nhaliday + nibble   1489

soft question - What are good non-English languages for mathematicians to know? - MathOverflow
I'm with Deane here: I think learning foreign languages is not a very mathematically productive thing to do; of course, there are lots of good reasons to learn foreign languages, but doing mathematics is not one of them. Not only are there few modern mathematics papers written in languages other than English, but the primary other language they are written (French) in is pretty easy to read without actually knowing it.

Even though I've been to France several times, my spoken French mostly consists of "merci," "si vous plait," "d'accord" and some food words; I've still skimmed 100 page long papers in French without a lot of trouble.

If nothing else, think of reading a paper in French as a good opportunity to teach Google Translate some mathematical French.
q-n-a  overflow  math  academia  learning  foreign-lang  publishing  science  french  soft-question  math.AG  nibble  quixotic 
10 weeks ago by nhaliday
[1804.04268] Incomplete Contracting and AI Alignment
We suggest that the analysis of incomplete contracting developed by law and economics researchers can provide a useful framework for understanding the AI alignment problem and help to generate a systematic approach to finding solutions. We first provide an overview of the incomplete contracting literature and explore parallels between this work and the problem of AI alignment. As we emphasize, misalignment between principal and agent is a core focus of economic analysis. We highlight some technical results from the economics literature on incomplete contracts that may provide insights for AI alignment researchers. Our core contribution, however, is to bring to bear an insight that economists have been urged to absorb from legal scholars and other behavioral scientists: the fact that human contracting is supported by substantial amounts of external structure, such as generally available institutions (culture, law) that can supply implied terms to fill the gaps in incomplete contracts. We propose a research agenda for AI alignment work that focuses on the problem of how to build AI that can replicate the human cognitive processes that connect individual incomplete contracts with this supporting external structure.
nibble  preprint  org:mat  papers  ai  ai-control  alignment  coordination  contracts  law  economics  interests  culture  institutions  number  context  behavioral-econ  composition-decomposition  rent-seeking  whole-partial-many 
april 2018 by nhaliday
Theory of Self-Reproducing Automata - John von Neumann
Fourth Lecture: THE ROLE OF HIGH AND OF EXTREMELY HIGH COMPLICATION

Comparisons between computing machines and the nervous systems. Estimates of size for computing machines, present and near future.

Estimates for size for the human central nervous system. Excursus about the “mixed” character of living organisms. Analog and digital elements. Observations about the “mixed” character of all componentry, artificial as well as natural. Interpretation of the position to be taken with respect to these.

Evaluation of the discrepancy in size between artificial and natural automata. Interpretation of this discrepancy in terms of physical factors. Nature of the materials used.

The probability of the presence of other intellectual factors. The role of complication and the theoretical penetration that it requires.

Questions of reliability and errors reconsidered. Probability of individual errors and length of procedure. Typical lengths of procedure for computing machines and for living organisms--that is, for artificial and for natural automata. Upper limits on acceptable probability of error in individual operations. Compensation by checking and self-correcting features.

Differences of principle in the way in which errors are dealt with in artificial and in natural automata. The “single error” principle in artificial automata. Crudeness of our approach in this case, due to the lack of adequate theory. More sophisticated treatment of this problem in natural automata: The role of the autonomy of parts. Connections between this autonomy and evolution.

- 10^10 neurons in brain, 10^4 vacuum tubes in largest computer at time
- machines faster: 5 ms from neuron potential to neuron potential, 10^-3 ms for vacuum tubes

https://en.wikipedia.org/wiki/John_von_Neumann#Computing
pdf  article  papers  essay  nibble  math  cs  computation  bio  neuro  neuro-nitgrit  scale  magnitude  comparison  acm  von-neumann  giants  thermo  phys-energy  speed  performance  time  density  frequency  hardware  ems  efficiency  dirty-hands  street-fighting  fermi  estimate  retention  physics  interdisciplinary  multi  wiki  links  people  🔬  atoms  automata  duplication  iteration-recursion  turing  complexity  measure  nature  technology  complex-systems  bits  information-theory  circuits  robust  structure  composition-decomposition  evolution  mutation  axioms  analogy  thinking  input-output  hi-order-bits  coding-theory  flexibility  rigidity 
april 2018 by nhaliday
Ultimate fate of the universe - Wikipedia
The fate of the universe is determined by its density. The preponderance of evidence to date, based on measurements of the rate of expansion and the mass density, favors a universe that will continue to expand indefinitely, resulting in the "Big Freeze" scenario below.[8] However, observations are not conclusive, and alternative models are still possible.[9]

