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Emergence of Power Laws
Published on Apr 03, 20172415 Views
Where do power laws come from? There exist a handful of famous mechanisms that dynamically lead to scaling laws in complex dynamical systems, including preferential attachment processes and self-or
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Chapter list
On the origin of power laws in complex systems00:00
with Rudolf Hanel and Bernat Corominas-Murtra01:47
Power laws are pests - 101:59
Power laws are pests - 202:07
City size02:35
Rainfall05:14
Landslides05:37
Hurrican damages05:52
Financial interbank loans06:13
Forrest res in various regions06:39
Moon crater diameters07:04
Gamma rays from solar wind07:57
Movie sales08:13
Healthcare costs08:20
Particle physics08:28
Words in books09:09
Citations of scienti c articles11:12
Website hits11:18
Book sales11:54
Telephone calls11:57
Earth quake magnitude12:01
Seismic events12:14
War intensity12:17
Killings in wars12:21
Size of war12:24
Wealth distribution12:33
Family names13:14
More power laws ...13:20
Where do they come from?16:27
Classical routes to understand power laws16:33
Power laws at phase transitions17:26
Power laws through self-organised criticality21:09
Power laws through multiplicative processes22:04
Power laws through preferential processes26:57
Power laws through other mechanisms31:18
Did we miss something?32:17
Many processes are history- or path dependent32:58
Example: History-dependent processes34:28
Sentence-formation is SSR35:53
Sample-Space Reducing Processes (SSR) - 137:30
SSR lead to exact power laws!38:57
Proof by induction39:35
Sample-Space Reducing Processes (SSR) - 239:48
The role of noise41:21
The role of noise - result is exact too42:28
History-dependent processes with noise42:32
SSR based Zipf law is extremely robust42:48
Prior probabilities are practically irrelevant!45:20
Zipf law is remarkably robust - accelerated SSR45:22
What does this have to do with networks?45:35
SSR = targeted random walk on networks47:04
Graph - 148:04
Graph - 248:08
Graph - 348:13
Graph - 448:22
Graph - 548:25
Simple routing algorithm48:42
SSR is a random walk on directed ordered NW48:58
All diffusion processes on DAG are SSR49:20
Zipf holds for any link probability49:39
Does the topology of the network matter?50:06
Prior probabilities are practically irrelevant!50:32
What happens if introduce cycles?50:40
Prior probabilities are practically irrelevant!50:52
What happens if introduce cycles?50:53
Zipf's law is an immense attractor!51:41
Zipf's law is an attractor51:44
What about exponents > 1?52:08
Multiplication factor52:22
And reality?53:47
Every good search process is SSR!53:50
What is good search?53:56
Clicking on web page is often result of search process54:55
Result of a search process54:57
Searching behavior of employees55:25
Other problems that are of SSR nature56:13
Conclusions57:28