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🧵 "#Criticality: A Balance Between #Robustness and #Adaptability"

Today's SFI Seminar by @cgershen @cgg_mx:
Regarding systems at the #EdgeOfChaos
Identifying #PhaseTransition dynamics
Citing @WagnerEvolution on #Robustness
Contrasting it with #Chaos (fragile, hard to predict, etc.)
And then #Criticality, somewhere in the middle... ImageImageImageImage
With #criticality, due to #PowerLaw(-like) distributions:

"Most of the changes will be small, but for some, you can have large changes."

See also #fractals

Key history point: Stuart Kauffman's #random #Boolean #networks (1969!)

Updated by @cgershen in 2004 ImageImageImageImage
Read 12 tweets

"A. Notation and Terminology

Throughout this paper, the phrase ›log-ratio‹ for a pair of positive real numbers refers to the ratio of their logarithms (to a common base, the choice of which cancels out)..

All logarithms without an indicated base
>are understood to be taken to the base 𝑒..

II. Review of Definitions and History
Our treatment here is based on a recent survey by Mitzenmacher [#Internet #Mathematics 1(2), 226‒251 (2004)], to which we refer the reader for more information.[ Footnote: For instance,
>this survey describes another argument that leads to a #PowerLaw of word frequency based on preferential attachment, originally due to Simon [Biometrika 42(3/4), 425–440 (1955)]. We do not present this argument here.]
In what follows, we let 𝑓ⱼ be the (asymptotic) fraction of>
Read 9 tweets

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