Big Freeze or heat death
Main articles: Future of an expanding universe and Heat death of the universe
The Big Freeze is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature.[10] This scenario, in combination with the Big Rip scenario, is currently gaining ground as the most important hypothesis.[11] It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry. With a positive cosmological constant, it could also occur in a closed universe. In this scenario, stars are expected to form normally for 1012 to 1014 (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. Eventually black holes will dominate the universe, which themselves will disappear over time as they emit Hawking radiation.[12] Over infinite time, there would be a spontaneous entropy decrease by the Poincaré recurrence theorem, thermal fluctuations,[13][14] and the fluctuation theorem.[15][16]

A related scenario is heat death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed and there are no gradients—which are needed to sustain information processing, one form of which is life. The heat death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.[17]
physics  big-picture  world  space  long-short-run  futurism  singularity  wiki  reference  article  nibble  thermo  temperature  entropy-like  order-disorder  death  nihil  bio  complex-systems  cybernetics  increase-decrease  trends  computation  local-global  prediction  time  spatial  spreading  density  distribution  manifolds  geometry  janus 
april 2018 by nhaliday
Eternity in six hours: intergalactic spreading of intelligent life and sharpening the Fermi paradox
We do this by demonstrating that traveling between galaxies – indeed even launching a colonisation project for the entire reachable universe – is a relatively simple task for a star-spanning civilization, requiring modest amounts of energy and resources. We start by demonstrating that humanity itself could likely accomplish such a colonisation project in the foreseeable future, should we want to, and then demonstrate that there are millions of galaxies that could have reached us by now, using similar methods. This results in a considerable sharpening of the Fermi paradox.
pdf  study  article  essay  anthropic  fermi  space  expansionism  bostrom  ratty  philosophy  xenobio  ideas  threat-modeling  intricacy  time  civilization  🔬  futurism  questions  paradox  risk  physics  engineering  interdisciplinary  frontier  technology  volo-avolo  dirty-hands  ai  automation  robotics  duplication  iteration-recursion  von-neumann  data  scale  magnitude  skunkworks  the-world-is-just-atoms  hard-tech  ems  bio  bits  speedometer  nature  model-organism  mechanics  phys-energy  relativity  electromag  analysis  spock  nitty-gritty  spreading  hanson  street-fighting  speed  gedanken  nibble 
march 2018 by nhaliday
Prisoner's dilemma - Wikipedia
caveat to result below:
An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).[14]

Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is bigger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.[8]

https://alfanl.com/2018/04/12/defection/
Nature boils down to a few simple concepts.

Haters will point out that I oversimplify. The haters are wrong. I am good at saying a lot with few words. Nature indeed boils down to a few simple concepts.

In life, you can either cooperate or defect.

Used to be that defection was the dominant strategy, say in the time when the Roman empire started to crumble. Everybody complained about everybody and in the end nothing got done. Then came Jesus, who told people to be loving and cooperative, and boom: 1800 years later we get the industrial revolution.

Because of Jesus we now find ourselves in a situation where cooperation is the dominant strategy. A normie engages in a ton of cooperation: with the tax collector who wants more and more of his money, with schools who want more and more of his kid’s time, with media who wants him to repeat more and more party lines, with the Zeitgeist of the Collective Spirit of the People’s Progress Towards a New Utopia. Essentially, our normie is cooperating himself into a crumbling Western empire.

Turns out that if everyone blindly cooperates, parasites sprout up like weeds until defection once again becomes the standard.

The point of a post-Christian religion is to once again create conditions for the kind of cooperation that led to the industrial revolution. This necessitates throwing out undead Christianity: you do not blindly cooperate. You cooperate with people that cooperate with you, you defect on people that defect on you. Christianity mixed with Darwinism. God and Gnon meet.

This also means we re-establish spiritual hierarchy, which, like regular hierarchy, is a prerequisite for cooperation. It is this hierarchical cooperation that turns a household into a force to be reckoned with, that allows a group of men to unite as a front against their enemies, that allows a tribe to conquer the world. Remember: Scientology bullied the Cathedral’s tax department into submission.

