Math papers from original isomorphisms PR (#587)

* 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>

data_compression/README.md

@@ -1,4 +1,5 @@
 # Data Compression
 
-* :scroll: [Data Compression](data-compression.pdf)
+* :scroll: [Data Compression](https://github.com/papers-we-love/papers-we-love/blob/master/data-compression/data-compression.pdf)
+
     > This paper surveys a variety of data compression methods spanning almost 40 years of research, from the work of Shannon, Fano and Huffman in the 40's, to a technique developed in 1986.

machine_learning/README.md

@@ -2,28 +2,52 @@
 
 ## External Papers
 
-* [Top 10 algorithms in data mining](http://www.cs.uvm.edu/~icdm/algorithms/10Algorithms-08.pdf) - While it is difficult to identify the top 10, this paper contains 10 very important data mining/machine learning algorithms
-* [A Few Useful Things to Know about Machine Learning](http://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf) - Just like the title says, it contains many useful tips and gotchas for machine learning
-* [Random Forests](https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf) - The initial paper on random forests
-* [Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data](http://repository.upenn.edu/cgi/viewcontent.cgi?article=1162&context=cis_papers) - The paper introducing conditional random fields as a framework for building probabilistic models.
-* [Support-Vector Networks](http://rd.springer.com/content/pdf/10.1007%2FBF00994018.pdf) - The initial paper on support-vector networks for classification.
+* [Top 10 algorithms in data mining](http://www.cs.uvm.edu/~icdm/algorithms/10Algorithms-08.pdf)
+
+  While it is difficult to identify the top 10, this paper contains 10 very important data mining/machine learning algorithms
+
+* [A Few Useful Things to Know about Machine Learning](http://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf)
+
+  Just like the title says, it contains many useful tips and gotchas for machine learning
+* [Random Forests](https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf)
+
+  The initial paper on random forests
+* [Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data](http://repository.upenn.edu/cgi/viewcontent.cgi?article=1162&context=cis_papers)
+
+  The paper introducing conditional random fields as a framework for building probabilistic models.
+* [Support-Vector Networks](http://rd.springer.com/content/pdf/10.1007%2FBF00994018.pdf)
+
+  The initial paper on support-vector networks for classification.
+
 * [The Fast Johnson-Lindenstrauss Transforms](https://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf)
 
     The Johnson-Lindenstrauss transform (JLT) prescribes that there exists a matrix of size `k x d`, where `k = O(1/eps^2 log d)` such that with high probability, a matrix A drawn from this distribution preserves pairwise distances up to epsilon (e.g. `(1-eps) * ||x-y|| < ||Ax - Ay|| < (1+eps) ||x-y||`). This paper was the first paper to show that you can actually compute the JLT in less that `O(kd)` operations (e.g. you don't need to do the full matrix multiplication). They used their faster algorithm to construct one of the fastest known approximate nearest neighbor algorithms.
 
     *Ailon, Nir, and Bernard Chazelle. "The fast Johnson-Lindenstrauss transform and approximate nearest neighbors." SIAM Journal on Computing 39.1 (2009): 302-322. Available: https://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf*
 
-* [Applications of Machine Learning to Location Data](http://www.berkkapicioglu.com/wp-content/uploads/2013/11/thesis_final.pdf) -  Using machine learning to design and analyze novel algorithms that leverage location data.
+* [Applications of Machine Learning to Location Data](http://www.berkkapicioglu.com/wp-content/uploads/2013/11/thesis_final.pdf) 
 
-* ["Why Should I Trust You?" Explaining the Predictions of Any Classifier](http://www.kdd.org/kdd2016/papers/files/rfp0573-ribeiroA.pdf) - This paper introduces an explanation technique for any classifier in a interpretable manner. 
+  Using machine learning to design and analyze novel algorithms that leverage location data.
 
-* [Multiple Narrative Disentanglement: Unraveling *Infinite Jest*](http://dreammachin.es/p1-wallace.pdf) - uses an unsupervised approach to natural language processing to classify narrators in David Foster Wallace's 1,000-page novel.
+* ["Why Should I Trust You?" Explaining the Predictions of Any Classifier](http://www.kdd.org/kdd2016/papers/files/rfp0573-ribeiroA.pdf)
 
-* [ImageNet Classification with Deep Convolutional Neural Networks](http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) - This paper introduces AlexNet, a neural network architecture which dramatically improved over the state-of-the-art in image classification algorithms and is widely regarded as a breakthrough moment for deep learning.
+  This paper introduces an explanation technique for any classifier in a interpretable manner. 
 
