Optimal Number of Hierarchical Facilities with Failures

This article proposes a continuous approximation model for determining the number of hierarchical facilities when lower level facilities are subject to failures. The average distance from customers to the nearest open facility is derived for two types of customer behavior. The optimal number of facilities that minimizes the average distance is then obtained. The analytical expression for the optimal number of facilities demonstrates how the location of facilities, the failure probability, and the customer behavior affect the optimal hierarchy and the average distance. The result shows that introducing the hierarchy can reduce the average distance if the failure probability is small and the penalty for failing to use facilities is large. The model provides a fundamental understanding of the optimal hierarchy and is useful for designing hierarchical facility systems.     

Order Distance in Regular Point Patterns

This article examines the k th nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the k th nearest distance and the average k th nearest distances are theoretically derived for k =1, 2, …, 7. As an application of the k th nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances.     

Multiple Facilities Location in the Plane Using the Gravity Model

Two problems are considered in this article. Both problems seek the location of p facilities. The first problem is the p median where the total distance traveled by customers is minimized. The second problem focuses on equalizing demand across facilities by minimizing the variance of total demand attracted to each facility. These models are unique in that the gravity rule is used for the allocation of demand among facilities rather than assuming that each customer selects the closest facility. In addition, we also consider a multiobjective approach, which combines the two objectives. We propose heuristic solution procedures for the problem in the plane. Extensive computational results are presented.     

Neighbor-based Properties of Some Orderings of Two-dimensional Space

An ordering of a two-dimensional matrix assigns consecutive integers to the cells in that matrix. This paper evaluates such orderings by concentrating on the differences between each cell's order key and the keys of its spatial neighbors. In all, ten systematically generated orderings and two hundred random trials from a newly defined class of orderings are compared. The row-by-row (raster) ordering often used in remote sensing and in matrix ordering within computer programs minimizes the mean absolute difference, the root-mean-squared difference (and hence the Geary statistic), and the mean maximum absolute difference for both 8-by-8 and 256-by-256 matrices; of the quadrant-recursive (“quadtree-compatible”) orderings examined, the Morton order had the lowest values for both mean absolute difference measures, whereas the Hilbert order had the lowest root-mean-squared neighbor difference. The Morton order has the overall minimum value for the Moran statistic. Heuristic search procedures applied to the 8-by-8 case found orderings which had considerably “better” values for these statistics (higher for Moran; lower for the others) than did any of the above, suggesting that it will be possible to define new systematic orderings with better scores than any ordering currently in the literature.     

基于GIS的徐州市城乡交通基础设施通达性研究

以徐州市城乡交通网络数据为数据源,利用GIS空间分析技术,选取长度-半径维数、分枝维数、距离可达性、时间可达性和可达性系数5个指标对该区交通网络的空间形态、空间分布、距离关系、时间关系等进行多角度分析。结果表明,徐州市城乡交通网络长度-半径维数呈现明显的空间分异,徐州市区及周边地区交通网络密度最大,其次是东部,西北部县域交通网络密度最小,分枝维数和长度-半径维数的空间分布基本一致。区内各节点的时间和距离可达性均随距离徐州市区的增大而增大,通达性高于全区平均水平的节点有徐州市辖区各节点,接近全区平均水平的节点有邳州市、沛县和睢宁县,而丰县和新沂市的通达性水平则低于全区平均通达性水平。     

SPATIAL COMPETITION AND THE JOINT CONSUMPTION OF SERVICES*

In Hotelling location models, an implicit assumption has been made that a customer uses the service provided by the firm, independent of other customers. However, for firms that supply meeting rooms, wedding halls, tennis courts, and golf links it is essential to incorporate the fact that the customer only uses the service in conjunction with other customers. The objective of this paper is to formulate the Hotelling location model n consideration of the interdependence among customers in one-dimensional space, and to characterize the state of equilibrium. In our model, each group of members within a given distance enjoys a fixed amount of service of the firms, under the assumption that the travel cost incurred by each group is defined as the travel cost of the farthest customer in the group.     

COMPETITIVE FACILITIES: MARKET SHARE AND LOCATION WITH RANDOM UTILITY*

ABSTRACT. A new approach is proposed for calculating the expected market share. It is assumed that consumers patronize a facility according to a utility function, selecting the facility with the highest utility value. However, consumers'ratings of the utility components are stochastic by some random distribution. Therefore, the buying power of customers located at the same point is divided among several facilities. A probability that a consumer patronizes a certain facility can be calculated. Consequently, the expected market share by competing facilities can be estimated. This calculation is more than 1,000 times faster than repeating a simulation enough times to achieve a reasonable accuracy. The distance decay calculated using the new approach is approximately exponential. A procedure for finding the optimal location anywhere in the plane for a new facility that maximizes the market share is also introduced.     

