abraham-Shrauner, B.
1981-01-01
The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...... of convergence consistent with the moments conserved by the applied smoothing function. In the hybrid particle-mesh method of Hockney and Eastwood (HE) the particles are interpolated onto a regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values...... and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight...
Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions
Directory of Open Access Journals (Sweden)
Liu Jinn-Liang
2017-10-01
Full Text Available We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.
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).
Double generalized linear compound poisson models to insurance claims data
DEFF Research Database (Denmark)
Andersen, Daniel Arnfeldt; Bonat, Wagner Hugo
2017-01-01
This paper describes the specification, estimation and comparison of double generalized linear compound Poisson models based on the likelihood paradigm. The models are motivated by insurance applications, where the distribution of the response variable is composed by a degenerate distribution...... implementation and illustrate the application of double generalized linear compound Poisson models using a data set about car insurances....
A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture
Van Nguyen, Thu
2011-01-01
In the present paper we prove the following conjecture in Kingman, J.F.C., Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerning a famous Raikov's theorem of decomposition of Poisson random variables: "If a radial sum of two independent random variables X and Y is radial Poisson, then each of them must be radial Poisson."
Poisson-Boltzmann-Nernst-Planck model
International Nuclear Information System (INIS)
Zheng Qiong; Wei Guowei
2011-01-01
The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.
Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger
2016-11-01
In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.
A Note On the Estimation of the Poisson Parameter
Directory of Open Access Journals (Sweden)
S. S. Chitgopekar
1985-01-01
distribution when there are errors in observing the zeros and ones and obtains both the maximum likelihood and moments estimates of the Poisson mean and the error probabilities. It is interesting to note that either method fails to give unique estimates of these parameters unless the error probabilities are functionally related. However, it is equally interesting to observe that the estimate of the Poisson mean does not depend on the functional relationship between the error probabilities.
Efficient triangulation of Poisson-disk sampled point sets
Guo, Jianwei
2014-05-06
In this paper, we present a simple yet efficient algorithm for triangulating a 2D input domain containing a Poisson-disk sampled point set. The proposed algorithm combines a regular grid and a discrete clustering approach to speedup the triangulation. Moreover, our triangulation algorithm is flexible and performs well on more general point sets such as adaptive, non-maximal Poisson-disk sets. The experimental results demonstrate that our algorithm is robust for a wide range of input domains and achieves significant performance improvement compared to the current state-of-the-art approaches. © 2014 Springer-Verlag Berlin Heidelberg.
Poisson equation for weak gravitational lensing
International Nuclear Information System (INIS)
Kling, Thomas P.; Campbell, Bryan
2008-01-01
Using the Newman and Penrose [E. T. Newman and R. Penrose, J. Math. Phys. (N.Y.) 3, 566 (1962).] spin-coefficient formalism, we examine the full Bianchi identities of general relativity in the context of gravitational lensing, where the matter and space-time curvature are projected into a lens plane perpendicular to the line of sight. From one component of the Bianchi identity, we provide a rigorous, new derivation of a Poisson equation for the projected matter density where the source term involves second derivatives of the observed weak gravitational lensing shear. We also show that the other components of the Bianchi identity reveal no new results. Numerical integration of the Poisson equation in test cases shows an accurate mass map can be constructed from the combination of a ground-based, wide-field image and a Hubble Space Telescope image of the same system
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.
Outcome of Blunt Abdominal Traumas with Stable Hemodynamic and Positive FAST Findings.
Behboodi, Firooz; Mohtasham-Amiri, Zahra; Masjedi, Navid; Shojaie, Reza; Sadri, Peyman
2016-01-01
Focused assessment with sonography for trauma (FAST) is a highly effective first screening tool for initial classification of abdominal trauma patients. The present study was designed to evaluate the outcome of patients with blunt abdominal trauma and positive FAST findings. The present prospective cross-sectional study was done on patients over 7 years old with normal abdominal examination, positive FAST findings, and available abdominopelvic computed tomography (CT) scan findings. The frequency of need for laparotomy as well as its probable risk factors were calculated. 180 patients were enrolled (mean age: 28.0 ± 11.5 years; 76.7% male). FAST findings were confirmed by abdominopelvic CT scan in only 124 (68.9%) cases. Finally, 12 (6.6%) patients needed laparotomy. Mean age of those in need of laparotomy was significantly higher than others (36.75 ± 11.37 versus 27.34 ± 11.37, p = 0.006). Higher grading of spleen (p = 0.001) and hepatic (p = 0.038) ruptures increased the probability of need for laparotomy. 68.9% of the positive FAST findings in patients with blunt abdominal trauma and stable hemodynamics was confirmed by abdominopelvic CT scan and only 6.6% needed laparotomy. Simultaneous presence of free fluid and air in the abdominal area, old age, and higher grading o solid organ injuries were factors that had a significant correlation with need for laparotomy.
Area-to-Area Poisson Kriging and Spatial Bayesian Analysis
Asmarian, Naeimehossadat; Jafari-Koshki, Tohid; Soleimani, Ali; Taghi Ayatollahi, Seyyed Mohammad
2016-10-01
Background: In many countries gastric cancer has the highest incidence among the gastrointestinal cancers and is the second most common cancer in Iran. The aim of this study was to identify and map high risk gastric cancer regions at the county-level in Iran. Methods: In this study we analyzed gastric cancer data for Iran in the years 2003-2010. Areato- area Poisson kriging and Besag, York and Mollie (BYM) spatial models were applied to smoothing the standardized incidence ratios of gastric cancer for the 373 counties surveyed in this study. The two methods were compared in term of accuracy and precision in identifying high risk regions. Result: The highest smoothed standardized incidence rate (SIR) according to area-to-area Poisson kriging was in Meshkinshahr county in Ardabil province in north-western Iran (2.4,SD=0.05), while the highest smoothed standardized incidence rate (SIR) according to the BYM model was in Ardabil, the capital of that province (2.9,SD=0.09). Conclusion: Both methods of mapping, ATA Poisson kriging and BYM, showed the gastric cancer incidence rate to be highest in north and north-west Iran. However, area-to-area Poisson kriging was more precise than the BYM model and required less smoothing. According to the results obtained, preventive measures and treatment programs should be focused on particular counties of Iran. Creative Commons Attribution License
1983-05-20
Poisson processes is introduced: the amplitude has a law which is spherically invariant and the filter is real, linear and causal. It is shown how such a model can be identified from experimental data. (Author)
Generalization of Poisson distribution for the case of changing probability of consequential events
International Nuclear Information System (INIS)
Kushnirenko, E.
1995-01-01
The generalization of the Poisson distribution for the case of changing probabilities of the consequential events is done. It is shown that the classical Poisson distribution is the special case of this generalized distribution when the probabilities of the consequential events are constant. The using of the generalized Poisson distribution gives the possibility in some cases to obtain analytical result instead of making Monte-Carlo calculation
Guo, Jianqiang; Wang, Wansheng
2014-01-01
This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable.
Dilaton gravity, Poisson sigma models and loop quantum gravity
International Nuclear Information System (INIS)
Bojowald, Martin; Reyes, Juan D
2009-01-01
Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum-corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D spacetime dimensions.
Efficient maximal Poisson-disk sampling and remeshing on surfaces
Guo, Jianwei; Yan, Dongming; Jia, Xiaohong; Zhang, Xiaopeng
2015-01-01
Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.
Efficient maximal Poisson-disk sampling and remeshing on surfaces
Guo, Jianwei
2015-02-01
Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.
Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics
International Nuclear Information System (INIS)
Czachor, M.
1996-01-01
Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)
Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation
International Nuclear Information System (INIS)
Bardsley, Johnathan M; Goldes, John
2009-01-01
In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is ill-posed, regularization is needed. Regularized Poisson likelihood estimation has been studied extensively by the authors, though a problem of high importance remains: the choice of the regularization parameter. We will present three statistically motivated methods for choosing the regularization parameter, and numerical examples will be presented to illustrate their effectiveness
A generalized Poisson solver for first-principles device simulations
Energy Technology Data Exchange (ETDEWEB)
Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch [Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland); Brück, Sascha; Luisier, Mathieu [Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Poisson point processes imaging, tracking, and sensing
Streit, Roy L
2010-01-01
This overview of non-homogeneous and multidimensional Poisson point processes and their applications features mathematical tools and applications from emission- and transmission-computed tomography to multiple target tracking and distributed sensor detection.
Amalia, Junita; Purhadi, Otok, Bambang Widjanarko
2017-11-01
Poisson distribution is a discrete distribution with count data as the random variables and it has one parameter defines both mean and variance. Poisson regression assumes mean and variance should be same (equidispersion). Nonetheless, some case of the count data unsatisfied this assumption because variance exceeds mean (over-dispersion). The ignorance of over-dispersion causes underestimates in standard error. Furthermore, it causes incorrect decision in the statistical test. Previously, paired count data has a correlation and it has bivariate Poisson distribution. If there is over-dispersion, modeling paired count data is not sufficient with simple bivariate Poisson regression. Bivariate Poisson Inverse Gaussian Regression (BPIGR) model is mix Poisson regression for modeling paired count data within over-dispersion. BPIGR model produces a global model for all locations. In another hand, each location has different geographic conditions, social, cultural and economic so that Geographically Weighted Regression (GWR) is needed. The weighting function of each location in GWR generates a different local model. Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) model is used to solve over-dispersion and to generate local models. Parameter estimation of GWBPIGR model obtained by Maximum Likelihood Estimation (MLE) method. Meanwhile, hypothesis testing of GWBPIGR model acquired by Maximum Likelihood Ratio Test (MLRT) method.
Wang, Yiyi; Kockelman, Kara M
2013-11-01
This work examines the relationship between 3-year pedestrian crash counts across Census tracts in Austin, Texas, and various land use, network, and demographic attributes, such as land use balance, residents' access to commercial land uses, sidewalk density, lane-mile densities (by roadway class), and population and employment densities (by type). The model specification allows for region-specific heterogeneity, correlation across response types, and spatial autocorrelation via a Poisson-based multivariate conditional auto-regressive (CAR) framework and is estimated using Bayesian Markov chain Monte Carlo methods. Least-squares regression estimates of walk-miles traveled per zone serve as the exposure measure. Here, the Poisson-lognormal multivariate CAR model outperforms an aspatial Poisson-lognormal multivariate model and a spatial model (without cross-severity correlation), both in terms of fit and inference. Positive spatial autocorrelation emerges across neighborhoods, as expected (due to latent heterogeneity or missing variables that trend in space, resulting in spatial clustering of crash counts). In comparison, the positive aspatial, bivariate cross correlation of severe (fatal or incapacitating) and non-severe crash rates reflects latent covariates that have impacts across severity levels but are more local in nature (such as lighting conditions and local sight obstructions), along with spatially lagged cross correlation. Results also suggest greater mixing of residences and commercial land uses is associated with higher pedestrian crash risk across different severity levels, ceteris paribus, presumably since such access produces more potential conflicts between pedestrian and vehicle movements. Interestingly, network densities show variable effects, and sidewalk provision is associated with lower severe-crash rates. Copyright © 2013 Elsevier Ltd. All rights reserved.
The Hitchin model, Poisson-quasi-Nijenhuis, geometry and symmetry reduction
International Nuclear Information System (INIS)
Zucchini, Roberto
2007-01-01
We revisit our earlier work on the AKSZ-like formulation of topological sigma model on generalized complex manifolds, or Hitchin model, [20]. We show that the target space geometry geometry implied by the BV master equations is Poisson-quasi-Nijenhuis geometry recently introduced and studied by Stienon and Xu (in the untwisted case) in [44]. Poisson-quasi-Nijenhuis geometry is more general than generalized complex geometry and comprises it as a particular case. Next, we show how gauging and reduction can be implemented in the Hitchin model. We find that the geometry resulting form the BV master equation is closely related to but more general than that recently described by Lin and Tolman in [40, 41], suggesting a natural framework for the study of reduction of Poisson-quasi-Nijenhuis manifolds
Lord, Dominique; Geedipally, Srinivas Reddy; Guikema, Seth D
2010-08-01
The objective of this article is to evaluate the performance of the COM-Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM-Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over- or underdispersion. Over the last year, the COM-Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson-gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM-Poisson models were estimated using crash data collected at 162 railway-highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM-Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.
On the Fedosov deformation quantization beyond the regular Poisson manifolds
International Nuclear Information System (INIS)
Dolgushev, V.A.; Isaev, A.P.; Lyakhovich, S.L.; Sharapov, A.A.
2002-01-01
A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane
Versteeg, Inge; Mens, Petra F.
2009-01-01
The objective of this study is to develop and evaluate a simple, cheap, and stable positive control for the quality control and quality assurance (QA) of rapid diagnostic tests (RDT) for the diagnosis of malaria. Plasmodium falciparum in vitro culture of known parasite concentrations was dried on a
Measuring Poisson Ratios at Low Temperatures
Boozon, R. S.; Shepic, J. A.
1987-01-01
Simple extensometer ring measures bulges of specimens in compression. New method of measuring Poisson's ratio used on brittle ceramic materials at cryogenic temperatures. Extensometer ring encircles cylindrical specimen. Four strain gauges connected in fully active Wheatstone bridge self-temperature-compensating. Used at temperatures as low as liquid helium.
Efficient information transfer by Poisson neurons
Czech Academy of Sciences Publication Activity Database
Košťál, Lubomír; Shinomoto, S.
2016-01-01
Roč. 13, č. 3 (2016), s. 509-520 ISSN 1547-1063 R&D Projects: GA ČR(CZ) GA15-08066S Institutional support: RVO:67985823 Keywords : information capacity * Poisson neuron * metabolic cost * decoding error Subject RIV: BD - Theory of Information Impact factor: 1.035, year: 2016
Quantization of Poisson Manifolds from the Integrability of the Modular Function
Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.
2014-10-01
We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.
Poisson structure of dynamical systems with three degrees of freedom
Gümral, Hasan; Nutku, Yavuz
1993-12-01
It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of three-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack-McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka-Volterra, May-Leonard, and Maxwell-Bloch systems admit globally integrable bi-Hamiltonian structure.
Comment on: 'A Poisson resampling method for simulating reduced counts in nuclear medicine images'
DEFF Research Database (Denmark)
de Nijs, Robin
2015-01-01
In order to be able to calculate half-count images from already acquired data, White and Lawson published their method based on Poisson resampling. They verified their method experimentally by measurements with a Co-57 flood source. In this comment their results are reproduced and confirmed...... by a direct numerical simulation in Matlab. Not only Poisson resampling, but also two direct redrawing methods were investigated. Redrawing methods were based on a Poisson and a Gaussian distribution. Mean, standard deviation, skewness and excess kurtosis half-count/full-count ratios were determined for all...... methods, and compared to the theoretical values for a Poisson distribution. Statistical parameters showed the same behavior as in the original note and showed the superiority of the Poisson resampling method. Rounding off before saving of the half count image had a severe impact on counting statistics...
