Recursive partition and amalgamation with the exponential family: Theory and applications

The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.     

On a poisson reduction for Gel'fand-Zakharevich manifolds

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

稀疏过程在破产问题中的应用

本讨论一类人寿保险的风险过程，其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏．对此模型给出其破产概率的具体上界，并与其它一类风险模型进行比较．     

Saturated Commutative Spaces of Heisenberg Type

In this paper, we give a partial classification of commutative spaces of Heisenberg type. Several classification results were known previously. In order to avoid complicated technical details, we restrict ourselves to saturated commutative spaces. Our results are presented in Table II.     

完备可分度量群上的齐次Levy过程的复合Poisson逼近

该文利用算子半群的方法给出了取值于具有左不变度量的完备可分群的齐次Levy过程是复合Poisson过程的弱极限这一结论．     

Local existence for the one‐dimensional Vlasov–Poisson system with infinite mass

A collisionless plasma is modelled by the Vlasov–Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as ∣x∣ → ∞. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behaviour are shown to exist locally in time, and criteria for the continuation of these solutions are established. Copyright © 2006 John Wiley & Sons, Ltd.     

Quantum Dot and Antidot Infrared Photodetectors: Iterative Methods for Solving the Laplace Equation in Domains with Involved Geometry

We propose iteration methods for solving the Dirichlet problem in domains with involved geometry. Such problems arise in relation to the problem of optimizing quantum dot and antidot infrared detectors. We estimate the deviation of an approximate solution from the exact solution.