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Linear Thinking in a Nonlinear World
Test yourself with this word problem: Imagine you’re responsible for your company’s car fleet. You manage two models, an SUV that gets 10 miles to the gallon and a sedan that gets 20. The fleet has equal numbers of each, and all the cars travel 10,000 miles a year. You have enough capital to replace one model with more-fuel-efficient vehicles to lower operational costs and help meet sustainability goals.

Which upgrade is better?

A. Replacing the 10 MPG vehicles with 20 MPG vehicles

B. Replacing the 20 MPG vehicles with 50 MPG vehicles

Intuitively, option B seems more impressive—an increase of 30 MPG is a lot larger than a 10 MPG one. And the percentage increase is greater, too. But B is not the better deal. In fact, it’s not even close. Let’s compare.
nonlinearity 
july 2018 by zryb
Book of Extremes: Why the 21st Century Isn’t Like the 20th Century
"What makes the 21st century different from the 20th century? This century is the century of extremes -- political, economic, social, and global black-swan events happening with increasing frequency and severity.

Book of Extremes is a tour of the current reality as seen through the lens of complexity theory – the only theory capable of explaining why the Arab Spring happened and why it will happen again; why social networks in the virtual world behave like flashmobs in the physical world; why financial bubbles blow up in our faces and will grow and burst again; why the rich get richer and will continue to get richer regardless of governmental policies; why the future of economic wealth and national power lies in comparative advantage and global trade; why natural disasters will continue to get bigger and happen more frequently; and why the Internet – invented by the US -- is headed for a global monopoly controlled by a non-US corporation. It is also about the extreme innovations and heroic innovators yet to be discovered and recognized over the next 100 years.

Complexity theory combines the predictable with the unpredictable. It assumes a nonlinear world of long-tailed distributions instead of the classical linear world of normal distributions. In the complex 21st century, almost nothing is linear or normal. Instead, the world is highly connected, conditional, nonlinear, fractal, and punctuated. Life in the 21st century is a long-tailed random walk – Levy walks -- through extreme events of unprecedented impact. It is an exciting time to be alive."
nonlinearity  to-read 
june 2018 by jaypcross
Complexity no Bar to AI - Gwern.net
Critics of AI risk suggest diminishing returns to computing (formalized asymptotically) means AI will be weak; this argument relies on a large number of questionable premises and ignoring additional resources, constant factors, and nonlinear returns to small intelligence advantages, and is highly unlikely. (computer science, transhumanism, AI, R)
created: 1 June 2014; modified: 01 Feb 2018; status: finished; confidence: likely; importance: 10
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april 2018 by nhaliday
The Nonlinear God -- What Does Nonlinearity Look Like? Six Visual Models (Part 1/2)
"I find that many of the grand paradoxes in thinking that people have about God come from a too-shallow understanding of nonlinearity. Calvinism, Molinism, or even just the basic "problem of evil" all bring up a long list of difficult questions when asked from the normal linear human perspective because they also have a preconceived assumption that God is also linear.

But what does nonlinearity even look like? Glad you asked."
god  nonlinearity  cognition  hunters 
december 2017 by jaypcross
Open Thread, 11/26/2017 – Gene Expression
A few days ago there was a Twitter thing about top five books that have influenced you. It’s hard for me to name five, but I put three books down for three different reasons:

- Principles of Population Genetics, because it gives you a model for how to analyze and understand evolutionary processes. There are other books out there besides Principles of Population Genetics. But if you buy this book you don’t need to buy another (at SMBE this year I confused Andy Clark with Mike Lynch for a second when introducing myself. #awkward)
- The Fall of Rome. A lot of historical writing can be tendentious. I’ve also noticed an unfortunate tendency of historians dropping into contemporary arguments and pretty much lying through omission or elision to support their political side (it usually goes “actually, I’m a specialist in this topic and my side is 100% correct because of obscure-stuff where I’m shading the facts”). The Fall of Rome illustrates the solidity that an archaeological and materialist take can give the field. This sort of materialism isn’t the final word, but it needs to be the start of the conversation.
- From Dawn to Decadence: 1500 to the Present: 500 Years of Western Cultural Life. To know things is important in and of itself. My own personal experience is that the returns to knowing things in a particular domain or area do not exhibit a linear return. Rather, it exhibits a logistic curve. Initially, it’s hard to make sense of anything from the facts, but at some point comprehension and insight increase rapidly, until you reach the plateau of diminishing marginal returns.

