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Functions are vectors
Conceptualizing functions as infinite-dimensional vectors lets us apply the tools of linear algebra to a vast landscape of new problems, from image and geometry processing to curve fitting and machine learning.
New
The latest blog posts to take off on Hacker News. 2,851 posts.
812
Data diffs: Algorithms for explaining what changed in a dataset (2022)
tl;dr: part 1 explains what an explanation algorithm is, and part 2 describes an open source SQL data differ.
813
We're not Platonists, we've just learned the bitter lesson
Machine Alignment Monday, 7/24/23
814
Sub-pixel distance transform
High quality font rendering for WebGPU
815
Refusing to teach kids math will not improve equity
We have public schools for a reason.
816
Statistical Arbitrage – An Easy Walkthrough
Statistical arbitrage (stat arb) is a pillar of quantitative trading that relies on mean reversion to predict the future returns of an asset. Mean reversion believes that if a stock has risen higher it’s more likely to revert in the short term which is the opposite of a momentum strategy that believes if a stock has…
817
A tutorial quantum interpreter in 150 lines of Lisp
a personal blog
818
Penrose 3.0
Create beautiful diagrams just by typing math notation in plain text.
819
Matrices and Graph
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices
820
2048 Bit RSA and the Year 2030
The Call of the Open Sidewalk [The Call of the Open…2023239 points149 commentsSecurity & Privacy details
Update: NIST released a draft that modified their recommendations (Oct 2024) 1) . RSA 2048 is to be only considered “deprecated” after 2030. The draft states:
821
Hilbert Transform
Concise summary of the Hilbert transform: mathematics, effects on signals, and applications in telecommunications.
822
California needs real math education, not gimmicks
A guest post by Armand Domalewski.
823
Can a Rubik's Cube be brute-forced?
a personal blog
824
How to keep lambda calculus simple
Once upon a time, my curiosity of dependent types transitioned into an endeavour to learn how they work under the bonnet. Then I found the paper called “A Tutorial Implementation of a Dependently Typed Lambda Calculus” or just “Simply Easy” – and began reading it. However, the affairs happening there were so complex…
825
Superrational
“Will Vicktoreya Keyneslee Beauxpensees please come see the principal right now?” said the voice over the intercom.
826
Regex engine internals as a library
Over the last several years, I’ve rewritten Rust’s regex crate to enable better internal composition, and to make it easier to add optimizations while maintaining correctness. In the course of this rewrite I created a new crate, regex-automata , which exposes much of the regex crate internals as their own APIs for…
827
A Dive into the Math Behind Bitcoin Schnorr Signatures
Get up close and personal with Schnorr and his now patent-free linear signature algorithm.
828
A trick to eliminate 2π (sometimes)
As a physicist, I’ve learned that the presence of 2 π 2\pi 2 π [▼] [ Or rather τ \tau τ , as it should actually be called . ] in a formula usually spells trouble. It’s kind of annoying to write by hand, easy to forget, and it’s dimensionless, so you can’t easily check if you forgot to divide or multiply by it…
829
Solving “Two Sum” in C with a tiny hash table
I came across a question: How does one efficiently solve Two Sum in C? There’s a naive quadratic time solution, but also an amortized linear time solution using a hash table. Without a built-in or standard library hash table, the latter sounds onerous. However, a mask-step-index table , a hash table construction…
830
Every factorial approximates a power
For every n, there is a base b such that n! = b^n. The relation between n and b(n) is surprisingly close to linear.
831
832
4D Toys Update 8: Rotating the 3D Slice, 2D Faces Projections, Marble Scenes
This is a Mega-Update ®™ that focuses on features that people have been requesting for a long time. I have a ton of stuff in Miegakure that could be shared with 4D Toys but what takes development time is not the cool 4D stuff but all the UI/UX around it. First of all because there is the VR version, the mouse/keyboard…
833
Finally getting two's complement
A different view on two's complement math.
834
How to create a game using hyperbolic geometry? (2020)
puzzle roguelike on a hyperbolic plane
835
A regular expression to check for prime numbers (2007)
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.
836
A Bayesian view of Amazon resellers (2011)
I was buying a used book through Amazon this evening. Three resellers offered the book at essentially the same price. Here were their ratings: 94% positive out of 85,193 reviews 98% positive out of 20,785 reviews 99% positive out of 840 reviews Which reseller is likely to give the best service? Before you assume it's
837
Hashing
A visual, interactive introduction to hash functions.
838
Shannon’s Source Coding Theorem (2020)
The mathematical field of information theory attempts to mathematically describe the concept of “information”. In the first two posts, we discussed the concepts of self-information and information entropy. In this post, we step through Shannon’s Source Coding Theorem to see how the information entropy of a probability…
839
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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