Anticipating the Next Half‐Century of Geographical Analysis

Prompted by a series of panel sessions at a recent American Association of Geographers annual meeting entitled “A Globe‐Shaped Crystal Ball: The Next Fifty Years of Geographical Analysis,” participants were asked to speculate on the future of the journal, which of course has broader implications for spatial and geographic analytics. In what follows, I provide my thoughts on the journal as a reader, contributor, referee, and former editor of Geographical Analysis. The major points touched upon include the following. First, application to address substantive concerns will come to dominate the field. Second, the spatial data deluge will continue unabated, but will lead to important advances because of better detail and less abstraction of reality. Third, analytical methods will evolve specifically for big data. Fourth, the point‐and‐click revolution will result in ever more use of spatial analytics, but also will lend itself to greater and more widespread abuse of these methods. Fifth, addressing assumptions and theoretical foundations of long utilized approaches will revolutionize a new generation of spatial analytics. Sixth, geographic uncertainty and bias will be more than an afterthought, and methods will emerge to support meaningful analysis. Finally, spatial optimization will have increased prominence in fundamental analysis, particularly associated with establishing and evaluating significance.     

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.