A Note on the Extremities of Local Moran's Iis and Their Impact on Global Moran's I

By defining local Moran's I_i as a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's I_i expressed by the local linkage degree. Depending on whether we use the W- or C-coding of the spatial connectivity matrix, the variance of local Moran's I_i for a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's I_i with a large variance affect the global statistic much more than spatial objects associated with a local Moran's I_i with a small variance. Counterintuitively, global Moran's I defined in the W-coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C-coding. Second, we investigate the impact of the empirical data on local Moran's I_i and show that local Moran's I_i will only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's I_i. Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation.     

基于可见光谱特征提取的敦煌壁画颜料识别方法研究

为了对壁画颜料种类进行无损识别,根据不同的物质对光的吸收特性不同,决定着光谱反射率不同这一特性,提出一种基于可见光谱的颜料识别方法,并对敦煌壁画所用颜料进行了分析。提取可见光谱曲线二阶导数负数部分表征曲线峰值区域的几何轮廓,利用中值金字塔对提取结果进行三层分辨率表征以突出曲线峰值位置信息,归一化三种表征尺度并组合构建特征空间F,以欧氏距离为准则对壁画采样点与颜料库样本进行相似度判别,从而识别出壁画用颜料信息。结果表明,本研究构建的识别方法能够对壁画颜料种类进行无损识别,在壁画数字存档及修复领域具有一定的应用前景。     

Probabilistic, Maximal Covering Location—Allocation Models forCongested Systems

When dealing with the design of service networks, such as health andemergency medical services, banking or distributed ticket-selling services, the location of servicecenters has a strong influence on the congestion at each of them, and, consequently, on thequality of service. In this paper, several probabilistic maximal coveringlocation—allocation models with constrained waiting time for queue length are presentedto consider service congestion. The first model considers the location of a given number ofsingle-server centers such that the maximum population is served within a standard distance, andnobody stands in line for longer than a given time or with more than a predetermined number ofother users. Several maximal coverage models are then formulated with one or more servers perservice center. A new heuristic is developed to solve the models and tested in a 30-node network.     

Biological Kinship,Postmarital Residence and the Emergence of Cemetery Formalisation at Prehistoric Marathon

This paper examines the role of kinship and postmarital residence in the emergence of organised cemeteries during the transition from the Final Neolithic to the Early Bronze Age at Marathon, Attica. Focusing on the cemetery of Tsepi, we performed intra‐cemetery biodistance analysis to test whether biological relatedness structured spatial organisation of tombs, and whether postmarital residence was matrilocal or patrilocal. Dental metric, dental morphological and cranial non‐metric data were collected from 293 individuals and subjected to multivariate analysis (principal component analysis, Euclidean distance ordination via multidimensional scaling), binomial probability calculations, Ripley's K analysis and determinant ratio analysis. Results indicated phenotypic similarity among some tomb co‐interments; however, outliers suggested that within‐tomb burial depended on a variety of factors that could include affinal, fictive or practical kinship. There was strong evidence for phenotypic patterning by tomb row, indicating that cemetery structure at Tsepi was organised according to biological lineages. This was especially evident for females. Male phenotypic variation was higher than that of females, though not significantly so. The results of intra‐cemetery biodistance analysis at Tsepi reveal a complex mortuary programme that emphasised biological kinship within an exogamous and likely matrilocal system of mate exchange. When considered in light of ethnographic evidence, the practice of male exogamy may correlate with the coastal location of the community and the maritime activities that structured the economy during the emergence of social complexity in the region. This paper illustrates the potential of biodistance analyses for elucidating aspects of social life in the Aegean. Copyright © 2017 John Wiley & Sons, Ltd.     

LOCATING A SINGLE NEW FACILITY AMONG EXISTING,UNEQUALLY ATTRACTIVE FACILITIES*

ABSTRACT. The location of a new facility in a competitive environment is investigated. It is assumed that customers patronize the facility with the highest utility value rather than the closest facility. Simulations show that the new approach yields a superior location in terms of market size captured. Sensitivity analyses of the problem parameters illustrate the sensitivity of the location and the sensitivity of the market size captured to the facility's quality.     

