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Finite state machines as data structure for representing ordered sets and maps
It turns out that finite state machines are useful for things other than expressing computation. Finite state machines can also be used to compactly represent ordered sets or maps of strings that can be searched very quickly.
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A Beginner’s Guide to Recurrent Networks and LSTMs
The Eclipse Deeplearning4j Project. Eclipse Deeplearning4j has 5 repositories available. Follow their code on GitHub.
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Quadratic Voting (2014)
Glen Weyl has uploaded a new version of his paper, Quadratic Voting (written with Steven Lalley), to SSRN, which now includes the completed proofs. Quadratic voting is the most important idea for l…
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What Is Spacetime, Really?
On the 100th anniversary of Einstein’s Theory of Relativity, Stephen Wolfram discusses the nature of space and time, and fundamental theory of physics.
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If 1+x is 1, how much is 1-x?
► Versión en Español (The title should be "if (= (+ 1 x) 1), how much is (- 1 x)?", but ...) Toy floating point Mathematically, if we...
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Computer scientists prove that a 40-year-old algorithm is optimal
Computer scientists from MIT find that a 40-year-old algorithm for determining the “edit distance” between symbols cannot be optimized any further.
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Is there such a thing as half a derivative?
The original question was: Another one of those questions of the type “does this make sense”. You have first derivatives and second derivatives. f'(x), f”(x) or sometimes dy/dx …
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A Beginner’s Guide to Eigenvectors, Covariance, PCA and Entropy
The Eclipse Deeplearning4j Project. Eclipse Deeplearning4j has 5 repositories available. Follow their code on GitHub.
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A regular expression to check for prime numbers
Regular expressions are extremely powerful. This is something I read at least once or twice every day while reading articles and blogs on the Web.
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MathBox 2: PowerPoint Must Die
PowerPoint must die.
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Gravity's Oldest Puzzles
Every now and then the orbital motion of a body doesn’t match our prediction. And that might lead to interesting discoveries.
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Why it’s harder to forge a SHA-1 certificate than to find a SHA-1 collision
It’s well known that SHA-1 is no longer considered a secure cryptographic hash function. Researchers now believe that finding a hash collision (two values that result in the same value when SHA-1 is applied) is inevitable and likely to happen.
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Federal Reserve Bank of NY converts major economic model to Julia
Marco Del Negro, Marc Giannoni, Pearl Li, Erica Moszkowski, and Micah Smith We have implemented the FRBNY DSGE model in a free and open-source language called Julia. The code is posted here on GitHub, a public repository hosting service. This effort is the result of a collaboration between New York Fed staff and folks…
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How to implement a spreadsheet
My friend Lindsey Kuper recently remarked on Twitter that spreadsheets were commonly understood to be the most widely used dataflow program...
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12-minute Mandelbrot: fractals on a 50 year old IBM 1401 mainframe
When I found out that the Computer History Museum has a working IBM 1401 computer [1] , I wondered if it could generate the Mandelbrot frac...
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Introduction to Monte Carlo Tree Search
The subject of game AI generally begins with so-called perfect information games. These are turn-based games where the players have no information hidden from each other and there is no element of chance in the game mechanics (such as by rolling dice or drawing cards from a shuffled deck). Tic Tac Toe, Connect 4…
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Path Tracing 3D Fractals
In some ways path tracing is one of the simplest and most intuitive ways to do ray tracing.
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Algorithmic surrealism: A slow-motion guide to high-frequency trading
Please note: Part 1 of this essay appeared in the Feb 2015 edition of Contributoria . It is published and modified here under a...
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Deriving the Reddit Formula
A few things about Reddit’s hot formula have always bothered me. The formula has obviously been a success when it comes to setting the Internet on fire, but I have to wonder:
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Impossible Escape?
Can you use math to escape from, what seems like, an impossible prison escape problem based on coins and a chessboard?
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Google’s S2, geometry on the sphere, cells and Hilbert curve
Update - 05 Dec 2017: Google just announced that it will be commited to the development of a new released version of the S2 library, amazing news, repository can be found here. Google's S2 library is a real treasure, not only due to its capabilities for spatial indexing but also because it is a library that
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Bayesian ranking of items with up and downvotes or 5 star ratings
Evan Miller wrote a great article How Not To Sort By Average Rating . He shows that simple formulas like score = upvotes - downvotes or score = upvotes / (upvotes + downvotes) don’t work. He proposes to use the lower bound of the Wilson score confidence interval. The formula is complicated and somewhat of a hack…
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