Outcome of Blunt Abdominal Traumas with Stable Hemodynamic and Positive FAST Findings
Directory of Open Access Journals (Sweden)
Firooz Behboodi
2016-04-01
Full Text Available Introduction: Focused assessment with sonography for trauma (FAST is a highly effective first screening tool for initial classification of abdominal trauma patients. The present study was designed to evaluate the outcome of patients with blunt abdominal trauma and positive FAST findings. Methods: The present prospective cross-sectional study was done on patients over 7 years old with normal abdominal examination, positive FAST findings, and available abdominopelvic computed tomography (CT scan findings. The frequency of need for laparotomy as well as its probable risk factors were calculated. Results: 180 patients were enrolled (mean age: 28.0 ± 11.5 years; 76.7% male. FAST findings were confirmed by abdominopelvic CT scan in only 124 (68.9% cases. Finally, 12 (6.6% patients needed laparotomy. Mean age of those in need of laparotomy was significantly higher than others (36.75 ± 11.37 versus 27.34 ± 11.37, p = 0.006. Higher grading of spleen (p = 0.001 and hepatic (p = 0.038 ruptures increased the probability of need for laparotomy. Conclusion: 68.9% of the positive FAST findings in patients with blunt abdominal trauma and stable hemodynamics was confirmed by abdominopelvic CT scan and only 6.6% needed laparotomy. Simultaneous presence of free fluid and air in the abdominal area, old age, and higher grading o solid organ injuries were factors that had a significant correlation with need for laparotomy.
Markov modulated Poisson process models incorporating covariates for rainfall intensity.
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 generalized right truncated bivariate Poisson regression model with applications to health data.
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.
Yelland, Lisa N; Salter, Amy B; Ryan, Philip
2011-10-15
Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.
Null canonical formalism 1, Maxwell field. [Poisson brackets, boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Wodkiewicz, K [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej
1975-01-01
The purpose of this paper is to formulate the canonical formalism on null hypersurfaces for the Maxwell electrodynamics. The set of the Poisson brackets relations for null variables of the Maxwell field is obtained. The asymptotic properties of the theory are investigated. The Poisson bracket relations for the news-functions of the Maxwell field are computed. The Hamiltonian form of the asymptotic Maxwell equations in terms of these news-functions is obtained.
Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems
Directory of Open Access Journals (Sweden)
Hailiang Li
2003-09-01
Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.
State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.
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
Independent production and Poisson distribution
International Nuclear Information System (INIS)
Golokhvastov, A.I.
1994-01-01
The well-known statement of factorization of inclusive cross-sections in case of independent production of particles (or clusters, jets etc.) and the conclusion of Poisson distribution over their multiplicity arising from it do not follow from the probability theory in any way. Using accurately the theorem of the product of independent probabilities, quite different equations are obtained and no consequences relative to multiplicity distributions are obtained. 11 refs
A generalized gyrokinetic Poisson solver
International Nuclear Information System (INIS)
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms
Penyelesaian Persamaan Poisson 2D dengan Menggunakan Metode Gauss-Seidel dan Conjugate Gradien
Mahmudah, Dewi Erla; Naf'an, Muhammad Zidny
2017-01-01
In this paper we focus on solution of 2D Poisson equation numerically. 2D Poisson equation is a partial differential equation of second order elliptical type. This equation is a particular form or non-homogeneous form of the Laplace equation. The solution of 2D Poisson equation is performed numerically using Gauss Seidel method and Conjugate Gradient method. The result is the value using Gauss Seidel method and Conjugate Gradient method is same. But, consider the iteration process, the conver...
Ifremer
1992-01-01
Vous trouverez dans ce document les 24 poissons les plus courants de Guyane (sur un nombre d'espèces approchant les 200) avec leurs principales caractéristiques, leurs noms scientifiques, français, anglais et espagnol et leurs photographies. Ils sont classés, de l'acoupa au vivaneau ti yeux, par ordre alphabétique. Si vous ne trouvez pas de chiffres sur la production de telle ou telle espèce, c'est parce qu'ils n'existent pas, mais aussi et surtout parce qu'ils ne signifieraient rien, l...
TCP (truncated compound Poisson) process for multiplicity distributions in high energy collisions
International Nuclear Information System (INIS)
Srivastave, P.P.
1990-01-01
On using the Poisson distribution truncated at zero for intermediate cluster decay in a compound Poisson process, the authors obtain TCP distribution which describes quite well the multiplicity distributions in high energy collisions. A detailed comparison is made between TCP and NB for UA5 data. The reduced moments up to the fifth agree very well with the observed ones. The TCP curves are narrower than NB at high multiplicity tail, look narrower at very high energy and develop shoulders and oscillations which become increasingly pronounced as the energy grows. At lower energies the distributions, of the data for fixed intervals of rapidity for UA5 data and for the data (at low energy) for e + e - annihilation and pion-proton, proton-proton and muon-proton scattering. A discussion of compound Poisson distribution, expression of reduced moments and Poisson transforms are also given. The TCP curves and curves of the reduced moments for different values of the parameters are also presented
Poisson regression for modeling count and frequency outcomes in trauma research.
Gagnon, David R; Doron-LaMarca, Susan; Bell, Margret; O'Farrell, Timothy J; Taft, Casey T
2008-10-01
The authors describe how the Poisson regression method for analyzing count or frequency outcome variables can be applied in trauma studies. The outcome of interest in trauma research may represent a count of the number of incidents of behavior occurring in a given time interval, such as acts of physical aggression or substance abuse. Traditional linear regression approaches assume a normally distributed outcome variable with equal variances over the range of predictor variables, and may not be optimal for modeling count outcomes. An application of Poisson regression is presented using data from a study of intimate partner aggression among male patients in an alcohol treatment program and their female partners. Results of Poisson regression and linear regression models are compared.
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-Boltzmann-Nernst-Planck model.
Zheng, Qiong; Wei, Guo-Wei
2011-05-21
The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external
Zhong, Jie; Zhao, Honggang; Yang, Haibin; Yin, Jianfei; Wen, Jihong
2018-06-01
Rubbery coatings embedded with air cavities are commonly used on underwater structures to reduce reflection of incoming sound waves. In this paper, the relationships between Poisson's and modulus loss factors of rubbery materials are theoretically derived, the different effects of the tiny Poisson's loss factor on characterizing the loss factors of shear and longitudinal moduli are revealed. Given complex Young's modulus and dynamic Poisson's ratio, it is found that the shear loss factor has almost invisible variation with the Poisson's loss factor and is very close to the loss factor of Young's modulus, while the longitudinal loss factor almost linearly decreases with the increase of Poisson's loss factor. Then, a finite element (FE) model is used to investigate the effect of the tiny Poisson's loss factor, which is generally neglected in some FE models, on the underwater sound absorption of rubbery coatings. Results show that the tiny Poisson's loss factor has a significant effect on the sound absorption of homogeneous coatings within the concerned frequency range, while it has both frequency- and structure-dependent influence on the sound absorption of inhomogeneous coatings with embedded air cavities. Given the material parameters and cavity dimensions, more obvious effect can be observed for the rubbery coating with a larger lattice constant and/or a thicker cover layer.
Adaptive maximal poisson-disk sampling on surfaces
Yan, Dongming; Wonka, Peter
2012-01-01
In this paper, we study the generation of maximal Poisson-disk sets with varying radii on surfaces. Based on the concepts of power diagram and regular triangulation, we present a geometric analysis of gaps in such disk sets on surfaces, which
Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.
Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie
2017-07-01
For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 (22α̂)0.50 for 0.020.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 Poisson model dose-response curve. © 2016 Society for Risk Analysis.
Poisson regression approach for modeling fatal injury rates amongst Malaysian workers
International Nuclear Information System (INIS)
Kamarulzaman Ibrahim; Heng Khai Theng
2005-01-01
Many safety studies are based on the analysis carried out on injury surveillance data. The injury surveillance data gathered for the analysis include information on number of employees at risk of injury in each of several strata where the strata are defined in terms of a series of important predictor variables. Further insight into the relationship between fatal injury rates and predictor variables may be obtained by the poisson regression approach. Poisson regression is widely used in analyzing count data. In this study, poisson regression is used to model the relationship between fatal injury rates and predictor variables which are year (1995-2002), gender, recording system and industry type. Data for the analysis were obtained from PERKESO and Jabatan Perangkaan Malaysia. It is found that the assumption that the data follow poisson distribution has been violated. After correction for the problem of over dispersion, the predictor variables that are found to be significant in the model are gender, system of recording, industry type, two interaction effects (interaction between recording system and industry type and between year and industry type). Introduction Regression analysis is one of the most popular
Easy Demonstration of the Poisson Spot
Gluck, Paul
2010-01-01
Many physics teachers have a set of slides of single, double and multiple slits to show their students the phenomena of interference and diffraction. Thomas Young's historic experiments with double slits were indeed a milestone in proving the wave nature of light. But another experiment, namely the Poisson spot, was also important historically and…
Modifications in the AUTOMESH and other POISSON Group Codes
International Nuclear Information System (INIS)
Gupta, R.C.
1986-01-01
Improvements in the POISSON Group Codes are discussed. These improvements allow one to compute magnetic field to an accuracy of a few parts in 100,000 in quite complicated geometries with a reduced requirement on computational time and computer memory. This can be accomplished mainly by making the mesh dense at some places and sparse at other places. AUTOMESH has been modified so that one can use variable mesh size conveniently and efficiently at a number of places. We will present an example to illustrate these techniques. Several other improvements in the codes AUTOMESH, LATTICE and POISSON will also be discussed
Modeling Repeated Count Data : Some Extensions of the Rasch Poisson Counts Model
van Duijn, M.A.J.; Jansen, Margo
1995-01-01
We consider data that can be summarized as an N X K table of counts-for example, test data obtained by administering K tests to N subjects. The cell entries y(ij) are assumed to be conditionally independent Poisson-distributed random variables, given the NK Poisson intensity parameters mu(ij). The
Zero-inflated Poisson model based likelihood ratio test for drug safety signal detection.
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.
Poisson structure of the equations of ideal multispecies fluid electrodynamics
International Nuclear Information System (INIS)
Spencer, R.G.
1984-01-01
The equations of the two- (or multi-) fluid model of plasma physics are recast in Hamiltonian form, following general methods of symplectic geometry. The dynamical variables are the fields of physical interest, but are noncanonical, so that the Poisson bracket in the theory is not the standard one. However, it is a skew-symmetric bilinear form which, from the method of derivation, automatically satisfies the Jacobi identity; therefore, this noncanonical structure has all the essential properties of a canonical Poisson bracket
Modelling infant mortality rate in Central Java, Indonesia use generalized poisson regression method
Prahutama, Alan; Sudarno
2018-05-01
The infant mortality rate is the number of deaths under one year of age occurring among the live births in a given geographical area during a given year, per 1,000 live births occurring among the population of the given geographical area during the same year. This problem needs to be addressed because it is an important element of a country’s economic development. High infant mortality rate will disrupt the stability of a country as it relates to the sustainability of the population in the country. One of regression model that can be used to analyze the relationship between dependent variable Y in the form of discrete data and independent variable X is Poisson regression model. Recently The regression modeling used for data with dependent variable is discrete, among others, poisson regression, negative binomial regression and generalized poisson regression. In this research, generalized poisson regression modeling gives better AIC value than poisson regression. The most significant variable is the Number of health facilities (X1), while the variable that gives the most influence to infant mortality rate is the average breastfeeding (X9).
Affine Poisson Groups and WZW Model
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Ctirad Klimcík
2008-01-01
Full Text Available We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the q → ∞ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.
Poisson brackets for fluids and plasmas
International Nuclear Information System (INIS)
Morrison, P.J.
1982-01-01
Noncanonical yet Hamiltonian descriptions are presented of many of the non-dissipative field equations that govern fluids and plasmas. The dynamical variables are the usually encountered physical variables. These descriptions have the advantage that gauge conditions are absent, but at the expense of introducing peculiar Poisson brackets. Clebsch-like potential descriptions that reverse this situations are also introduced
Maximum-likelihood fitting of data dominated by Poisson statistical uncertainties
International Nuclear Information System (INIS)
Stoneking, M.R.; Den Hartog, D.J.
1996-06-01
The fitting of data by χ 2 -minimization is valid only when the uncertainties in the data are normally distributed. When analyzing spectroscopic or particle counting data at very low signal level (e.g., a Thomson scattering diagnostic), the uncertainties are distributed with a Poisson distribution. The authors have developed a maximum-likelihood method for fitting data that correctly treats the Poisson statistical character of the uncertainties. This method maximizes the total probability that the observed data are drawn from the assumed fit function using the Poisson probability function to determine the probability for each data point. The algorithm also returns uncertainty estimates for the fit parameters. They compare this method with a χ 2 -minimization routine applied to both simulated and real data. Differences in the returned fits are greater at low signal level (less than ∼20 counts per measurement). the maximum-likelihood method is found to be more accurate and robust, returning a narrower distribution of values for the fit parameters with fewer outliers
The Poisson alignment reference system implementation at the Advanced Photon Source
International Nuclear Information System (INIS)
Feier, I.
1998-01-01
The Poisson spot was established using a collimated laser beam from a 3-mW diode laser. It was monitored on a quadrant detector and found to be very sensitive to vibration and air disturbances. Therefore, for future work we strongly recommend a sealed vacuum tube in which the Poisson line may be propagated. A digital single-axis feedback system was employed to generate an straight line reference (SLR) on the X axis. Pointing accuracy was better than 8 ± 2 microns at a distance of 5 m. The digital system was found to be quite slow with a maximum bandwidth of 47 ± 9 Hz. Slow drifts were easily corrected but any vibration over 5 Hz was not. We recommend an analog proportional-integral-derivative (PID) controller for high bandwidth and smooth operation of the kinematic mirror. Although the Poisson alignment system (PAS) at the Advanced Photon Source is still in its infancy, it already shows great promise as a possible alignment system for the low-energy undulator test line (LEUTL). Since components such as wigglers and quadruples will initially be aligned with respect to each other using conventional means and mounted on some kind of rigid rail, the goal would be to align six to ten such rails over a distance of about 30 m. The PAS could be used to align these rails by mounting a sphere at the joint between two rails. These spheres would need to be in a vacuum pipe to eliminate the refractive effects of air. Each sphere would not be attached to either rail but instead to a flange connecting the vacuum pipes of each rail. Thus the whole line would be made up of straight, rigid segments that could be aligned by moving the joints. Each sphere would have its own detector, allowing the operators to actively monitor the position of each joint and therefore the overall alignment of the system
Approximation by some combinations of Poisson integrals for Hermite and Laguerre expansions
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Grażyna Krech
2013-02-01
Full Text Available The aim of this paper is the study of a rate of convergence of some combinations of Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over the Poisson integrals. We prove also the Voronovskaya type theorem for these new operators.
Tests of a homogeneous Poisson process against clustering and other alternatives
International Nuclear Information System (INIS)
Atwood, C.L.
1994-05-01
This report presents three closely related tests of the hypothesis that data points come from a homogeneous Poisson process. If there is too much observed variation among the log-transformed between-point distances, the hypothesis is rejected. The tests are more powerful than the standard chi-squared test against the alternative hypothesis of event clustering, but not against the alternative hypothesis of a Poisson process with smoothly varying intensity
Doubly stochastic Poisson processes in artificial neural learning.
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.
