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Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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How to turn a biased coin into a Fair Coin
Fair Coins are the currency of Userland. A Fair Coin flips fifty-fifty with mathematical exactness. In the real world most coins are pretty fair, but you never know whether there might be a small bias to one side or another. This presents Lauren Ipsum , a girl who's lost in Userland, with a problem. No one wants her…
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Why Hacker News should use a different Deterministic Algorithm, Not a Random One
NetworkSolutions.com - Original domain name registration and reservation services with variety of internet-related business offerings. Quick, dependable and reliable.
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Quasi-Polynomial Algorithm for Graph Isomorphism
Update (Dec. 14): The long wait is over! Here’s Laci’s paper on the arXiv. So far, I’ve read it only deeply enough to note that it contains the following sentence: A group G ≤ S…
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Random Attractors – Found using Lyapunov Exponents (2001)
Contribution by Philip Ham: attractor.basic and Python implementation by Johan Bichel Lindegaard.
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The Kalman filter: helping chickens cross the road
The Kalman Filter. Helping Chickens Cross the Road. David Austin Grand Valley State University I was running some errands recently when I spied the Chicken Robot ambling down the sidewalk, then vee…
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Projective Geometric Algebra Done Right
[This is part one of a two-part series. The second part can be found here: Symmetries in Projective Geometric Algebra .]
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An illustrated guide to automatic sparse differentiation
In numerous applications of machine learning, Hessians and Jacobians exhibit sparsity, a property that can be leveraged to vastly accelerate their computation. While the usage of automatic differentiation in machine learning is ubiquitous, automatic sparse differentiation (ASD) remains largely unknown. This post…
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Damn Cool Algorithms: Quadtrees and Hilbert Curves
Last Thursday night at Oredev, after the sessions, was "Birds of a Feather" - a sort of mini-unconference. Anyone could write up a topic on the whiteboard; interested individuals added their names, and each group got allocated a room to chat about the topic. I joined the "Spatial Indexing" group, and we spent a…
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John Coltrane illustrates the mathematics of jazz
The Jazz of Physics: Albert Einstein and John Coltrane had a lot in common. The so-called “Coltrane circle” or “Circle of Fifths,” but incorporates Coltrane’s own innovations. Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in the Repository of Scales and
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A very casual introduction to Fully Homomorphic Encryption (2012)
Craig Gentry on board the mothership. (credit) A couple of weeks ago I polled readers for the subjects that they were interested in. You gave me some excellent responses, and I promise they’r…
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The Contagion of Concern: Game theory of how anxiety spreads
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The Algorithm for Hard Problems: Shake and Pull Gently
(Or, “regularized greedy algorithms and their applications.”) James Gilles “Algorithm” is one of those words that sounds fancier than it really deserves. We hear all the time about the “facebook algorithm”, the “youtube algorithm”, “high frequency trading algorithms”, “artificial intelligence algorithms”, and so on…
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Cleaner parallel curves with Euler spirals
Blog of Raph Levien.
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A New Angle on L2 Regularization
Deep neural networks have been shown to be vulnerable to the adversarial example phenomenon: all models tested so far can have their classifications dramatically altered by small image perturbations . The following predictions were for instance made by a state-of-the-art network trained to recognize celebrities :
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Sharing everything I could understand about gradient noise
You've most likely heard about gradient noise through the name Perlin noise , which refers to one particular implementation with various CPU optimizations. Because it's an incredible tool for creative work, it's used virtually everywhere: visual effects, video games, procedural mathematical art, etc. While getting it…
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Better Intuition for Information Theory
Better visual explanations of information theoretic quantities like entropy and mutual information using I-diagrams. Based on Raymond W. Yeung's "A new outlook on Shannon's information measures" paper from 1991.
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God created the real numbers
W. Jherek Swanger writes in his introduction to Camillo 7 Agrippa's "A Treatise on the Science of Arms, with a philosophical Dialogue (1553)" that:
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Signed integers are asymmetrical
An edge case in integer safety.
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Just teach my kid the math
This is a new thing for me - I'm hosting a blog post by a colleague/friend - James Tanton. You can find James' original post here. One reason it's being re-hosted here is because Medium is apparently blocked in some countries: Egypt Malaysia ..... possibly others. It is astounding to me that mathematics - of all…
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Some thoughts about the reports of supposed evidence of election irregularities
The Internet lit up on Monday over the news, reported in New York Magazine , that a team of computer scientists and lawyers had reported to the Clinton campaign that “they’ve found persuasive evidence that results in Wisconsin, Michigan, and Pennsylvania may have been manipulated or hacked. ”
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Why don't machine learning research agents overfit?
New research indicates that AI agents learn compressible models of data, which don’t have enough space to enable memorization.
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Clifford Algebra: A visual introduction (2014)
Clifford Algebra, a.k.a. Geometric Algebra, is a most extraordinary synergistic confluence of a diverse range of specialized mathematical fields, each with its own methods and formalisms, all of wh…
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A triangle whose interior angles sum to zero
In hyperbolic geometry, the sum of a the interior angles of a triangle can be any value less than π. If the sum is zero the triangle has area π.
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Limits on Matrix Multiplication
Can 2.3728639 be best? Personal site; note puzzles Josh Alman is a graduate student at a technical school in the Boston area. He is working on matrix multiplication, among other problems in complex…
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Optimizing 128-bit Division
When it comes to hashing, sometimes 64 bit is not enough, for example, because of birthday paradox — the hacker can iterate through random $latex 2^{32}$ entities and it can be proven that wi…
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The Block Stacking Problem
John D. Norton Department of History and Philosophy of Science University of Pittsburgh https://sites.pitt.edu/~jdnorton/jdnorton.html
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MathJax Turns 3.0
When I launched bit-player.org in 2006, displaying any sort of mathematical notation on the web was torture. I would typeset an equation in LaTeX, convert the output to a JPEG image, upload the image file to a directory on the server, and embed a reference to the file in an HTML img tag. The process was cumbersome and…