nhaliday + math.ds   37

Stability of the Solar System - Wikipedia
The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways. For this reason (among others) the Solar System is chaotic,[1] and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years.[2]

The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]


The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996
nibble  wiki  reference  article  physics  mechanics  space  gravity  flux-stasis  uncertainty  robust  perturbation  math  dynamical  math.DS  volo-avolo  multi  org:edu  org:inst  papers  preprint  time  data  org:mat 
november 2017 by nhaliday
How to Escape Saddle Points Efficiently – Off the convex path
A core, emerging problem in nonconvex optimization involves the escape of saddle points. While recent research has shown that gradient descent (GD) generically escapes saddle points asymptotically (see Rong Ge’s and Ben Recht’s blog posts), the critical open problem is one of efficiency — is GD able to move past saddle points quickly, or can it be slowed down significantly? How does the rate of escape scale with the ambient dimensionality? In this post, we describe our recent work with Rong Ge, Praneeth Netrapalli and Sham Kakade, that provides the first provable positive answer to the efficiency question, showing that, rather surprisingly, GD augmented with suitable perturbations escapes saddle points efficiently; indeed, in terms of rate and dimension dependence it is almost as if the saddle points aren’t there!
acmtariat  org:bleg  nibble  liner-notes  machine-learning  acm  optimization  gradient-descent  local-global  off-convex  time-complexity  random  perturbation  michael-jordan  iterative-methods  research  learning-theory  math.DS  iteration-recursion  org:popup 
july 2017 by nhaliday
Mixing (mathematics) - Wikipedia
One way to describe this is that strong mixing implies that for any two possible states of the system (realizations of the random variable), when given a sufficient amount of time between the two states, the occurrence of the states is independent.

Mixing coefficient is
α(n) = sup{|P(A∪B) - P(A)P(B)| : A in σ(X_0, ..., X_{t-1}), B in σ(X_{t+n}, ...), t >= 0}
for σ(...) the sigma algebra generated by those r.v.s.

So it's a notion of total variational distance between the true distribution and the product distribution.
concept  math  acm  physics  probability  stochastic-processes  definition  mixing  iidness  wiki  reference  nibble  limits  ergodic  math.DS  measure  dependence-independence 
february 2017 by nhaliday
Information Geometry (Part 16) | Azimuth
While preparing this talk, I discovered a cool fact. I doubt it’s new, but I haven’t exactly seen it elsewhere. I came up with it while trying to give a precise and general statement of ‘Fisher’s fundamental theorem of natural selection’. I won’t start by explaining that theorem, since my version looks rather different than Fisher’s, and I came up with mine precisely because I had trouble understanding his. I’ll say a bit more about this at the end.

Here’s my version:
The square of the rate at which a population learns information is the variance of its fitness.
baez  mathtariat  evolution  bio  genetics  population-genetics  bits  interdisciplinary  models  exposition  math.DS  giants  information-theory  entropy-like  org:bleg  nibble  fisher  EGT  dynamical 
february 2017 by nhaliday
China invents the digital totalitarian state | The Economist
PROGRAMMING CHINA: The Communist Party’s autonomic approach to managing state security: https://www.merics.org/sites/default/files/2017-12/171212_China_Monitor_44_Programming_China_EN__0.pdf
- The Chinese Communist Party (CCP) has developed a form of authoritarianism that cannot be measured through traditional political scales like reform versus retrenchment. This version of authoritarianism involves both “hard” and “soft” authoritarian methods that constantly act together.
- To describe the social management process, this paper introduces a new analytical framework called China’s “Autonomic Nervous System” (ANS). This approach explains China’s social management process through a complex systems engineering framework. This framework mirrors the CCP’s Leninist way of thinking.
- The framework describes four key parts of social management, visualized through ANS’s “self-configuring,” “self-healing,” “self-optimizing” and “self-protecting” objectives.

China's Social Credit System: An Evolving Practice of Control: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3175792

The Chinese government is not the only entity that has access to millions of faces + identifying information. So do Google, Facebook, Instagram, and anyone who has scraped information from similar social networks (e.g., US security services, hackers, etc.).

In light of such ML capabilities it seems clear that anti-ship ballistic missiles can easily target a carrier during the final maneuver phase of descent, using optical or infrared sensors (let alone radar).

China goes all-in on technology the US is afraid to do right.
US won't learn its lesson in time for CRISPR or AI.

Artificial intelligence is developing fast in China. But is it likely to enable the suppression of freedoms? One of China's most successful investors, Neil Shen, has a short answer to that question. Also, Chinese AI companies now have the potential to overtake their Western rivals -- we explain why. Anne McElvoy hosts with The Economist's AI expert, Tom Standage

the dude just stonewalls when asked at 7:50, completely zipped lips

What you’re looking at above is the work of SenseTime, a Chinese computer vision startup. The software in question, called SenseVideo, is a visual scenario analytics system. Basically, it can analyse video footage to pinpoint whether moving objects are humans, cars, or other entities. It’s even sophisticated enough to detect gender, clothing, and the type of vehicle it’s looking at, all in real time.


