A Combined Cluster and Interaction Model: The Hierarchical Assignment Problem

This article presents a new spatial modeling approach that deals with interactions between individual geographic entities. The developed model represents a generalization of the transportation problem and the classical assignment problem and is termed the hierarchical assignment problem (HAP). The HAP optimizes the spatial flow pattern between individual origin and destination locations, given that some grouping, or aggregation of individual origins and destinations is permitted to occur. The level of aggregation is user specified, and the aggregation step is endogenous to the model itself. This allows for the direct accounting of aggregation costs in pursuit of optimal problem solutions. The HAP is formulated and solved with several sample data sets using commercial optimization software. Trials illustrate how HAP solutions respond to changes in levels of aggregation, as well as reveal the diverse network designs and allocation schemes obtainable with the HAP. Connections between the HAP and the literature on the p-median problem, cluster analysis, and hub-and-spoke networks are discussed and suggestions for future research are made.     

Bivariate Correlation with Spatial Data

The paper examines the use of the Pearson product moment correlation coefficient and the Spearman rank correlation coefficient on map data that are spatially correlated. Research has shown that in this case standard estimators underestimate the true sampling variance of the Pearson coefficient. The Clifford and Richardson “effective sample size” solution to this problem is described, methods for implementing the procedure are considered, and properties of the technique examined. The method is also used to adjust the Spearman test. Two applications are given and the method of Clifford and Richardson contrasted with the method of data “prewhitening.”     

The Modifiable Areal Unit Problem,in a Regression Model Whose Independent Variable Is a Distance from a Predetermined Point

This paper deals with the modifiable areal unit problem in the context of a regression model where a dependent variable is an attribute value (say, income) of an atomic data unit (say, a household) and an independent variable is a distance from a predetermined point (say, a central business district) to the atomic data unit (a disaggregated model). We apply this disaggregated model to spatially aggregated data in which the dependent variable is the average income over a spatial unit and the independent variable is the average distance from each household in a spatial unit to the predetermined point (an aggregated model). First, estimating the slope coefficient by the least squares method, we prove that the variance of the estimator for the slope coefficient in the aggregated model is larger than that in the disaggregated model. Second, focusing on variations in the variance of the estimator for the slope coefficient in the aggregated model with respect to the number of zones, we obtain the number of zones in which the variance is close to that in the disaggregated model. Third, we obtain the zoning system that has the minimum variance for a fixed number of zones. We also calculate the maximum variance in order to examine the range of the variance.     

Aggregation and Ecological Effects in Geographically Based Data

Statistics calculated using the means of geographic areas can differ substantially from the corresponding statistics based on data from individuals. Analysts who base their conclusions about individual-level relationships on area-level analyses run the risk of committing the ecological fallacy. Statistical models are proposed that capture the essential features of the structure of a population composed of geographically defined groups and can encompass grouping processes and contextual effects. These models are used to show how small effects in the analysis of individual-level data can be magnified substantially when the corresponding analysis based on aggregated data is carried out. Thus the source of aggregation effects is exposed. While aggregation effects have been studied by many authors, no general approach has been offered to the problem of adjusting an area-level analysis so as to correct for aggregation effects and hence remove, or at least reduce, the bias that leads to the ecological fallacy. The statistical models proposed are used to provide an approach to this problem. Data from the 1991 U.K. Census of Housing and Population are used to illustrate the size of the aggregation effects and the extent to which the proposed adjustments succeed in their objective.     

