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🧵 "#Criticality: A Balance Between #Robustness and #Adaptability"
Today's SFI Seminar by @cgershen @cgg_mx:
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...
Identifying #PhaseTransition dynamics
Citing @WagnerEvolution on #Robustness
Contrasting it with #Chaos (fragile, hard to predict, etc.)
And then #Criticality, somewhere in the middle...
#ConradMitzenmacher-7
"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
>
"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,
>
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>
In what follows, we let 𝑓ⱼ be the (asymptotic) fraction of>
