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A Lisp interpreter implemented in Conway's Game of Life (2021)
Lisp in Life is a Lisp interpreter implemented in Conway’s Game of Life.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
2252
A New Way To Solve Linear Equations (over finite fields)
Impossible but true: a new approach to linear systems Prasad Raghavendra is an expert in many aspects of complexity theory, especially the foundations of approximation theory. He recently was a col…
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Map Simplification with Visvalingam's Algorithm
An interesting challenge in cartography is getting data of the appropriate resolution. As Lewis Fry Richardson observed , the more precisely you measure the length of a coastline, the longer it appears; geographic shapes have infinite complexity. Digital displays, in contrast, are limited by pixels. Choosing too high…
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MathCode, Mathematical Coding Agent
A terminal AI coding agent that formalizes math problems into Lean 4 theorems and proves them.
2255
Dumb statistical models, always making people look bad
This is Jessica. In my Prediction for Decision-making class last quarter we talked about human predictions and decisions relative to algorithmic ones. This led to a discussion about why it’s often hard to demonstrate the value of human knowledge once you have a decent statistical model.
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Alpha Compositing
Interactive article explaining alpha compositing concepts.
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Evolution Strategies as a Scalable Alternative to Reinforcement Learning
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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Prolly Trees
A deep dive into the Probabilistic B-tree or Prolly Tree data structure including examples. Prolly Trees are used to create version controlled databases.
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Clojure Numerics: Orthogonalization and Least Squares
How to solve linear systems that have many solutions, or those that have no solutions at all? That's the theme for a thick math textbook, of course, but from...
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Defining Statistical Models in Jax?
This is Bob. And I’d like to know the best way for us to code a bunch of models in JAX to use to evaluate parallel algorithms including normalizing flows. I’m going to dump out my current thinking, but I’m really hoping to get feedback from experts on the best way to do this without starting a flame war in the…
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Modeling the World in 280 Characters
An exploration of the mindset, methods, and motivations behind crafting tiny, expressive shaders that combine code, art, and constraint.
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Eytzinger Binary Search
This tutorial is loosely based on a 46-page paper by Paul-Virak Khuong and Pat Morin “Array layouts for comparison-based searching” and describes one particular way of performing efficient binary search by rearranging elements of a sorted array in a cache-friendly way.
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Nibble Sort
A while back, John Regehr posted the Nibble Sort Programming Contest on his blog. The objective was to write a program that sorts the 4-bit components (nibbles) of 64-bit words as fast as possible. For example, 0x42badc0ffeed00d5 should result in 0xffeedddcba542000 after sorting.
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Dungeon Generation in Enter The Gungeon
I’ve been playing a lot of Enter The Gungeon recently. It’s a great, brutally hard, twin stick bullet hell that reminded me a lot of Binding of Isaac. But as I’ve been playing it …
2269
Hinge and Its Implementation of the Gale–Shapley algorithm
https://thetab.com/uk/2020/05/20/this-is-how-the-nobel-prize-winning-hinge-algorithm-actually-works-157740
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The Dome: A simple violation of determinism in Newtonian mechanics (2005)
John D. Norton Department of History and Philosophy of Science, University of Pittsburgh Pittsburgh PA 15260. Homepage: www.pitt.edu/~jdnorton This page is available at www.pitt.edu/~jdnorton/goodies
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Why I decided not to enter the $100k global warming time-series challenge
Interesting applied project for your students , or as a warning for decisions under uncertainty / statistical significance. Real money on the line so the length of time and number of entries required to get a winner may be an interesting dataset after this is all done.
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Breaking 256-Bit Elliptic Curve Encryption with a Quantum Computer
Researchers have calculated the quantum computer size necessary to break 256-bit elliptic curve public-key cryptography: Finally, we calculate the number of physical qubits required to break the 256-bit elliptic curve encryption of keys in the Bitcoin network within the small available time frame in which it would…
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Not all graphs are trees
It's pretty easy to imagine how to represent relational algebra expressions as a tree—they are already structurally rooted trees where each operator has its...
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Reinventing the Wheel: Discovering the Optimal Rolling Shape with PyTorch (2019)
It is thought that the wheel was invented more than five thousand years ago, yet modern machine learning tools were only developed in the past few decade...
2275
Embeddings, vectors, and arithmetic
An embedding is the representation of a piece of text like a word, sentence, or paragraph. Traditionally this value is in the form of a mathematical vector - a point in space. You can think of it as analogous to coordinates on a map that just happens to have many, many dimensions.
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DARPA’s 23 Challenge Questions
DARPA challenges The Defense Advanced Research Projects Agency (DARPA) has issued 23 mathematical challenges. DARPA says the solution of any one of these challenges would have the effect of “…
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One night in Uzbekistan: Why was this one data point so influential?
We have a comment coming out in Nature next week that is going to cause the retraction of a high-profile paper by Kotz et al. from last year (the second most cited climate paper in the news in 2024).
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Short algorithm, long-range consequences
A new technique for solving ‘graph Laplacians’ is drastically simpler than its predecessors, with implications for a huge range of practical problems.
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Provably space-efficient parallel functional programming
You have heard your grandmother tell you many times: parallel programming is hard. In 2022, does it still have to be? Back in grandma’s heyday, they knew a cool and breezy way to do paralleli…
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Category Theory Illustrated – Types
In this chapter we will talk about types. This might be disappointing for you, if you expected to learn about as many new categories as possible (which you don’t even suspect are really categories till the unexpected reveal)—we’ve been talking about the category of types in a given programming language ever since the…