Entropy in Urban and Regional Modelling: Retrospect and Prospect. 城市和区域建模中的熵：回顾与展望

Abstract

Entropy in Urban and Regional Modelling introduced a new framework for constructing spatial interaction and associated location models. These ideas are reviewed briefly and then set in the wider context of the application of entropy in a range of disciplines. Related developments since 1970 are examined with particular reference to extensions of the core model, links to mathematical programming, the relationship to economics, and the introduction of a dynamic spatial structure hypothesis. The role of entropy maximizing in geography, and more widely in complexity science, is reviewed and two conclusions are drawn beyond the continued effective deployment of entropy models: geography could be a leading player as complexity science develops; and geography can use these ideas to update the presentation of its classic theories. The ongoing research agenda is extensive-particularly in relation to the modeling of imperfect markets in economics-in its links with network science and agent-based modeling. Recent developments in physics suggest a new role for entropy in understanding spatial structure. This article is organized into five main sections. The first summarizes the ideas of the book; the second sets this discussion in a wider context; the third surveys the developments that have taken place since its publication. The fourth summarizes the role of entropy maximizing in geography in the context of complexity science, and the fifth presents an ongoing research agenda.

Statistical mechanics of multiedge networks

“…On the other hand, not fixing any binary related quantity implies that as T → ∞,p ij = 1 − e − t ij → 1 (fully connected topology) and we are lead to (15). Finally, not fixing any constraints, t + ij = t ij =t, we recover (17). For simplicity, the only example we report in this section corresponds to the very relevant case in which both strength and degree sequences are fixed, the rest of the cases being easily derivable from the general theory exposed.…”

“…A final comment deserves the seminal work by Wilson on transport theory [17]. He followed a similar scheme and found expressions for the expected number of events connecting two arbitrary nodes according to some considered constraints.…”

Časoprostorové modely nákupního chování české populace

“…Sheppard (1978), Senior (1979), Haynes, Fotheringham (1984), Fotheringham, O'Kelly (1989), Pooler (1994), Fotheringham et al (2000), či Wilson (2010), zde však stručně představíme také milníky v jejich vývoji. Modelování toků a pohybů v humánní geografii bylo inspirováno fyzikou (Newtonovým zákonem univerzální gravitace) a první práce využívající fyzikální analogie v geografii se objevily již koncem 19. století (Ravenstein, 1885).…”

Shopping and Services Related Travel in the Hinterland of Brno: Changes From the Socialist Period to the Present / Spádovost Za Obchodem A Službami V Zázemí Brna: Srovnání Období Socialismu A Současnosti

“…Löffler (1998), pointed to different shapes of distance functions for various centre sizes; he also provided a detailed overview of available input data for Reilly's model, specifically mass-and distancerelated data. Fotheringham et al (2000) and Wilson (2010) represent more recent work, expanding upon the theoretical starting points and the historical development of spatial interaction modelling, including possible future utilization.…”