Sentence examples for critical branching process from inspiring English sources

This is the mean-field exponent of a critical branching process [10].

A critical branching process will display power-law dynamics, however, a number of assumptions underlying branching processes do not hold true in neurophysiological systems.

A critical branching process is a process such that one active node will activate on average one other node at the next time step and so one can discern how this would relate to neuronal systems whereby the system is critical if one active neuron on average activates one other neuron at the next time step.

In our model, in particular, one could conjecture that the set of parameters that give maximum dynamic range and power law response function for the ganglion cell would correspond to a critical branching process [41] in the information transmission in the retina.

Aldous and Popovic [ 38] proposed a continuous-time critical branching process conditioned on the number of species in the present, with the assumption that the birth and death rates are identical in macroevolution, which was later relaxed by Gernhard [ 39, 40] to allow uncorrelated birth and death rates.

Additionally, re-entrant connections invalidate the standard theory of branching processes [21] and so this brings into question the idea that neuronal systems can be modelled as critical branching processes.

Universality in waiting time distributions is abundant in a wide range of complex systems in nature, e.g. earthquake occurrences [10], [11], human communication [1], [2], and in neuronal avalanches [12] [14], where it has been associated with critical branching processes [15], [16], and in systems showing (on-off) intermittent dynamics [17].

These show behaviour that is typical of near-critical branching processes, which often becoming extinct early but also often grows to significant size before extinction.

The population model is defined to be a super-critical Markovian branching process, or more specifically, a super-critical linear birth-and-death (B D) process.

A third class of applications is branching process constructions which are used to gain greater understanding of other mathematical structures, such as critical phenomena in percolation.

That one collision 65 million years ago represented a critical branching in the possibilities of life.