If you haven’t, I recommend you subscribe to Patrick Wyman’s Tides of History podcast. I pretty much wait now for every new episode.
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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
Reconsidering the Heritability of Intelligence in Adulthood: Taking Assortative Mating and Cultural Transmission into Account
Heritability estimates of general intelligence in adulthood generally range from 75 to 85%, with all heritability due to additive genetic influences, while genetic dominance and shared environmental factors are absent, or too small to be detected. These estimates are derived from studies based on the classical twin design and are based on the assumption of random mating. Yet, considerable positive assortative mating has been reported for general intelligence. Unmodeled assortative mating may lead to biased estimates of the relative magnitude of genetic and environmental factors.

...

Under the preferred phenotypic assortment model, the variance of intelligence in adulthood was not only due to non-shared environmental (18%) and additive genetic factors (44%) but also to non-additive genetic factors (27%) and phenotypic assortment (11%).This non-additive nature of genetic influences on intelligence needs to be accommodated in future GWAS studies for intelligence.
study  biodet  behavioral-gen  psychology  cog-psych  iq  twin-study  sib-study  biases  gotchas  models  map-territory  assortative-mating  variance-components  🌞  nonlinearity  regularizer  intricacy 
november 2017 by nhaliday
1 Genetics and Crime
The broader construct of antisocial behavior – which includes criminal offending, as well as aggression – also shows substantial genetic influence. In a meta-analysis combining effect sizes in 51 twin and adoption studies, Rhee and Waldman (2002) reported a heritability estimate of 41 per cent, with the remaining 59 per cent of variance being due to environmental factors. Interestingly, when comparing results for various definitions of antisocial behavior, only criminal offending appeared to be influenced by both additive genetic effects and non-additive genetic effects – possibly due to genetic dominance and epistatic interactions between genes – based on a pattern of results whereby, on average, identical (monozygotic) twin correlations are more than twice the value of fraternal (dizygotic) twin correlations, and also that biological parent–offspring correlations are less than fraternal twin correlations. Such non-additive genetic effects could arise if one or more high risk alleles act in a recessive fashion, or if certain alleles at one locus affect gene expression at other loci (epistasis).

One intriguing aspect of the literature on genetics and crime is that the strong and consistent genetic influence seen for property offending does not hold true for violent criminal convictions. None of the major adoption studies in Scandinavia or the United States found any elevated risk for violent convictions as a function of either biological or adoptive parent criminal offending, although one early twin study did find greater identical (monozygotic) than fraternal (dizygotic) concordance for violent convictions (see Cloninger and Gottesman, 1987). This pattern of twin, but not parent-offspring, similarity for violent criminal behavior suggests the possibility of non-additive genetic effects due to dominance or epistasis, which would result in increased resemblance for siblings (and twins), but not for parents and offspring. Thus, there may be genetic risk for violent crimes such as murder and rape, which may stem from rare recessive genes, or specific combinations of alleles that do not appear in studies of vertical transmission across generations.

A Swedish national twin study of criminal behavior and its violent, white-collar and property subtypes: https://www.cambridge.org/core/journals/psychological-medicine/article/a-swedish-national-twin-study-of-criminal-behavior-and-its-violent-white-collar-and-property-subtypes/0D9A88185ED0FD5525A5EBD5D2EBA117
For all criminal convictions, heritability was estimated at around 45% in both sexes, with the shared environment accounting for 18% of the variance in liability in females and 27% in males. The correlation of these risk factors across sexes was estimated at +0.63. In men, the magnitudes of genetic and environmental influence were similar in the three criminal conviction subtypes. However, for violent and white-collar convictions, nearly half and one-third of the genetic effects were respectively unique to that criminal subtype. About half of the familial environmental effects were unique to property convictions.

Heritability, Assortative Mating and Gender Differences in Violent Crime: Results from a Total Population Sample Using Twin, Adoption, and Sibling Models: https://link.springer.com/article/10.1007/s10519-011-9483-0
Using 36k twins, violent crime was moderately heritable (~ 55%) w/ 13% shared environment influence. Using 1.5 mil siblings, heritability was higher for males, & family environment higher for females. Moderate assortative mating for violent crime (r = .4).

The impact of neighbourhood deprivation on adolescent violent criminality and substance misuse: A longitudinal, quasi-experimental study of the total Swedish population: https://academic.oup.com/ije/article/42/4/1057/656274/The-impact-of-neighbourhood-deprivation-on
In the crude model, an increase of 1 SD in neighbourhood deprivation was associated with a 57% increase in the odds of being convicted of a violent crime (95% CI 52%–63%). The effect was greatly attenuated when adjustment was made for a number of observed confounders (OR 1.09, 95% CI 1.06–1.11). When we additionally adjusted for unobserved familial confounders, the effect was no longer present (OR 0.96, 95% CI 0.84–1.10). Similar results were observed for substance misuse. The results were not due to poor variability either between neighbourhoods or within families.

