Many interesting C∗-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C∗-algebra of a symplectic groupoid. Toward this end, I define polarizations for Lie groupoids and sketch the construction of this algebra. A large number of examples show that this idea unifies previous geometric constructions, ...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

and key words Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem : how an optical field is converted into a sequence of photoelectrons upon detection . Their choice of problem could not have been better, nor thei r timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when qua...

In this paper we consider the Poisson algebraic structure associated with a classical r-matrix, i.e. with a solution of the modified classical Yang–Baxter equation. In Section 1 we recall the concept and basic facts of the r-matrix type Poisson orbits. Then we describe the r-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or CPn-type orbits of SL(n,C). Here we ca...

Let Y be an affine symplectic variety of dimension 2n, and let π : X → Y be a crepant resolution. By the definition, there is a symplectic 2-form σ̄ on the smooth part Yreg ∼= π (Yreg), and it extends to a 2-form σ on X. Since π is crepant, σ is a symplectic 2-form on X. The symplectic structures on X and Y define Poisson structures on them in a natural manner. One can define a Poisson deformati...

BACKGROUND AND OBJECTIVES 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. METHODS The data was collected from a longitudinal study during 2005-20...

In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and C∗-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid which deals with a big enough class of functions to include the above mentioned example. As an ...

In this article we study the properties of the hyperinterpolation operator on the unit disk D in R. We show how the hyperinterpolation can be used in connection with the Kumar-Sloan method to approximate the solution of a nonlinear Poisson equation on the unit disk (discrete Galerkin method). A bound for the norm of the hyperinterpolation operator in the space C(D) is derived. Our results prove...

• Count data are often modeled using a Poisson model. • If y ∼ Poisson(μ) then E(y) = var(y) = μ. • When counts are assumed exchangeable given μ and the rates μ can also be assumed to be exchangeable, a Gamma population model for the rates is often chosen. • The hierarchical model is then yi ∼ Poisson(μi) μi ∼ Gamma(α, β). • Priors for the hyperparameters are often taken to be Gamma (or exponen...