MEDIAN,MEAN, AND OPTIMUM AS FACILITY LOCATIONS*

ABSTRACT The mean and the median are both measures of centrality. In one dimension, the median minimizes the average absolute distance from a facility to a set of customers {x_i}, and the mean minimizes the average squared distance. In two dimensions, the median minimizes the average rectangular distance, and the mean minimizes the average squared distance. This paper investigates the “location penalty” when a nonoptimal location is substituted for the optimal location. In one dimension, the average absolute distance at the mean is never more than twice the average absolute distance at the median. Surprisingly, this happens when the median and mean are close together. In two dimensions, the ratio of the average Euclidean distance at the median to the average Euclidean distance at the optimum is never more than . However, this upper bound depends on an unlikely scenario with just two customers. With three equal-sized customers, this ratio is never more than 1.12. However, if the triangle formed by the customers is rotated relative to the rectangular grid, the ratio never exceeds 1.028.     

OBNOXIOUS FACILITY LOCATION IN THE INTERIOR OF A PLANAR NETWORK*

ABSTRACT. The problem of locating a point that is as far as possible from arcs and nodes of a network is investigated. Each arc or node may have a different multiplicative factor (weight) for its distance. A graphical solution approach, as well as a computational algorithm, is presented.     

THE OPTIMAL LOCATIONS OF MULTIPLE BRIDGES,CONNECTING FACILITIES,OR PRODUCT VARIETIES*

ABSTRACT This paper considers the optimal locations of two or more facilities, and the optimal number of facilities, when trips are made in pairs. The results are the same as standard models of spatial competition when there is perfect matching, but not when there is random matching. The first interpretation is bridges across a river, with residential locations on one side matched perfectly or randomly to jobs on the other side. The second interpretation is connecting facilities, such as tennis courts or restaurants where pairs of consumers meet. The third interpretation is product differentiation, with husbands and wives jointly choosing from among varieties.     

NEW ARCHAEOMAGNETIC STUDIES NEAR XI'AN,CHINA*

Archaeomagnetic and mineral magnetic studies were made of known-age samples from fired structures and sediments from archaeological sites near Xi'an, China. The fired materials retained a stable record of the direction of the past geomagnetic field, which compared well with previous investigations and could contribute to an archaeomagnetic calibration curve. However, discrepancies with documented observations of the field were noted.     

A REGIONAL CONSUMER DEMAND MODEL FOR NEW ZEALAND*

ABSTRACT. This paper discusses the formulation and estimation of sets of demand systems for six New Zealand regions. The chosen model is based on the Linear Expenditure System, constrained in various ways to take account of interregional differences in consumer behaviour. Our results suggest that income and price elasticities of demand vary significantly between regions, suggesting that regional employment and output patterns are likely to differ in their responses to changes in aggregate demand.     

ONE NAME,MANY GROUNDS: LAND,MARRIAGE AND SOCIAL STRUCTURE AMONG THE OROKAIVA OF PAPUA NEW GUINEA

It is proposed, through an examination of published materials on the Orokaiva, that established and even competing models and concepts of ‘kinship’ and marriage (generalized and direct exchange, agnatic descent, clan, balanced reciprocity) have little or no explanatory power since they either do not fit the published facts or they predict the same results, despite published assertions to the contrary. An hypothesis linking relationship terminology, marriage ‘systems’ and land use is proposed. Some features in the ‘system’ of ‘kinship’ terminology appear to be expressive of the ideology of gardening rather than ‘kinship’ and marriage per se.     

COMPOSITIONAL CHARACTERIZATION OF FRENCH LIMESTONE: A NEW TOOL FOR ART HISTORIANS*

Limestone from quarries known to medieval craftsmen and from the monuments they built and embellished, as well as from carvings now in museum collections, has been characterized by neutron activation analysis. Specimens from 38 quarries in the Lutetian and Jurassic limestone formations of France and from sculptures in American and French museums have been tested, and the results have been compiled in a data base to which art historians may refer when attempting to determine provenance for sculptures. Multivariate statistical analysis of concentration data shows stone from a particular quarry in the Paris basin to be compositionally homogeneous and distinguishable from other quarries in the same formation. The same approach to data related to quarries near the Burgundian abbey of Cluny finds general agreement between classifications based on compositional and on petrographic data, but the number of samples available for analysis at the time of writing was insufficient to achieve the finer distinctions reported for the Paris basin.     

ARTIFICIAL NEURAL NETWORKS: A NEW APPROACH TO MODELING INTERREGIONAL TELECOMMUNICATION FLOWS*

ABSTRACT. During the last thirty years there has been much research effort in regional science devoted to modeling interactions over geographic space. Theoretical approaches for studying these phenomena have been modified considerably. This paper suggests a new modeling approach, based upon a general nested sigmoid neural network model. Its feasibility is illustrated in the context of modeling interregional telecommunication traffic in Austria, and its performance is evaluated in comparison with the classical regression approach of the gravity type. The application of this neural network approach may be viewed as a three-stage process. The first stage refers to the identification of an appropriate network from the family of two-layered feedforward networks with 3 input nodes, one layer of (sigmoidal) intermediate nodes and one (sigmoidal) output node (logistic activation function). There is no general procedure to address this problem. We solved this issue experimentally. The input-output dimensions have been chosen in order to make the comparison with the gravity model as close as possible. The second stage involves the estimation of the network parameters of the selected neural network model. This is performed via the adaptive setting of the network parameters (training, estimation) by means of the application of a least mean squared error goal and the error back propagating technique, a recursive learning procedure using a gradient search to minimize the error goal. Particular emphasis is laid on the sensitivity of the network performance to the choice of the initial network parameters, as well as on the problem of overfitting. The final stage of applying the neural network approach refers to the testing of the interregional teletraffic flows predicted. Prediction quality is analyzed by means of two performance measures, average relative variance and the coefficient of determination, as well as by the use of residual analysis. The analysis shows that the neural network model approach outperforms the classical regression approach to modeling telecommunication traffic in Austria.     

SOIL PHOSPHATE ANALYSIS: A NEW TECHNIQUE FOR MEASUREMENT IN THE FIELD USING A TEST STRIP*

A new method for soil phosphate analysis has been developed for field measurement which will increase the applicability of phosphate mapping in archaeological prospection.