5,107 research outputs found
Poisson algebras via model theory and differential-algebraic geometry
No full textBrown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry and model theory. In particular, it is shown that while the sets of Poisson rational and Poisson primitive ideals do coincide, in every Krull dimension at least four there are complex affine Poisson algebras with Poisson rational ideals that are not Poisson locally closed. These counterexamples also give rise to counterexamples to the classical (noncommutative) Dixmier–Moeglin equivalence in finite GK dimension. A weaker version of the Poisson Dixmier–Moeglin equivalence is proven for all complex affine Poisson algebras, from which it follows that the full equivalence holds in Krull dimension three or less. Finally, it is shown that everything, except possibly that rationality implies primitivity, can be done over an arbitrary base field of characteristic zero
Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
No full textWe study random spatial permutations on ℤ3 where each jump x↦π(x) is penalized by a factor e−T∥x−π(x)∥2 . The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the lengths of such cycles are distributed according to Poisson-Dirichlet. This can be explained heuristically using a stochastic coagulation-fragmentation process for long cycles, which is supported by numerical data
Using Computational and Mathematical Methods to Explore a New Distribution: The ν-Poisson
No full textA new distribution (the v-Poisson) and its conjugate density are introduced and explored using computational and mathematical methods. The v-Poisson is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli, Geometric). It also leads to the generalization of distributions derived from these discrete distributions (viz. the Binomial and Negative Binomial). We use mathematics as far as we can and then employ computational and graphical methods to explore the distribution and its conjugate density further. Three methods are presented for estimating the v-Poisson parameters: The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method of maximum likelihood can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the v-Poisson parameters is easily computed. We derive the necessary and sufficient condition for the conjugate family to be proper. The v-Poisson is a flexible distribution that can account for over/under dispersion commonly encountered in count data. We also explore an empirical application demonstrating this flexibility of the v-Poisson to fit count data which does not seem to follow the Poisson distribution.</p
Franç. dard, nom de poisson
No full textThomas Antoine. Franç. dard, nom de poisson. In: Romania, tome 36 n°141, 1907. pp. 91-96
Consistent estimation of zero-inflated count models
No full textApplications of zero-inflated count data models have proliferated in health economics. However, zero-inflated Poisson or zero-inflated negative binomial maximum likelihood estimators are not robust to misspecification. This paper proposes Poisson quasi-likelihood estimators as an alternative. These estimators are consistent in the presence of excess zeros without having to specify the full distribution. The advantages of the Poisson quasi-likelihood approach are illustrated in a series of Monte Carlo simulations and in an application to the demand for health services.Excess zeros, Poisson, logit, unobserved heterogeneity, misspecification
On the Equivalence of Location Choice Models: Conditional Logit, Nested Logit and Poisson
No full textIt is well understood that the two most popular empirical models of location choice - conditional logit and Poisson - return identical coefficient estimates when the regressors are not individual specific. We show that these two models differ starkly in terms of their implied predictions. The conditional logit model represents a zero-sum world, in which one region's gain is the other regions' loss. In contrast, the Poisson model implies a positive-sum economy, in which one region's gain is no other region's loss. We also show that all intermediate cases can be represented as a nested logit model with a single outside option. The nested logit turns out to be a linear combination of the conditional logit and Poisson models. Conditional logit and Poisson elasticities mark the polar cases and can therefore serve as boundary values in applied research.firm location, residential choice, conditional logit, nested logit, Poisson count model
Poisson–Lie sigma models on Drinfel’d double
No full textsummary:Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle.
The elegant form of equations of motion for so called Poisson-Lie groups is derived.
Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using the adjoint representation of Lie group and Drinfel’d double we show that Poisson-Lie group can be constructed for general Lie bialgebra
Normal deviation and Poisson approximation of a security market by the geometric Markov renewal processes
No full textWe consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. European call option pricing formulas for GMRP are presented. [ABSTRACT FROM AUTHOR
Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps
No full textThe multiple disorder problem consists of finding a sequence of stopping times which are as close as possible to the (unknown) times of "disorder" when the distribution of an observed process changes its probability characteristics. We present a formulation and solution of the multiple disorder problem for a Wiener and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial optimal switching problems to the corresponding coupled optimal stopping problems and solving the equivalent coupled free-boundary problems by means of the smooth- and continuous-fit conditions.Multiple disorder problem, Wiener process, compound Poisson process, optimal switching, coupled optimal stopping problem, (integro-differential) coupled free-boundary problem, smooth and continuous fit, Ito-Tanaka-Meyer formula.
Bending Poisson Effect in Two-Dimensional Crystals
No full textAs the Poisson effect formulates, lateral strains in a material can be caused by a uniaxial stress in the perpendicular direction, but no net lateral strain should be induced in a thin homogeneous elastic plate subjected to a pure bending load. Here, we demonstrated by ab initio simulations that significant exotic lateral strains can be induced by pure bending in two-dimensional crystals, in which the lateral components of chemical bonds can respond to bending curvature directly. The bending Poisson ratio, defined as the ratio of lateral strain to the curvature, is a function of curvature depending on chemical constitution, bonding structure, and atomic interaction of the crystal, and is anisotropic
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