Fractal Simplification of Lines Using Convex Hulls

We investigate the problem of the simplification of a curve from a geometric viewpoint. Starting from a fractal hypothesis, we consider that the best methods are those that keep an estimated value of the fractal dimension constant, before and after simplification. We propose a simplification rule based on the use of local convex hulls that corresponds to a new algorithm for computing fractal dimension. This algorithm is both accurate and universal, and does not imply the need to make arbitrary hypotheses regarding the structure of the curve. A comparison is made with other fractal approaches and with the well-known Douglas-Peucker method.     

A SPATIAL HEDONIC APPROACH ON LAND USE CHANGE ANTICIPATIONS*

ABSTRACT This paper estimates land use conversion anticipation when zoning is the primary tool of land use regulation. Extending the Capozza and Helsey model (1989) to the case of uncertainty in future land use zoning, a spatialized hedonic model is proposed to estimate such anticipation phenomena at a fine level (cadastral unit). Estimations use Mixed Geographically Weighted Regression (MGWR) techniques with a two‐stage model that links agricultural and developable land markets. This allows for mapping varying spatial parameters that measure anticipation effects within the theoretical framework. Results confirm the influence of anticipation on agricultural land prices in the Provence region. Moreover, the level of data spatialization allows us to take into account intra‐municipalities' heterogeneity of land use conversion anticipation.     

The SpatialARMED Framework: Handling Complex Spatial Components in Spatial Association Rule Mining

Recent research has identified spatial association rule (SAR) mining as a promising technique for geographic pattern mining and knowledge discovery. Nevertheless, important spatial components embedded in the studied phenomenon, in particular complex spatial functional relations such as neighborhood effects and spatial spillover effects have largely been neglected. This article unravels this specific problem to enhance the effective application of SAR mining practices in spatial data analytics. The main discussion focuses on the specification of complex spatial components by means of spatial dependence properties of the data and on how to integrate them in the process of SAR mining. A comprehensive framework dubbed SpatialARMED is proposed for the effective extraction of spatial patterns. The framework is then showcased through its application to crime analysis.     

Histoire de la logique floue une approche sociologique des pratiques de démonstration

Starting from an historical case study, this article addresses the general issue of the development of a social history of mathematics and logic. It aims at giving an account of certain features of recent history of fuzzy logic. For this purpose, it develops an approach based on a sociology of methods of demonstration and on the material analysis of logical activity, in particular of writing and reading activities. The formation of a social history of forms of demonstration is outlined.