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Win your fantasy league using operations research
I’ve never been good at playing football 1 . I started playing again last year and I have scored more own goals than goals for my team. Also, I support the RCD Espanyol 2 , which has spent last season in the second division and has miraculously ascended to the first division last week. And to be honest, I only watch…
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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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Constructing a Four-Point Egg
For reasons beyond the scope of this entry, I have been investigating elliptical and ovoid shapes. The Wikipedia article for Moss’s egg has a link to a tutorial on Euclidean Eggs by Freyja Hreinsdóttir which (amongst other things) describes how to construct the “four point egg”. I think it is a nicer shape than Moss’s…
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Scoped Propagators
A programming model for spatial canvases
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Algorithmic Mathematical Art (2004)
In the early 1990s, they were merely visualization aids in the study of mathematics. Gradually, the complexity and artistry of the images becomes an end itself.
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Dividing unsigned 8-bit numbers
Division is quite an expensive operation. For instance, latency of the 32-bit division varies between 10 and 15 cycles on the Cannon Lake CPU, and for Zen4 this range is from 9 to 14 cycles. The latency of 32-bit multiplication is 3 or 4 cycles on both CPU models.
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Math as a habit
Making math a daily habit
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Planes in 3D Space
Visual and interactive introduction to 2D planes in 3D space.
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AI for math resources, and erdosproblems.com
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistan…
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Evaluating a class of infinite sums in closed form
A family of infinite sums that evaluate to rational numbers, sometimes integers, and and effective algorithm for finding the sum.
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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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Wide angle lens distortion correction from lines
Hugo Hadfield - Cross stack robotics engineer and computer vision researcher specializing in deep learning, sensor fusion, geometric algebra and applications in self-driving cars and robotic manipulation.
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RSA is deceptively simple and fun
While reading Real-World Cryptography , I came across the "million message attack" . This is an attack that Daniel Bleichenbacher demonstrated in 1998, which effectively broke RSA with a particular encoding function called PKCS #1 . It was only mentioned briefly, so I dug in and decided to try to understand the…
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Floats Are Weird
Compute this limit more accurately with one weird trick!
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Solving SAT via Positive Supercompilation
The boolean satisfiability problem (“SAT” for short) is arguably the most famous NP-complete problem in theoretical computer science. According to Wikipedia, it is “the problem of determining if there exists an interpretation that satisfies a given Boolean formula ”; or, in simpler terms, if there is at least one…
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Generating Mazes
Visualizations and techniques for different maze generation algorithms.
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SQL, Homomorphisms and Constraint Satisfaction Problems
Database queries are a pretty surprisingly powerful tool that can solve seemingly intractable problems.
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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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Unprojecting text with ellipses (2016)
Using transformed ellipses to estimate perspective transformations of text.
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The Invention of Zero
“If you look at zero you see nothing; but look through it and you will see the world.”
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How to get from high school math to cutting-edge ML/AI
1) Foundational math. 2) Classical machine learning. 3) Deep learning. 4) Cutting-edge machine learning.
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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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The game theory of seduction and marriage with Jane Austen
The enduring success of her early 19th century novels are in large part due to their persistent relevance
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Trying Kolmogorov-Arnold Networks in Practice
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
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The Second Law of Thermodynamics (2011)
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
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Optimizing a bignum library for fun
Can I make math operations run 100x faster on really, really big numbers?
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Nash equilibria in Ballmer's binary-search interview game
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a…