经济转型期陕北公路交通与经济发展的关联分析

结合陕北公路交通与经济发展的实际,应用1998-2007年度的数据,运用主成分析、相关性、回归模型、弹性分析等方法,对经济转型期陕北公路交通与经济发展效率进行了综合分析评价。结果发现,陕北公路交通与经济发展之间相关度较高,两者之间的最优回归方程可表示为Logistic曲线函数,交通发展指数对经济发展指数的平均弹性系数大体在0.42-0.58之间波动。在综合经济发展过程中,原来较为落后地区的公路交通基础设施与经济发展会逐步趋向协调;公路交通基础设施的改善是经济发展不可缺少的条件之一,但其边际效益会逐渐减小。最后,建议在当前阶段,为实现陕北经济的顺利转型和健康发展,应建设形成多种运输方式协调发展的综合交通运输体系。     

Determination of the turbulent spectrum in the ionosphere by a tomographic method

A theory of tomographic reconstruction of the statistical properties of the random turbulent ionospheric plasma is presented. Derived integral equations for the coherence functions of the measured fields allow the determination of inhomogeneous layer coordinates and the reconstruction of cross-sections of the electron density correlation functions. For statistically homogeneous layers and a transmitter on board a moving satellite with a linear receiving array on the ground, we have the possibility of determining the three-dimensional correlation function structure or its spectrum using a set of two-dimensional cross-sections. One receiver allows the reconstruction of the spectrum of the two-dimensional cross-section of the correlation function. We also consider the solution of the inverse problem for non-homogeneous fluctuations. In this case the distribution of the electron density fluctuations, its variance and the correlation coefficient, characterizing the spatial structure of fluctuations may be reconstructed by a tomographic technique. Experimental results on the identification of the layer height of the irregularities and on the spectrum of the two-dimensional cross-sections of the correlation function measurements are presented.     

基于空间自相关和时空扫描统计量的聚集比较分析

聚集是区域经济研究中的重点问题之一,而聚集定位问题又是深入分析聚集需要解决的首要问题。由于聚集具有高度的尺度敏感性,采用空间自相关方法分析时,尺度选择容易受研究者主观判断的影响,而且空间自相关方法也未考虑聚集的时间特征。与之相比,Kulldorff等学者提出的扫描统计量方法表现出了明显的优势。研究探索性地选用浙江省各市、县工业从业人口的聚集问题,从尺度选择、尺度转换和时空融合三个方面,比较了空间自相关和时空扫描统计量方法在探测聚集问题上的差异性,进而证实了时空扫描统计量方法不仅有效解决了人为选择尺度的偏倚问题,实现了尺度推绎、转换的自动化,而且更加有利地融合了立体、动态、多尺度的时空分析优势。     

云冈石窟顶部土层水盐分布特征研究

可溶盐是石质文物风化的重要原因,其聚集、运移与水密不可分。石窟顶部土层中的盐是云冈石质文物内部盐分的重要来源,因而研究石窟顶部土层中的水盐分布特征对未来减小可溶盐在石质文物内部的聚集具有十分重要的意义。本研究对云冈石窟顶部不同位置、不同深度土层的饱和渗透系数、含水率、孔隙比、可溶盐含量进行了系统的分析测试,并结合取土位置的坡度和植被覆盖率,研究了云冈石窟顶部土层中水盐分布特征。结果表明:植被覆盖率越高,土体含水量越高;坡度越大,土体含水率越低;土体孔隙比与饱和渗透系数呈线性关系。植被覆盖率、坡度及土体的渗透性能是影响石窟顶部土层水盐分布的主要原因。     

Spatial Entropy

A major problem in information theory concerns the derivation of a continuous measure of entropy from the discrete measure. Many analysts have shown that Shannon's treatment of this problem is incomplete, but few have gone on to rework his analysis. In this paper, it is suggested that a new measure of discrete entropy which incorporates interval size explicitly is required; such a measure is fundamental to geography and this statistic has been called spatial entropy. The use of the measure is first illustrated by application to one-and two-dimensional aggregation problems, and then the implications of this statistic for Wilson's entropy-maximizing method are traced. Theil's aggregation statistic is reinterpreted in spatial terms, and finally, some heuristics are suggested for the design of real and idealized spatial systems in which entropy is at a maximum.     