With a functioning hierarchy, men still gossip, lie and scheme, but they will do so in whispers behind closed doors. In your face they cooperate and contribute to the group’s wellbeing because incentives are thus that contributing to group wellbeing heightens status.

Without a functioning hierarchy, men gossip, lie and scheme, but they do so in your face, and they tell you that you are positively deluded for accusing them of gossiping, lying and scheming. Seeds will not sprout in such ground.

Spiritual dominance is established in the same way any sort of dominance is established: fought for, taken. But the fight is ritualistic. You can’t force spiritual dominance if no one listens, or if you are silenced the ritual is not allowed to happen.

If one of our priests is forbidden from establishing spiritual dominance, that is a sure sign an enemy priest is in better control and has vested interest in preventing you from establishing spiritual dominance..

They defect on you, you defect on them. Let them suffer the consequences of enemy priesthood, among others characterized by the annoying tendency that very little is said with very many words.

https://contingentnotarbitrary.com/2018/04/14/rederiving-christianity/
To recap, we started with a secular definition of Logos and noted that its telos is existence. Given human nature, game theory and the power of cooperation, the highest expression of that telos is freely chosen universal love, tempered by constant vigilance against defection while maintaining compassion for the defectors and forgiving those who repent. In addition, we must know the telos in order to fulfill it.

In Christian terms, looks like we got over half of the Ten Commandments (know Logos for the First, don’t defect or tempt yourself to defect for the rest), the importance of free will, the indestructibility of evil (group cooperation vs individual defection), loving the sinner and hating the sin (with defection as the sin), forgiveness (with conditions), and love and compassion toward all, assuming only secular knowledge and that it’s good to exist.

Iterated Prisoner's Dilemma is an Ultimatum Game: http://infoproc.blogspot.com/2012/07/iterated-prisoners-dilemma-is-ultimatum.html
The history of IPD shows that bounded cognition prevented the dominant strategies from being discovered for over over 60 years, despite significant attention from game theorists, computer scientists, economists, evolutionary biologists, etc. Press and Dyson have shown that IPD is effectively an ultimatum game, which is very different from the Tit for Tat stories told by generations of people who worked on IPD (Axelrod, Dawkins, etc., etc.).

...

For evolutionary biologists: Dyson clearly thinks this result has implications for multilevel (group vs individual selection):
... Cooperation loses and defection wins. The ZD strategies confirm this conclusion and make it sharper. ... The system evolved to give cooperative tribes an advantage over non-cooperative tribes, using punishment to give cooperation an evolutionary advantage within the tribe. This double selection of tribes and individuals goes way beyond the Prisoners' Dilemma model.

implications for fractionalized Europe vis-a-vis unified China?

and more broadly does this just imply we're doomed in the long run RE: cooperation, morality, the "good society", so on...? war and group-selection is the only way to get a non-crab bucket civilization?

Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent:
http://www.pnas.org/content/109/26/10409.full
http://www.pnas.org/content/109/26/10409.full.pdf
https://www.edge.org/conversation/william_h_press-freeman_dyson-on-iterated-prisoners-dilemma-contains-strategies-that

https://en.wikipedia.org/wiki/Ultimatum_game

analogy for ultimatum game: the state gives the demos a bargain take-it-or-leave-it, and...if the demos refuses...violence?

The nature of human altruism: http://sci-hub.tw/https://www.nature.com/articles/nature02043
- Ernst Fehr & Urs Fischbacher

Some of the most fundamental questions concerning our evolutionary origins, our social relations, and the organization of society are centred around issues of altruism and selfishness. Experimental evidence indicates that human altruism is a powerful force and is unique in the animal world. However, there is much individual heterogeneity and the interaction between altruists and selfish individuals is vital to human cooperation. Depending on the environment, a minority of altruists can force a majority of selfish individuals to cooperate or, conversely, a few egoists can induce a large number of altruists to defect. Current gene-based evolutionary theories cannot explain important patterns of human altruism, pointing towards the importance of both theories of cultural evolution as well as gene–culture co-evolution.

...

