Abstract
A distance bias is imposed on the probability of direct connection between every pair of points in a random net. The probability that there exists a path from a given point in the net to another point is now a function of both the axone density and the distance between the points. A recursion formula is derived in terms of which this probability can be computed.
The rate of spread of an epidemic where probability of contact depends on the distance between the individuals can also be computed from the recursion formula.
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Literature
Solomonoff, R. and A. Rapoport. 1951. “Connectivity of Random Nets.”Bull. Math. Biophysics.,13, 107–117.
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Rapoport, A. Nets with distance bias. Bulletin of Mathematical Biophysics 13, 85–91 (1951). https://doi.org/10.1007/BF02478355
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DOI: https://doi.org/10.1007/BF02478355