Analysis of Errors Due to Demand Data Aggregation in the Set Covering and Maximal Covering Location Problems

In this paper, we extend the concepts of demand data aggregation error to location problems involving coverage. These errors, which arise from losses in locational information, may lead to suboptimal location patterns. They are potentially more significant in covering problems than in p-median problems because the distance metric is binary in covering problems. We examine the Hillsman and Rhoda (1978) Source A, B, and C errors, identify their coverage counterparts, and relate them to the cost and optimality errors that may result. Three rules are then presented which, when applied during data aggregation, will reduce these errors. The third rule will, in fact, eliminate all loss of locational information, but may also limit the amount of aggregation possible. Results of computational tests on a large-scale problem are presented to demonstrate the performance of rule 3.     

Elimination of Source A and B Errors in p-Median Location Problems

The p-median problem is a powerful tool in analyzing facility location options when the goal of the location scheme is to minimize the average distance that demand must traverse to reach its nearest facility. It may be used to determine the number of facilities to site, as well as the actual facility locations. Demand data are frequently aggregated in p-median location problems to reduce the computational complexity of the problem. Demand data aggregation, however, results in the loss of locational information. This loss may lead to suboptimal facility location configurations (optimality errors) and inaccurate measures of the resulting travel distances (cost errors). Hillsman and Rhoda (1978) have identified three error components: Source A, B, and C errors, which may result from demand data aggregation. In this article, a method to measure weighted travel distances in p-median problems which eliminates Source A and B errors is proposed. Test problem results indicate that the proposed measurement scheme yields solutions with lower optimality and cost errors than does the traditional distance measurement scheme.     

甘肃城镇体系地域空间结构研究

在分析甘肃城镇体系地域空间结构现状的基础上,运用分形理论和方法对甘肃城镇体系地域空间结构的聚集维数、网格维数和关联维数进行了测算和分析,表明甘肃城镇体系的空间分布是分形的,以14个主要城市为研究对象,甘肃省城市体系在空间分布上比较集中;以甘肃省内75个城镇为研究对象,城镇分布的总体均衡性适中;以中部城镇密集地区为研究对象,城镇体系在空间上分布比较均匀。并据此提出了甘肃城镇体系地域空间结构合理化的建议。     

COMPLEX MODE SUPERPOSITION ALGORITHM FOR SEISMIC RESPONSES OF NON-CLASSICALLY DAMPED LINEAR MDOF SYSTEM

This paper deals with a complex mode superposition method for the seismic responses of general multiple degrees of freedom (MDOF) discrete system with complex eigenvectors and eigenvalues. A delicate general solution, completely in real value form, for calculat-ing seismic time history response of the MDOF system which cannot be uncoupled by normal modes, is deduced based on the algorithms of the complex superposition method. This solution comprises of two parts which are in relation to the Duhamel integration to sine and cosine function respectively. The related term of the Duhamel integration to sine function is actually the displacement response of the oscillator with corresponding modal frequency and the damping ratio. The other can be transferred into a combina-tion of the displacement and velocity responses of the same oscillator. In order to meet the practical needs of seismic design based on code design spectra for various kinds of structures equipped by viscous dampers, the complex complete quadratic combination (CCQC) method is deduced following similar procedures such as the well-known CQC method, in which a new modal velocity correlation coefficient, together with a new modal displacement-velocity correlation coefficient are involved besides the modal displacement correlation coefficient in normal CQC formula. The new algorithm of CCQC is not only as concise as that of the normal CQC but also has explicit physical meaning. The results obtained from complex mode superposition approaches are discussed and verified in some examples through step by step integration computation under a prescribed earth-quake motion input. From these examplary analyses, it may be pointed that the CCQC algorithm normally yields conservative outcome and that the forced mode uncoupling approach has good approximation even the discussed examplary structures are strongly non-proportional.     

