Glad to be granted a patent on prediction & control of blowout in combustion systems by United States Patent and Trademark Office. Our invention predicts the exact blowout time significantly earlier using a log periodic power law & performs control action to prevent the blowout.
#USPatents #IntellectualProperty #Blowout #IITMadras #Aviation #Innovation #JetEngine #STEM #Aerospace #Statisticalphysics #powerlaw #Complexsystems #Sustainability #scaleinvariance #Logperiodicity #Combustion
@skewray True!
1/f distributions --- one of my advisors told me not to study that because it would destroy my career. His name was Per Bak. I ignored him. He was right tho
Lévy distributions are a nice example of a convolutionally stable power law with non-Gaussian behavior. Cauchy distributions, despite having no finite mean or variance are also stable. α-stable.
You do need infinite data to know the true asymptotic shape of a distribution ...
It is possible to measure the fatness of the tails of a distribution ... But I've been told that "α-stable laws are both beautiful and frustrating: they’re mathematically neat, but empirically very hard to confirm.", so yeah, what Bak said
Stanford study confirms what entrepreneurs suspected: 46% of VCs are basically expensive Magic 8-balls with worse odds 🎱
Out of 12,069 middle-to-senior VC professionals studied, nearly half never achieved even a 2x return on any investment. To be fair, VC works on power law - most bets fail, but the few big wins compensate. Still... yikes 📊
The mysterious maths at work in the Tour de France
If you look at where previous winners of the world's most famous cycling race are from, a surprisingly common pattern emerges.
#Zipf #PowerLaw
https://www.bbc.com/future/article/20240716-the-mysterious-mathematical-law-behind-tour-de-france-winners?ocid=global_future_rss
@LeonardoDiOttio
It would be cool to graph all fediverse accounts by followers. That would be a #PowerLaw graph with a very, very, very long tail....
📉 The human cell count and size distribution
(I'm reflexively skeptical of the tendency to draw a line on a log-log graph and call it a power law, but at least these guys admit the fit isn't perfect and don't particularly claim there is a universal scaling principle but it would be nice to see this tried w/ some other organisms.)
https://phys.org/news/2023-09-common-statistical-principles-scaling-nature.html
@davidzipper “There is a persistent cohort of drivers who are getting five, six, seven, ten, 15, 20 speeding tickets — and driving on our streets recklessly without any consequences whatsoever” #safestreets #powerlaw
#til Yoda's Law
Und es hat nix mit #StarWars zu tun, sondern mit #Pflanzenökologie #PowerLaw
https://persquaremile.com/2011/10/05/floral-metabolic-densities/
#GeoffreyWest - Why Do #PowerLaws Work So Widely?
https://www.youtube.com/watch?v=6Gw07lDU8-Y&ab_channel=CloserToTruth
#Philosophy #PhilosophyOfScience #Math #Maths #Mathematics #Physics #UniversalLaws #LawsOfNature #LawsOfPhysics #Systems #ComplexAdaptiveSystems #Biology #Metabolism #Ageing #Aging #Emergence #ScalingLaw #ScalingLaws #PowerLaw #CloserToTruth #RobertKuhn
@darioringach This preprint is an excellent read on the #adaptation of the #firing rate of primary #visual #cortex neurons - showing a #powerlaw scaling between the ratio of #probabilities and the ratio of observed firing rates, and also relative invariance of directional scatter (though I am puzzled by the use of cosine similarity instead of more standard distances between distributions...).
An interesting result is that the log firing rate is linearly proportional to the negative surprise of a stimulus, which will certainly bring a smile to proponents of #probabilistic representations in the brain or #predictive processing...
The study extends these observations to more ecological distributions, but - as far as I understand it - still samples individual orientations. One can predict that this would extend to showing textures with different levels of anisotropy (as defined by the tuple $(n_x, n_y)$ in the Ringach, 2002 paper, for example), creating a stimulus set ${ s_i }$ that better covers the space of visual features.
@ldebowsk Adding variants of the #HashTags ...
#MutualInformation
#InformationTheory
#StochasticProcess
#ExcessEntropy
#KolmogorovComplexity
#AlgorithmicRandomness
#LargeLanguageModel
#NeuralNetwork
#PowerLaw
#UniversalCoding
(Just to help discoverability)
6/10) We find that activations across different layers have an #eigenspectrum that follows a #powerlaw. Furthermore, well-defined intervals exist for the power law decay coefficient, α, where models exhibit excellent #OoD #generalization! 📈🎉🥳
This is going to sound really weird and #Nerd, but without specific controls (and even with them) the #fediverse is probably ultimately going to sort out into a #PowerLaw distribution of users/server. #DataScience #Probability #ChaosTheory
A #PowerLaw Keeps the Brain’s Perceptions Balanced https://getpocket.com/explore/item/a-power-law-keeps-the-brain-s-perceptions-balanced?utm_source=twtrsynd&utm_medium=social via @Pocket@twitter.com
A #toymodel explores the role of #luck vs. #talent in determining #success and #failure:
The #distribution of #wealth follows a well-known pattern sometimes called an 80:20 rule~ 80% of the wealth is owned by 20% of the people–a well-studied #pattern called a #powerlaw that crops up in a wide range of social phenomena.
"Talent vs Luck: the role of randomness in success and failure"
A. Pluchino. A. E. Biondo,
A. Rapisarda
paper: https://arxiv.org/abs/1802.07068
…
review:
https://www.technologyreview.com/s/610395/if-youre-so-smart-why-arent-you-rich-turns-out-its-just-chance/#
