Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Starting from the question: What is the accident risk of an insured individual?, we consider that the customer has contracted policies in different insurance lines: motor and home. Three models based on the multivariate Sarmanov distribution are analyzed. Driven by a real data set that takes into account three types of accident risks, two for motor and one for home, three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals are considered and fitted to the data. To estimate the parameters of these three models, we discuss a method for approaching the maximum likelihood (ML) estimators. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM and with elliptical copula based models.     

理解和应用疏水相互作用的尺度依赖原理

Lum,Chandler 和Week 三人建立起来的尺度依赖的疏水相互作用理论为人们提供了一个 重要的理论框架（LCW 理论）去理解和进一步研究与疏水相互作用相关的现象。按照LCW 理 论,当一个疏水粒子的半径小于1 纳米,它的疏水水合自由能与其半径的三次方成线性关系;而当 一个疏水粒子的半径大于1 纳米,它的疏水水合自由能与其半径的二次方成线性关系。1 纳米是一 个较为普适的转变半径。小于这个尺度,水合的热力学过程是由熵主导的,大于这个尺度,水合的 热力学过程是由焓主导的。在这篇综述里,我们介绍了温度,压强和水里面的添加物对疏水水合自 由能的影响。在实验上,我们对基于原子力显微镜的单分子力谱方法研究疏水高分子水合能作了重 点介绍。同时,对这一理论在蛋白质折叠和膜组装等体系中的应用也做了介绍。     

Tail asymptotics for the sum of two heavy-tailed dependent risks

Let X ₁ , X ₂ denote positive heavy-tailed random variables with continuous marginal distribution functions F ₁ and F ₂, respectively. The asymptotic behavior of the tail of X ₁ +X ₂ is studied in a general copula framework and some bounds and extremal properties are provided. For more specific assumptions on F ₁ , F ₂ and the underlying dependence structure of X ₁ and X ₂, we survey explicit asymptotic results available in the literature and add several new cases.Supported by the Austrian Science Fund Project P-18392.     

Dependence on parameters for a discrete Emden-Fowler equation

We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden-Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigating the dependence on parameters of discrete boundary value problems.     

Open problems and conjectures

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

High-speed optical digital transmitter/receiver module operating at 1.3 μm wavelength

Taking benefit of optical fibers' wide bandwidth and low attenuation, research and development were conducted in order to apply fiber optics to public telecommunications' networks mainly for long-distance and large-capacity transmissions. However, application of fiber has rapidly spread toward cornrnunication networks having relatively short transmission distances (within several kilometers) such as local area networks (LAN) and computer networks. Thus, requirements for the fiber optic transmitters and receivers used as electro-optic transducers, such as small-size, low-price, high-reliability and low-supply voltage operations, become stricter than those of the public telecommunication network.     

Generating random correlation matrices based on vines and extended onion method

We extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.G. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276–294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, Journal of Multivariate Analysis 97 (2006) 2177–2189] based on partial correlations. The latter is based on the so-called D-vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions.