39fd04bdce
* Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem" (who cares) ). But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things. This <10-page paper also uses 𝔰𝔩₂(ℂ), a simple mathematical object you haven’t heard of, but which is a nice lead-in to an area of real mathematics—rep theory—that (1) contains actual insights (1a) that you aren’t using (2) is simple (3) isn’t pretentious. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre This is a higher-level paper, but still a survey (so more readable). It ties together disparate areas like Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra. It has pictures and you’ll get a better sense of what mathematics is like from skimming it. * Create see.machine.learning * tropical geometry Recently there have been some papers posted about tropical geometry of neural nets. Tropical is also said to be derived from CS. This is a good introduction. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org> |
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| from-dominoes-to-hexagons.pdf | ||
| graph-isomorphism-and-representation-theory.pdf | ||
| intro-to-tropical-algebraic-geometry.pdf | ||
| README.md | ||
| tilings.pdf | ||
| transcendence-of-pi.pdf | ||
Mathematics
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📜 The Transcendence of Pi by Steve Mayer
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📜 Tilings by Ardila
The paper covers a broad swath of the topic on analysis of tiling, and related strategies.
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📜 From Dominoes to Hexagons by Thurston
A paper on the generalization of tilings across different base planes.
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📜 Graph Isomorphism and Representation Theory by Daniel Litt
The graph isomorphism problem shows how to construct graphs using a simple building-block ("basis"). The same method applies to finding different building blocks to construct the same things. This technique can be applied to file systems, greplin, trees, virtual DOM, etc.
A short paper, it also shows how to use
𝔰𝔩₂(ℂ)as a simple mathematical object that leads into the area of real mathematics—represention theory. -
📜 Conway's ZIP proof by George Francis and Jeffrey Weeks
This paper presents a classification proof: "How can it be that you know something about all possible
X, even thexϵXyou haven’t seen yet?" The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels. -
📜 Packing of Spheres by N. Sloane Discusses the role of E8 & Leech lattices in optimal codes for mathematically-ideal compression. Ikosahedrons, a tool in this investigation, are also presented.
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📜 Some Underlying Geometric Notions by Hatcher
High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra.
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📜 What is a Young Tableaux? by Alexander Yong
Young Tableau appear in combinatoric problems, representation theory, and the calculus of Grassmannians. Another common topic is sorting, and smarter ways to organise sub-sorts.
Topology
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📜 Topology of Numbers by hatcher
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Applied Algebraic Topology and Sensor Networks by Robert Ghrist
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📜 Intro to Tropical Algebra Geometry
Recently there have been some papers posted about tropical geometry of neural nets. Tropical is also said to be derived from CS. This is a good introduction.
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📜 Elements of Algebraic Topology: Sheaves by Ghrist
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'