Even China’s Backwater Cities Are Going Smart: http://www.sixthtone.com/news/1001452/even-chinas-backwater-cities-are-going-smart

remember that tweet with the ML readout of Chinese surveilance cameras? Get ready for the future (via @triviumchina)

XI praised the organization and promised to help it beef up its operations (China
- "China will 'help ... 100 developing countries build or upgrade communication systems and crime labs in the next five years'"
- "The Chinese government will establish an international law enforcement institute under the Ministry of Public Security which will train 20,000 police for developing nations in the coming five years"

The Chinese connection to the Zimbabwe 'coup': http://www.cnn.com/2017/11/17/africa/china-zimbabwe-mugabe-diplomacy/index.html

China to create national name-and-shame system for ‘deadbeat borrowers’: http://www.scmp.com/news/china/economy/article/2114768/china-create-national-name-and-shame-system-deadbeat-borrowers
Anyone who fails to repay a bank loan will be blacklisted and have their personal details made public

China Snares Innocent and Guilty Alike to Build World’s Biggest DNA Database: https://www.wsj.com/articles/china-snares-innocent-and-guilty-alike-to-build-worlds-biggest-dna-database-1514310353
Police gather blood and saliva samples from many who aren’t criminals, including those who forget ID cards, write critically of the state or are just in the wrong place

Many of the ways Chinese police are collecting samples are impermissible in the U.S. In China, DNA saliva swabs or blood samples are routinely gathered from people detained for violations such as forgetting to carry identity cards or writing blogs critical of the state, according to documents from a national police DNA conference in September and official forensic journals.

Others aren’t suspected of any crime. Police target certain groups considered a higher risk to social stability. These include migrant workers and, in one city, coal miners and home renters, the documents show.


In parts of the country, law enforcement has stored DNA profiles with a subject’s other biometric information, including fingerprints, portraits and voice prints, the heads of the DNA program wrote in the Chinese journal Forensic Science and Technology last year. One provincial police force has floated plans to link the data to a person’s information such as online shopping records and entertainment habits, according to a paper presented at the national police DNA conference. Such high-tech files would create more sophisticated versions of paper dossiers that police have long relied on to keep tabs on citizens.

Marrying DNA profiles with real-time surveillance tools, such as monitoring online activity and cameras hooked to facial-recognition software, would help China’s ruling Communist Party develop an all-encompassing “digital totalitarian state,” says Xiao Qiang, adjunct professor at the University of California at Berkeley’s School of Information.


A teenage boy studying in one of the county’s high schools recalled that a policeman came into his class after lunch one day this spring and passed out the collection boxes. Male students were told to clean their mouths, spit into the boxes and place them into envelopes on which they had written their names.


Chinese police sometimes try to draw connections between ethnic background or place of origin and propensity for crime. Police officers in northwestern China’s Ningxia region studied data on local prisoners and noticed that a large number came from three towns. They decided to collect genetic material from boys and men from every clan to bolster the local DNA database, police said at the law-enforcement DNA conference in September.

China is certainly in the lead in the arena of digital-biometric monitoring. Particularly “interesting” is the proposal to merge DNA info with online behavioral profiling.



This is the thing I find the most disenchanting about the current political spectrum. It's all reheated ideas that are a century old, at least. Everyone wants to run our iPhone society with power structures dating to the abacus.
Thank God for the forward-thinking Chinese Communist Party and its high-tech social credit system!


INSIDE CHINA'S VAST NEW EXPERIMENT IN SOCIAL RANKING: https://www.wired.com/story/age-of-social-credit/

The government thinks "social credit" will fix the country's lack of trust — and the public agrees.

To be Chinese today is to live in a society of distrust, where every opportunity is a potential con and every act of generosity a risk of exploitation. When old people fall on the street, it’s common that no one offers to help them up, afraid that they might be accused of pushing them in the first place and sued. The problem has grown steadily since the start of the country’s economic boom in the 1980s. But only recently has the deficit of social trust started to threaten not just individual lives, but the country’s economy and system of politics as a whole. The less people trust each other, the more the social pact that the government has with its citizens — of social stability and harmony in exchange for a lack of political rights — disintegrates.

All of which explains why Chinese state media has recently started to acknowledge the phenomenon — and why the government has started searching for solutions. But rather than promoting the organic return of traditional morality to reduce the gulf of distrust, the Chinese government has preferred to invest its energy in technological fixes. It’s now rolling out systems of data-driven “social credit” that will purportedly address the problem by tracking “good” and “bad” behavior, with rewards and punishments meted out accordingly. In the West, plans of this sort have tended to spark fears about the reach of the surveillance state. Yet in China, it’s being welcomed by a public fed up of not knowing who to trust.

