Critical Pólya urn

Abstract

We propose a variant model of the Pólya urn process, where the dynamics consist of two competing elements: suppression of growth and enhancement of dormant character. Here the level of such features is controlled by an internal parameter in a random manner, so that the system self-organizes and characteristic observables exhibit scale invariance, suggesting the existence of criticality. Varying the internal control parameter, one can explain interesting universality classes for avalanche-type events. We also discuss different versions of the model. It is pointed out that such an underlying mechanism has earlier been noted to operate in a neural network.

From the synthesis and characterization of methacrylated fatty acid based precursors to shape memory polymers

“…can be implemented with triglycerides and fatty acids to obtain precursors of thermoset resins. 8 Probably the most frequent modification applied to vegetable oils, as well as to their derived fatty acids, is epoxidation (including the cases where the oxirane ring is opened to synthesize biopolyols). These modified products can be further reacted with anhydrides, isocyanates, can be cationically polymerized, or modified using olefin metathesis, thiol-ene addition etc.…”

The diffusion of opposite opinions in a randomly biased environment

“…In a memory lapse situation, the process is occurring independently of the past. Similar ideas have been 1 used in [3,5,17]. Now we state our first result.…”

Scaling in simple continued fraction

“…On the contrary, the occurrence of power-law may have a few different dynamical routes. The most common underlying mechanisms include: criticality [10][11][12][13], self-organized criticality [4][5][6], first passage properties for random walk [14][15][16], preferential process [17], multiplicative stochastic process with constraint [18][19][20][21], and sample space reducing (SSR) process [22][23][24][25][26]. The SSR is pertinent to this work.…”