Hoen, Petra W; Denollet, Johan; de Jonge, Peter; Whooley, Mary A
2013-07-01
Positive affect can improve survival, but the mechanisms responsible for this association are unknown. We sought to evaluate the association between positive affect and mortality in patients with stable coronary heart disease and to determine biological and behavioral factors that might explain this association. The Heart and Soul Study is a prospective cohort study of 1,018 outpatients with stable coronary heart disease. Participants were recruited between September 11, 2000, and December 20, 2002, and were followed up to June 2011. Baseline positive affect was assessed by using the 10-item positive affect subscale of the Positive and Negative Affect Schedule. Cox proportional hazards regression was used to estimate the risk of mortality (primary outcome measure) and cardiovascular events (heart failure, myocardial infarction, stroke, transient ischemic attack) associated with positive affect, adjusting for baseline cardiac disease severity and depression. We also evaluated the extent to which these associations were explained by potential biological and behavioral mediators. A total of 369 patients (36%) died during a mean ± SD follow-up period of 7.1 ± 2.5 years. Positive affect was not significantly associated with cardiovascular events (hazard ratio [HR]: 0.89; 95% CI, 0.79-1.00; P = .06). However, each standard deviation (8.8-point) increase in positive affect score was associated with a 16% decreased risk of all-cause mortality (HR: 0.84; 95% CI, 0.76-0.92; P = .001). After adjustment for cardiac disease severity and depressive symptoms, positive affect remained significantly associated with improved survival (HR: 0.87; 95% CI, 0.78-0.97; P = .01). The association was no longer significant after adjustment for behavioral factors, and particularly physical activity (HR: 0.92; 95% CI, 0.82-1.03; P = .16). Further adjustment for C-reactive protein and omega-3 fatty acids did not result in any meaningful changes (HR: 0.94; 95% CI, 0.84-1.06; P = .31). In this
Equal-Time and Equal-Space Poisson Brackets of the N -Component Coupled NLS Equation
International Nuclear Information System (INIS)
Zhou Ru-Guang; Li Pei-Yao; Gao Yuan
2017-01-01
Two Poisson brackets for the N-component coupled nonlinear Schrödinger (NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation. (paper)
Modeling environmental noise exceedances using non-homogeneous Poisson processes.
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.
International Nuclear Information System (INIS)
Vinaixa, Maria; Yanes, Oscar; Rodriguez, Miguel A.; Capellades, Jordi; Aivio, Suvi; Stracker, Travis H.; Gomez, Josep; Canyellas, Nicolau
2017-01-01
A novel metabolomics approach for NMR-based stable isotope tracer studies called PEPA is presented, and its performance validated using human cancer cells. PEPA detects the position of carbon label in isotopically enriched metabolites and quantifies fractional enrichment by indirect determination of "1"3C-satellite peaks using 1D-"1H-NMR spectra. In comparison with "1"3C-NMR, TOCSY and HSQC, PEPA improves sensitivity, accelerates the elucidation of "1"3C positions in labeled metabolites and the quantification of the percentage of stable isotope enrichment. Altogether, PEPA provides a novel framework for extending the high-throughput of "1H-NMR metabolic profiling to stable isotope tracing in metabolomics, facilitating and complementing the information derived from 2D-NMR experiments and expanding the range of isotopically enriched metabolites detected in cellular extracts. (copyright 2017 The Authors. Published by Wiley-VCH Verlag GmbH and Co. KGaA.)
Robust iterative observer for source localization for Poisson equation
Majeed, Muhammad Usman
2017-01-05
Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.
Robust iterative observer for source localization for Poisson equation
Majeed, Muhammad Usman; Laleg-Kirati, Taous-Meriem
2017-01-01
Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.
Detecting overdispersion in count data: A zero-inflated Poisson regression analysis
Afiqah Muhamad Jamil, Siti; Asrul Affendi Abdullah, M.; Kek, Sie Long; Nor, Maria Elena; Mohamed, Maryati; Ismail, Norradihah
2017-09-01
This study focusing on analysing count data of butterflies communities in Jasin, Melaka. In analysing count dependent variable, the Poisson regression model has been known as a benchmark model for regression analysis. Continuing from the previous literature that used Poisson regression analysis, this study comprising the used of zero-inflated Poisson (ZIP) regression analysis to gain acute precision on analysing the count data of butterfly communities in Jasin, Melaka. On the other hands, Poisson regression should be abandoned in the favour of count data models, which are capable of taking into account the extra zeros explicitly. By far, one of the most popular models include ZIP regression model. The data of butterfly communities which had been called as the number of subjects in this study had been taken in Jasin, Melaka and consisted of 131 number of subjects visits Jasin, Melaka. Since the researchers are considering the number of subjects, this data set consists of five families of butterfly and represent the five variables involve in the analysis which are the types of subjects. Besides, the analysis of ZIP used the SAS procedure of overdispersion in analysing zeros value and the main purpose of continuing the previous study is to compare which models would be better than when exists zero values for the observation of the count data. The analysis used AIC, BIC and Voung test of 5% level significance in order to achieve the objectives. The finding indicates that there is a presence of over-dispersion in analysing zero value. The ZIP regression model is better than Poisson regression model when zero values exist.
The Poisson model limits in NBA basketball: Complexity in team sports
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.
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.
Poisson/Superfish codes for personal computers
International Nuclear Information System (INIS)
Humphries, S.
1992-01-01
The Poisson/Superfish codes calculate static E or B fields in two-dimensions and electromagnetic fields in resonant structures. New versions for 386/486 PCs and Macintosh computers have capabilities that exceed the mainframe versions. Notable improvements are interactive graphical post-processors, improved field calculation routines, and a new program for charged particle orbit tracking. (author). 4 refs., 1 tab., figs
Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus
Buring, Ricardo; Kiselev, Arthemy V.; Rutten, Nina
2018-02-01
Let \\mathscr{P} be a Poisson structure on a finite-dimensional affine real manifold. Can \\mathscr{P} be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach - with respect to all affine Poisson manifolds - to finding a class of solutions to this deformation problem. For that reasoning, several types of graphs are needed. In this paper we outline the algorithms to generate those graphs. The graphs that encode deformations are classified by the number of internal vertices k; for k ≤ 4 we present all solutions of the deformation problem. For k ≥ 5, first reproducing the pentagon-wheel picture suggested at k = 6 by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that yields a new unique solution without 2-loops and tadpoles at k = 8.
Directory of Open Access Journals (Sweden)
Ramona C. Polexe
2013-07-01
Full Text Available In this study, we describe the elaboration of multifunctional positively charged polyelectrolyte complex (PEC nanoparticles, designed to be stable at physiological salt concentration and pH, for effective targeted delivery. These nanoparticles were obtained by charge neutralization between chitosan (CS as polycation and hyaluronic acid (HA as polyanion. We showed that the course of the complexation process and the physico-chemical properties of the resulting colloids were impacted by (i internal parameters such as the Degree of Acetylation (DA, i.e., the molar ration of acetyl glucosamine residues and molar mass of CS, the HA molar mass and (ii external parameters like the charge mixing ratio and the polymer concentrations. As a result, nonstoichiometric colloidal PECs were obtained in water or PBS (pH 7.4 and remained stable over one month. The polymer interactions were characterized by thermal analysis (DSC and TGA and the morphology was studied by scanning electron microscopy. A model antibody, anti-ovalbumine (OVA immunoglobulin A (IgA was sorbed on the particle surface in water and PBS quantitatively in 4 h. The CS-HA/IgA nanoparticles average size was between 425–665 nm with a positive zeta potential. These results pointed out that CS-HA can be effective carriers for use in targeted drug delivery.
A regularization method for solving the Poisson equation for mixed unbounded-periodic domains
DEFF Research Database (Denmark)
Spietz, Henrik Juul; Mølholm Hejlesen, Mads; Walther, Jens Honoré
2018-01-01
the regularized unbounded-periodic Green's functions can be implemented in an FFT-based Poisson solver to obtain a convergence rate corresponding to the regularization order of the Green's function. The high order is achieved without any additional computational cost from the conventional FFT-based Poisson solver...... and enables the calculation of the derivative of the solution to the same high order by direct spectral differentiation. We illustrate an application of the FFT-based Poisson solver by using it with a vortex particle mesh method for the approximation of incompressible flow for a problem with a single periodic...
Renewal characterization of Markov modulated Poisson processes
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Marcel F. Neuts
1989-01-01
Full Text Available A Markov Modulated Poisson Process (MMPP M(t defined on a Markov chain J(t is a pure jump process where jumps of M(t occur according to a Poisson process with intensity λi whenever the Markov chain J(t is in state i. M(t is called strongly renewal (SR if M(t is a renewal process for an arbitrary initial probability vector of J(t with full support on P={i:λi>0}. M(t is called weakly renewal (WR if there exists an initial probability vector of J(t such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t,M(t]. Relevance to the lumpability of J(t is also studied.
Modeling spiking behavior of neurons with time-dependent Poisson processes.
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.
Numerical solution of continuous-time DSGE models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...... classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very...
A new non-commutative representation of the Wiener and Poisson processes
International Nuclear Information System (INIS)
Privault, N.
1996-01-01
Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs
Nonlocal surface plasmons by Poisson Green's function matching
International Nuclear Information System (INIS)
Morgenstern Horing, Norman J
2006-01-01
The Poisson Green's function for all space is derived for the case in which an interface divides space into two separate semi-infinite media, using the Green's function matching method. Each of the separate semi-infinite constituent parts has its own dynamic, nonlocal polarizability, which is taken to be unaffected by the presence of the interface and is represented by the corresponding bulk response property. While this eliminates Friedel oscillatory phenomenology near the interface with p ∼ 2p F , it is nevertheless quite reasonable and useful for a broad range of lower (nonvanishing) wavenumbers, p F . The resulting full-space Poisson Green's function is dynamic, nonlocal and spatially inhomogeneous, and its frequency pole yields the surface plasmon dispersion relation, replete with dynamic and nonlocal features. It also accommodates an ambient magnetic field
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.
The Jackson Queueing Network Model Built Using Poisson Measures. Application To A Bank Model
Directory of Open Access Journals (Sweden)
Ciuiu Daniel
2014-07-01
Full Text Available In this paper we will build a bank model using Poisson measures and Jackson queueing networks. We take into account the relationship between the Poisson and the exponential distributions, and we consider for each credit/deposit type a node where shocks are modeled as the compound Poisson processes. The transmissions of the shocks are modeled as moving between nodes in Jackson queueing networks, the external shocks are modeled as external arrivals, and the absorption of shocks as departures from the network.
Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates
International Nuclear Information System (INIS)
Laurence, T.; Chromy, B.
2010-01-01
Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms of counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE
Reference manual for the POISSON/SUPERFISH Group of Codes
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
The POISSON/SUPERFISH Group codes were set up to solve two separate problems: the design of magnets and the design of rf cavities in a two-dimensional geometry. The first stage of either problem is to describe the layout of the magnet or cavity in a way that can be used as input to solve the generalized Poisson equation for magnets or the Helmholtz equations for cavities. The computer codes require that the problems be discretized by replacing the differentials (dx,dy) by finite differences ({delta}X,{delta}Y). Instead of defining the function everywhere in a plane, the function is defined only at a finite number of points on a mesh in the plane.
Directory of Open Access Journals (Sweden)
Hubert Gojzewski
2017-06-01
Full Text Available UV-curable polymer composites are of importance in industry, biomedical applications, scientific fields, and daily life. Outstanding physical properties of polymer composites were achieved with nanoparticles as filler, primarily in enhancing mechanical strength or barrier properties. Structure-property relationships of the resulting nanocomposites are dictated by the polymer-filler molecular architecture, i.e. interactions between polymer matrix and filler, and high surface area to volume ratio of the filler particles. Among monomers, acrylates and methacrylates attracted wide attention due to their ease of polymerization and excellent physicochemical and mechanical properties of the derived polymers. We prepared and photopolymerized two series of formulations containing hydrophobized silica nanofiller (Aerosil R7200 dispersed in 2-hydroxyethyl acrylate (HEA or polyethylene glycol diacrylate (PEGDA monomers. We compared selected physical properties of the formulations, both before and after photocuring; specifically the viscosity of formulations and dispersion of the filler in the polymer matrices. Additionally, we estimated the bulk Poisson׳s ratio of the investigated nanocomposites. This article contains data related to the research article entitled “Nanoscale Young׳s modulus and surface morphology in photocurable polyacrylate/nanosilica composites” (Gojzewski et al., 2017 [1].
Marques, Alexandre; Nave, Jean-Christophe; Rosales, Ruben
2011-11-01
The Poisson equation is of central importance in the description of fluid flows and other physical phenomena. In prior work, Marques, Nave, and Rosales introduced the Correction Function Method (CFM) to obtain fourth-order accurate solutions for the constant coefficient Poisson problem with prescribed jump conditions for the solution and its normal derivative across arbitrary interfaces. Here we combine this method with the ideas introduced by Mayo to solve other Poisson problems involving complex geometries. In summary, we are able to rewrite the problem as a boundary integral equation in terms of a potential distribution over the boundary or interface. The solution of this integral equation is discontinuous across the boundary or interface. Hence, after this integral equation is solved using standard techniques, the potential distribution can be used to determine the jump discontinuities. We are then able to use the CFM to solve the resulting Poisson equation with jump discontinuities. The outcome is a fourth-order accurate scheme to solve general Poisson problems which, over arbitrary geometries, has a cost that is approximately twice that of a fast Poisson solver using FFT on a rectangular geometry of the same size. Details of the method and applications will be presented.
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
Koehl, Patrice; Delarue, Marc
2010-02-14
The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE
International Nuclear Information System (INIS)
Grigoriu, Mircea; Samorodnitsky, Gennady
2004-01-01
Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method
Application of Poisson random effect models for highway network screening.
Jiang, Ximiao; Abdel-Aty, Mohamed; Alamili, Samer
2014-02-01
In recent years, Bayesian random effect models that account for the temporal and spatial correlations of crash data became popular in traffic safety research. This study employs random effect Poisson Log-Normal models for crash risk hotspot identification. Both the temporal and spatial correlations of crash data were considered. Potential for Safety Improvement (PSI) were adopted as a measure of the crash risk. Using the fatal and injury crashes that occurred on urban 4-lane divided arterials from 2006 to 2009 in the Central Florida area, the random effect approaches were compared to the traditional Empirical Bayesian (EB) method and the conventional Bayesian Poisson Log-Normal model. A series of method examination tests were conducted to evaluate the performance of different approaches. These tests include the previously developed site consistence test, method consistence test, total rank difference test, and the modified total score test, as well as the newly proposed total safety performance measure difference test. Results show that the Bayesian Poisson model accounting for both temporal and spatial random effects (PTSRE) outperforms the model that with only temporal random effect, and both are superior to the conventional Poisson Log-Normal model (PLN) and the EB model in the fitting of crash data. Additionally, the method evaluation tests indicate that the PTSRE model is significantly superior to the PLN model and the EB model in consistently identifying hotspots during successive time periods. The results suggest that the PTSRE model is a superior alternative for road site crash risk hotspot identification. Copyright © 2013 Elsevier Ltd. All rights reserved.
A covariant Poisson deformation quantization with separation of variables up to the third order
Karabegov, Alexander
2002-01-01
We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a K\\"ahler manifold M. Unlike C_1 and C_2, this operator can not be expressed in terms of the K\\"ahler-Poisson tensor on M. We modify C_3 to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and thus can be defined on an arbitrary complex manifold endowed with a Poisson bivecto...
