Canalization is a form of network robustness found in genetic regulatory networks that results in a reduction of the variation of phenotypic expression relative to the complexity of the genome. Recently, it was discovered that canalization can evolve in a complex network through a self-organization of node (gene) behavior resulting from a competition of a network's nodes that selects for a diversity of behavior [K.E. Bassler, C. Lee, and Y. Lee, Phys. Rev. Lett. 93, 038101 (2004)]. Previously, this "self-organized" mechanism for the evolution of canalization has been studied only in deterministic model systems. This paper considers the effects of stochastic noise in the signals exchanged between nodes on the self-organized evolution of canalization. We find that small levels of stochastic noise increase the amount of canalization produced. At higher levels of noise, the amount of canalization produced levels off and reaches a maximum value, before it reduces at large levels of noise.
A diffusive model with a price dependent diffusion coefficient was recently proposed to explain the occurrence of non-Gaussian price return distributions observed empirically in real markets
[J.L. McCauley and G.H. Gunaratne, Physica A 329, 178 (2003)].
Depending on the functional form of the diffusion coefficient, the exactly solved continuum limit of the model can produce either an exponential distribution, or a "fat-tailed" power-law distribution of returns. Real markets, however, are discrete, and, in this paper, the effects of discreteness on the model are explored. Discrete distributions from simulations and from numerically exact calculations are presented and compared to the corresponding distributions of the continuum model. A type of phase transition is discovered in discrete models that lead to fat-tailed distributions in the continuum limit, sheading light on the nature of such distributions. The transition is to a phase in which infinite price changes can occur in finite time.
We explore the phase diagram of a recently introduced gradient driven anisotropic 3D sandpile model of vortex dynamics. Two distinct phases are observed: one is a self-organized critical state characterized by avalanches of vortex motion that obey finite-size scaling and that has a finite critical current density; the other one has vortices that cluster together and occupy only every other lattice site in the X-Y plane. The critical current density is zero in the clustered phase. Detailed results of a finite-size scaling analysis of the avalanches in the self-organized phase is discussed, including critical exponents that differ from the corresponding 2D model.