32,257 research outputs found
Stochastic Physics, Complex Systems and Biology
In complex systems, the interplay between nonlinear and stochastic dynamics,
e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in
Darwinian sense, in terms of discrete jumps among attractors, with punctuated
equilibrium, spontaneous random "mutations" and "adaptations". On an
evlutionary time scale it produces sustainable diversity among individuals in a
homogeneous population rather than convergence as usually predicted by a
deterministic dynamics. The emergent discrete states in such a system, i.e.,
attractors, have natural robustness against both internal and external
perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear
stochastic open biochemical system, could be understood through such a
perspective.Comment: 10 page
Criticality and Continuity of Explosive Site Percolation in Random Networks
This Letter studies the critical point as well as the discontinuity of a
class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random
network. The class of the percolation is implemented by introducing a best-of-m
rule. Two major results are found: i). For any specific , the critical
percolation point scales with the average degree of the network while its
exponent associated with is bounded by -1 and . ii).
Discontinuous percolation could occur on sparse networks if and only if
approaches infinite. These results not only generalize some conclusions of
ordinary percolation but also provide new insights to the network robustness.Comment: 5 pages, 5 figure
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