Abstract
A number of agents can arrange themselves equidistantly in a row via a sequence of adjustments, based on a simple “local” interaction. The convergence of the configuration to the desired one is exponentially fast. A similarity is shown between this phenomenon and the dynamics of pulse propagation along a distributedRC line, and a conjecture is made concerning the evolution of a similar system with a probabilistic rule of behavior.
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References
W. F. Ames,Nonlinear Ordinary Differential Equations in Transport Processes, Academic Press, New York, 1968.
J. Antinone and G. W. Brown, The modelling of resistive interconnects for integrated circuits,IEEE J. Solid-State Circuits, April 1983, pp. 200–203; see also: G. De May, A comment on “The modeling of resistive interconnects for integrated circuits,”IEEE J. Solid-State Circuits, August 1983, pp. 542–543.
E. R. Berlekamp, E. N. Gilbert, and F. S. Sinden, A polygon problemThe American Mathematical Monthly 72, pp. 233–241, 1965.
A. M. Bruckstein, G. Sapiro, and D. Shaked, Evolutions of planar polygons, CIS Report #9202, Technion, Israel, 1993, to appear inIntl. J. Pattern Recognition, 1994/5.
J. H. Cadwell, A property of linear cyclic transformations,Math. Gaz. 37, pp. 85–89, 1953.
R. J. Clarke, Sequences of polygons,Mathematics Magazine 52, pp. 102–105, 1979.
M. G. Darboux, Sur un probleme de geometrie elementaire,Bull. Sci. Math. 2, pp. 298–304.
P. J. Davis, Cyclic transformations of polygons and the generalized inverse,Can. J. Math. 29, pp. 756–770, 1977.
S. Gueron and S. Levin, Self organization of front patterns in large wildebeest herds,J. Theor. Biology,165, pp. 541–552, 1994.
F. B. Hildebrand,Introduction to Numerical Analysis, second edition, Dover, New York, 1987.
M. Kac, Random walk and the theory of Brownian motion, inSelected Papers on Noise and Stochastic Processes, edited by N. Wax, Dover, New York, 1954.
A. B. Kahng and S. Muddu, Delay analysis of VLSI interconnections using the diffusion equation model,31st ACM/IEEE Design Automation Conference, 1994.
M. Kijima, Numerical calculation of ruin probabilities for skip-free Markov chains,SIAM Review 53 (4), December 1993, pp 621–624.
P. Lancaster and M. Tismenetsky,The Theory of Matrices, second edition, Academic Press, New York, 1985.
T. Sakurai, Approximation of wiring delay in MOSFETLSI,IEEE J. Solid-State Circuits, August 1983, pp. 418–426.
M. R. Spiegel,Mathematical Handbook of Formulas and Tables, McGraw-Hill, New York, 1968.
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On temporary leave from IBM Israel-Science and Technology, Matam, Haifa 31905, Israel.
On sabbatical at AT&T Bell Laboratories at Murray-Hill, NJ 07974, USA.
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Wagner, I.A., Bruckstein, A.M. Row Straightening via local interactions. Circuits Systems and Signal Process 16, 287–305 (1997). https://doi.org/10.1007/BF01246714
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DOI: https://doi.org/10.1007/BF01246714