4 ms·

The dynamics of correlated novelties

9 points by foolrush 12y ago

foolrush 12y ago
On chance and correlation to other discoveries. “Novelties are a familiar part of daily life. They are also fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called “expanding the adjacent possible”.”
MrQuincle 12y ago
Although these models are highly abstract that very fact enables them to form a foundation for many different fields. * In thermodynamics the Ehrenfest model (or dog-flea model) was developed: http://www.wikiwand.com/en/Ehrenfest_model http://www.wikiwand.com/en/Ehrenfest_model * In spread of infectious diseases and vaccine efficacy models Polya urn models can be used. * In exchangeable models (e.g. in classification where labels are assigned but without semantics!!) the Pitman-Yor (PY) process can be described as an urn model and exhibits power-law distribution (of items over the different classes) as well. The Pitman-Yor process is a (two-parameter) generalization of the Poisson-Dirichlet process. The "proper" distribution over the space of all partitions. The urn model for PY is as follows. Start with a black ball with weight "b". At each step sample a ball proportional to its weight. If you sample a black ball, put it back in, along with another one black ball of weight "a", plus(!) a ball of a color - sampled from a base distribution H - with weight "1-a". If you sample a colored ball, put it back in, along with a ball of the same color and weight "1". The model from Tria et al. is also a two-parameter model, but I've to check if it is indeed different. I guess it is, Strogatz rulez. ;-) Edit: paper by Teh that describes Zipf's law (proportion of tables with n customers scales as O(n^{-1-d})) and Heap's law (total number of tables with n customers scales as O(n^d)) for the PY process: http://www.stats.ox.ac.uk/~teh/research/npbayes/TehJor2010a.pdf http://www.stats.ox.ac.uk/~teh/research/npbayes/TehJor2010a....
deleted 12y ago
[deleted]

9 points by foolrush 12y ago

On chance and correlation to other discoveries. “Novelties are a familiar part of daily life. They are also fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called “expanding the adjacent possible”.”

MrQuincle 12y ago

Although these models are highly abstract that very fact enables them to form a foundation for many different fields. * In thermodynamics the Ehrenfest model (or dog-flea model) was developed: http://www.wikiwand.com/en/Ehrenfest_model http://www.wikiwand.com/en/Ehrenfest_model * In spread of infectious diseases and vaccine efficacy models Polya urn models can be used. * In exchangeable models (e.g. in classification where labels are assigned but without semantics!!) the Pitman-Yor (PY) process can be described as an urn model and exhibits power-law distribution (of items over the different classes) as well. The Pitman-Yor process is a (two-parameter) generalization of the Poisson-Dirichlet process. The "proper" distribution over the space of all partitions. The urn model for PY is as follows. Start with a black ball with weight "b". At each step sample a ball proportional to its weight. If you sample a black ball, put it back in, along with another one black ball of weight "a", plus(!) a ball of a color - sampled from a base distribution H - with weight "1-a". If you sample a colored ball, put it back in, along with a ball of the same color and weight "1". The model from Tria et al. is also a two-parameter model, but I've to check if it is indeed different. I guess it is, Strogatz rulez. ;-) Edit: paper by Teh that describes Zipf's law (proportion of tables with n customers scales as O(n^{-1-d})) and Heap's law (total number of tables with n customers scales as O(n^d)) for the PY process: http://www.stats.ox.ac.uk/~teh/research/npbayes/TehJor2010a.pdf http://www.stats.ox.ac.uk/~teh/research/npbayes/TehJor2010a....

deleted 12y ago

[deleted]