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Nomogram - Wikipedia
Mythology and psychology are like the outer axes on a nomogram, allowing plotting of an unknown in between
mathematics  analog  graphical  calculator  harvest 
20 hours ago by bdwc
A simple mechanism could have been decisive for the development of life | Hacker News
This is one in a number of papers exploring how biological phase separation/condensation may have provided favourable microenvironments for early life development.

For a nice primer on what biological phase separation is, see this (non-paywalled) general audience article from earlier this year in Nature (https://www.nature.com/articles/d41586-018-03070-2).

Some other work on phase separation as a means for primordial evolution and biochemistry includes a paper from Christine Keating in 2012 (WAY WAY ahead of the curve) [1], elegant work by Frank Jülicher [2], and more recently a nice paper from Keating and Phil Bevilacqua [3].

These papers (IMO) tie rather nicely into some theoretical predictions on self-organization from Jeremy England [4].

[1] Keating, C.D. (2012). Aqueous phase separation as a possible route to compartmentalization of biological molecules. Acc. Chem. Res. 45, 2114–2124.

[2] Zwicker, D., Seyboldt, R., Weber, C.A., Hyman, A.A., and Jülicher, F. (2016). Growth and division of active droplets provides a model for protocells. Nat. Phys. 13, 408.

[3] Poudyal, R.R., Pir Cakmak, F., Keating, C.D., and Bevilacqua, P.C. (2018). Physical Principles and Extant Biology Reveal Roles for RNA-Containing Membraneless Compartments in Origins of Life Chemistry. Biochemistry 57, 2509–2519.

[4] England, J.L. (2013). Statistical physics of self-replication. J. Chem. Phys. 139, 121923.

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mxwsn 1 day ago [-]

Phase separation really seems to be a hot topic in biology beyond early life development too, extending at least to the field of gene regulation.

A Phase Separation Model for Transcriptional Control. https://www.ncbi.nlm.nih.gov/pubmed/28340338

which already has 70 citations despite being published just 14 months ago.
science  chemistry  biology  physics  mathematics  to:Read  HN-comments  ****  exploration 
23 hours ago by MarcK
Declarative equations, compositional strategies: solving differential systems with lazy splines
A simple Haskell encoding of Euler’s method of integration is presented. From this encoding, a general solver for continuous differential equations is developed, by way of lazy splines. Various
refinement strategies are introduced to improve accuracy. The result is a declarative, compositional library for solving differential
equations.
pdf  article  haskell  mathematics 
yesterday by doneata
What Sequential Games, the Tychonoff Theorem, and the Double-Negation Shift have in Common
This is a tutorial for mathematically inclined functional programmers, based on previously published, peered reviewed theoretical work. We discuss a higher-type functional, written here in the functional programming language Haskell, which

1. optimally plays sequential games,
2. implements a computational version of the Tychonoff Theorem from topology, and
3. realizes the Double-Negation Shift from logic and proof theory.

The functional makes sense for finite and infinite (lazy) lists, and in the binary case it amounts to an operation that is available in any (strong) monad.

In fact, once we define this monad in Haskell, it turns out that this amazingly versatile functional is already available in Haskell, in the standard prelude, called sequence, which iterates this binary operation. Therefore Haskell proves that this functional is even more versatile than anticipated, as the function sequence was introduced for other purposes by the language designers, in particular the iteration of a list of monadic effects (but effects are not what we discuss here).

Checkout related resources as well:
http://www.cs.bham.ac.uk/~mhe/papers/msfp2010/
http://homepages.inf.ed.ac.uk/wadler/papers/tychonoff/tychonoff.lhs
article  pdf  programming  haskell  mathematics  logic 
yesterday by doneata
Linear logic and deep learning
To summarise the talk: deep learning has become a popular tool for image classification, playing Go, and a range of other tasks. Recent work at Facebook, Google and within academia has discovered how to couple deep neural nets to more general programmatic elements in the Von Neumann style, for example external memories. I’ve presented today my joint work with Huiyi Hu, where we for the first time show how using the polynomial semantics of linear logic, one can also couple deep neural nets to functional programming elements.
slides  pdf  deep-learning  logic  mathematics 
yesterday by doneata
Immersive Math
The world's first linear algebra book with fully interactive figures.
kb_cpu  mathematics  tutorial  book 
yesterday by rootis0
Chapter 15 – Key Mathematic Principles for Performance Testers | Microsoft Docs
Helpful illustrations, definitions, and explanations (including standard deviation, which I can never remember)
mathematics  statistics  stats  performance  metrics  standarddeviation 
yesterday by mccutchen
On David Foster Wallace, Georg Cantor, and Infinity
Few ideas have had a racier history than the idea of infinity. It arose amid ancient paradoxes, proceeded to baffle philosophers for a couple of millennia, and then, by a daring feat of intellect, was finally made to yield its secrets in the late 19th century, though not without leaving a new batch of paradoxes. You
books  philosophy  mathematics  davidfosterwallace  infinity  georgcantor 
2 days ago by coldbrain
Les mathématiques au cinéma, une liste exhaustive et définitive - Liste de 23 films - SensCritique
Pour une obscure raison, le cinéma aime parler de mathématiques, ce qui a pour conséquence de créer une catégorie de film à part, les films mathématiques....
cinema  mathematics 
3 days ago by doegox
Immersive Math
"The world's first linear algebra book with fully interactive figures."
linearalgebra  textbooks  free  math  mathematics 
3 days ago by robertogreco

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