Abstract
Two-dimensional networks have been very successful for representing a wide class of problems in the physical and social sciences. The idea that the connectivity of the network constrains the flows on a network can be generalized to a much wider class of complex systems. Multidimensional polyhedra are the analogues of links in networks, and these too have a connectivity through their shared vertices. This combinatorial mathematics underlies a methodology for representing and analyzing very large hierarchical and heterarchical systems, while ensuring compatibility between data at all levels of aggregation. The goal of the methodology is to provide means of analyzing and understanding the dynamic behavior of systems of all degrees of complexity. No prior knowledge of the approach is assumed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atkin, R. H. Mathematical Structure in Human Affairs. London: Heinemann Educational Books, 1974.
Atkin, R. H. Combinatorial Connectivities in Social Systems. Basel: Birkhäser, 1977.
Atkin, R. H. Multidimensional Man. Harmondsworth: Penguin Books, 1981.
Casti, J. “The Geometry of Human Affairs.” In Reality Rules: II, Ch. 8, 229–286. New York: Wiley Inter-Science, 1992.
Dawkins, R. The Blind Watchmaker. London: Penguin Books, 1988.
Gould, P., J. Johnson, and G. Chapman. The Structure of Television. London: Pion Books, 1984.
Haight, F. Mathematical Theories of Traffic Flow. London: Academic Press, 1963.
Holtier, S. “Patterns of Structural-Qualitative Changes in the Development of Complex Systems.” Planning and Design 19 (1992): 375–402.
Leutbach, W. Introduction to the Theory of Traffic Flows. Berlin: Springer-Verlag, 1986.
Johnson, J. H. “The Q-Analysis of Road Intersection.” I. J. Man-Machine Studies 8 (1976): 531–548.
Johnson, J. H. “The Q-Analysis of Road Traffic Systems.” Environment and Planning B 8 (1981): 141–189.
Johnson, J. H. “Q-Transmission in Simplicial Complexes.” I. J. Man-Machine Studies 16 (1982): 351–377.
Johnson J. H. “Hierarchical Backcloth-Traffic Simulation.” Planning and Design 13 (1986) 415–446.
Johnson, J. H. “A Theory of Stars in Complex Systems.” In Complexity, Language, and Life: Mathematical Approaches, edited by J. Casti & A. Karlqvist, 21–61. New York: Springer-Verlag, 1986.
Johnson, J. H. “Gradient Polygons: Fundamental Primitives in Hierarchical Computer Vision.” In Proc. Symposium in Honor of Prof. J-C Simon, AFCET, University of Paris, 156 boulevard Péreire-75017, Paris, October, 1990.
Johnson, J. H. “The Mathematics of Complex Systems.” In The Mathematical Revolution Inspired by Computing, edited by J. Johnson and M. Loomes, 165–186. Oxford: Oxford University Press, 1991.
Johnson, J. H. “The Dynamics of Large Complex Road Systems.” In Mathematics in Transport Planning and Control, edited by J. D. Griffiths, 395–409. Oxford: Oxford University Press, 1992.
Johnson, J. H. “Representation, Knowledge Elicitation, and Mathematical Science.” In Artificial Intelligence in Mathematics, edited by J. Johnson, S. McKee, and A. Vella, 313–328. Oxford: Oxford University Press, 1994.
Johnson, J. H. “Links, Arrows, and Networks: Fundamental Metaphors in Human Thought.” This volume.
Ross-Ashby, W. An Introduction to Cybernetics. London: Methuen, 1984. (Reprint of 1956 original.)
Salter, R. J. Highway Traffic Analysis and Design. London: Macmillan, 1976.
Wardrop, J. G. “Some Theoretical Aspects of Road Traffic Research.” Proc. Inst. Civil Eng. Part II (1952): 325-378.
Winston, M. E., and R. Chaffin. “A Taxonomy of Part-Whole Relations.” Cog. Sci. 11 (1987): 417–444.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Johnson, J. (1995). The Multidimensional Networks of Complex Systems. In: Batten, D., Casti, J., Thord, R. (eds) Networks in Action. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57843-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-57843-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63376-8
Online ISBN: 978-3-642-57843-4
eBook Packages: Springer Book Archive