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New
The latest blog posts to take off on Hacker News. 266 posts.
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How Chordcat works – a chord naming algorithm
chordcat is a chord-naming application and a pet project of mine. It is written in C++ and SFML.
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Diffusion models are evolutionary algorithms
Authors: Yanbo Zhang, Benedikt Hartl, Hananel Hazan, Michael Levin
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My Notes on Apple Math Notes
Apple's effort to improve the UX of math.
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Perceptually lossless (talking head) video compression at 22kbit/s
Achieving extreme video compression rates using the LivePortrait model for talking head videos.
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Alonzo Church: Architect of computer intelligence
The man who gave us the solution to the Entscheidungsproblem
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Adventures in Probability
I hope everyone had a good weekend. I went on a hike. It was great. Statistics One of my great school regrets, next to “taking three years of business...
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A Hamiltonian Circuit for Rubik's Cube
At last, the Hamiltonian circuit problem for Rubik's Cube has a solution! To be a little more mathematically precise, a Hamiltonian circuit of the quarter-turn metric Cayley graph for the Rubik's Cube group has been found.
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Demystifying the regular expression that checks if a number is prime (2016)
Ever wondered how the ^.?$|^(..+?)\1+$ regular expression can tell you if a number is not prime? In this blog post you'll learn how and why it works. Code examples in Java, JavaScript, Python and Perl are provided.
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Probability-generating functions
I have long struggled with understanding what probability-generating functions are and how to intuit them. There were two pieces of the puzzle missing for me, and we’ll go through both in this article.
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Sets, types and type checking
My currently understanding of types
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Goodhart’s law isn’t as useful as you might think (2023)
Goodhart's Law is useless. It tells you about a phenomenon, but it doesn't tell you how to solve it. We look at how organisations actually prevent Goodhart's Law, and illustrate this with Amazon's Weekly Business Review as an example.
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Adventures in algorithmic trading on the Runescape Grand Exchange
Runescape has been a game near and dear to my heart since I was a child. Though I do not actively play anymore, it still functions as an interesting programming project substrate. Most recently, I created a bot that automatically executes trades on the Grand Exchange in order to conduct market making via common…
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Category Theory Illustrated: Logic (2021)
Now let’s talk about one more seemingly unrelated topic just so we can “surprise” ourselves when we realize it’s category theory. By the way, in this chapter there will be another surprise in addition to that, so don’t fall asleep.
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Sinusoidal Sunlight
The graph of daylight over the course of a year looks like a sine wave, but is it?
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Yes, we did discover the Higgs
Ben Recht got my attention with a tweet about his blog post "The Higgs discovery did not take place.” I’m generally a fan of Ben’s writing, but I think he’s off base on a number of issues, and I’ll explain why. [Updated Oct 23rd, 2024] Ben's …
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TLA from First Principles
Building an intuition for the mathematics behind the "TLA" in "TLA+"
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Adding row polymorphism to Damas-Hindley-Milner
Intro to HM
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Tog's Paradox
Tog’s Paradox (also known as The Complexity Paradox or Tog’s ComplexityParadox) is an observation that products aiming to simplify a task for users tend toinspire new, more complex tasks. It’s one ...
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One Plus One Equals Two (2006)
From the highly eclectic blog of Mark Dominus
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Understanding Gaussians
The **Gaussian distribution**, or **normal distribution** is a key subject in statistics, machine learning, physics, and pretty much any other field that deals with data and probability.
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Using Euro coins as weights (2004)
Here is a cheap way to obtain a set of standard weights, for measuring weights up to about 100 gram, to an accuracy of about 0.5 gram : Use the coins of the currency of your country. Thus one can make use of the fact that these coins are fabricated in mass production, and because of that have not only a constant shape…
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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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Damas-Hindley-Milner inference two ways
What is Damas-Hindley-Milner?
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Faster convergence for diffusion models
Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think
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Counterintuitive Properties of High Dimensional Space (2018)
Our geometric intuition developed in our three-dimensional world often fails us in higher dimensions. Many properties of even simple objects, such as higher dimensional analogs of cubes and spheres, are very counterintuitive. Below we discuss just a few of these properties in an attempt to convey some of the weirdness…
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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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LLMs don't do formal reasoning
Important new study from Apple
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