A Synthesis of Aggregation Methods for Multifacility Location Problems: Strategies for Containing Error

When solving a location problem using aggregated units to represent demand, it is well known that the process of aggregation introduces error. Research has focussed on individual components of error, with little work on identifying and controlling total error. We provide a focussed review of some of this literature and suggest a strategy for controlling total error. Consideration of alternative criteria for evaluating aggregation schemes shows that the method selected should be compatible with the objectives of the analyses in which it is used. Experiments are described that show that two different measures of error are related in a nonlinear way to the number of aggregate demand points (q), for any value of the number of facilities (p). We focus on the parameter q/p and show that it is critical for determining the expected severity of the error. Many practical implementations of location algorithms operate within the range of q/p where the rate of change of error with respect to q/p is highest.     

Aggregation Decomposition and Aggregation Guidelines for a Class of Minimax and Covering Location Models

Facility location problems often involve movement between facilities to be located and customers/demand points, with distances between the two being important. For problems with many customers, demand point aggregation may be needed to obtain a computationally tractable model. Aggregation causes error, which should be kept small. We consider a class of minimax location models for which the aggregation may be viewed as a second‐order location problem, and use error bounds as aggregation error measures. We provide easily computed approximate “square root” formulas to assist in the aggregation process. The formulas establish that the law of diminishing returns applies when doing aggregation. Our approach can also facilitate aggregation decomposition for location problems involving multiple “separate” communities.     

Theoretical Underpinnings of the Gravity Hypothesis

Various theoretical rationalizations of the gravity hypothesis for spatial interaction are examined. Deterministic utility theory cannot account for variability in individual behavior. Choice models based on Luce's axiom contain some inconsistencies. Random utility theory provides a probabilistic formulation that is internally consistent, and also solves the aggregation problem. However, investigation reveals that, although this provides a theoretical justification for gravity-like behavior, the assumptions made are sufficiently unrealistic to cast doubt on the empirical validity of the gravity hypothesis.     

快速城镇化背景下乡村聚落分形特征及影响因素研究——以广东省茂名市为例

本文基于分形理论,借助聚集维数、空间关联维数及形态维数,对茂名县域、市域及镇域乡村聚落分形特征进行研究,并从自然地理、人口、设施建设和经济发展方面构建指标体系,运用Pearson相关性分析法,探讨分形影响因素.研究表明:①乡村聚落呈多尺度、多分形特征.聚集性从市域到镇域呈从地理导向到行政导向的趋势,高城镇化水平地区聚集...     

Some Thoughts on the Origin,Development and Retreat of Slopes

A senior Moscow University geomorphologist suggests that the limited Russian literature on slope development interprets “slope processes” too narrowly, restricting the term largely to mass wasting. Moreover, the convex-concave slope profile is viewed as the mature type under all climatic conditions. Such an approach tends to ignore the common phenomenon of slope retreat, which is presented as a more significant factor in slope development than the processes taking place on the slope itself. Several examples of slope retreat over long distances are given, suggesting that the profiles of retreating slopes depart from the convex-concave model. The author also takes issue with the view that stepped slope profiles tend to be smoothed by mass wasting. In his view, stepped profiles may in fact be further accentuated in slope development, for example, on valley sides made up of alternating soft and hard rock layers and in the case of so-called antiplanation terraces in high-latitude mountains. The author also takes issue with the view that “cattle tracks” are primary slope forms. He suggests they are secondary formations superimposed on ridges and other microrelief forms produced by mass wasting on the slope.     

城市舒适性视角下长春市创新产出的空间特征及影响因素

基于长春市2009—2018年专利授权数，以城市街道为创新产出基本分析单元，从城市舒适性视角探讨城市创新产出的空间格局及其影响因素。研究发现：2009—2018年长春市城市内部创新发展差异逐渐增大，局部区域相对均衡，整体呈现“西南集聚，东南分散”的空间特征；创新产出的空间单元数量逐渐增多，并形成“北低南高，四大核心”的空间格局；且伴随显著的高值集聚现象，企业、大学与研究机构的空间聚集性促进了知识溢出效应；城市舒适性对于长春市创新产出的空间集聚有一定影响，休闲舒适性因子与长春市创新产出的空间分布整体相关性较强。