FT-IR measurements of petroleum fluid inclusions: methane, n-alkanes and carbon dioxide quantitative analysis

A recent advancement in petroleum geochemistry is to model fossil oil composition using microthermometric and volumetric data acquired from individual fluid inclusion analysis. Fourier transform infrared (FT‐IR) microspectroscopy can record compositional information related to gas (CH₄ and CO₂) and alkane contents of petroleum inclusions. In this study, a quantitative procedure for FT‐IR microspectrometry has been developed to obtain, from individual fluid inclusions, mol percentage concentrations of methane, alkanes and carbon dioxide as constraints to thermodynamic modelling. A petroleum inclusion in a sample from the Québec City Promontory nappe area was used as standard to record a reference spectrum of methane. The analytical procedure is based on the measurement of CH₄/alkane and CH₄/CO₂ band area ratios. CH₄/alkane infrared band area ratio is obtained after spectral subtraction of the reference methane spectrum. This area ratio, affected by absolute absorption intensities of methane, methyl and methylene, provides a molar CH₄/alkane ratio. Methyl/methylene ratio (CH₂/CH₃) ratio is obtained following procedures established in previous work. CO₂/CH₄ concentration ratio is estimated from relative absolute absorption intensities. Application to natural inclusions from different environments shows good correlation between FT‐IR quantification and PIT (petroleum inclusion thermodynamic) modelling.     

Simple Iterative Use of Lyapunov's Solution for the Linear Optimal Seismic Design of Passive Devices in Framed Buildings

This article presents a Lyapunov-based analysis/redesign approach for the optimal seismic design of added viscous dampers in 3D framed structures. The optimal solution minimizes the total added damping while the mean squared drifts at the peripheral frames are constrained to allowable values under a white noise excitation. The proposed approach uses Lyapunov equation for analysis and an optimality criterion that dictates “fully stressedness” for redesign. Hence, the design process is actually comprised of an iterative solution of a set of algebraic equations. Three examples are solved so as to highlight the advantages of the proposed approach — a 3-story shear frame, an 8-story, 3-bay by 3-bay setback frame, and a 10-story industrial frame.     

Experimental study of polycrystal growth from an advecting supersaturated fluid in a model fracture

We present real‐time observations of polycrystal growth experiments in transmitted light in an accurately controlled flow system with the analogue material alum [KAl(SO₄)₂·12H₂O]. The aim of the experiments is to obtain a better insight into the evolution of vein microstructures. A first series of experiments shows the evolution of a polycrystal at supersaturations between 0.095 and 0.263. The average growth rate of the crystals is influenced by growth competition and the depletion of the solute along fracture length. Growth competition is controlled by crystallographic orientation, crystal size and crystal location. In addition, the growth rate of an individual crystal facet also shows variations depending on the facet index, facet size and flow velocity. These variations can influence the morphology of the grain boundaries and the microstructures. The aim of the second series of experiments is to investigate the growth evolution of rough/dissolved facets in detail. The growth distance required for the development of facets is around 15 μm. In all the experiments, we observe that the measured growth rates have a much larger range than predicted by alum single‐crystal growth kinetics. This is due to the combined effect of the facet index and the crystal size. Furthermore, at high supersaturations, the facet growth rate measurements do not fit the same growth rate equation as for the experiments at lower supersaturations (<0.176). This can be explained by a change in the growth mechanism at high supersaturations with more influence of volume diffusion, relative to advection of the bulk solution on the growth rate. This effect can also cause a more homogeneous sealing pattern over fracture length. At high supersaturations, the larger crystals in these experiments incorporate regularly spaced fluid inclusion bands and we propose that these can be used as an indicator for high palaeo‐supersaturation. The final microstructures of the experiments show no asymmetry with respect to the flow direction.     

Funerary practices and kinship in an Early Bronze Age society: a Bayesian approach applied to the radiocarbon dating of Argaric double tombs

The main aim of this paper is to test the hypothesis on kinship relations (affinity/marriage vs descent/consanguinity, and matrilocality) expressed in the funerary record of the El Argar Bronze Age society (South-east Iberia, 2200–1550 cal BCE), taking into account the absolute chronological dimension of double adult tombs. A set of 23 double tombs having radiocarbon dates for both skeletons were selected, and radiocarbon calibration and Bayesian probability analysis was conducted. The results support the ‘descent’ hypothesis, since for most of the cases the chronological distance between individuals buried together was larger than two decades. Finally, several guidelines for future research are suggested in order to overcome shortages in current chronological and archaeological data.     