Energy Technology Data Exchange (ETDEWEB)
Vinaixa, Maria; Yanes, Oscar [Department of Electronic Engineering-Universitat Rovira i Virgili, Spanish Biomedical Research Center in Diabetes and Associated Metabolic Disorders (CIBERDEM), Reus (Spain); Rodriguez, Miguel A.; Capellades, Jordi [Universitat Rovira i Virgili, Spanish Biomedical Research Center in Diabetes and Associated Metabolic Disorders (CIBERDEM), Reus (Spain); Aivio, Suvi; Stracker, Travis H. [Institute for Research in Biomedicine (IRB Barcelona), Barcelona Institute of Science and Technology (Spain); Gomez, Josep; Canyellas, Nicolau [Department of Electronic Engineering-, Universitat Rovira i Virgili, Tarragona (Spain)
2017-03-20
A novel metabolomics approach for NMR-based stable isotope tracer studies called PEPA is presented, and its performance validated using human cancer cells. PEPA detects the position of carbon label in isotopically enriched metabolites and quantifies fractional enrichment by indirect determination of {sup 13}C-satellite peaks using 1D-{sup 1}H-NMR spectra. In comparison with {sup 13}C-NMR, TOCSY and HSQC, PEPA improves sensitivity, accelerates the elucidation of {sup 13}C positions in labeled metabolites and the quantification of the percentage of stable isotope enrichment. Altogether, PEPA provides a novel framework for extending the high-throughput of {sup 1}H-NMR metabolic profiling to stable isotope tracing in metabolomics, facilitating and complementing the information derived from 2D-NMR experiments and expanding the range of isotopically enriched metabolites detected in cellular extracts. (copyright 2017 The Authors. Published by Wiley-VCH Verlag GmbH and Co. KGaA.)
Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2010-01-25
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.
Poisson's equation in de Sitter space-time
Energy Technology Data Exchange (ETDEWEB)
Pessa, E [Rome Univ. (Italy). Ist. di Matematica
1980-11-01
Based on a suitable generalization of Poisson's equation for de Sitter space-time the form of gravitation's law in 'projective relativity' is examined; it is found that, in the interior case, a small difference with the customary Newtonian law arises. This difference, of a repulsive character, can be very important in cosmological problems.
Poisson filtering of laser ranging data
Ricklefs, Randall L.; Shelus, Peter J.
1993-01-01
The filtering of data in a high noise, low signal strength environment is a situation encountered routinely in lunar laser ranging (LLR) and, to a lesser extent, in artificial satellite laser ranging (SLR). The use of Poisson statistics as one of the tools for filtering LLR data is described first in a historical context. The more recent application of this statistical technique to noisy SLR data is also described.
Quasineutral Limit of the Schrödinger-Poisson System in Coulomb Gauge
Lin, Chi-Kun; Wong, Yau-Shu; Wu, Kung-Chien
2012-01-01
The zero Debye length asymptotic of the Schrödinger-Poisson system in Coulomb gauge for ill-prepared initial data is studied. We prove that when the scaled Debye length λ → 0, the current density defined by the solution of the Schrödinger-Poisson system in the Coulomb gauge converges to the solution of the rotating incompressible Euler equation plus a fast singular oscillating gradient vector field.
Poisson processes and a Bessel function integral
Steutel, F.W.
1985-01-01
The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily
A Conway-Maxwell-Poisson (CMP) model to address data dispersion on positron emission tomography.
Santarelli, Maria Filomena; Della Latta, Daniele; Scipioni, Michele; Positano, Vincenzo; Landini, Luigi
2016-10-01
Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.
Histogram bin width selection for time-dependent Poisson processes
International Nuclear Information System (INIS)
Koyama, Shinsuke; Shinomoto, Shigeru
2004-01-01
In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method
Histogram bin width selection for time-dependent Poisson processes
Energy Technology Data Exchange (ETDEWEB)
Koyama, Shinsuke; Shinomoto, Shigeru [Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan)
2004-07-23
In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.
Binomial vs poisson statistics in radiation studies
International Nuclear Information System (INIS)
Foster, J.; Kouris, K.; Spyrou, N.M.; Matthews, I.P.; Welsh National School of Medicine, Cardiff
1983-01-01
The processes of radioactive decay, decay and growth of radioactive species in a radioactive chain, prompt emission(s) from nuclear reactions, conventional activation and cyclic activation are discussed with respect to their underlying statistical density function. By considering the transformation(s) that each nucleus may undergo it is shown that all these processes are fundamentally binomial. Formally, when the number of experiments N is large and the probability of success p is close to zero, the binomial is closely approximated by the Poisson density function. In radiation and nuclear physics, N is always large: each experiment can be conceived of as the observation of the fate of each of the N nuclei initially present. Whether p, the probability that a given nucleus undergoes a prescribed transformation, is close to zero depends on the process and nuclide(s) concerned. Hence, although a binomial description is always valid, the Poisson approximation is not always adequate. Therefore further clarification is provided as to when the binomial distribution must be used in the statistical treatment of detected events. (orig.)
Poisson statistics application in modelling of neutron detection
International Nuclear Information System (INIS)
Avdic, S.; Marinkovic, P.
1996-01-01
The main purpose of this study is taking into account statistical analysis of the experimental data which were measured by 3 He neutron spectrometer. The unfolding method based on principle of maximum likelihood incorporates the Poisson approximation of counting statistics applied (aithor)
Variational Gaussian approximation for Poisson data
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
2D sigma models and differential Poisson algebras
International Nuclear Information System (INIS)
Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander
2015-01-01
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
Improved mesh generator for the POISSON Group Codes
International Nuclear Information System (INIS)
Gupta, R.C.
1987-01-01
This paper describes the improved mesh generator of the POISSON Group Codes. These improvements enable one to have full control over the way the mesh is generated and in particular the way the mesh density is distributed throughout this model. A higher mesh density in certain regions coupled with a successively lower mesh density in others keeps the accuracy of the field computation high and the requirements on the computer time and computer memory low. The mesh is generated with the help of codes AUTOMESH and LATTICE; both have gone through a major upgrade. Modifications have also been made in the POISSON part of these codes. We shall present an example of a superconducting dipole magnet to explain how to use this code. The results of field computations are found to be reliable within a few parts in a hundred thousand even in such complex geometries
Beta-Poisson model for single-cell RNA-seq data analyses.
Vu, Trung Nghia; Wills, Quin F; Kalari, Krishna R; Niu, Nifang; Wang, Liewei; Rantalainen, Mattias; Pawitan, Yudi
2016-07-15
Single-cell RNA-sequencing technology allows detection of gene expression at the single-cell level. One typical feature of the data is a bimodality in the cellular distribution even for highly expressed genes, primarily caused by a proportion of non-expressing cells. The standard and the over-dispersed gamma-Poisson models that are commonly used in bulk-cell RNA-sequencing are not able to capture this property. We introduce a beta-Poisson mixture model that can capture the bimodality of the single-cell gene expression distribution. We further integrate the model into the generalized linear model framework in order to perform differential expression analyses. The whole analytical procedure is called BPSC. The results from several real single-cell RNA-seq datasets indicate that ∼90% of the transcripts are well characterized by the beta-Poisson model; the model-fit from BPSC is better than the fit of the standard gamma-Poisson model in > 80% of the transcripts. Moreover, in differential expression analyses of simulated and real datasets, BPSC performs well against edgeR, a conventional method widely used in bulk-cell RNA-sequencing data, and against scde and MAST, two recent methods specifically designed for single-cell RNA-seq data. An R package BPSC for model fitting and differential expression analyses of single-cell RNA-seq data is available under GPL-3 license at https://github.com/nghiavtr/BPSC CONTACT: yudi.pawitan@ki.se or mattias.rantalainen@ki.se Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Hadayeghi, Alireza; Shalaby, Amer S; Persaud, Bhagwant N
2010-03-01
A common technique used for the calibration of collision prediction models is the Generalized Linear Modeling (GLM) procedure with the assumption of Negative Binomial or Poisson error distribution. In this technique, fixed coefficients that represent the average relationship between the dependent variable and each explanatory variable are estimated. However, the stationary relationship assumed may hide some important spatial factors of the number of collisions at a particular traffic analysis zone. Consequently, the accuracy of such models for explaining the relationship between the dependent variable and the explanatory variables may be suspected since collision frequency is likely influenced by many spatially defined factors such as land use, demographic characteristics, and traffic volume patterns. The primary objective of this study is to investigate the spatial variations in the relationship between the number of zonal collisions and potential transportation planning predictors, using the Geographically Weighted Poisson Regression modeling technique. The secondary objective is to build on knowledge comparing the accuracy of Geographically Weighted Poisson Regression models to that of Generalized Linear Models. The results show that the Geographically Weighted Poisson Regression models are useful for capturing spatially dependent relationships and generally perform better than the conventional Generalized Linear Models. Copyright 2009 Elsevier Ltd. All rights reserved.
Quantum fields and Poisson processes. Pt. 2
International Nuclear Information System (INIS)
Bertrand, J.; Gaveau, B.; Rideau, G.
1985-01-01
Quantum field evolutions are written as expectation values with respect to Poisson processes in two simple models; interaction of two boson fields (with conservation of the number of particles in one field) and interaction of a boson with a fermion field. The introduction of a cutt-off ensures that the expectation values are well-defined. (orig.)
Nonhomogeneous fractional Poisson processes
International Nuclear Information System (INIS)
Wang Xiaotian; Zhang Shiying; Fan Shen
2007-01-01
In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W H (j) (t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W H (j) (t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function λ(t) strongly influences the existence of the highest finite moment of W H (j) (t) and the behaviour of the tail probability of W H (j) (t)
On the Magnetic Shield for a Vlasov-Poisson Plasma
Caprino, Silvia; Cavallaro, Guido; Marchioro, Carlo
2017-12-01
We study the screening of a bounded body Γ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of Γ . The charged wind is modeled by a Vlasov-Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of Γ . We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body. Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved.
POISSON, Analysis Solution of Poisson Problems in Probabilistic Risk Assessment
International Nuclear Information System (INIS)
Froehner, F.H.
1986-01-01
1 - Description of program or function: Purpose of program: Analytic treatment of two-stage Poisson problem in Probabilistic Risk Assessment. Input: estimated a-priori mean failure rate and error factor of system considered (for calculation of stage-1 prior), number of failures and operating times for similar systems (for calculation of stage-2 prior). Output: a-posteriori probability distributions on linear and logarithmic time scale (on specified time grid) and expectation values of failure rate and error factors are calculated for: - stage-1 a-priori distribution, - stage-1 a-posteriori distribution, - stage-2 a-priori distribution, - stage-2 a-posteriori distribution. 2 - Method of solution: Bayesian approach with conjugate stage-1 prior, improved with experience from similar systems to yield stage-2 prior, and likelihood function from experience with system under study (documentation see below under 10.). 3 - Restrictions on the complexity of the problem: Up to 100 similar systems (including the system considered), arbitrary number of problems (failure types) with same grid
The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models
Evangelista, Luiz Roberto; Lenzi, Ervin Kaminski; Barbero, Giovanni
2013-01-01
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual (PNP) or anomalous (PNPA) diffusional models that satisfy Poisson's equation in a finite-length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these re...
The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models.
Evangelista, Luiz Roberto; Lenzi, Ervin Kaminski; Barbero, Giovanni
2013-11-20
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.
High-Order Finite-Difference Solution of the Poisson Equation with Interface Jump Conditions II
Marques, Alexandre; Nave, Jean-Christophe; Rosales, Rodolfo
2010-11-01
The Poisson equation with jump discontinuities across an interface is of central importance in Computational Fluid Dynamics. In prior work, Marques, Nave, and Rosales have introduced a method to obtain fourth-order accurate solutions for the constant coefficient Poisson problem. Here we present an extension of this method to solve the variable coefficient Poisson problem to fourth-order of accuracy. The extended method is based on local smooth extrapolations of the solution field across the interface. The extrapolation procedure uses a combination of cubic Hermite interpolants and a high-order representation of the interface using the Gradient-Augmented Level-Set technique. This procedure is compatible with the use of standard discretizations for the Laplace operator, and leads to modified linear systems which have the same sparsity pattern as the standard discretizations. As a result, standard Poisson solvers can be used with only minimal modifications. Details of the method and applications will be presented.
Differential expression analysis for RNAseq using Poisson mixed models.
Sun, Shiquan; Hood, Michelle; Scott, Laura; Peng, Qinke; Mukherjee, Sayan; Tung, Jenny; Zhou, Xiang
2017-06-20
Identifying differentially expressed (DE) genes from RNA sequencing (RNAseq) studies is among the most common analyses in genomics. However, RNAseq DE analysis presents several statistical and computational challenges, including over-dispersed read counts and, in some settings, sample non-independence. Previous count-based methods rely on simple hierarchical Poisson models (e.g. negative binomial) to model independent over-dispersion, but do not account for sample non-independence due to relatedness, population structure and/or hidden confounders. Here, we present a Poisson mixed model with two random effects terms that account for both independent over-dispersion and sample non-independence. We also develop a scalable sampling-based inference algorithm using a latent variable representation of the Poisson distribution. With simulations, we show that our method properly controls for type I error and is generally more powerful than other widely used approaches, except in small samples (n <15) with other unfavorable properties (e.g. small effect sizes). We also apply our method to three real datasets that contain related individuals, population stratification or hidden confounders. Our results show that our method increases power in all three data compared to other approaches, though the power gain is smallest in the smallest sample (n = 6). Our method is implemented in MACAU, freely available at www.xzlab.org/software.html. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.
Doubly stochastic Poisson process models for precipitation at fine time-scales
Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao
2012-09-01
This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.
Is neutron evaporation from highly excited nuclei a poisson random process
International Nuclear Information System (INIS)
Simbel, M.H.
1982-01-01
It is suggested that neutron emission from highly excited nuclei follows a Poisson random process. The continuous variable of the process is the excitation energy excess over the binding energy of the emitted neutrons and the discrete variable is the number of emitted neutrons. Cross sections for (HI,xn) reactions are analyzed using a formula containing a Poisson distribution function. The post- and pre-equilibrium components of the cross section are treated separately. The agreement between the predictions of this formula and the experimental results is very good. (orig.)
Measurements of the Poisson ratio and fragility of glass-forming liquids
DEFF Research Database (Denmark)
Christensen, Tage Emil; Olsen, Niels Boye
Recently much attention has been given to models and phenomenology of glass-forming liquids that correlates fast and slow degrees of freedom . In particular the Poisson ratio has been correlated with fragility. We present data on shear - and bulk modulus obtained by the techniques...... of the piezoelectric transducers PBG and PSG on a number of glass-forming liquids. Hereby the Poisson ratio can be found. Furthermore the PSG also gives the temperature dependence of shear viscosity and thereby the fragility. The validity of the conjectured relation is discussed...
Família composta Poisson-Truncada: propriedades e aplicações
ARAÚJO, Raphaela Lima Belchior de
2015-01-01
Este trabalho analisa propriedades da família de distribuições de probabilidade Composta N e propõe a sub-família Composta Poisson-Truncada como um meio de compor distribuições de probabilidade. Suas propriedades foram estudadas e uma nova distribuição foi investigada: a distribuição Composta Poisson-Truncada Normal. Esta distribuição possui três parâmetros e tem uma flexibilidade para modelar dados multimodais. Demonstramos que sua densidade é dada por uma mistura infinita de densidades norm...