-* [Interpretable machine learning: definitions, methods, and applications](https://arxiv.org/pdf/1901.04592.pdf) - This paper introduces the foundations of the rapidly emerging field of interpretable machine learning.
+* [Multiple Narrative Disentanglement: Unraveling *Infinite Jest*](http://dreammachin.es/p1-wallace.pdf)
 
-* [Distilling the Knowledge in a Neural Network](https://arxiv.org/pdf/1503.02531.pdf) - This seminal paper introduces a method to distill information from an ensemble of neural networks into a single model.
+  Uses an unsupervised approach to natural language processing that classifies narrators in David Foster Wallace's 1,000-page novel.
+
+* [ImageNet Classification with Deep Convolutional Neural Networks](http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf)
+
+  This paper introduces AlexNet, a neural network architecture which dramatically improved over the state-of-the-art in image classification algorithms and is widely regarded as a breakthrough moment for deep learning.
+
+* [Interpretable machine learning: definitions, methods, and applications](https://arxiv.org/pdf/1901.04592.pdf)
+
+  This paper introduces the foundations of the rapidly emerging field of interpretable machine learning.
+
+* [Distilling the Knowledge in a Neural Network](https://arxiv.org/pdf/1503.02531.pdf)
+
+  This seminal paper introduces a method to distill information from an ensemble of neural networks into a single model.
 
 ## Hosted Papers
 
@@ -39,3 +63,14 @@
 
     *Bourgain, Jean, and Jelani Nelson. "Toward a unified theory of sparse dimensionality reduction in euclidean space." arXiv preprint arXiv:1311.2542; Accepted in an AMS Journal but unpublished at the moment  (2013). Available: http://arxiv.org/abs/1311.2542*
 
+* :scroll: **[Truncation of Wavelet Matrices: Edge Effects and the Reduction of Topological Control](https://reader.elsevier.com/reader/sd/pii/0024379594000395?token=EB0AA78D59A9648480596F018EFB72E0A02FD5FA70326B24B9D501E1A6869FE72CC4D97FA9ACC8BAB56060D6C908EC83)** by Freedman
+  
+  In this paper by Michael Hartley Freedman, he applies Robion Kirby “torus trick”, via wavelets, to the problem of compression.
+
+* :scroll: **[Understanding Deep Convolutional Networks](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/Understanding-Deep-Convolutional-Networks.pdf)** by Mallat
+
+  Stéphane Mallat proposes a model by which renormalisation can identify self-similar structures in deep networks.  [This video of Curt MacMullen discussing renormalization](https://www.youtube.com/watch?v=_qjPFF5Gv1I) can help with more context. 
+  
+* :scroll: **[General self-similarity: an overview](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/General-self-similarity--an-overview.pdf)** by Leinster
+
+Dr Leinster's paper provides a concise, straightforward, picture of self-similarity, and its role in renormalization.

mathematics/README.md

@@ -1,5 +1,45 @@
 ## Mathematics
 
-* [:scroll:](transcendence-of-pi.pdf) [The Transcendence of pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer
+* :scroll: [The Transcendence of Pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer
+
+* :scroll: [Tilings](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/tilings.pdf) by Ardila
+
+  The paper covers a broad swath of the topic on analysis of tiling, and related strategies.
+
+* :scroll: [From Dominoes to Hexagons](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/from-dominoes-to-hexagons.pdf) by Thurston
+
+  A paper on the generalization of tilings across different base planes.
+
+* :scroll: [Graph Isomorphism and Representation Theory](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/graph-isomorphism-and-representation-theory.pdf) 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.
+
+* :scroll: [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) 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 the `xϵX` you haven’t seen yet?"  The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels.
+
+* :scroll: [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) 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.
+
+* :scroll: [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher
+
+  High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra.
+
+* :scroll: [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) 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 
+* :scroll: [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher
+* [Applied Algebraic Topology and Sensor Networks](https://www.math.upenn.edu/~ghrist/preprints/ATSN.pdf) by Robert Ghrist
+* :scroll: [Intro to Tropical Algebra Geometry](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/intro-to-tropical-algebraic-geometry.pdf)
+
+  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.
+
+* :scroll: [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist
+
+  Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'