Why are humans so unusual among animals in this respect? We propose that quantitatively, and probably even qualitatively, unique patterns of human altruism provide the answer to this question. Human altruism goes far beyond that which has been observed in the animal world. Among animals, fitness-reducing acts that confer fitness benefits on other individuals are largely restricted to kin groups; despite several decades of research, evidence for reciprocal altruism in pair-wise repeated encounters4,5 remains scarce6–8. Likewise, there is little evidence so far that individual reputation building affects cooperation in animals, which contrasts strongly with what we find in humans. If we randomly pick two human strangers from a modern society and give them the chance to engage in repeated anonymous exchanges in a laboratory experiment, there is a high probability that reciprocally altruistic behaviour will emerge spontaneously9,10.

However, human altruism extends far beyond reciprocal altruism and reputation-based cooperation, taking the form of strong reciprocity11,12. Strong reciprocity is a combination of altruistic rewarding, which is a predisposition to reward others for cooperative, norm-abiding behaviours, and altruistic punishment, which is a propensity to impose sanctions on others for norm violations. Strong reciprocators bear the cost of rewarding or punishing even if they gain no individual economic benefit whatsoever from their acts. In contrast, reciprocal altruists, as they have been defined in the biological literature4,5, reward and punish only if this is in their long-term self-interest. Strong reciprocity thus constitutes a powerful incentive for cooperation even in non-repeated interactions and when reputation gains are absent, because strong reciprocators will reward those who cooperate and punish those who defect.

...

We will show that the interaction between selfish and strongly reciprocal … [more]
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march 2018 by nhaliday
Stein's example - Wikipedia
Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named after Charles Stein of Stanford University, who discovered the phenomenon in 1955.[1]

An intuitive explanation is that optimizing for the mean-squared error of a combined estimator is not the same as optimizing for the errors of separate estimators of the individual parameters. In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent; this occurs in channel estimation in telecommunications, for instance (different factors affect overall channel performance). On the other hand, if one is instead interested in estimating an individual parameter, then using a combined estimator does not help and is in fact worse.

...

Many simple, practical estimators achieve better performance than the ordinary estimator. The best-known example is the James–Stein estimator, which works by starting at X and moving towards a particular point (such as the origin) by an amount inversely proportional to the distance of X from that point.
nibble  concept  levers  wiki  reference  acm  stats  probability  decision-theory  estimate  distribution  atoms 
february 2018 by nhaliday
Information Processing: Mathematical Theory of Deep Neural Networks (Princeton workshop)
"Recently, long-past-due theoretical results have begun to emerge. These results, and those that will follow in their wake, will begin to shed light on the properties of large, adaptive, distributed learning architectures, and stand to revolutionize how computer science and neuroscience understand these systems."
hsu  scitariat  commentary  links  research  research-program  workshop  events  princeton  sanjeev-arora  deep-learning  machine-learning  ai  generalization  explanans  off-convex  nibble  frontier  speedometer  state-of-art  big-surf  announcement 
january 2018 by nhaliday
orbit - Best approximation for Sun's trajectory around galactic center? - Astronomy Stack Exchange
The Sun orbits in the Galactic potential. The motion is complex; it takes about 230 million years to make a circuit with an orbital speed of around 220 km/s, but at the same time it oscillates up and down with respect to the Galactic plane every ∼70∼70 million years and also wobbles in and out every ∼150∼150 million years (this is called epicyclic motion). The spatial amplitudes of these oscillations are around 100 pc vertically and 300 pc in the radial direction inwards and outwards around an average orbital radius (I am unable to locate a precise figure for the latter).
nibble  q-n-a  overflow  space  oscillation  time  cycles  spatial  trivia  manifolds 
december 2017 by nhaliday
Why do stars twinkle?
According to many astronomers and educators, twinkle (stellar scintillation) is caused by atmospheric structure that works like ordinary lenses and prisms. Pockets of variable temperature - and hence index of refraction - randomly shift and focus starlight, perceived by eye as changes in brightness. Pockets also disperse colors like prisms, explaining the flashes of color often seen in bright stars. Stars appear to twinkle more than planets because they are points of light, whereas the twinkling points on planetary disks are averaged to a uniform appearance. Below, figure 1 is a simulation in glass of the kind of turbulence structure posited in the lens-and-prism theory of stellar scintillation, shown over the Penrose tile floor to demonstrate the random lensing effects.