Trophic position of soil nematodes in boreal forests as indicated by stable isotope analysis
Kudrin, Alexey; Tsurikov, Sergey
2016-04-01
Despite the well-developed trophic classification of soil nematodes, their position in soil food webs is still little understood. Observed deviations from the typical feeding strategy indicate that a simplified trophic classification probably does not fully reflect actual trophic interactions. Furthermore, the extent and functional significance of nematodes as prey for other soil animals remains unknown. Stable isotope analysis (SIA) is powerful tool for investigating the structure of soil food webs, but its application to the study of soil nematodes has been limited to only a few studies. We used stable isotope analysis to gain a better understanding of trophic links of several groups of soil nematodes in two boreal forests on albeluvisol. We investigated four taxonomic groups of nematodes: Mononchida, Dorylaimida, Plectidae and Tylenchidae (mostly from the genus Filenchus), that according to the conventional trophic classification represent predators, omnivores, bacterivores and root-fungal feeders, respectively. To assess the trophic position of nematodes, we used a comparison against a set of reference species including herbivorous, saprophagous and predatory macro-invertebrates, oribatid and mesostigmatid mites, and collembolans. Our results suggest that trophic position of the investigated groups of soil nematodes generally corresponds to the conventional classification. All nematodes were enriched in 13C relative to Picea abies roots and litter, and mycorrhizal fungal mycelium. Root-fungal feeders Tylenchidae had δ15N values similar to those of earthworms, enchytraeids and Entomobrya collembolans, but slightly lower δ13C values. Bacterivorous Plectidae were either equal or enriched in 15N compared with saprophagous macroinvertebrates and most mesofauna species. Omnivorous Dorylaimida and predatory Mononchida were further enriched in 15N and their isotopic signature was similar to that of predatory arthropods. These data confirm a clear separation of
Positive-definite matrix processes of finite variation
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Stelzer, Robert
2007-01-01
Processes of finite variation, which take values in the positive semidefinite matrices and are representable as the sum of an integral with respect to time and one with respect to an extended Poisson random measure, are considered. For such processes we derive conditions for the square root (and ...
Positive-Definite Matrix Processes of Finite Variation
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Stelzer, Robert
Processes of finite variation, which take values in the positive semidefinite matrices and are representable as the sum of an integral with respect to time and one with respect to an extended Poisson random measure, are considered. For such processes we derive conditions for the square root (and ...
Optimal linear filtering of Poisson process with dead time
International Nuclear Information System (INIS)
Glukhova, E.V.
1993-01-01
The paper presents a derivation of an integral equation defining the impulsed transient of optimum linear filtering for evaluation of the intensity of the fluctuating Poisson process with allowance for dead time of transducers
Nonparametric Bayesian inference for multidimensional compound Poisson processes
Gugushvili, S.; van der Meulen, F.; Spreij, P.
2015-01-01
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density r0 and intensity λ0. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context,
Poisson equation in the Kohn-Sham Coulomb problem
Manby, F. R.; Knowles, Peter James
2001-01-01
We apply the Poisson equation to the quantum mechanical Coulomb problem for many-particle systems. By introducing a suitable basis set, the two-electron Coulomb integrals become simple overlaps. This offers the possibility of very rapid linear-scaling treatment of the Coulomb contribution to Kohn-Sham theory.
A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space
International Nuclear Information System (INIS)
Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel
2006-01-01
Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations
Hyperbolically Patterned 3D Graphene Metamaterial with Negative Poisson's Ratio and Superelasticity.
Zhang, Qiangqiang; Xu, Xiang; Lin, Dong; Chen, Wenli; Xiong, Guoping; Yu, Yikang; Fisher, Timothy S; Li, Hui
2016-03-16
A hyperbolically patterned 3D graphene metamaterial (GM) with negative Poisson's ratio and superelasticity is highlighted. It is synthesized by a modified hydrothermal approach and subsequent oriented freeze-casting strategy. GM presents a tunable Poisson's ratio by adjusting the structural porosity, macroscopic aspect ratio (L/D), and freeze-casting conditions. Such a GM suggests promising applications as soft actuators, sensors, robust shock absorbers, and environmental remediation. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Wavelets, ridgelets, and curvelets for Poisson noise removal.
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.
Sense of Humor, Stable Affect, and Psychological Well-Being
Directory of Open Access Journals (Sweden)
Arnie Cann
2014-08-01
Full Text Available A good sense of humor has been implicated as a quality that could contribute to psychological well-being. The mechanisms through which sense of humor might operate include helping to reappraise threats, serving as a character strength, or facilitating happiness. The current research attempts to integrate these possibilities by examining whether a good sense of humor might operate globally by helping to maintain a more stable positive affect. Stable positive affect has been shown to facilitate more effective problem solving and to build resilience. However, not all humor is adaptive humor, so we also examine the roles that different styles of humor use might play. Individual differences in humor styles were used to predict stable levels of affect. Then, in a longitudinal design, humor styles and stable affect were used to predict subsequent resilience and psychological health. The results indicated that stable affect was related to resilience and psychological well-being, and that a sense of humor that involves self-enhancing humor, humor based on maintaining a humorous perspective about one’s experiences, was positively related to stable positive affect, negatively related to stable negative affect, and was mediated through stable affect in influencing resilience, well-being and distress. Thus, while a good sense of humor can lead to greater resilience and better psychological health, the current results, focusing on stable affect, find only self-enhancing humor provides reliable benefits.
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-06-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering
Bayesian spatial modeling of HIV mortality via zero-inflated Poisson models.
Musal, Muzaffer; Aktekin, Tevfik
2013-01-30
In this paper, we investigate the effects of poverty and inequality on the number of HIV-related deaths in 62 New York counties via Bayesian zero-inflated Poisson models that exhibit spatial dependence. We quantify inequality via the Theil index and poverty via the ratios of two Census 2000 variables, the number of people under the poverty line and the number of people for whom poverty status is determined, in each Zip Code Tabulation Area. The purpose of this study was to investigate the effects of inequality and poverty in addition to spatial dependence between neighboring regions on HIV mortality rate, which can lead to improved health resource allocation decisions. In modeling county-specific HIV counts, we propose Bayesian zero-inflated Poisson models whose rates are functions of both covariate and spatial/random effects. To show how the proposed models work, we used three different publicly available data sets: TIGER Shapefiles, Census 2000, and mortality index files. In addition, we introduce parameter estimation issues of Bayesian zero-inflated Poisson models and discuss MCMC method implications. Copyright © 2012 John Wiley & Sons, Ltd.
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.
Poisson processes on groups and Feynman path integrals
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.
1979-09-01
An expression is given for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems
Monitoring Poisson time series using multi-process models
DEFF Research Database (Denmark)
Engebjerg, Malene Dahl Skov; Lundbye-Christensen, Søren; Kjær, Birgitte B.
aspects of health resource management may also be addressed. In this paper we center on the detection of outbreaks of infectious diseases. This is achieved by a multi-process Poisson state space model taking autocorrelation and overdispersion into account, which has been applied to a data set concerning...
Poisson-generalized gamma empirical Bayes model for disease ...
African Journals Online (AJOL)
In spatial disease mapping, the use of Bayesian models of estimation technique is becoming popular for smoothing relative risks estimates for disease mapping. The most common Bayesian conjugate model for disease mapping is the Poisson-Gamma Model (PG). To explore further the activity of smoothing of relative risk ...
Nonhomogeneous fractional Poisson processes
Energy Technology Data Exchange (ETDEWEB)
Wang Xiaotian [School of Management, Tianjin University, Tianjin 300072 (China)]. E-mail: swa001@126.com; Zhang Shiying [School of Management, Tianjin University, Tianjin 300072 (China); Fan Shen [Computer and Information School, Zhejiang Wanli University, Ningbo 315100 (China)
2007-01-15
In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W{sub H}{sup (j)}(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W{sub H}{sup (j)}(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function {lambda}(t) strongly influences the existence of the highest finite moment of W{sub H}{sup (j)}(t) and the behaviour of the tail probability of W{sub H}{sup (j)}(t)
Casimir meets Poisson: improved quark/gluon discrimination with counting observables
Frye, Christopher; Larkoski, Andrew J.; Thaler, Jesse; Zhou, Kevin
2017-09-01
Charged track multiplicity is among the most powerful observables for discriminating quark- from gluon-initiated jets. Despite its utility, it is not infrared and collinear (IRC) safe, so perturbative calculations are limited to studying the energy evolution of multiplicity moments. While IRC-safe observables, like jet mass, are perturbatively calculable, their distributions often exhibit Casimir scaling, such that their quark/gluon discrimination power is limited by the ratio of quark to gluon color factors. In this paper, we introduce new IRC-safe counting observables whose discrimination performance exceeds that of jet mass and approaches that of track multiplicity. The key observation is that track multiplicity is approximately Poisson distributed, with more suppressed tails than the Sudakov peak structure from jet mass. By using an iterated version of the soft drop jet grooming algorithm, we can define a "soft drop multiplicity" which is Poisson distributed at leading-logarithmic accuracy. In addition, we calculate the next-to-leading-logarithmic corrections to this Poisson structure. If we allow the soft drop groomer to proceed to the end of the jet branching history, we can define a collinear-unsafe (but still infrared-safe) counting observable. Exploiting the universality of the collinear limit, we define generalized fragmentation functions to study the perturbative energy evolution of collinear-unsafe multiplicity.
On Poisson's ratio for metal matrix composite laminates. [aluminum boron composites
Herakovich, C. T.; Shuart, M. J.
1978-01-01
The definition of Poisson's ratio for nonlinear behavior of metal matrix composite laminates is discussed and experimental results for tensile and compressive loading of five different boron-aluminum laminates are presented. It is shown that there may be considerable difference in the value of Poisson's ratio as defined by a total strain or an incremental strain definition. It is argued that the incremental definition is more appropriate for nonlinear material behavior. Results from a (0) laminate indicate that the incremental definition provides a precursor to failure which is not evident if the total strain definition is used.
Measurement of Poisson's ratio of nonmetallic materials by laser holographic interferometry
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.
Spatial variation of natural radiation and childhood leukaemia incidence in Great Britain
International Nuclear Information System (INIS)
Richardson, Sylvia; Monfort, Christine; Green, Martyn; Muirhead, Colin; Draper, Gerald
1995-01-01
This paper describes an analysis of the geographical variation of childhood leukaemia incidence in Great Britain over a 15 year period in relation to natural radiation (gamma and radon). Data at the level of the 459 district level local authorities in England, Wales and regional districts in Scotland are analysed in two complementary ways: first, by Poisson regressions with the inclusion of environmental covariates and a smooth spatial structure; secondly, by a hierarchical Bayesian model in which extra-Poisson variability is modelled explicitly in terms of spatial and non-spatial components. From this analysis, we deduce a strong indication that a main part of the variability is accounted for by a local neighbourhood 'clustering' structure. This structure is furthermore relatively stable over the 15 year period for the lymphocytic leukaemias which make up the majority of observed cases. We found no evidence of a positive association of childhood leukaemia incidence with outdoor or indoor gamma radiation levels. There is no consistent evidence of any association with radon levels. Indeed, in the Poisson regressions, a significant positive association was only observed for one 5-year period, a result which is not compatible with a stable environmental effect. Moreover, this positive association became clearly non-significant when over-dispersion relative to the Poisson distribution was taken into account. (author)
The Rasch Poisson counts model for incomplete data : An application of the EM algorithm
Jansen, G.G.H.
Rasch's Poisson counts model is a latent trait model for the situation in which K tests are administered to N examinees and the test score is a count [e.g., the repeated occurrence of some event, such as the number of items completed or the number of items answered (in)correctly]. The Rasch Poisson
Poisson processes on groups and Feynamn path integrals
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Aix-Marseille-2 Univ., 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.
1980-01-01
We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems. (orig.)
International Nuclear Information System (INIS)
Hernandez-Bermejo, Benito
2011-01-01
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: → A new family of Poisson structures is globally characterized and analyzed. → Such family is globally defined for arbitrary values of the dimension and the rank. → Global construction of Casimir invariants and Darboux canonical form is provided. → Very diverse and previously known solutions of physical interest are generalized.
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2011-05-09
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: A new family of Poisson structures is globally characterized and analyzed. Such family is globally defined for arbitrary values of the dimension and the rank. Global construction of Casimir invariants and Darboux canonical form is provided. Very diverse and previously known solutions of physical interest are generalized.
Experimental dead-time distortions of Poisson processes
International Nuclear Information System (INIS)
Faraci, G.; Pennisi, A.R.; Consiglio Nazionale delle Ricerche, Catania
1983-01-01
In order to check the distortions, introduced by a non-extended dead time on the Poisson statistics, accurate experiments have been made in single channel counting. At a given measuring time, the dependence on the choice of the time origin and on the width of the dead time has been verified. An excellent agreement has been found between the theoretical expressions and the experimental curves. (orig.)
Error-Rate Bounds for Coded PPM on a Poisson Channel
Moision, Bruce; Hamkins, Jon
2009-01-01
Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.
Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations
Blossey, R.; Maggs, A. C.; Podgornik, R.
2017-06-01
We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.
Generic Schemes for Single-Molecule Kinetics. 2: Information Content of the Poisson Indicator.
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.
A physiologically based nonhomogeneous Poisson counter model of visual identification
DEFF Research Database (Denmark)
Christensen, Jeppe H; Markussen, Bo; Bundesen, Claus
2018-01-01
A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects that are ......A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects...... that mimicked the dynamics of receptive field selectivity as found in neurophysiological studies. Furthermore, the initial sensory response yielded theoretical hazard rate functions that closely resembled empirically estimated ones. Finally, supplied with a Naka-Rushton type contrast gain control, the model...
Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science
Li, Shilong; Yin, Chuancun; Zhao, Xia; Dai, Hongshuai
2017-01-01
Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigat...
Log-normal frailty models fitted as Poisson generalized linear mixed models.
Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver
2016-12-01
The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
A Local Poisson Graphical Model for inferring networks from sequencing data.
Allen, Genevera I; Liu, Zhandong
2013-09-01
Gaussian graphical models, a class of undirected graphs or Markov Networks, are often used to infer gene networks based on microarray expression data. Many scientists, however, have begun using high-throughput sequencing technologies such as RNA-sequencing or next generation sequencing to measure gene expression. As the resulting data consists of counts of sequencing reads for each gene, Gaussian graphical models are not optimal for this discrete data. In this paper, we propose a novel method for inferring gene networks from sequencing data: the Local Poisson Graphical Model. Our model assumes a Local Markov property where each variable conditional on all other variables is Poisson distributed. We develop a neighborhood selection algorithm to fit our model locally by performing a series of l1 penalized Poisson, or log-linear, regressions. This yields a fast parallel algorithm for estimating networks from next generation sequencing data. In simulations, we illustrate the effectiveness of our methods for recovering network structure from count data. A case study on breast cancer microRNAs (miRNAs), a novel application of graphical models, finds known regulators of breast cancer genes and discovers novel miRNA clusters and hubs that are targets for future research.
The transverse Poisson's ratio of composites.
Foye, R. L.
1972-01-01
An expression is developed that makes possible the prediction of Poisson's ratio for unidirectional composites with reference to any pair of orthogonal axes that are normal to the direction of the reinforcing fibers. This prediction appears to be a reasonable one in that it follows the trends of the finite element analysis and the bounding estimates, and has the correct limiting value for zero fiber content. It can only be expected to apply to composites containing stiff, circular, isotropic fibers bonded to a soft matrix material.
A Generalized QMRA Beta-Poisson Dose-Response Model.
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 0Poisson model, PI(d|α,β), is a special case of the generalized model with K min = 1 (which implies r*=1). The generalized beta-Poisson model is based on a conceptual model with greater detail in the dose-response mechanism. Since a maximum likelihood solution is not easily available, a likelihood-free approximate Bayesian computation (ABC) algorithm is employed for parameter estimation. By fitting the generalized model to four experimental data sets from the literature, this study reveals that the posterior median r* estimates produced fall short of meeting the required condition of r* = 1 for single-hit assumption. However, three out of four data sets fitted by the generalized models could not achieve an improvement in goodness of fit. These combined results imply that, at least in some cases, a single-hit assumption for characterizing the dose-response process may not be appropriate, but that the more complex models may be difficult to support especially if the sample size is small. The three-parameter generalized model provides a possibility to investigate the mechanism of a dose-response process in greater detail than is possible under a single-hit model. © 2016 Society for Risk Analysis.