Sensitivity of Dental Phenotypic Data for the Identification of Biological Relatives

Using modern samples of known kin, this paper evaluates two fundamental aspects of kinship analysis in archaeological contexts: (1) choice of data (dental metrics or morphology) and (2) analytical approach (multivariate, distance‐based approach or a ‘rare trait’ analysis). Stone dental casts were analysed from 155 female individuals from four sampling locations in Kenya. Of these 155 individuals, only three pairs were close kin: mother–daughter, sister–sister, and first‐cousin–first‐cousin dyads. After variable winnowing, inter‐individual distances or similarities were calculated using 11 odontometric variables and 25 dental morphological variables. Resulting distance matrices were ordinated in two dimensions using multidimensional scaling. Odontometric data performed relatively well at identifying known relative pairs, but the results were heavily affected by choice of similarity measure (e.g. Euclidean distances vs. Gower coefficients) and pre‐analysis data treatments (e.g. raw data vs. principal components). Dental morphological data performed comparably with odontometric data but were slightly less effective. Rare traits were identified and compared among relative pairs for concordance, with mixed results. Rare morphological features were randomly distributed throughout the population and were not exclusively found in close kin. In combination, results indicated the sister–sister dyad was most consistently identified; however, in no analysis were relatives more phenotypically similar than all random pairs of unrelated individuals. A multivariate, distance‐based approach was more effective than rare traits at identifying relative pairs, but even under ideal circumstances, there is not enough variation present in the dentition to faithfully identify close relatives in the absence of contextual archaeological data. Copyright © 2017 John Wiley & Sons, Ltd.     

The K‐Function Method on a Network and Its Computational Implementation

This paper proposes two statistical methods, called the network K‐function method and the network cross K‐function method, for analyzing the distribution of points on a network. First, by extending the ordinary K‐function method defined on a homogeneous infinite plane with the Euclidean distance, the paper formulates the K‐function method and the cross K‐function method on a finite irregular network with the shortest‐path distance. Second, the paper shows advantages of the network K‐function methods, such as that the network K‐function methods can deal with spatial point processes on a street network in a small district, and that they can exactly take the boundary effect into account. Third, the paper develops the computational implementation of the network K‐functions, and shows that the computational order of the K‐function method is O(n²_Q log n_Q) and that of the network cross K‐function is O(n_Q log U3Q), where n_Q is the number of nodes of a network.     

A Cost-Based Ripley’s <Emphasis Type="Italic">K</Emphasis> Function to Assess Social Strategies in Settlement Patterning

Most quantitative approaches to distributional analysis in archaeology assume a homogeneous study surface that is amenable to easy generalisations. This framework has been widely used to describe settlement processes, disregarding the spatial heterogeneity inherent to geographic reality. In other words, researchers have often assumed that the correlation between the elements of a spatial distribution is a function of the Euclidean distance (i.e. straight line distance) between them. Other archaeological studies have tested alternative measures to Euclidean distances, such as cost-based ones, both to describe optimal routes and to assess spatial autocorrelation in a point pattern. Nevertheless, until now there has been no suitable model to introduce these measures into spatial statistical equations. In order to overcome this obstacle, we approach the implementation problem inversely by embedding the spatial pattern under study into a Euclidean frame of reference based on its cost-distance pairwise matrix. This paper describes the application of this methodology on one of the main tools used by archaeologists to assess settlement patterns: Ripley’s K function. We present two case studies, covering both macroscale and mesoscale, with significant variations in the results depending on the use of the Euclidean or cost-based approach. Data, functions and results have been R-packaged for the sake of reproducibility and reusability, allowing other researchers to build upon our methods.     

A Covering Tour Model for Planning Mobile Health Care Facilities in SuhumDistrict, Ghama

The provision of adequate primary health care in developing countries is often troublesome. The problem is to provide a sufficient number of facilities to be geographically accessible, yet few enough to be properly stocked and staffed. In many less developed countries accessibility problems are exacerbated by extensive rainy seasons in which travel is only possible on paved roads. Using the covering tour model we investigate the use of mobile facilities to resolve this dilemma in Suhum District, Ghana. The model minimizes a mobile facility's travel while serving all population centers within range of a feasible stop. Computational results show that in the rainy season the model cannot provide full coverage; over six percent of the population is beyond a covering distance of eight kilometers. In the dry season, 99 percent of the population can be served by a tour at a covering distance of seven kilometers.Beyond a distance of four kilometers, the dry season problem becomes a trade-off between the distance traveled by healthcare patrons and mobile facilities. These results illustrate the importance of flexibility of mobile systems: if accessibility cannot be provided in all seasons it may still be provided at favorable times of the year.