Modelling heterogeneous space–time occurrences of earthquakes and its residual analysis

Summary. Earthquake intensities are modelled as a function of previous activity whose specific form is based on established empirical laws in seismology, but whose parameter values can vary from place to place. This model is used for characterizing regional features of seismic activities in and around Japan, and also for exploring regions where the actual seismicity rate systematically deviates from that of the modelled rate.     

Monte carlo estimates of the distributions of the random polygons of the voronoi tessellation with respect to a poisson process

A large-scale study, in which two million random Voronoi polygons (with respect to a homogeneous Poisson point process) were generated and mensurated, is described. The polygon characteristics recorded are number of sides (or vertices), perimeter, area and interior angles. A feature is the efficient “quantile” method of replicating Poisson-type random structures, which it is hoped may find useful application elsewhere.     

鄱阳县农村居民点空间分布特征及影响因素分析

以鄱阳县第二次土地利用现状调查成果数据为基础,借助GIS为工具,计算Voronoi图面积变异系数与最邻近点指数,结合GIS查询工具、缓冲分区、SQL统计等功能论证鄱阳县农村居民点在空间上的分布特征的同时,定量的研究地形、公路交通、河流等因素对农村居民点空间分布的影响。研究的结果表明:平原地区农村居民点分布数量较大,分布相对集中。交通因素对农村居民点分布有重要的作用,随着距公路距离越远,居民点分布逐渐减少。河流对农村居民点分布也有一定程度的影响作用,当地鄱阳湖湖泊水面特殊情况,制约湖泊周边居民点的空间分布情况。     

Modeling of Acoustic Signal Energies with a Generalized Frank Copula. A Linguistic Conjecture is Reviewed

In this article a generalized Frank copula was selected to model the dependence between the energy on two frequency bands of the speech signal, coming from eight languages. An algorithm was developed that uses maximum likelihood to choose the best fitting copula’s parameters. Through bootstrap, the algorithm estimates the variability of the parameters for each language and also computes confidence regions by means of Voronoi tesselations. A linguistic conjecture which claims that the languages are organized in three rhythmic classes, was confirmed by the Voronoi regions. Modeling with a uniparametric Frank copula, the different degrees of dependence between the energies were quantified.     

Practical Maximum Pseudolikelihood for Spatial Point Patterns(with Discussion)

This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner's (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class of spatial point process models the likelihood is intractable, while the pseudolikelihood is known explicitly, except for the computation of an integral over the sampling region. Approximation of this integral by a finite sum in a special way yields an approximate pseudolikelihood which is formally equivalent to the (weighted) likelihood of a loglinear model with Poisson responses. This can be maximized using standard statistical software for generalized linear or additive models, provided the conditional intensity of the process takes an 'exponential family' form. Using this approach a wide variety of spatial point process models of Gibbs type can be fitted rapidly, incorporating spatial trends, interaction between points, dependence on spatial covariates, and mark information.     

Clustering via nonparametric density estimation

Although Hartigan (1975) had already put forward the idea of connecting identification of subpopulations with regions with high density of the underlying probability distribution, the actual development of methods for cluster analysis has largely shifted towards other directions, for computational convenience. Current computational resources allow us to reconsider this formulation and to develop clustering techniques directly in order to identify local modes of the density. Given a set of observations, a nonparametric estimate of the underlying density function is constructed, and subsets of points with high density are formed through suitable manipulation of the associated Delaunay triangulation. The method is illustrated with some numerical examples.     

Calculating the proportion of triangles in a poisson – voronoi tessellation of the plane

The proportion of triangles in a Poisson – Voronoi tessellation has been recently represented as a five-fold integral. Here we give a simpler representation, reduce it to a fourfold integral and discuss its numerical evaluation.     

横向并购初期固位策略销售服务网络结构优化

本文着眼于当今世界企业经营领域的前沿,对企业横向购并初期的销售服务网络的集成优化进行了深入研究,本文基于固定位置策略建立了优化模型,给出了模型的求解算法与计算复杂性。同时,本文以合并后5个销售服务中心30个客户为背景,给出了算法的仿真计算结果。     

Modelling spatial intensity for replicated inhomogeneous point patterns in brain imaging

Summary.  Pharmacological experiments in brain microscopy study patterns of cellular activ- ation in response to psychotropic drugs for connected neuroanatomic regions. A typical ex- perimental design produces replicated point patterns having highly complex spatial variability. Modelling this variability hierarchically can enhance the inference for comparing treatments. We propose a semiparametric formulation that combines the robustness of a nonparametric kernel method with the efficiency of likelihood-based parameter estimation. In the convenient framework of a generalized linear mixed model, we decompose pattern variation by kriging the intensities of a hierarchically heterogeneous spatial point process. This approximation entails discretizing the inhomogeneous Poisson likelihood by Voronoi tiling of augmented point patterns. The resulting intensity-weighted log-linear model accommodates spatial smoothing through a reduced rank penalized linear spline. To correct for anatomic distortion between subjects, we interpolate point locations via an isomorphic mapping so that smoothing occurs relative to common neuroanatomical atlas co-ordinates. We propose a criterion for choosing the degree and spatial locale of smoothing based on truncating the ordered set of smoothing covariates to minimize residual extra-dispersion. Additional spatial covariates, experimental design factors, hierarchical random effects and intensity functions are readily accommodated in the linear predictor, enabling comprehensive analyses of the salient properties underlying replicated point patterns. We illustrate our method through application to data from a novel study of drug effects on neuronal activation patterns in the brain of rats.     

Fitting three-dimensional Laguerre tessellations to foam structures

Foam models, especially random tessellations, are powerful tools to study the relations between the geometric structure of foams and their physical properties. In this paper, we propose the use of random Laguerre tessellations, weighted versions of the well-known Voronoi tessellations, as models for the microstructure of foams. Based on geometric characteristics estimated from a tomographic image of a closed-cell polymer foam, we fit a Laguerre tessellation model to the material. It is shown that this model allows for a better fit of the geometric structure of the foam than some classical Voronoi tessellation models.