Minimum-Cost Distances in Spatial Analysis

An axiomatic approach to distance is developed which focuses on those behavioral concepts of distance related to movement in space. In particular, spatial movement by behaving units is postulated to involve a choice from among some set of abstract trips in space, and implicitly, to involve the minimization of some relevant notion of trip costs. In this context, the relevant behavioral notion of distance in space is taken to be the minimum-cost distance generated by this choice process. These trip-cost concepts extend the classical notions of paths, path lengths, and shortest paths in metric spaces. Hence many of the analytical results of the paper involve extensions of classical shortest-path distance properties to minimum-cost distances. In addition to these extensions, a characterization theorem is given which specifies the possible functional relationships between trip costs and their associated path lengths. These relationships include most functional forms which are commonly employed in the literature.     

Going round in circles: Some new evidence for population in the later middle ages

The Myntling Register contains some little known and, in some respects, highly unusual demographic evidence relating to the period from around the later fourteenth century up to the 1970s and to the wealthy Lincolnshire Priory of Spalding. It is in the form of hundreds of ‘family trees’ relating to the villein families of the priory's major manors. It has evidence of interest to economic historians of medieval England on several fronts, the three of which dealt with here are proportions of males to females, percentages of females marrying, and most particularly numbers of surviving children per family. This evidence, whilst by no means perfect, is of a much more direct kind than that often used in attempts to calculate later medieval population. As such it has a contribution to make to the very vexed question of later medieval demography.     

ESR dating of the Neanderthal site, Kebara Cave, Israel

In 1985 a Neanderthal skeleton was found in the cave of Kebara in southern Mt. Carmel. Electron spin resonance (ESR) dates have been obtained on tooth enamel of gazelles found in layer X, just overlying the layer in which the skeleton was found. Assuming early uptake of uranium by the teeth, they yield an age of 60 ± 6 ka; assuming gradual, linear uptake of uranium yields an age of 64 ± 6 ka. Both age estimates are consistent with a previous estimate for the skeleton, based on TL dating of burnt flint, of 60 ± 4 ka.