However appealing and ubiquitous on the internet, this popular explanation is wrong, and my aim is to debunk the myth. This research is mostly about showing that the lens-and-prism theory just doesn't work, but I also have a stellar list of references that explain the actual cause of scintillation, starting with two classic papers by C.G. Little and S. Chandrasekhar.
nibble  org:junk  space  sky  visuo  illusion  explanans  physics  electromag  trivia  cocktail  critique  contrarianism  explanation  waves  simulation  experiment  hmm  magnitude  atmosphere  roots  idk 
december 2017 by nhaliday
light - Why doesn't the moon twinkle? - Astronomy Stack Exchange
As you mention, when light enters our atmosphere, it goes through several parcels of gas with varying density, temperature, pressure, and humidity. These differences make the refractive index of the parcels different, and since they move around (the scientific term for air moving around is "wind"), the light rays take slightly different paths through the atmosphere.

Stars are point sources
…the Moon is not
nibble  q-n-a  overflow  space  physics  trivia  cocktail  navigation  sky  visuo  illusion  measure  random  electromag  signal-noise  flux-stasis  explanation  explanans  magnitude  atmosphere  roots 
december 2017 by nhaliday
galaxy - How do astronomers estimate the total mass of dust in clouds and galaxies? - Astronomy Stack Exchange
Dust absorbs stellar light (primarily in the ultraviolet), and is heated up. Subsequently it cools by emitting infrared, "thermal" radiation. Assuming a dust composition and grain size distribution, the amount of emitted IR light per unit dust mass can be calculated as a function of temperature. Observing the object at several different IR wavelengths, a Planck curve can be fitted to the data points, yielding the dust temperature. The more UV light incident on the dust, the higher the temperature.

The result is somewhat sensitive to the assumptions, and thus the uncertainties are sometimes quite large. The more IR data points obtained, the better. If only one IR point is available, the temperature cannot be calculated. Then there's a degeneracy between incident UV light and the amount of dust, and the mass can only be estimated to within some orders of magnitude (I think).
nibble  q-n-a  overflow  space  measurement  measure  estimate  physics  electromag  visuo  methodology 
december 2017 by nhaliday
How do you measure the mass of a star? (Beginner) - Curious About Astronomy? Ask an Astronomer
Measuring the mass of stars in binary systems is easy. Binary systems are sets of two or more stars in orbit about each other. By measuring the size of the orbit, the stars' orbital speeds, and their orbital periods, we can determine exactly what the masses of the stars are. We can take that knowledge and then apply it to similar stars not in multiple systems.

We also can easily measure the luminosity and temperature of any star. A plot of luminocity versus temperature for a set of stars is called a Hertsprung-Russel (H-R) diagram, and it turns out that most stars lie along a thin band in this diagram known as the main Sequence. Stars arrange themselves by mass on the Main Sequence, with massive stars being hotter and brighter than their small-mass bretheren. If a star falls on the Main Sequence, we therefore immediately know its mass.

In addition to these methods, we also have an excellent understanding of how stars work. Our models of stellar structure are excellent predictors of the properties and evolution of stars. As it turns out, the mass of a star determines its life history from day 1, for all times thereafter, not only when the star is on the Main Sequence. So actually, the position of a star on the H-R diagram is a good indicator of its mass, regardless of whether it's on the Main Sequence or not.
nibble  q-n-a  org:junk  org:edu  popsci  space  physics  electromag  measurement  mechanics  gravity  cycles  oscillation  temperature  visuo  plots  correlation  metrics  explanation  measure  methodology 
december 2017 by nhaliday
Sequence Modeling with CTC
A visual guide to Connectionist Temporal Classification, an algorithm used to train deep neural networks in speech recognition, handwriting recognition and other sequence problems.
acmtariat  techtariat  org:bleg  nibble  better-explained  machine-learning  deep-learning  visual-understanding  visualization  analysis  let-me-see  research  sequential  audio  classification  model-class  exposition  language  acm  approximation  comparison  markov  iteration-recursion  concept  atoms  distribution  orders  DP  heuristic  optimization  trees  greedy  matching  gradient-descent 
december 2017 by nhaliday
Is the speed of light really constant?
So what if the speed of light isn’t the same when moving toward or away from us? Are there any observable consequences? Not to the limits of observation so far. We know, for example, that any one-way speed of light is independent of the motion of the light source to 2 parts in a billion. We know it has no effect on the color of the light emitted to a few parts in 1020. Aspects such as polarization and interference are also indistinguishable from standard relativity. But that’s not surprising, because you don’t need to assume isotropy for relativity to work. In the 1970s, John Winnie and others showed that all the results of relativity could be modeled with anisotropic light so long as the two-way speed was a constant. The “extra” assumption that the speed of light is a uniform constant doesn’t change the physics, but it does make the mathematics much simpler. Since Einstein’s relativity is the simpler of two equivalent models, it’s the model we use. You could argue that it’s the right one citing Occam’s razor, or you could take Newton’s position that anything untestable isn’t worth arguing over.