Childhood family income, adolescent violent criminality and substance misuse: quasi-experimental total population study: http://bjp.rcpsych.org/content/early/2014/08/14/bjp.bp.113.136200
https://www.economist.com/news/science-and-technology/21613303-disturbing-study-link-between-incomes-and-criminal-behaviour-have-and
What did surprise him was that when he looked at families which had started poor and got richer, the younger children—those born into relative affluence—were just as likely to misbehave when they were teenagers as their elder siblings had been. Family income was not, per se, the determining factor.

Indicators of domestic/intimate partner violence are structured by genetic and nonshared environmental influences: https://www.researchgate.net/publication/233737219_Indicators_of_domesticintimate_partner_violence_are_structured_by_genetic_and_nonshared_environmental_influences
Three indicators of IPV were measured and genetic factors accounted for 24% of the variance in hitting one's partner, 54% of the variance in injuring one's partner, and 51% of the variance in forcing sexual activity on one's partner. The shared environment explained none of the variance across all three indicators and the nonshared environment explained the remainder of the variance.
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october 2017 by nhaliday
Why are children in the same family so different from one another? - PubMed - NCBI
- Plomin et al

The article has three goals: (1) To describe quantitative genetic methods and research that lead to the conclusion that nonshared environment is responsible for most environmental variation relevant to psychological development, (2) to discuss specific nonshared environmental influences that have been studied to date, and (3) to consider relationships between nonshared environmental influences and behavioral differences between children in the same family. The reason for presenting this article in BBS is to draw attention to the far-reaching implications of finding that psychologically relevant environmental influences make children in a family different from, not similar to, one another.
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october 2017 by nhaliday
Stages of Diversification
This paper studies the evolution of sectoral concentration in relation to the level of per capita income. We show that various measures of sectoral concentration follow a U-shaped pattern across a wide variety of data sources: countries first diversify, in the sense that economic activity is spread more equally across sectors, but there exists, relatively late in the development process, a point at which they start specializing again. We discuss this finding in light of existing theories of trade and growth, which generally predict a monotonic relationship between income and diversification. (JEL F43, F15, O40)

seems unhealthy to me (complacency)
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june 2017 by nhaliday
There Is No Such Thing as Decreasing Returns to Scale — Confessions of a Supply-Side Liberal
Besides pedagogical inertia—enforced to some extent by textbook publishers—I am not quite sure what motivates the devotion in so many economics curricula to U-shaped average cost curves. Let me make one guess: there is a desire to explain why firms are the size they are rather than larger or smaller. To my mind, such an explanation should proceed in one of three ways, appropriate to three different situations.
econotariat  economics  micro  plots  scale  marginal  industrial-org  business  econ-productivity  efficiency  cost-benefit  explanation  critique  clarity  intricacy  curvature  convexity-curvature  nonlinearity  input-output 
may 2017 by nhaliday
Estimating the number of unseen variants in the human genome
To find all common variants (frequency at least 1%) the number of individuals that need to be sequenced is small (∼350) and does not differ much among the different populations; our data show that, subject to sequence accuracy, the 1000 Genomes Project is likely to find most of these common variants and a high proportion of the rarer ones (frequency between 0.1 and 1%). The data reveal a rule of diminishing returns: a small number of individuals (∼150) is sufficient to identify 80% of variants with a frequency of at least 0.1%, while a much larger number (> 3,000 individuals) is necessary to find all of those variants.

A map of human genome variation from population-scale sequencing: http://www.internationalgenome.org/sites/1000genomes.org/files/docs/nature09534.pdf

Scientists using data from the 1000 Genomes Project, which sequenced one thousand individuals from 26 human populations, found that "a typical [individual] genome differs from the reference human genome at 4.1 million to 5.0 million sites … affecting 20 million bases of sequence."[11] Nearly all (>99.9%) of these sites are small differences, either single nucleotide polymorphisms or brief insertion-deletions in the genetic sequence, but structural variations account for a greater number of base-pairs than the SNPs and indels.[11]

