Abstract
In the present chapter, we discuss the graph representations of urban spatial patterns (maps) and suggest a computationally feasible technique for understanding urban forms based on scale-dependent random walks that can be used in order to spot the relatively isolated locations and neighborhoods, to detect urban sprawl, and to illuminate the hidden community structures in complex urban textures. The approach may be implemented for the detailed expertise of any urban pattern and the associated transport networks that may include many transportation modes.
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“We Shape our Buildings; thereafter They Shape Us”. In his speech to the meeting in the House of Lords, October 28, 1943, W. Churchill had requested that the House of Commons bombed out in May 1941 be rebuilt exactly as before, since the configuration of space and even its scarcity in the House of Commons played a greater role in effectual parliament activity. In his view, “giving each member a desk to sit at and a lid to bang” would be unreasonable, since “the House would be mostly empty most of the time; whereas, at critical votes and moments, it would fill beyond capacity, with members spilling out into the aisles, giving a suitable sense of crowd and urgency” (Churchill 2019). The old House of Commons was rebuilt in 1950 in its original form, remaining insufficient to seat all its members.
References
Blanchard, Ph., Volchenkov, D., Mathematical Analysis of Urban Spatial Networks, Springer Series Understanding Complex Systems, Berlin / Heidelberg. ISBN 978-3-540-87828-5, 181 pages (2009)
Chung, F.R.K., Lecture notes on spectral graph theory, AMS Publications Providence (1997)
Churchill, W., Famous Quotations/Stories of Winston Churchill at http://www.winstonchurchill.org (2019)
Hanson, J.M., Order and Structure in Urban Space: A Morphological History of London, Ph.D. Thesis, University College London (1989)
Hillier, B., Hanson, J., The Social Logic of Space (1993, reprint, paperback edition ed.). Cambridge: Cambridge University Press (1984)
Iida, S., Hillier, B., “Network and psychological effects in urban movement”, in A.G. Cohn, D.M. Mark (eds) Proc. of Int. Conf. in Spatial Information Theory: COSIT 2005 published in Lecture Notes in Computer Science 3693, 475-490, Springer-Verlag (2005)
Kac, M., “On the Notion of Recurrence in Discrete Stochastic Processes”, Bull. Am. Math. Soc.53, 1002 (1947) [Reprinted in M. Kac Probability, Number Theory, and Statistical Physics: Selected Papers, K. Baclawski, M.D. Donsker (eds.), Cambridge, Mass.: MIT Press, Series: Mathematicians of our time Vol. 14, 231 (1979)]
Lovász, L., “Random Walks On Graphs: A Survey.” Bolyai Society Mathematical Studies2: Combinatorics, Paul Erdös is Eighty, 1 Keszthely (Hungary) (1993)
Orford, S., Dorling, D., Mitchell, R., Shaw M. & Davey-Smith, G., “Life and death of the people of London: a historical GIS of Charles Booth’s inquiry.” Health and Place 8 (1), 25-35 (2002)
Ortega-Andeane, P., Jiménez-Rosas, E., Mercado-Doménech, S., & Estrada-Rodrýguez, C., “Space syntax as a determinant of spatial orientation perception.” Int. J. of Psychology, 40 (1), 11-18 (2005)
Rankin, B., After the Map: Cartography, Navigation, and the Transformation of Territory in the Twentieth Century. Chicago: University of Chicago Press (2016)
Shlesinger, M.F., “First encounters” Nature 450(1) 40 (2007)
Vaughan, L., “The relationship between physical segregation and social marginalization in the urban environment.” World Architecture, 185, pp. 88-96 (2005)
Vaughan, L., Chatford, D., & Sahbaz, O., Space and Exclusion: The Relationship between physical segregation. economic marginalization and poverty in the city, Paper presented to Fifth Intern. Space Syntax Symposium, Delft, Holland (2005)
Volchenkov, D., “Grammar Of Complexity: From Mathematics to a Sustainable World”, in World Scientific Series Nonlinear Physical Science (2018)
Volchenkov, D., Blanchard, Ph., “Intelligibility and first passage times in complex urban networks”, Proc. R. Soc. A464 2153-2167; https://doi.org/10.1098/rspa.2007.0329 (2008a)
Volchenkov, D., Blanchard, Ph., “Random Walks Along the Streets and Channels in Compact Cities : Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics”, Phys. Rev. E75, 026104 (2007)
Volchenkov, D., Blanchard, Ph., Scaling and Universality in City Space Syntax: between Zipf and Matthew. Physica A387(10), 2353 (2008b)
Wirth, L., The Ghetto (edition 1988) Studies in Ethnicity, transaction Publishers, New Brunswick (USA), London (UK) (1928)
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Volchenkov, D. (2019). Assessing Complexity of Urban Spatial Networks. In: D'Acci, L. (eds) The Mathematics of Urban Morphology. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12381-9_9
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DOI: https://doi.org/10.1007/978-3-030-12381-9_9
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