1531
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…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
1532
Random Attractors – Found using Lyapunov Exponents (2001)
Contribution by Philip Ham: attractor.basic and Python implementation by Johan Bichel Lindegaard.
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1534
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 .]
1535
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…
1536
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…
1537
The Contagion of Concern: Game theory of how anxiety spreads
Founder, Investor, Author
1538
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…
1539
Cleaner parallel curves with Euler spirals
Blog of Raph Levien.
1540
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 :
1541
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…
1542
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.
1543
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:
1544
Signed integers are asymmetrical
An edge case in integer safety.
1545
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…
1546
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…
1547
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.
1548
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…
1551
The Block Stacking Problem
John D. Norton Department of History and Philosophy of Science University of Pittsburgh https://sites.pitt.edu/~jdnorton/jdnorton.html
1552
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…
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Using calculus to do number theory
Calculus is the mathematics of approximations of continuous quantities ; number theory asks exact problems about discrete quantities. These seem, therefore, to be unrelated studies.
1555
Industrious Dice
I’m a professional mathematician. That means somebody pays me to do math. I’m also a recreational mathematician. That means you might have to pay me to get me to stop. Wearing my recreational mathe…
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Math Team
and other horrible things you do to get into stanford
1558
What is algebra?
NOVEMBER 20, 2011. We hear a lot about the importance that all children master algebra before they graduate from high school. But what exactly is algebra, and is it really as important as everyone …
1559
Gravitational attraction of stars and cows
One attempt at rationalizing astrology is to say that the gravitational effects of celestial bodies impact our bodies. To get an idea how hard the stars and planets pull on us, let's compare their gravitational attraction to that of cows at various distances. Newton's law of gravity says that the gravitational…
1560
Busy Beaver Updates: Now Even Busier
Way back in the covid-filled summer of 2020, I wrote a survey article about the ridiculously-rapidly-growing Busy Beaver function. My survey then expanded to nearly twice its original length, with …