Abstract
Random cellular structures (froths, foams, undifferentiated biological tissues) are in statistical equilibrium thanks to elementary local transformations. They form a statistical ensemble, with universal properties (structural equation of state, and distribution of cell shapes, up to priors). Notably, all natural random cellular structures in two dimensions follow a unique relation -that can be obtained by maximum entropy inference- between the variance of the cell shape distributions, and the probability that a cell has six neighbours (Lemaitre’s Law) .By obtaining the distributions of cell shapes thanks to coupled rate equations, one is able to propose a mechanism for the renewal of biological tissues like the mammal epidermis. No prior probabilities are necessary, but some assumptions on the division kernel are needed. The solutions are very restricted, and agree with those obtained by MaxEnt and with experimental data.Random cellular structures offer therefore an excellent testing ground for Maxent inference.
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