It’s unsurprising that a system that promises to place a check on unfiltered power has proven popular — although it’s… [more]
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january 2017 by nhaliday
Shtetl-Optimized » Blog Archive » Why I Am Not An Integrated Information Theorist (or, The Unconscious Expander)
In my opinion, how to construct a theory that tells us which physical systems are conscious and which aren’t—giving answers that agree with “common sense” whenever the latter renders a verdict—is one of the deepest, most fascinating problems in all of science. Since I don’t know a standard name for the problem, I hereby call it the Pretty-Hard Problem of Consciousness. Unlike with the Hard Hard Problem, I don’t know of any philosophical reason why the Pretty-Hard Problem should be inherently unsolvable; but on the other hand, humans seem nowhere close to solving it (if we had solved it, then we could reduce the abortion, animal rights, and strong AI debates to “gentlemen, let us calculate!”).

Now, I regard IIT as a serious, honorable attempt to grapple with the Pretty-Hard Problem of Consciousness: something concrete enough to move the discussion forward. But I also regard IIT as a failed attempt on the problem. And I wish people would recognize its failure, learn from it, and move on.

In my view, IIT fails to solve the Pretty-Hard Problem because it unavoidably predicts vast amounts of consciousness in physical systems that no sane person would regard as particularly “conscious” at all: indeed, systems that do nothing but apply a low-density parity-check code, or other simple transformations of their input data. Moreover, IIT predicts not merely that these systems are “slightly” conscious (which would be fine), but that they can be unboundedly more conscious than humans are.

To justify that claim, I first need to define Φ. Strikingly, despite the large literature about Φ, I had a hard time finding a clear mathematical definition of it—one that not only listed formulas but fully defined the structures that the formulas were talking about. Complicating matters further, there are several competing definitions of Φ in the literature, including ΦDM (discrete memoryless), ΦE (empirical), and ΦAR (autoregressive), which apply in different contexts (e.g., some take time evolution into account and others don’t). Nevertheless, I think I can define Φ in a way that will make sense to theoretical computer scientists. And crucially, the broad point I want to make about Φ won’t depend much on the details of its formalization anyway.

We consider a discrete system in a state x=(x1,…,xn)∈Sn, where S is a finite alphabet (the simplest case is S={0,1}). We imagine that the system evolves via an “updating function” f:Sn→Sn. Then the question that interests us is whether the xi‘s can be partitioned into two sets A and B, of roughly comparable size, such that the updates to the variables in A don’t depend very much on the variables in B and vice versa. If such a partition exists, then we say that the computation of f does not involve “global integration of information,” which on Tononi’s theory is a defining aspect of consciousness.
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january 2017 by nhaliday
Noise: dinosaurs, syphilis, and all that | West Hunter
Generally speaking, I thought the paleontologists were a waste of space: innumerate, ignorant about evolution, and simply not very smart.

None of them seemed to understand that a sharp, short unpleasant event is better at causing a mass extinction, since it doesn’t give flora and fauna time to adapt.

Most seemed to think that gradual change caused by slow geological and erosion forces was ‘natural’, while extraterrestrial impact was not. But if you look at the Moon, or Mars, or the Kirkwood gaps in the asteroids, or think about the KAM theorem, it is apparent that Newtonian dynamics implies that orbits will be perturbed, and that sometimes there will be catastrophic cosmic collisions. Newtonian dynamics is as ‘natural’ as it gets: paleontologists not studying it in school and not having much math hardly makes it ‘unnatural’.

One of the more interesting general errors was not understanding how to to deal with noise – incorrect observations. There’s a lot of noise in the paleontological record. Dinosaur bones can be eroded and redeposited well after their life times – well after the extinction of all dinosaurs. The fossil record is patchy: if a species is rare, it can easily look as if it went extinct well before it actually did. This means that the data we have is never going to agree with a perfectly correct hypothesis – because some of the data is always wrong. Particularly true if the hypothesis is specific and falsifiable. If your hypothesis is vague and imprecise – not even wrong – it isn’t nearly as susceptible to noise. As far as I can tell, a lot of paleontologists [ along with everyone in the social sciences] think of of unfalsifiability as a strength.

Done Quickly: https://westhunt.wordpress.com/2011/12/03/done-quickly/
I’ve never seen anyone talk about it much, but when you think about mass extinctions, you also have to think about rates of change

You can think of a species occupying a point in a many-dimensional space, where each dimension represents some parameter that influences survival and/or reproduction: temperature, insolation, nutrient concentrations, oxygen partial pressure, toxin levels, yada yada yada. That point lies within a zone of habitability – the set of environmental conditions that the species can survive. Mass extinction occurs when environmental changes are so large that many species are outside their comfort zone.

The key point is that, with gradual change, species adapt. In just a few generations, you can see significant heritable responses to a new environment. Frogs have evolved much greater tolerance of acidification in 40 years (about 15 generations). Some plants in California have evolved much greater tolerance of copper in just 70 years.

As this happens, the boundaries of the comfort zone move. Extinctions occur when the rate of environmental change is greater than the rate of adaptation, or when the amount of environmental change exceeds the limit of feasible adaptation. There are such limits: bar-headed geese fly over Mt. Everest, where the oxygen partial pressure is about a third of that at sea level, but I’m pretty sure that no bird could survive on the Moon.


Paleontologists prefer gradualist explanations for mass extinctions, but they must be wrong, for the most part.
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september 2016 by nhaliday

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