CENTER POINTS, EQUILIBRIUM POSITIONS, AND THE OBNOXIOUS LOCATION PROBLEM

ABSTRACT. Real variable analysis has een used to great benefit in a variety of classical problems in location theory. In this paper we explore basic complex variable techniques in one formulation of the obnoxious location problem. A general definition of center points is first given and used to formulate several alternate versions of the obnoxious location problem. A logarithmic transformation is then used to demonstrate some equivalences between these families of distinct location problems (defined via center points). A prototype logarithmic potential function which results from this formulation is then investigated, and it is demonstrated that the extremal solutions with this objective reside on the boundary of its domain of definition. An application using zero- and one-dimensional centers is discussed, and a generalization to the spatial obnoxious problem is also briefly examined. We define a zero-dimensional center as a critical point of the logarithmic potential function, and it is shown that these centers are equivalent to the solutions of the Complex Moment Problem.     

The Encoding-Error Model of Pathway Completion without Vision

We present a model that accounts for errors in short-cutting to complete a triangular pathway by individuals deprived of visual input. The model assumes that systematic error arises from components of navigation concerned with encoding an internal representation of the pathway, rather than the computation of a homeward trajectory or motor output per se. Subjects' tendency to compress the range of actually produced turns and distances, in comparison to the range of correct values, is attributed to regression toward the mean of encoded values during encoding of segments and turns, in the face of uncertainty about the actual values. Individual-subject variations are attributed to differences in the encoding-function parameters, not to variations in the processes themselves. The model provides excellent accounts of data obtained with triangular pathways but fares less well when pathway complexity increases, at which point errors do not appear to be solely attributable to encoding processes. The sources of error identified by the model are likely to play a role in navigation more generally.     

PLACE AND SPACE IN CONTEMPORARY EUROPE: SOME LESSONS AND REFLECTIONS*

The “localities debate,” stimulated by the Economic and Social Research Council's “Changing Urban and Regional Systems” initiative, was conducted in the pages of Antipode and Society and Space at a length that showed scant regard for emerging environmental sensitivities. Much of it involved politically contentious claims and increasingly exhausted theory; it resolved very little and in that sense was little more than a storm in a pretty familiar pudding basin. A later flirtation with postmodernism simply pushed aside questions of explanation while raising the political stakes as celebration of the differences between places became the order of the day. Nonetheless, important issues emerge from or relate to that debate, and we draw on our experiences to comment on three of them: (i) agents, structures, the production of space and the material bases of place: some issues of theory; (ii) the production of places, people's attachment to place, and place-based political strategies: some issues of practice; (iii) localities, postmodernism and the difference that place makes: is the regressive turn to postmodernism as approach avoidable?     

New Dimensions in Infrastructure Evaluation: The Case of Non-Technical Issues in Intelligent Vehicle-Highway Systems

Traditional infrastructure evaluation focuses primarily on technical criteria, such as the completion of a designated, interconnected system of facilities or a particular project's capacity to reduce costs borne by suppliers or end users. In the contemporary policymaking environment, however, nontechnical criteria are often of great importance in determining the success or failure of a particular infrastructure enterprise. Institutional considerations, for example, can often delay the implementation of a project or undermine its effectiveness. This paper examines the importance of non-technical criteria in infrastructure evaluation through a case study of the implementation of a major highway investment program in advanced communication and control technologies, known as intelligent vehicle -highway systems (IVHS). The case study focuses on the role of institutional issues as well as environmental issues, in the implementation of IVHS in the US. surface transportation system. The case emphasizes, first, the significance of institutional and environmental issues, and second, mechanisms for evaluating these issues in the context of a major infrastructure investment program.