SPECIAL RELATIVITY WITHOUT ONE-WAY VELOCITY ASSUMPTIONS:
https://sci-hub.bz/https://www.jstor.org/stable/186029
https://sci-hub.bz/https://www.jstor.org/stable/186671
nibble  scitariat  org:bleg  physics  relativity  electromag  speed  invariance  absolute-relative  curiosity  philosophy  direction  gedanken  axioms  definition  models  experiment  space  science  measurement  volo-avolo  synchrony  uniqueness  multi  pdf  piracy  study  article 
november 2017 by nhaliday
Estimation of effect size distribution from genome-wide association studies and implications for future discoveries
We report a set of tools to estimate the number of susceptibility loci and the distribution of their effect sizes for a trait on the basis of discoveries from existing genome-wide association studies (GWASs). We propose statistical power calculations for future GWASs using estimated distributions of effect sizes. Using reported GWAS findings for height, Crohn’s disease and breast, prostate and colorectal (BPC) cancers, we determine that each of these traits is likely to harbor additional loci within the spectrum of low-penetrance common variants. These loci, which can be identified from sufficiently powerful GWASs, together could explain at least 15–20% of the known heritability of these traits. However, for BPC cancers, which have modest familial aggregation, our analysis suggests that risk models based on common variants alone will have modest discriminatory power (63.5% area under curve), even with new discoveries.

later paper:
Distribution of allele frequencies and effect sizes and their interrelationships for common genetic susceptibility variants: http://www.pnas.org/content/108/44/18026.full

Recent discoveries of hundreds of common susceptibility SNPs from genome-wide association studies provide a unique opportunity to examine population genetic models for complex traits. In this report, we investigate distributions of various population genetic parameters and their interrelationships using estimates of allele frequencies and effect-size parameters for about 400 susceptibility SNPs across a spectrum of qualitative and quantitative traits. We calibrate our analysis by statistical power for detection of SNPs to account for overrepresentation of variants with larger effect sizes in currently known SNPs that are expected due to statistical power for discovery. Across all qualitative disease traits, minor alleles conferred “risk” more often than “protection.” Across all traits, an inverse relationship existed between “regression effects” and allele frequencies. Both of these trends were remarkably strong for type I diabetes, a trait that is most likely to be influenced by selection, but were modest for other traits such as human height or late-onset diseases such as type II diabetes and cancers. Across all traits, the estimated effect-size distribution suggested the existence of increasingly large numbers of susceptibility SNPs with decreasingly small effects. For most traits, the set of SNPs with intermediate minor allele frequencies (5–20%) contained an unusually small number of susceptibility loci and explained a relatively small fraction of heritability compared with what would be expected from the distribution of SNPs in the general population. These trends could have several implications for future studies of common and uncommon variants.

...

Relationship Between Allele Frequency and Effect Size. We explored the relationship between allele frequency and effect size in different scales. An inverse relationship between the squared regression coefficient and f(1 − f) was observed consistently across different traits (Fig. 3). For a number of these traits, however, the strengths of these relationships become less pronounced after adjustment for ascertainment due to study power. The strength of the trend, as captured by the slope of the fitted line (Table 2), markedly varies between traits, with an almost 10-fold change between the two extremes of distinct types of traits. After adjustment, the most pronounced trend was seen for type I diabetes and Crohn’s disease among qualitative traits and LDL level among quantitative traits. In exploring the relationship between the frequency of the risk allele and the magnitude of the associated risk coefficient (Fig. S4), we observed a quadratic pattern that indicates increasing risk coefficients as the risk-allele frequency diverges away from 0.50 either toward 0 or toward 1. Thus, it appears that regression coefficients for common susceptibility SNPs increase in magnitude monotonically with decreasing minor-allele frequency, irrespective of whether the minor allele confers risk or protection. However, for some traits, such as type I diabetes, risk alleles were predominantly minor alleles, that is, they had frequencies of less than 0.50.
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november 2017 by nhaliday
Use and Interpretation of LD Score Regression
LD Score regression distinguishes confounding from polygenicity in genome-wide association studies: https://sci-hub.bz/10.1038/ng.3211
- Po-Ru Loh, Nick Patterson, et al.