Human genetic variation: https://en.wikipedia.org/wiki/Human_genetic_variation

Singleton Variants Dominate the Genetic Architecture of Human Gene Expression: https://www.biorxiv.org/content/early/2017/12/15/219238
study  sapiens  genetics  genomics  population-genetics  bioinformatics  data  prediction  cost-benefit  scale  scaling-up  org:nat  QTL  methodology  multi  pdf  curvature  convexity-curvature  nonlinearity  measurement  magnitude  🌞  distribution  missing-heritability  pop-structure  genetic-load  mutation  wiki  reference  article  structure  bio  preprint  biodet  variance-components  nibble  chart 
may 2017 by nhaliday
Concentration and Growth | Dietrich Vollrath
Ultimately, and this is my impression, not some kind of established fact, concentration likely lowers innovative activity. Put it this way, the null hypothesis should probably be that concentration lowers innovation. An individual industry needs to provide evidence they are on the “right side of the curve” in the first AAH figure to believe concentration would be good for productivity growth in the long run.
econotariat  commentary  links  economics  growth-econ  trends  market-power  business  industrial-org  flexibility  innovation  malaise  stagnation  econ-productivity  madisonian  rent-seeking  competition  correlation  frontier  stylized-facts  chart  🎩  entrepreneurialism  rot  scale  curvature  corporation  convexity-curvature  nonlinearity 
may 2017 by nhaliday
Missing heritability problem - Wikipedia
The "missing heritability" problem[1][2][3][4][5][6] can be defined as the fact that single genetic variations cannot account for much of the heritability of diseases, behaviors, and other phenotypes. This is a problem that has significant implications for medicine, since a person's susceptibility to disease may depend more on "the combined effect of all the genes in the background than on the disease genes in the foreground", or the role of genes may have been severely overestimated.

The 'missing heritability' problem was named as such in 2008. The Human Genome Project led to optimistic forecasts that the large genetic contributions to many traits and diseases (which were identified by quantitative genetics and behavioral genetics in particular) would soon be mapped and pinned down to specific genes and their genetic variants by methods such as candidate-gene studies which used small samples with limited genetic sequencing to focus on specific genes believed to be involved, examining the SNP kinds of variants. While many hits were found, they often failed to replicate in other studies.

The exponential fall in genome sequencing costs led to the use of GWAS studies which could simultaneously examine all candidate-genes in larger samples than the original finding, where the candidate-gene hits were found to almost always be false positives and only 2-6% replicate;[7][8][9][10][11][12] in the specific case of intelligence candidate-gene hits, only 1 candidate-gene hit replicated,[13] and of 15 neuroimaging hits, none did.[14] The editorial board of Behavior Genetics noted, in setting more stringent requirements for candidate-gene publications, that "the literature on candidate gene associations is full of reports that have not stood up to rigorous replication...it now seems likely that many of the published findings of the last decade are wrong or misleading and have not contributed to real advances in knowledge".[15] Other researchers have characterized the literature as having "yielded an infinitude of publications with very few consistent replications" and called for a phase out of candidate-gene studies in favor of polygenic scores.[16]

This led to a dilemma. Standard genetics methods have long estimated large heritabilities such as 80% for traits such as height or intelligence, yet none of the genes had been found despite sample sizes that, while small, should have been able to detect variants of reasonable effect size such as 1 inch or 5 IQ points. If genes have such strong cumulative effects - where were they? Several resolutions have been proposed, that the missing heritability is some combination of:

...

7. Genetic effects are indeed through common SNPs acting additively, but are highly polygenic: dispersed over hundreds or thousands of variants each of small effect like a fraction of an inch or a fifth of an IQ point and with low prior probability: unexpected enough that a candidate-gene study is unlikely to select the right SNP out of hundreds of thousands of known SNPs, and GWASes up to 2010, with n<20000, would be unable to find hits which reach genome-wide statistical-significance thresholds. Much larger GWAS sample sizes, often n>100k, would be required to find any hits at all, and would steadily increase after that.
This resolution to the missing heritability problem was supported by the introduction of Genome-wide complex trait analysis (GCTA) in 2010, which demonstrated that trait similarity could be predicted by the genetic similarity of unrelated strangers on common SNPs treated additively, and for many traits the SNP heritability was indeed a substantial fraction of the overall heritability. The GCTA results were further buttressed by findings that a small percent of trait variance could be predicted in GWASes without any genome-wide statistically-significant hits by a linear model including all SNPs regardless of p-value; if there were no SNP contribution, this would be unlikely, but it would be what one expected from SNPs whose effects were very imprecisely estimated by a too-small sample. Combined with the upper bound on maximum effect sizes set by the GWASes up to then, this strongly implied that the highly polygenic theory was correct. Examples of complex traits where increasingly large-scale GWASes have yielded the initial hits and then increasing numbers of hits as sample sizes increased from n<20k to n>100k or n>300k include height,[23] intelligence,[24] and schizophrenia.
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may 2017 by nhaliday

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