An Analysis of Urban Structure Using Concepts of Algebraic Topology

Atkin, R.H.; Johnson, Jeffrey; Mancini, Victor H.

doi:10.1080/00420987120080421

Cited by 15 publications

(8 citation statements)

References 2 publications

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“…As Paasi argues, Lundberg was a "neopositivist" who "strived to make sociology a science in the spirit of law-seeking physical sciences" (2011a: 300). During the high point of quantitative geography and after, geographers too have turned to topology in their search for a mathematical language that would capture the spatial, social, and cultural structures of urban life (Atkin et al, 1971;Yeats, 2001). …”

Section: From Mathematical To Post-mathematical Topologiesmentioning

confidence: 99%

Towards a post-mathematical topology

Martin

Secor

2013

Progress in Human Geography

195

136

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Pre-proof version.Abstract: This paper aims to bring clarity to the term topology as it has been deployed in human geography. We summarize the insights that geographers have garnered from thinking topologically about space and power. We find that many deployments of topology both overstretch topology's conceptual merit and limit its insights for spatial thinking. We show how topology, with its structuralist and modernist baggage, requires some theoretical reworking to be put to work by poststructuralist geographers. Our purpose is not to consolidate a specific topological approach for geographers, but to call for an ongoing consideration of what topology offers poststructuralist spatial theories.

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Section: From Mathematical To Post-mathematical Topologiesmentioning

confidence: 99%

Towards a post-mathematical topology

Martin

Secor

2013

Progress in Human Geography

195

136

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“…Hence, the calculation of similarity between entropies at two successive moments, performed for the whole time period, may shed light on understanding the transitions in data structure under the changes of entropy. The comparison of vector-like quantities that characterize the simplicial complex can be performed in different ways, for example by finding the critical dimension [47,48] or calculation of the cosine of an angle between two vectors [38]; we have chosen the latter one for the following reasons. Namely, we are interested in the changes of the structure of the dataset under the filtration of the simplicial complex through the successive time steps by calculating the entropies of the nested sequence of simplicial complexes.…”

Section: Results Of the Calculationsmentioning

confidence: 99%

“…The applications of Q-analysis span through different fields and problems, like studying the qualitative and quantitative structure of television programs [41], analysis of the content of newspaper stories [42], social networks [43][44][45][46], urban planning [47,48], relationships among geological regions [49], distribution systems [50], decision making [51], diagnosis of failure in large systems [52], controllability of dynamical systems [53] and the game of chess [54], to mention a few. These applications, and many others, express the usefulness of Q-analysis in data analysis; nevertheless, in most of the cases, it was applied to the analysis of small datasets suggesting possible inadequacy for handling the modern explosion of large datasets.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets

Maletić

Zhao

2017

Entropy

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Abstract:The emergence of complex datasets permeates versatile research disciplines leading to the necessity to develop methods for tackling complexity through finding the patterns inherent in datasets. The challenge lies in transforming the extracted patterns into pragmatic knowledge. In this paper, new information entropy measures for the characterization of the multidimensional structure extracted from complex datasets are proposed, complementing the conventionally-applied algebraic topology methods. Derived from topological relationships embedded in datasets, multilevel entropy measures are used to track transitions in building the high dimensional structure of datasets captured by the stratified partition of a simplicial complex. The proposed entropies are found suitable for defining and operationalizing the intuitive notions of structural relationships in a cumulative experience of a taxi driver's cognitive map formed by origins and destinations. The comparison of multilevel integration entropies calculated after each new added ride to the data structure indicates slowing the pace of change over time in the origin-destination structure. The repetitiveness in taxi driver rides, and the stability of origin-destination structure, exhibits the relative invariance of rides in space and time. These results shed light on taxi driver's ride habits, as well as on the commuting of persons whom he/she drove.

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“…In this case, it may be said that x~ and x k are s-connected if they share at least (s + 1) properties. A number of authors have developed techniques for analysing such connectivity relations (Atkin et al, 1971;Abell, 1975). …”

Section: The Structure Of Organisational Relationsmentioning

confidence: 99%