Collision prediction models using multivariate Poisson-lognormal regression.
El-Basyouny, Karim; Sayed, Tarek
2009-07-01
This paper advocates the use of multivariate Poisson-lognormal (MVPLN) regression to develop models for collision count data. The MVPLN approach presents an opportunity to incorporate the correlations across collision severity levels and their influence on safety analyses. The paper introduces a new multivariate hazardous location identification technique, which generalizes the univariate posterior probability of excess that has been commonly proposed and applied in the literature. In addition, the paper presents an alternative approach for quantifying the effect of the multivariate structure on the precision of expected collision frequency. The MVPLN approach is compared with the independent (separate) univariate Poisson-lognormal (PLN) models with respect to model inference, goodness-of-fit, identification of hot spots and precision of expected collision frequency. The MVPLN is modeled using the WinBUGS platform which facilitates computation of posterior distributions as well as providing a goodness-of-fit measure for model comparisons. The results indicate that the estimates of the extra Poisson variation parameters were considerably smaller under MVPLN leading to higher precision. The improvement in precision is due mainly to the fact that MVPLN accounts for the correlation between the latent variables representing property damage only (PDO) and injuries plus fatalities (I+F). This correlation was estimated at 0.758, which is highly significant, suggesting that higher PDO rates are associated with higher I+F rates, as the collision likelihood for both types is likely to rise due to similar deficiencies in roadway design and/or other unobserved factors. In terms of goodness-of-fit, the MVPLN model provided a superior fit than the independent univariate models. The multivariate hazardous location identification results demonstrated that some hazardous locations could be overlooked if the analysis was restricted to the univariate models.
Irreversible thermodynamics of Poisson processes with reaction.
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.
Degenerate odd Poisson bracket on Grassmann variables
International Nuclear Information System (INIS)
Soroka, V.A.
2000-01-01
A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is proposed. It is revealed that this bracket has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, second and third orders with respect to the Grassmann derivatives. It is shown that these Δ-like operators, together with the Grassmann-odd nilpotent Casimir function of this bracket, form a finite-dimensional Lie superalgebra
Prediction of forest fires occurrences with area-level Poisson mixed models.
Boubeta, Miguel; Lombardía, María José; Marey-Pérez, Manuel Francisco; Morales, Domingo
2015-05-01
The number of fires in forest areas of Galicia (north-west of Spain) during the summer period is quite high. Local authorities are interested in analyzing the factors that explain this phenomenon. Poisson regression models are good tools for describing and predicting the number of fires per forest areas. This work employs area-level Poisson mixed models for treating real data about fires in forest areas. A parametric bootstrap method is applied for estimating the mean squared errors of fires predictors. The developed methodology and software are applied to a real data set of fires in forest areas of Galicia. Copyright © 2015 Elsevier Ltd. All rights reserved.
Poisson sampling - The adjusted and unadjusted estimator revisited
Michael S. Williams; Hans T. Schreuder; Gerardo H. Terrazas
1998-01-01
The prevailing assumption, that for Poisson sampling the adjusted estimator "Y-hat a" is always substantially more efficient than the unadjusted estimator "Y-hat u" , is shown to be incorrect. Some well known theoretical results are applicable since "Y-hat a" is a ratio-of-means estimator and "Y-hat u" a simple unbiased estimator...
Quadratic Poisson brackets compatible with an algebra structure
Balinsky, A. A.; Burman, Yu.
1994-01-01
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2012-01-01
This work improves upon Hockney and Eastwood's Fourier-based algorithm for the unbounded Poisson equation to formally achieve arbitrary high order of convergence without any additional computational cost. We assess the methodology on the kinematic relations between the velocity and vorticity fields....
An application of the Autoregressive Conditional Poisson (ACP) model
CSIR Research Space (South Africa)
Holloway, Jennifer P
2010-11-01
Full Text Available When modelling count data that comes in the form of a time series, the static Poisson regression and standard time series models are often not appropriate. A current study therefore involves the evaluation of several observation-driven and parameter...
A Family of Poisson Processes for Use in Stochastic Models of Precipitation
Penland, C.
2013-12-01
Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.
A physiologically based nonhomogeneous Poisson counter model of visual identification.
Christensen, Jeppe H; Markussen, Bo; Bundesen, Claus; Kyllingsbæk, Søren
2018-04-30
A physiologically based nonhomogeneous Poisson counter model of visual identification is presented. The model was developed in the framework of a Theory of Visual Attention (Bundesen, 1990; Kyllingsbæk, Markussen, & Bundesen, 2012) and meant for modeling visual identification of objects that are mutually confusable and hard to see. The model assumes that the visual system's initial sensory response consists in tentative visual categorizations, which are accumulated by leaky integration of both transient and sustained components comparable with those found in spike density patterns of early sensory neurons. The sensory response (tentative categorizations) feeds independent Poisson counters, each of which accumulates tentative object categorizations of a particular type to guide overt identification performance. We tested the model's ability to predict the effect of stimulus duration on observed distributions of responses in a nonspeeded (pure accuracy) identification task with eight response alternatives. The time courses of correct and erroneous categorizations were well accounted for when the event-rates of competing Poisson counters were allowed to vary independently over time in a way that mimicked the dynamics of receptive field selectivity as found in neurophysiological studies. Furthermore, the initial sensory response yielded theoretical hazard rate functions that closely resembled empirically estimated ones. Finally, supplied with a Naka-Rushton type contrast gain control, the model provided an explanation for Bloch's law. (PsycINFO Database Record (c) 2018 APA, all rights reserved).
A heterogeneous CPU+GPU Poisson solver for space charge calculations in beam dynamics studies
Energy Technology Data Exchange (ETDEWEB)
Zheng, Dawei; Rienen, Ursula van [University of Rostock, Institute of General Electrical Engineering (Germany)
2016-07-01
In beam dynamics studies in accelerator physics, space charge plays a central role in the low energy regime of an accelerator. Numerical space charge calculations are required, both, in the design phase and in the operation of the machines as well. Due to its efficiency, mostly the Particle-In-Cell (PIC) method is chosen for the space charge calculation. Then, the solution of Poisson's equation for the charge distribution in the rest frame is the most prominent part within the solution process. The Poisson solver directly affects the accuracy of the self-field applied on the charged particles when the equation of motion is solved in the laboratory frame. As the Poisson solver consumes the major part of the computing time in most simulations it has to be as fast as possible since it has to be carried out once per time step. In this work, we demonstrate a novel heterogeneous CPU+GPU routine for the Poisson solver. The novel solver also benefits from our new research results on the utilization of a discrete cosine transform within the classical Hockney and Eastwood's convolution routine.
Species Abundance in a Forest Community in South China: A Case of Poisson Lognormal Distribution
Institute of Scientific and Technical Information of China (English)
Zuo-Yun YIN; Hai REN; Qian-Mei ZHANG; Shao-Lin PENG; Qin-Feng GUO; Guo-Yi ZHOU
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 (σ andμ) 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 σ 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/σ should be an alternative measure of diversity.
Nonhomogeneous Poisson process with nonparametric frailty
International Nuclear Information System (INIS)
Slimacek, Vaclav; Lindqvist, Bo Henry
2016-01-01
The failure processes of heterogeneous repairable systems are often modeled by non-homogeneous Poisson processes. The common way to describe an unobserved heterogeneity between systems is to multiply the basic rate of occurrence of failures by a random variable (a so-called frailty) having a specified parametric distribution. Since the frailty is unobservable, the choice of its distribution is a problematic part of using these models, as are often the numerical computations needed in the estimation of these models. The main purpose of this paper is to develop a method for estimation of the parameters of a nonhomogeneous Poisson process with unobserved heterogeneity which does not require parametric assumptions about the heterogeneity and which avoids the frequently encountered numerical problems associated with the standard models for unobserved heterogeneity. The introduced method is illustrated on an example involving the power law process, and is compared to the standard gamma frailty model and to the classical model without unobserved heterogeneity. The derived results are confirmed in a simulation study which also reveals several not commonly known properties of the gamma frailty model and the classical model, and on a real life example. - Highlights: • A new method for estimation of a NHPP with frailty is introduced. • Introduced method does not require parametric assumptions about frailty. • The approach is illustrated on an example with the power law process. • The method is compared to the gamma frailty model and to the model without frailty.
Boundary singularity of Poisson and harmonic Bergman kernels
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav
2015-01-01
Roč. 429, č. 1 (2015), s. 233-272 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190802 Institutional support: RVO:67985840 Keywords : harmonic Bergman kernel * Poisson kernel * pseudodifferential boundary operators Subject RIV: BA - General Mathematics Impact factor: 1.014, year: 2015 http://www.sciencedirect.com/science/article/pii/S0022247X15003170
Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes
Belitser, E.; Andrade Serra, De P.J.; Zanten, van J.H.
2013-01-01
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys desirable theoretical optimality properties. The prior we use is
Coefficient Inverse Problem for Poisson's Equation in a Cylinder
Solov'ev, V. V.
2011-01-01
The inverse problem of determining the coefficient on the right-hand side of Poisson's equation in a cylindrical domain is considered. The Dirichlet boundary value problem is studied. Two types of additional information (overdetermination) can be specified: (i) the trace of the solution to the
Moments analysis of concurrent Poisson processes
International Nuclear Information System (INIS)
McBeth, G.W.; Cross, P.
1975-01-01
A moments analysis of concurrent Poisson processes has been carried out. Equations are given which relate combinations of distribution moments to sums of products involving the number of counts associated with the processes and the mean rate of the processes. Elimination of background is discussed and equations suitable for processing random radiation, parent-daughter pairs in the presence of background, and triple and double correlations in the presence of background are given. The theory of identification of the four principle radioactive series by moments analysis is discussed. (Auth.)
Lyapunov stability and poisson structure of the thermal TDHF and RPA equations
International Nuclear Information System (INIS)
Balian, R.; Veneroni, M.
1989-01-01
The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p) density ρ behave as classical dynamical variables. By introducing the Lie--Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a Hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered. copyright 1989 Academic Press, Inc
Lyapunov stability and Poisson structure of the thermal TDHF and RPA equations
International Nuclear Information System (INIS)
Veneroni, M.; Balian, R.
1989-01-01
The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p.) density ρ behave as classical dynamical variables. By introducing the Lie-Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered
Grafting and Poisson Structure in (2+1)-Gravity with Vanishing Cosmological Constant
Meusburger, C.
2006-09-01
We relate the geometrical construction of (2+1)-spacetimes via grafting to phase space and Poisson structure in the Chern-Simons formulation of (2+1)-dimensional gravity with vanishing cosmological constant on manifolds of topology mathbb{R} × S_g, where S g is an orientable two-surface of genus g>1. We show how grafting along simple closed geodesics λ is implemented in the Chern-Simons formalism and derive explicit expressions for its action on the holonomies of general closed curves on S g .We prove that this action is generated via the Poisson bracket by a gauge invariant observable associated to the holonomy of λ. We deduce a symmetry relation between the Poisson brackets of observables associated to the Lorentz and translational components of the holonomies of general closed curves on S g and discuss its physical interpretation. Finally, we relate the action of grafting on the phase space to the action of Dehn twists and show that grafting can be viewed as a Dehn twist with a formal parameter θ satisfying θ2 = 0.
International Nuclear Information System (INIS)
Zheng, Y P; Choi, A P C; Ling, H Y; Huang, Y P
2009-01-01
Indentation is commonly used to determine the mechanical properties of different kinds of biological tissues and engineering materials. With the force–deformation data obtained from an indentation test, Young's modulus of the tissue can be calculated using a linear elastic indentation model with a known Poisson's ratio. A novel method for simultaneous estimation of Young's modulus and Poisson's ratio of the tissue using a single indentation was proposed in this study. Finite element (FE) analysis using 3D models was first used to establish the relationship between Poisson's ratio and the deformation-dependent indentation stiffness for different aspect ratios (indentor radius/tissue original thickness) in the indentation test. From the FE results, it was found that the deformation-dependent indentation stiffness linearly increased with the deformation. Poisson's ratio could be extracted based on the deformation-dependent indentation stiffness obtained from the force–deformation data. Young's modulus was then further calculated with the estimated Poisson's ratio. The feasibility of this method was demonstrated in virtue of using the indentation models with different material properties in the FE analysis. The numerical results showed that the percentage errors of the estimated Poisson's ratios and the corresponding Young's moduli ranged from −1.7% to −3.2% and 3.0% to 7.2%, respectively, with the aspect ratio (indentor radius/tissue thickness) larger than 1. It is expected that this novel method can be potentially used for quantitative assessment of various kinds of engineering materials and biological tissues, such as articular cartilage
Higueras, Manuel; González, J E; Di Giorgio, Marina; Barquinero, J F
2018-05-18
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.
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.
Optimality of Poisson Processes Intensity Learning with Gaussian Processes
Kirichenko, A.; van Zanten, H.
2015-01-01
In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a d-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational
Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)
DEFF Research Database (Denmark)
Agosto, Arianna; Cavaliere, Guiseppe; Kristensen, Dennis
We develop a class of Poisson autoregressive models with additional covariates (PARX) that can be used to model and forecast time series of counts. We establish the time series properties of the models, including conditions for stationarity and existence of moments. These results are in turn used...
Poisson and Gaussian approximation of weighted local empirical processes
Einmahl, J.H.J.
1995-01-01
We consider the local empirical process indexed by sets, a greatly generalized version of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main
International Nuclear Information System (INIS)
Lacombe, J.P.
1985-12-01
Statistic study of Poisson non-homogeneous and spatial processes is the first part of this thesis. A Neyman-Pearson type test is defined concerning the intensity measurement of these processes. Conditions are given for which consistency of the test is assured, and others giving the asymptotic normality of the test statistics. Then some techniques of statistic processing of Poisson fields and their applications to a particle multidetector study are given. Quality tests of the device are proposed togetherwith signal extraction methods [fr
Generalized master equations for non-Poisson dynamics on networks.
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.
Dependent Neyman type A processes based on common shock Poisson approach
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.
Dynamics of a prey-predator system under Poisson white noise excitation
Pan, Shan-Shan; Zhu, Wei-Qiu
2014-10-01
The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.
Multitasking domain decomposition fast Poisson solvers on the Cray Y-MP
Chan, Tony F.; Fatoohi, Rod A.
1990-01-01
The results of multitasking implementation of a domain decomposition fast Poisson solver on eight processors of the Cray Y-MP are presented. The object of this research is to study the performance of domain decomposition methods on a Cray supercomputer and to analyze the performance of different multitasking techniques using highly parallel algorithms. Two implementations of multitasking are considered: macrotasking (parallelism at the subroutine level) and microtasking (parallelism at the do-loop level). A conventional FFT-based fast Poisson solver is also multitasked. The results of different implementations are compared and analyzed. A speedup of over 7.4 on the Cray Y-MP running in a dedicated environment is achieved for all cases.
International Nuclear Information System (INIS)
Kennedy, G.
1981-01-01
The question of whether to use Poisson or Ruark-Devol statistics for radioactivity measurements in which the counting time is long compared to the half-life is discussed. Experimental data are presented which are well described by Poisson statistics. The applications of Ruark-Devol statistics are found to be very limited, in disagreement with earlier publications. (author)
Ship-Track Models Based on Poisson-Distributed Port-Departure Times
National Research Council Canada - National Science Library
Heitmeyer, Richard
2006-01-01
... of those ships, and their nominal speeds. The probability law assumes that the ship departure times are Poisson-distributed with a time-varying departure rate and that the ship speeds and ship routes are statistically independent...