https://www.biorxiv.org/content/biorxiv/early/2014/02/21/002931.full.pdf

Both polygenicity (i.e. many small genetic effects) and confounding biases, such as cryptic relatedness and population stratification, can yield inflated distributions of test statistics in genome-wide association studies (GWAS). However, current methods cannot distinguish between inflation from bias and true signal from polygenicity. We have developed an approach that quantifies the contributions of each by examining the relationship between test statistics and linkage disequilibrium (LD). We term this approach LD Score regression. LD Score regression provides an upper bound on the contribution of confounding bias to the observed inflation in test statistics and can be used to estimate a more powerful correction factor than genomic control. We find strong evidence that polygenicity accounts for the majority of test statistic inflation in many GWAS of large sample size.

Supplementary Note: https://images.nature.com/original/nature-assets/ng/journal/v47/n3/extref/ng.3211-S1.pdf

An atlas of genetic correlations across human diseases
and traits: https://sci-hub.bz/10.1038/ng.3406

https://www.biorxiv.org/content/early/2015/01/27/014498.full.pdf

Supplementary Note: https://images.nature.com/original/nature-assets/ng/journal/v47/n11/extref/ng.3406-S1.pdf

https://github.com/bulik/ldsc
ldsc is a command line tool for estimating heritability and genetic correlation from GWAS summary statistics. ldsc also computes LD Scores.
nibble  pdf  slides  talks  bio  biodet  genetics  genomics  GWAS  genetic-correlation  correlation  methodology  bioinformatics  concept  levers  🌞  tutorial  explanation  pop-structure  gene-drift  ideas  multi  study  org:nat  article  repo  software  tools  libraries  stats  hypothesis-testing  biases  confounding  gotchas  QTL  simulation  survey  preprint  population-genetics 
november 2017 by nhaliday
Equilibrium thermodynamics - Wikipedia
Equilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its final equilibrium state, work is extracted.

In an equilibrium state the potentials, or driving forces, within the system, are in exact balance. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial state of thermodynamic equilibrium, subject to accurately specified constraints, to calculate, when the constraints are changed by an externally imposed intervention, what the state of the system will be once it has reached a new equilibrium. An equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components' Gibbs free energy and a maximum of their entropy.

Equilibrium thermodynamics differs from non-equilibrium thermodynamics, in that, with the latter, the state of the system under investigation will typically not be uniform but will vary locally in those as energy, entropy, and temperature distributions as gradients are imposed by dissipative thermodynamic fluxes. In equilibrium thermodynamics, by contrast, the state of the system will be considered uniform throughout, defined macroscopically by such quantities as temperature, pressure, or volume. Systems are studied in terms of change from one equilibrium state to another; such a change is called a thermodynamic process.
nibble  wiki  reference  concept  conceptual-vocab  explanation  definition  physics  stat-mech  thermo  equilibrium  summary 
november 2017 by nhaliday
Fitting a Structural Equation Model
seems rather unrigorous: nonlinear optimization, possibility of nonconvergence, doesn't even mention local vs. global optimality...
pdf  slides  lectures  acm  stats  hypothesis-testing  graphs  graphical-models  latent-variables  model-class  optimization  nonlinearity  gotchas  nibble  ML-MAP-E  iteration-recursion  convergence 
november 2017 by nhaliday
[1509.02504] Electric charge in hyperbolic motion: The early history and other geometrical aspects
We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material points are replaced by infinitesimal length elements.

SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay: http://web.mit.edu/redingtn/www/netadv/SP20130311.html
nibble  preprint  papers  org:mat  physics  electromag  relativity  exposition  history  mostly-modern  pre-ww2  science  the-trenches  discovery  intricacy  classic  explanation  einstein  giants  plots  manifolds  article  multi  liner-notes  org:junk  org:edu  absolute-relative 
november 2017 by nhaliday
Autoignition temperature - Wikipedia
The autoignition temperature or kindling point of a substance is the lowest temperature at which it spontaneously ignites in normal atmosphere without an external source of ignition, such as a flame or spark. This temperature is required to supply the activation energy needed for combustion. The temperature at which a chemical ignites decreases as the pressure or oxygen concentration increases. It is usually applied to a combustible fuel mixture.

