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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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The polls messed up
To continue our post-voting, pre-vote-counting assessment (see also here and here ), I want to separate two issues which can get conflated: 1. Problems with poll-based election forecasts.
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Gödel's Theorem
A much-abused result in mathematical logic , supposed by many authors who don't understand it to support their own favored brand of rubbish, and even subjected to surprisingly rough handling by some who really should know better.
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Reconstructing Public Keys from Signatures
One weird hobby of mine is reasonable properties of cryptographic schemes that nobody promised they do or don’t have. Whether that’s invisible salamanders or binding through shared secr…
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The Three Ways of XOR
We all know the XOR operation. It’s the cousin of NOT, AND and OR. Like AND and OR, it is a binary boolean function. Unlike them, most programming languages ...
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Bilinear interpolation on a quadrilateral using Barycentric coordinates
A new algebraic method for hardware-accelerated bilinear interpolation on convex quadrilaterals is presented, using the Barycentric coordinate feature of modern GPUs.
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Machine Learning, Kolmogorov Complexity, and Squishy Bunnies (2019)
Computer Science, Machine Learning, Programming, Art, Mathematics, Philosophy, and Short Fiction
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Options for giving math talks and lectures online
As part of social distancing efforts to slow down the spread of the novel coronavirus, several universities have now transitioned, or begun transitioning, to online teaching models. (My home unive…
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Monte Carlo Crash Course: Quasi-Monte Carlo
We’ve learned how to define and apply Monte Carlo integration—fundamentally, it’s the only tool we need. In the remaining chapters, we’ll explore ways to reduce variance and successfully sample difficult distributions.
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TLA+ in Practice and Theory, Part 4: Order in TLA+
We learn how to encapsulate and compose TLA+ specifications, of the precise mathematical definition of abstraction, and compare TLA+'s notion of abstraction with those of other formalisms. Plus some various cool stuff.
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Probability Theory — A Primer
It is a wonder that we have yet to officially write about probability theory on this blog. Probability theory underlies a huge portion of artificial intelligence, machine learning, and statistics, and a number of our future posts will rely on the ideas and terminology we lay out in this post. Our first formal theory…
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I am a statistician and I buy lottery tickets
When my friends hear me say that I’m buying a lottery ticket for a big draw I often get ...
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Court of Appeal bans Bayesian probability
As of the 23rd May 2022 this website is archived and will receive no further updates .
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Fully Homomorphic Encryption: Secret Key Homomorphic Encryption Over Integers
In the previous post we discussed homomorphic encryption in it’s most abstract terms we presented Paillier as a partially homomorphic encryption . Thank you @mortendahlcs for making a clarification about the terms described :
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Two-Stack Sliding-Window Aggregation
An aggregation is some kind of summary of a set of data. This can be the sum, length, minimum, etc. It is quite common to want to calculate such a summary repeatedly, e.g. “the maximum noise level in dB for the past 30 seconds” for a nuisance detector. In such a case we say there is a sliding window over our data, and…
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Clojure Linear Algebra Refresher: 1 – Vector Spaces
This article is a starting article in a series that is going to briefly skim through a good engineering textbook on linear algebra, making notes that help yo...
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Hello, Perceptron: An introduction to artificial neural networks
Generative AI tools like ChatGPT and Midjournery are able to replicate (and often exceed) human-like performance on tasks like taking exams, generating text and making art.
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String Diagrams for Linear Algebra
We have established that there is a homomorphism called θ from B, the PROP of diagrams, to Mat, the PROP of matrices. To do this, it was enough to say where θ takes the four stars of the story so f…
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A Grimoire of Functions
I'm the kind of person who reads encyclopedias front to back just for fun, and I've been fascinated by mathematical special functions at least since my first encounter with the gamma function as a teenager. My work implementing numerical and symbolic algorithms in mpmath , Arb and other software projects during the…
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An interactive intro to Elliptic Curve Cryptography
A hands-on introduction to elliptic curve cryptography. Start with curve geometry, build point addition and scalar multiplication, see why ECDLP is hard, and then use that math in ECDH, ECDSA, and ECIES.
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Transformers Are Graph Neural Networks
Engineer friends often ask me: Graph Deep Learning sounds great, but are there any big commercial success stories? Is it being deployed in practical applications? Besides the obvious ones–recommendation systems at Pinterest, Alibaba and Twitter–a slightly nuanced success story is the Transformer architecture, which…
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A Molecular Near Miss
I’m thrilled to report that I’m a co-author of the article “ An ultra-stable gold-coordinated protein cage displaying reversible assembly “, which was recently published in Nature . This work is the result of an exciting collaboration between biochemists, physicists, structural biologists, mathematicians, and others…