A SAS-macro for estimation of the cumulative incidence using Poisson regression
DEFF Research Database (Denmark)
Waltoft, Berit Lindum
2009-01-01
the hazard rates, and the hazard rates are often estimated by the Cox regression. This procedure may not be suitable for large studies due to limited computer resources. Instead one uses Poisson regression, which approximates the Cox regression. Rosthøj et al. presented a SAS-macro for the estimation...... of the cumulative incidences based on the Cox regression. I present the functional form of the probabilities and variances when using piecewise constant hazard rates and a SAS-macro for the estimation using Poisson regression. The use of the macro is demonstrated through examples and compared to the macro presented...
Top-down fabrication of vertical silicon nano-rings based on Poisson diffraction
International Nuclear Information System (INIS)
Ai Yujie; Huang Ru; Hao Zhihua; Wang Runsheng; Liu Changze; Fan Chunhui; Wang Yangyuan
2011-01-01
Vertical Si nano-rings with a uniform thickness of about 100 nm have been fabricated by conventional optical photolithography with a low cost based on Poisson diffraction. Moreover, the roughness of the Si nano-rings can be effectively reduced by sacrificial oxidation. In order to increase the density of the nano-rings, coaxial twin Si nano-rings have been fabricated by the Poisson diffraction method combined with the spacer technique. The thickness of both the inner and outer Si nano-rings is about 60 nm, and the gap between the twin nano-rings is about 100 nm.
The effects of filament magnetization in superconducting magnets as calculated by POISSON
International Nuclear Information System (INIS)
Caspi, S.; Gilbert, W.S.; Helm, M.; Laslett, L.J.
1986-09-01
Magnetization of superconducting material can be introduced into POISSON through a field dependent permeability table (in the same way that iron characteristics are introduced). This can be done by representing measured magnetization data of the increasing and decreasing field by two independent B-γ curves (γ = 1/μ). Magnetization curves of this type were incorporated into the current regions of the program POISSON and their effect on the field coefficients observed. We have used this technique to calculate the effect of magnetization on the multipole coefficients of a SSC superconducting dipole magnet and to compare these coefficients with measured values
Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation
Directory of Open Access Journals (Sweden)
Wantao Jia
2018-02-01
Full Text Available We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method.
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 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.
Prescription-induced jump distributions in multiplicative Poisson processes.
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
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.
Appearance of eigen modes for the linearized Vlasov-Poisson equation
International Nuclear Information System (INIS)
Degond, P.
1983-01-01
In order to determine the asymptotic behaviour, when the time goes to infinity, of the solution of the linearized Vlasov-Poisson equation, we use eigen modes, associated to continuous linear functionals on a Banach space of analytic functions [fr
Nambu-Poisson reformulation of the finite dimensional dynamical systems
International Nuclear Information System (INIS)
Baleanu, D.; Makhaldiani, N.
1998-01-01
A system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system is introduced. We found in two simplest cases the complete sets of the integrals of motion using Nambu-Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures
Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks
Frahm, Klaus M.; Shepelyansky, Dima L.
2014-04-01
We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.
Determination of maximum negative Poisson's ratio for laminated fiber composites
Energy Technology Data Exchange (ETDEWEB)
Shokrieh, M.M.; Assadi, A. [Composites Research Laboratory, Mechanical Engineering Department, Center of Excellence in Experimental Solid Mechanics and Dynamics, Iran University of Science and Technology, Tehran 16846-13114 (Iran, Islamic Republic of)
2011-05-15
Contrary to isotropic materials, composites always show complicated mechanical behavior under external loadings. In this article, an efficient algorithm is employed to obtain the maximum negative Poisson's ratio for laminated composite plates. We try to simplify the problem based on normalization of parameters and some manufacturing constraints to overlook the additional constraint of the optimization procedure. A genetic algorithm is used to find the optimal thickness of each lamina with a specified fiber direction. It is observed that the laminated composite with the configuration of (15/60/15) has the maximum negative Poisson's ratio. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Feelings of hopelessness in stable HIV-positive patients on antiretrovirals
Directory of Open Access Journals (Sweden)
M Y H Moosa
2010-04-01
Full Text Available Aim. The coping skills and styles individuals utilise to deal with the stress of HIV infection greatly influence the psychological impact of this illness and potential consequent feelings of hopelessness. The aim of this study was to describe levels of hopelessness in a group of stable, non-depressed HIV-positive patients receiving antiretroviral therapy, and factors associated with hopelessness. Method. Thirty randomly selected non-depressed patients (according to Diagnostic and Statistical Manual of Mental Disorders, 4th edition (DSM-IV criteria were included in this study. Demographic and other data were obtained from all subjects, who also completed the Beck’s Hopelessness Scale (BHS. The 20 true-false items of the BHS (29 measured three major aspects of hopelessness, which was interpreted on the total scale score as follows: ≤3 minimal, and >3 significant. Results. The study population comprised 30 patients with a mean age of 37.9 years (standard error (SE 1.18 ( range 28 - 51 years. The mean BHS score was 4.03 (SE 0.55, with a range from 0 to 12. There were no statistically significant correlations between BHS scores of the study population and gender, marital status, employment status, level of education, years since the diagnosis of HIV, or number of children (p>0.05. Eighteen subjects (60% scored 3 or less on the BHS, considered minimal levels of hopelessness. However, 12 (40% scored more than 3, which is considered significant; of these 23% had scores of 7 or more. There was no statistically significant association between BHS scores and gender, employment status, level of education, number of children or number of years since diagnosis (p>0.05. However, patients who were married or living with partners were statistically more likely to score higher on the hopelessness scale compared with those who were single (p
Comparing two Poisson populations sequentially: an application
International Nuclear Information System (INIS)
Halteman, E.J.
1986-01-01
Rocky Flats Plant in Golden, Colorado monitors each of its employees for radiation exposure. Excess exposure is detected by comparing the means of two Poisson populations. A sequential probability ratio test (SPRT) is proposed as a replacement for the fixed sample normal approximation test. A uniformly most efficient SPRT exists, however logistics suggest using a truncated SPRT. The truncated SPRT is evaluated in detail and shown to possess large potential savings in average time spent by employees in the monitoring process
Poisson noise reduction from X-ray images by region classification ...
Indian Academy of Sciences (India)
Thakur Kirti
means Poisson noise filter which is one of the current state-of-the-art methods. Benefits of the proposed ... This modality is used to detect fractures in bones, tumours, cough or ..... metric peak signal to noise ratio (PSNR). It is observed from ...
A LATENT CLASS POISSON REGRESSION-MODEL FOR HETEROGENEOUS COUNT DATA
WEDEL, M; DESARBO, WS; BULT, [No Value; RAMASWAMY, [No Value
1993-01-01
In this paper an approach is developed that accommodates heterogeneity in Poisson regression models for count data. The model developed assumes that heterogeneity arises from a distribution of both the intercept and the coefficients of the explanatory variables. We assume that the mixing
Hierarchy of Poisson brackets for elements of a scattering matrix
International Nuclear Information System (INIS)
Konopelchenko, B.G.; Dubrovsky, V.G.
1984-01-01
The infinite family of Poisson brackets [Ssub(i1k1) (lambda 1 ), Ssub(i2k2) (lambda 2 )]sub(n) (n=0, 1, 2, ...) between the elements of a scattering matrix is calculated for the linear matrix spectral problem. (orig.)
International Nuclear Information System (INIS)
Ka-Lin, Su; Yuan-Xi, Xie
2010-01-01
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)
Directory of Open Access Journals (Sweden)
Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
Zero inflated Poisson and negative binomial regression models: application in education.
Salehi, Masoud; Roudbari, Masoud
2015-01-01
The number of failed courses and semesters in students are indicators of their performance. These amounts have zero inflated (ZI) distributions. Using ZI Poisson and negative binomial distributions we can model these count data to find the associated factors and estimate the parameters. This study aims at to investigate the important factors related to the educational performance of students. This cross-sectional study performed in 2008-2009 at Iran University of Medical Sciences (IUMS) with a population of almost 6000 students, 670 students selected using stratified random sampling. The educational and demographical data were collected using the University records. The study design was approved at IUMS and the students' data kept confidential. The descriptive statistics and ZI Poisson and negative binomial regressions were used to analyze the data. The data were analyzed using STATA. In the number of failed semesters, Poisson and negative binomial distributions with ZI, students' total average and quota system had the most roles. For the number of failed courses, total average, and being in undergraduate or master levels had the most effect in both models. In all models the total average have the most effect on the number of failed courses or semesters. The next important factor is quota system in failed semester and undergraduate and master levels in failed courses. Therefore, average has an important inverse effect on the numbers of failed courses and semester.
Poisson goodness-of-fit tests for radiation-induced chromosome aberrations
International Nuclear Information System (INIS)
Merkle, W.
1981-01-01
Asymptotic and exact Poisson goodness-to-fit tests have been reviewed with regard to their applicability in analysing distributional properties of data on chromosome aberrations. It has been demonstrated that for typical cytogenetic samples, i.e. when the average number of aberrations per cell is smaller than one, results of asymptotic tests, especially of the most commonly used u-test, differ greatly from results of corresponding exact tests. While the u-statistic can serve as a qualitative index to indicate a tendency towards under- or over-dispersion, exact tests should be used if the assumption of a Poisson distribution is crucial, e.g. in investigating induction mechanisms. If the main interest is to detect a difference between the mean and the variance of a sample it is furthermore important to realize that a much larger sample size is required to detect underdispersion than it is to detect overdispersion. (author)
A Poisson-Fault Model for Testing Power Transformers in Service
Directory of Open Access Journals (Sweden)
Dengfu Zhao
2014-01-01
Full Text Available This paper presents a method for assessing the instant failure rate of a power transformer under different working conditions. The method can be applied to a dataset of a power transformer under periodic inspections and maintenance. We use a Poisson-fault model to describe failures of a power transformer. When investigating a Bayes estimate of the instant failure rate under the model, we find that complexities of a classical method and a Monte Carlo simulation are unacceptable. Through establishing a new filtered estimate of Poisson process observations, we propose a quick algorithm of the Bayes estimate of the instant failure rate. The proposed algorithm is tested by simulation datasets of a power transformer. For these datasets, the proposed estimators of parameters of the model have better performance than other estimators. The simulation results reveal the suggested algorithms are quickest among three candidates.
Critical elements on fitting the Bayesian multivariate Poisson Lognormal model
Zamzuri, Zamira Hasanah binti
2015-10-01
Motivated by a problem on fitting multivariate models to traffic accident data, a detailed discussion of the Multivariate Poisson Lognormal (MPL) model is presented. This paper reveals three critical elements on fitting the MPL model: the setting of initial estimates, hyperparameters and tuning parameters. These issues have not been highlighted in the literature. Based on simulation studies conducted, we have shown that to use the Univariate Poisson Model (UPM) estimates as starting values, at least 20,000 iterations are needed to obtain reliable final estimates. We also illustrated the sensitivity of the specific hyperparameter, which if it is not given extra attention, may affect the final estimates. The last issue is regarding the tuning parameters where they depend on the acceptance rate. Finally, a heuristic algorithm to fit the MPL model is presented. This acts as a guide to ensure that the model works satisfactorily given any data set.
Steady state solution of the Poisson-Nernst-Planck equations
International Nuclear Information System (INIS)
Golovnev, A.; Trimper, S.
2010-01-01
The exact steady state solution of the Poisson-Nernst-Planck equations (PNP) is given in terms of Jacobi elliptic functions. A more tractable approximate solution is derived which can be used to compare the results with experimental observations in binary electrolytes. The breakdown of the PNP for high concentration and high applied voltage is discussed.
On terminating Poisson processes in some shock models
Energy Technology Data Exchange (ETDEWEB)
Finkelstein, Maxim, E-mail: FinkelMI@ufs.ac.z [Department of Mathematical Statistics, University of the Free State, Bloemfontein (South Africa); Max Planck Institute for Demographic Research, Rostock (Germany); Marais, Francois, E-mail: fmarais@csc.co [CSC, Cape Town (South Africa)
2010-08-15
A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.
On terminating Poisson processes in some shock models
International Nuclear Information System (INIS)
Finkelstein, Maxim; Marais, Francois
2010-01-01
A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.
Poisson noise removal with pyramidal multi-scale transforms
Woiselle, Arnaud; Starck, Jean-Luc; Fadili, Jalal M.
2013-09-01
In this paper, we introduce a method to stabilize the variance of decimated transforms using one or two variance stabilizing transforms (VST). These VSTs are applied to the 3-D Meyer wavelet pyramidal transform which is the core of the first generation 3D curvelets. This allows us to extend these 3-D curvelets to handle Poisson noise, that we apply to the denoising of a simulated cosmological volume.
Chadha, Alka; Bora, Swaroop Nandan
2017-11-01
This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.
Geometric Optics for One-Dimensional Schr(o)dinger-Poisson System
Institute of Scientific and Technical Information of China (English)
Zhifei ZHANG; Qionglei CHEN
2006-01-01
This paper considers a family of Schr(o)dinger-Poisson system in one dimension,whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals,the authors obtain a uniform description of the solution outside the caustic, and near the caustic.
Risk Sensitive Filtering with Poisson Process Observations
International Nuclear Information System (INIS)
Malcolm, W. P.; James, M. R.; Elliott, R. J.
2000-01-01
In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter
Stationary response of multi-degree-of-freedom vibro-impact systems to Poisson white noises
International Nuclear Information System (INIS)
Wu, Y.; Zhu, W.Q.
2008-01-01
The stationary response of multi-degree-of-freedom (MDOF) vibro-impact (VI) systems to random pulse trains is studied. The system is formulated as a stochastically excited and dissipated Hamiltonian system. The constraints are modeled as non-linear springs according to the Hertz contact law. The random pulse trains are modeled as Poisson white noises. The approximate stationary probability density function (PDF) for the response of MDOF dissipated Hamiltonian systems to Poisson white noises is obtained by solving the fourth-order generalized Fokker-Planck-Kolmogorov (FPK) equation using perturbation approach. As examples, two-degree-of-freedom (2DOF) VI systems under external and parametric Poisson white noise excitations, respectively, are investigated. The validity of the proposed approach is confirmed by using the results obtained from Monte Carlo simulation. It is shown that the non-Gaussian behaviour depends on the product of the mean arrival rate of the impulses and the relaxation time of the oscillator
A test for judging the presence of additional scatter in a Poisson process
International Nuclear Information System (INIS)
Mueller, J.W.
1978-01-01
The effect of additional scatter on a Poisson process is studied. Possible causes for such fluctuations are insufficient stability of the detection efficiency or of the associated electronics. It is shown with a simple model that the presence of fluctuations results in a characteristic broadening of the counting distribution. Comparison of the observed distribution with the one expected for a Poisson process with the same mean value will show three different regions, each with predictable sign of the deviation; the presence of scatter can thus be decided upon by a sign test. Experimental results are in excellent agreement with this expectation
Poisson-Spot Intensity Reduction with a Partially-Transparent Petal-Shaped Optical Mask
Shiri, Shahram; Wasylkiwskyj, Wasyl
2013-01-01
The presence of Poisson's spot, also known as the spot of Arago, formed along the optical axis in the geometrical shadow behind an obstruction, has been known since the 18th century. The presence of this spot can best be described as the consequence of constructive interference of light waves diffracted on the edge of the obstruction where its central position can··be determined by the symmetry of the object More recently, the elimination of this spot has received attention in the fields of particle physics, high-energy lasers, astronomy and lithography. In this paper, we introduce a novel, partially transparent petaled mask shape that suppresses the bright spot by up to 10 orders of magnitude in intensity, with powerful applications to many of the above fields. The optimization technique formulated in this design can identify mask shapes having partial transparency only near the petal tips.