The time {\displaystyle t_{\text{ig}}} {\displaystyle t_{\text{ig}}} it takes for a material to reach its autoignition temperature {\displaystyle T_{\text{ig}}} {\displaystyle T_{\text{ig}}} when exposed to a heat flux {\displaystyle q''} {\displaystyle q''} is given by the following equation:
nibble  wiki  reference  concept  metrics  identity  physics  thermo  temperature  time  stock-flow  phys-energy  chemistry  article  street-fighting  fire  magnitude  data  list 
november 2017 by nhaliday
Static electricity - Wikipedia
Electrons can be exchanged between materials on contact; materials with weakly bound electrons tend to lose them while materials with sparsely filled outer shells tend to gain them. This is known as the triboelectric effect and results in one material becoming positively charged and the other negatively charged. The polarity and strength of the charge on a material once they are separated depends on their relative positions in the triboelectric series. The triboelectric effect is the main cause of static electricity as observed in everyday life, and in common high-school science demonstrations involving rubbing different materials together (e.g., fur against an acrylic rod). Contact-induced charge separation causes your hair to stand up and causes "static cling" (for example, a balloon rubbed against the hair becomes negatively charged; when near a wall, the charged balloon is attracted to positively charged particles in the wall, and can "cling" to it, appearing to be suspended against gravity).
nibble  wiki  reference  article  physics  electromag  embodied  curiosity  IEEE  dirty-hands  phys-energy  safety  data  magnitude  scale 
november 2017 by nhaliday
Hyperbolic angle - Wikipedia
A unit circle {\displaystyle x^{2}+y^{2}=1} x^2 + y^2 = 1 has a circular sector with an area half of the circular angle in radians. Analogously, a unit hyperbola {\displaystyle x^{2}-y^{2}=1} {\displaystyle x^{2}-y^{2}=1} has a hyperbolic sector with an area half of the hyperbolic angle.
nibble  math  trivia  wiki  reference  physics  relativity  concept  atoms  geometry  ground-up  characterization  measure  definition  plots  calculation  nitty-gritty  direction  metrics  manifolds 
november 2017 by nhaliday
general relativity - What if the universe is rotating as a whole? - Physics Stack Exchange
To find out whether the universe is rotating, in principle the most straightforward test is to watch the motion of a gyroscope relative to the distant galaxies. If it rotates at an angular velocity -ω relative to them, then the universe is rotating at angular velocity ω. In practice, we do not have mechanical gyroscopes with small enough random and systematic errors to put a very low limit on ω. However, we can use the entire solar system as a kind of gyroscope. Solar-system observations put a model-independent upper limit of 10^-7 radians/year on the rotation,[Clemence 1957] which is an order of magnitude too lax to rule out the Gödel metric.
nibble  q-n-a  overflow  physics  relativity  gedanken  direction  absolute-relative  big-picture  space  experiment  measurement  volo-avolo 
november 2017 by nhaliday
Ancient Admixture in Human History
- Patterson, Reich et al., 2012
Population mixture is an important process in biology. We present a suite of methods for learning about population mixtures, implemented in a software package called ADMIXTOOLS, that support formal tests for whether mixture occurred and make it possible to infer proportions and dates of mixture. We also describe the development of a new single nucleotide polymorphism (SNP) array consisting of 629,433 sites with clearly documented ascertainment that was specifically designed for population genetic analyses and that we genotyped in 934 individuals from 53 diverse populations. To illustrate the methods, we give a number of examples that provide new insights about the history of human admixture. The most striking finding is a clear signal of admixture into northern Europe, with one ancestral population related to present-day Basques and Sardinians and the other related to present-day populations of northeast Asia and the Americas. This likely reflects a history of admixture between Neolithic migrants and the indigenous Mesolithic population of Europe, consistent with recent analyses of ancient bones from Sweden and the sequencing of the genome of the Tyrolean “Iceman.”
nibble  pdf  study  article  methodology  bio  sapiens  genetics  genomics  population-genetics  migration  gene-flow  software  trees  concept  history  antiquity  europe  roots  gavisti  🌞  bioinformatics  metrics  hypothesis-testing  levers  ideas  libraries  tools  pop-structure 
november 2017 by nhaliday
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