Controlling Complexity in Spatial Modelling

The present complexity approach is based on two assumptions: A1: measurability of deviations of outcomes with respect to reference values; A2 : extension of A1 to multi-set analysis. Complexity is then defined in terms of multi-set deviation compared to single-set ones; an interpretation is given in terms of information costs; examples show the relevance of the interpretation. As a useful by-product the explicit solution of the quadratic part of the discrete logistic ? one of the examples ? is derived; a set of pij-numbers is introduced, and a workable method for generating them exposed. Extensions are considered, in particular controllability. A further application is then proposed, namely to hypergraph conflict analysis, in particular conflict resolution. Many decisional conflicts at the spatial level can be axiomatised in this form; it is shown how the use of particular structures ? in the mathematical sense of that word ? of the problem allows of reducing greatly the degree of complexity of the problem, and hence the difficulty of finding a solution.Chaos, complexity, conflict, dynamics, hypergraphs, information

On Diffusion of Ideas in the Academic World: the Case of Spatial Econometrics

Spatial econometrics is a fast-growing field in the series of quantitative disciplines, auxiliaries of economics and related social sciences. Space, friction, interdependence, spatiotemporal components, externalities and many other aspects interact and should be treated adequately in this field. The publication of the Paelinck and Klaassen book in the late 1970s generated virtually the field spatial econometrics This article studies the diffusion of spatial econometrics, through experienced history on the one hand, on the other through bibliometric methods. Although this field was an “Invisible College” up to 2006 (absence of any organization in form of association, conference, journal, etc.), the databases depict a fast diffusion in the past and strong prospects for the future.

Spatial-Structural Relations among Technology Industrial Clusters: A Comparative Analysis of Metropolitan Regions in the U.S

Technical industrial clusters are defined and analyzed for a sample of U.S. metropolitan regions. Economic structure, spatial proximity and shape of the clusters are examined across the metropolitan regions through various economic and spatial measures and statistics. The data for this research are used to test the hypothesis that close spatial proximity results in stronger economic functional interdependence. This hypothesis is examined and the implications of the test are explored.

ON POTENTIALIZED PARTIAL FINITE DIFFERENCE EQUATIONS: ANALYZING THE COMPLEXITY OF KNOWLEDGE-BASED SPATIAL ECONOMIC DEVELOPMENTS

Knowledge-based regional and urban studies are plentiful; some systematics might be in order at this junction, so first the different links between economic production units in geographical space have to be clearly defined. Then a tool to represent the dynamics of those links should be selected; potentialized partial differential equations (PPDEs) are an appropriate tool to represent space-time relations in pre-geographical space. In practice, however, only discrete data are available, hence the question of how finite differences could generate PPFDEs (potentialized partial finite difference equations). A case has been worked out and simulated, showing a high degree of spatio-temporal complexity. Spatial econometric estimation is possible, as other work has shown; so an application to empirical data for France could be presented. Different versions of the latter have been worked out; they are presented in succession, followed by a last exercise on US data.COMPLEXITY, SPATIAL ECONOMETRICS, POTENTIAL, FINITE DIFFERENCES

A bilinear programming solution to the quadratic assignment problem

The quadratic assignment problem (QAP) or maximum acyclical graph problem is well documented (see e.g. Pardalos and Wolkowicz, 1994). One of the authors has published some material, in which it was tried, by structuring the problem additionally, to bring it as closely as possible in the neighbourhood of a binary solution (see Paelinck, 1983, pp. 251-256 and 273-277); good but not optimal solutions could so be obtained (see Paelinck, 1985, pp. 247-254). The problem is taken up again here, in the same spirit but at the same time in a different vein

A Non-Parametric Approach to Spatial Causality

The purpose of this paper is to show the capacity of a new non-parametric test based on symbolic entropy and symbolic dynamics to deal with the detection of linear and non-linear spatial causality. The good performance of the new test in detecting spatial causality and causal weighting matrix is notable and gives rise to an expectation that it may form a adequate tool for constructive specification searches.Causality; Spatial Dependence; Spatial Weight Matrices

Modelos para datos espaciales con estructura transversal o de panel. Una revision

En este trabajo analizamos la situación actual de la Econometría espacial, como disciplina de naturaleza econométrica especializada en el manejo de datos y relaciones de tipo espacial. Se trata de un campo de investigación que ha evolucionado muy rápidamente en las últimas décadas produciendo una gran variedad de técnicas e instrumentos diferentes. El pequeño análisis bibliogáfico que realizamos en la primera parte del trabajo pone de manifiesto esta tensión. A continuación, la discusión sobre métodos se estructura en dos grandes apartados dedicados, respectivamente, a los modelos puros de corte transversal y a los modelos de datos panel. Esta revisión nos ha permitido identificar ciertas lagunas que deberían recibir mayor atención por parte de los usuarios, aunque la valoración global es positiva