International Nuclear Information System (INIS)
Xie Yigang; Chai Yong
1994-01-01
The charged multiplicity distributions of hadron final states in the e + e - annihilation at the 91.2 GeV Z 0 energy region are fitted with Poisson shape in different rapidity windows for double and single hemisphere. The multiplicities which are in Poisson-like shapes can be got according to the parameter /D and fitting qualities are compared with the results derived from the relevant theoretical models. The relationship between the Poisson-like shape and KNO scaling is discussed. The connection between the parameters expressing the deviation from the Poisson shape and non-independent particle emission and multiplicity correlation strength is analyzed. The 'shoulder structure' is observed in the central rapidity region and analyzed with multi-jets by using the JADE jet analysis algorithm
Simple dead-time corrections for discrete time series of non-Poisson data
International Nuclear Information System (INIS)
Larsen, Michael L; Kostinski, Alexander B
2009-01-01
The problem of dead time (instrumental insensitivity to detectable events due to electronic or mechanical reset time) is considered. Most existing algorithms to correct for event count errors due to dead time implicitly rely on Poisson counting statistics of the underlying phenomena. However, when the events to be measured are clustered in time, the Poisson statistics assumption results in underestimating both the true event count and any statistics associated with count variability; the 'busiest' part of the signal is partially missed. Using the formalism associated with the pair-correlation function, we develop first-order correction expressions for the general case of arbitrary counting statistics. The results are verified through simulation of a realistic clustering scenario
Bayesian Estimation Of Shift Point In Poisson Model Under Asymmetric Loss Functions
Directory of Open Access Journals (Sweden)
uma srivastava
2012-01-01
Full Text Available The paper deals with estimating shift point which occurs in any sequence of independent observations of Poisson model in statistical process control. This shift point occurs in the sequence when i.e. m life data are observed. The Bayes estimator on shift point 'm' and before and after shift process means are derived for symmetric and asymmetric loss functions under informative and non informative priors. The sensitivity analysis of Bayes estimators are carried out by simulation and numerical comparisons with R-programming. The results shows the effectiveness of shift in sequence of Poisson disribution .
Modeling of Electrokinetic Processes Using the Nernst-Plank-Poisson System
DEFF Research Database (Denmark)
Paz-Garcia, Juan Manuel; Johannesson, Björn; Ottosen, Lisbeth M.
2010-01-01
Electrokinetic processes are known as the mobilization of species within the pore solution of porous materials under the effect of an external electric field. A finite elements model was implemented and used for the integration of the coupled Nernst-Plank-Poisson system of equations in order...
On neutral plasma oscillations
International Nuclear Information System (INIS)
Shadwick, B.A.; Morrison, P.J.
1993-06-01
We examine the conditions for the existence of spectrally stable neutral modes in a Vlasov-Poisson plasma and show that for stable equilibria of systems that have unbounded spatial domain, the only possible neutral modes are those with phase velocities that correspond to stationary inflection points of the equilibrium distribution function. It is seen that these neutral modes can possess positive or negative free energy
On neutral plasma oscillations
International Nuclear Information System (INIS)
Shadwick, B.A.; Texas Univ., Austin; Morrison, P.J.; Texas Univ., Austin
1994-01-01
We examine the conditions for the existence of spectrally stable neutral modes in a Vlasov-Poisson plasma and show that for stable equilibria of systems that have unbounded spatial domain, the only possible neutral modes are those with phase velocities that correspond to stationary inflection points of the equilibrium distribution function. It is seen that these neutral modes can posses positive or negative free energy. (orig.)
Modifying Poisson equation for near-solute dielectric polarization and solvation free energy
Energy Technology Data Exchange (ETDEWEB)
Yang, Pei-Kun, E-mail: peikun@isu.edu.tw
2016-06-15
Highlights: • We modify the Poisson equation. • The dielectric polarization was calculated from the modified Poisson equation. • The solvation free energies of the solutes were calculated from the dielectric polarization. • The calculated solvation free energies were similar to those obtained from MD simulations. - Abstract: The dielectric polarization P is important for calculating the stability of protein conformation and the binding affinity of protein–protein/ligand interactions and for exploring the nonthermal effect of an external electric field on biomolecules. P was decomposed into the product of the electric dipole moment per molecule p; bulk solvent density N{sub bulk}; and relative solvent molecular density g. For a molecular solute, 4πr{sup 2}p(r) oscillates with the distance r to the solute, and g(r) has a large peak in the near-solute region, as observed in molecular dynamics (MD) simulations. Herein, the Poisson equation was modified for computing p based on the modified Gauss’s law of Maxwell’s equations, and the potential of the mean force was used for computing g. For one or two charged atoms in a water cluster, the solvation free energies of the solutes obtained by these equations were similar to those obtained from MD simulations.
Pricing Zero-Coupon Catastrophe Bonds Using EVT with Doubly Stochastic Poisson Arrivals
Directory of Open Access Journals (Sweden)
Zonggang Ma
2017-01-01
Full Text Available The frequency and severity of climate abnormal change displays an irregular upward cycle as global warming intensifies. Therefore, this paper employs a doubly stochastic Poisson process with Black Derman Toy (BDT intensity to describe the catastrophic characteristics. By using the Property Claim Services (PCS loss index data from 2001 to 2010 provided by the US Insurance Services Office (ISO, the empirical result reveals that the BDT arrival rate process is superior to the nonhomogeneous Poisson and lognormal intensity process due to its smaller RMSE, MAE, MRPE, and U and larger E and d. Secondly, to depict extreme features of catastrophic risks, this paper adopts the Peak Over Threshold (POT in extreme value theory (EVT to characterize the tail characteristics of catastrophic loss distribution. And then the loss distribution is analyzed and assessed using a quantile-quantile (QQ plot to visually check whether the PCS index observations meet the generalized Pareto distribution (GPD assumption. Furthermore, this paper derives a pricing formula for zero-coupon catastrophe bonds with a stochastic interest rate environment and aggregate losses generated by a compound doubly stochastic Poisson process under the forward measure. Finally, simulation results verify pricing model predictions and show how catastrophic risks and interest rate risk affect the prices of zero-coupon catastrophe bonds.
Information content of poisson images
International Nuclear Information System (INIS)
Cederlund, J.
1979-04-01
One major problem when producing images with the aid of Poisson distributed quanta is how best to compromise between spatial and contrast resolution. Increasing the number of image elements improves spatial resolution, but at the cost of fewer quanta per image element, which reduces contrast resolution. Information theory arguments are used to analyse this problem. It is argued that information capacity is a useful concept to describe an important property of the imaging device, but that in order to compute the information content of an image produced by this device some statistical properties (such as the a priori probability of the densities) of the object to be depicted must be taken into account. If these statistical properties are not known one cannot make a correct choice between spatial and contrast resolution. (author)
A one-level FETI method for the drift–diffusion-Poisson system with discontinuities at an interface
Baumgartner, Stefan
2013-06-01
A 3d feti method for the drift-diffusion-Poisson system including discontinuities at a 2d interface is developed. The motivation for this work is to provide a parallel numerical algorithm for a system of PDEs that are the basic model equations for the simulation of semiconductor devices such as transistors and sensors. Moreover, discontinuities or jumps in the potential and its normal derivative at a 2d surface are included for the simulation of nanowire sensors based on a homogenized model. Using the feti method, these jump conditions can be included with the usual numerical properties and the original Farhat-Roux feti method is extended to the drift-diffusion-Poisson equations including discontinuities. We show two numerical examples. The first example verifies the correct implementation including the discontinuities on a 2d grid divided into eight subdomains. The second example is 3d and shows the application of the algorithm to the simulation of nanowire sensors with high aspect ratios. The Poisson-Boltzmann equation and the drift-diffusion-Poisson system with jump conditions are solved on a 3d grid with real-world boundary conditions. © 2013 Elsevier Inc..
Poisson-Based Inference for Perturbation Models in Adaptive Spelling Training
Baschera, Gian-Marco; Gross, Markus
2010-01-01
We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…
Characterization and global analysis of a family of Poisson structures
International Nuclear Information System (INIS)
Hernandez-Bermejo, Benito
2006-01-01
A three-dimensional family of solutions of the Jacobi equations for Poisson systems is characterized. In spite of its general form it is possible the explicit and global determination of its main features, such as the symplectic structure and the construction of the Darboux canonical form. Examples are given
Characterization and global analysis of a family of Poisson structures
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito [Escuela Superior de Ciencias Experimentales y Tecnologia, Edificio Departamental II, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 (Mostoles), Madrid (Spain)]. E-mail: benito.hernandez@urjc.es
2006-06-26
A three-dimensional family of solutions of the Jacobi equations for Poisson systems is characterized. In spite of its general form it is possible the explicit and global determination of its main features, such as the symplectic structure and the construction of the Darboux canonical form. Examples are given.
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Konno, Hidetoshi; Tamura, Yoshiyasu
2018-01-01
In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-08-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
International Nuclear Information System (INIS)
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-01-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Energy Technology Data Exchange (ETDEWEB)
Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong; Jia, Wantao [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2016-08-15
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Ruin probabilities for a regenerative Poisson gap generated risk process
DEFF Research Database (Denmark)
Asmussen, Søren; Biard, Romain
A risk process with constant premium rate c and Poisson arrivals of claims is considered. A threshold r is deﬁned for claim interarrival times, such that if k consecutive interarrival times are larger than r, then the next claim has distribution G. Otherwise, the claim size distribution is F...
Directory of Open Access Journals (Sweden)
Min Chen
2014-01-01
Full Text Available We study the one-dimensional bipolar nonisentropic Euler-Poisson equations which can model various physical phenomena, such as the propagation of electron and hole in submicron semiconductor devices, the propagation of positive ion and negative ion in plasmas, and the biological transport of ions for channel proteins. We show the existence and large time behavior of global smooth solutions for the initial value problem, when the difference of two particles’ initial mass is nonzero, and the far field of two particles’ initial temperatures is not the ambient device temperature. This result improves that of Y.-P. Li, for the case that the difference of two particles’ initial mass is zero, and the far field of the initial temperature is the ambient device temperature.
Numerically stable fluid–structure interactions between compressible flow and solid structures
Grétarsson, Jón Tómas
2011-04-01
We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tn+1 using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluid-structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of [16]. Because our method handles the fluid-structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid-structure interactions are not considered) at the fluid-structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions. © 2011 Elsevier Inc.
Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
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Lothar Schlafer
2008-05-01
Full Text Available C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.
Cellular solutions for the Poisson equation in extended systems
International Nuclear Information System (INIS)
Zhang, X.; Butler, W.H.; MacLaren, J.M.; van Ek, J.
1994-01-01
The Poisson equation for the electrostatic potential in a solid is solved using three different cellular techniques. The relative merits of these different approaches are discussed for two test charge densities for which an analytic solution to the Poisson equation is known. The first approach uses full-cell multiple-scattering theory and results in the famililar structure constant and multipole moment expansion. This solution is shown to be valid everywhere inside the cell, although for points outside the muffin-tin sphere but inside the cell the sums must be performed in the correct order to yield meaningful results. A modification of the multiple-scattering-theory approach yields a second method, a Green-function cellular method, which only requires the solution of a nearest-neighbor linear system of equations. A third approach, a related variational cellular method, is also derived. The variational cellular approach is shown to be the most accurate and reliable, and to have the best convergence in angular momentum of the three methods. Coulomb energies accurate to within 10 -6 hartree are easily achieved with the variational cellular approach, demonstrating the practicality of the approach in electronic structure calculations
Directory of Open Access Journals (Sweden)
Chi Zhang
2015-05-01
Full Text Available To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP distributions by incorporating a multiplicative factor (or dependency parameter λ, named as Type I and Type II bivariate ZIGP distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over- or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.
Pal, Suvra; Balakrishnan, N
2017-10-01
In this paper, we consider a competing cause scenario and assume the number of competing causes to follow a Conway-Maxwell Poisson distribution which can capture both over and under dispersion that is usually encountered in discrete data. Assuming the population of interest having a component cure and the form of the data to be interval censored, as opposed to the usually considered right-censored data, the main contribution is in developing the steps of the expectation maximization algorithm for the determination of the maximum likelihood estimates of the model parameters of the flexible Conway-Maxwell Poisson cure rate model with Weibull lifetimes. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination within the Conway-Maxwell Poisson distribution is addressed using the likelihood ratio test and information-based criteria to select a suitable competing cause distribution that provides the best fit to the data. A simulation study is also carried out to demonstrate the loss in efficiency when selecting an improper competing cause distribution which justifies the use of a flexible family of distributions for the number of competing causes. Finally, the proposed methodology and the flexibility of the Conway-Maxwell Poisson distribution are illustrated with two known data sets from the literature: smoking cessation data and breast cosmesis data.
Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries
Morales Escalante, José A.; Gamba, Irene M.
2018-06-01
We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann-Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k →). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.
Poisson simulation for high voltage terminal of test stand for 1MV electrostatic accelerator
Energy Technology Data Exchange (ETDEWEB)
Park, Sae-Hoon; Kim, Jeong-Tae; Kwon, Hyeok-Jung; Cho, Yong-Sub [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Kim, Yu-Seok [Dongguk Univ.., Gyeongju (Korea, Republic of)
2014-10-15
KOMAC provide ion beam to user which energy range need to expand to MeV range and develop 1 MV electrostatic accelerator. The specifications of the electrostatic accelerator are 1MV acceleration voltage, 10 mA peak current and variable gas ion. We are developing test stand before set up 1 MV electrostatic accelerator. The test stand voltage is 300 kV and operating time is 8 hours. The test stand is consist of 300 kV high voltage terminal, DC-AC-DC inverter, power supply device inside terminal, 200MHz RF power, 5 kV extraction power supply, 300 kV accelerating tube and vacuum system.. The beam measurement system and beam dump will be installed next to accelerating tube. Poisson code simulation results of the high voltage terminal are presented in this paper. Poisson code has been used to calculate the electric field for high voltage terminal. The results of simulation were verified with reasonable results. The poisson code structure could be apply to the high voltage terminal of the test stand.
Poisson simulation for high voltage terminal of test stand for 1MV electrostatic accelerator
International Nuclear Information System (INIS)
Park, Sae-Hoon; Kim, Jeong-Tae; Kwon, Hyeok-Jung; Cho, Yong-Sub; Kim, Yu-Seok
2014-01-01
KOMAC provide ion beam to user which energy range need to expand to MeV range and develop 1 MV electrostatic accelerator. The specifications of the electrostatic accelerator are 1MV acceleration voltage, 10 mA peak current and variable gas ion. We are developing test stand before set up 1 MV electrostatic accelerator. The test stand voltage is 300 kV and operating time is 8 hours. The test stand is consist of 300 kV high voltage terminal, DC-AC-DC inverter, power supply device inside terminal, 200MHz RF power, 5 kV extraction power supply, 300 kV accelerating tube and vacuum system.. The beam measurement system and beam dump will be installed next to accelerating tube. Poisson code simulation results of the high voltage terminal are presented in this paper. Poisson code has been used to calculate the electric field for high voltage terminal. The results of simulation were verified with reasonable results. The poisson code structure could be apply to the high voltage terminal of the test stand