211
Missile defense is NP-complete
Exploring the Weapon-Target Assignment problem: how missile defense connects to NP-completeness, SSPK probability calculations, and how saturation attacks exploit computational limits.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
212
Calculus with Julia
This is a set of notes for learning calculus using the Julia language. Julia is an open-source programming language with an easy to learn syntax that is well suited for this task.
213
I Wrote My Fastest Hashtable
I had to get there eventually. I had a blog post called “I Wrote a Fast Hashtable” and another blog post called “I Wrote a Faster Hashtable.” Now I finally wrote the fastest…
214
Diffusion models from scratch, from a new theoretical perspective
This tutorial aims to give a gentle introduction to diffusion models, with a running example to illustrate how to build, train and sample from a simple diffusion model from scratch.
215
Anagram Scoring
From the highly eclectic blog of Mark Dominus
216
Quaternions
Introduction to quaternions and rotations in 3D.
217
218
When Random Isn't
This post is an anecdote from over a decade ago, of which I lost the actual code. So please forgive me if I do not accurately remember all the details. Some details are also simplified so that anyone that likes computer security can enjoy this article, not just those who have played World of Warcraft (although the…
219
The Pentium contains a complicated circuit to multiply by three
This article is available in German at Heise Online . In 1993, Intel released the high-performance Pentium processor, the start of the long...
220
Why do prime numbers make these spirals? (2019)
A curious pattern in polar plots with prime numbers, together with discussion of Dirichlet's theorem
221
My Favorite Algorithm: Linear Time Median Finding (2018)
Finding the median in a list seems like a trivial problem, but doing so in linear time turns out to be tricky. In this post I’m going to walk through one of my favorite algorithms, the median-of-medians approach to find the median of a list in deterministic linear time. Although proving that this algorithm runs in…
222
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.
223
Simpson’s Paradox (2016)
A riveting tale of how good data can lead to bad decisions.
224
Making any integer with four 2s
There's a cute math puzzle that can be interesting to folks on very different levels:
225
Modern SAT solvers: fast, neat and underused
Before I started doing research, I saw SAT solvers as academically interesting but without practical uses ouside of other academic applications. I've since then changed my mind, and I want to change yours, because modern SAT solvers are neat, fast and almost criminally underused by the industry.
226
Language models pack billions of concepts into 12k dimensions
In a recent 3Blue1Brown video series on transformer models, Grant Sanderson posed a fascinating question: How can a relatively modest embedding space of 12,288 dimensions (GPT-3) accommodate millions of distinct real-world concepts? The answer lies at the intersection of high-dimensional geometry and a remarkable…
227
Kalman Filter Explained Simply
Tired of equations and matrices? Ready to learn the easy way? This post explains the Kalman Filter simply with pictures and examples!
228
A Beginner's Guide to Understanding Convolutional Neural Networks
Engineering at Forward | UCLA CS '19
229
230
231
232
A neat XOR trick
Looking over the solutions mega-thread , it seems like not many people discovered this trick; when I posted about it , people found it to be noteworthy.
233
Image Kernels explained visually
An image kernel is a small matrix used to apply effects like the ones you might find in Photoshop or Gimp, such as blurring, sharpening, outlining or embossing. They're also used in machine learning for 'feature extraction', a technique for determining the most important portions of an image. In this context the…
234
235
Using Fibonacci numbers to convert from miles to kilometers and vice versa
I recently learned an interesting fact about Fibonacci numbers while watching a random number theory video on YouTube. Fibonacci numbers can be used to approximately convert from miles to kilometers and back. Here is how. Take two consecutive Fibonacci numbers, for example 5 and 8. And you're done converting. No...
236
Images Created from Prime Numbers
Inspired by James McKee’s Trinity Hall prime, physics researcher Gilles Esposito-Farese (of the self-descriptive pangram) has worked out that this 2,258-digit prime number: 53084469288402965415857953902888840109250315594591772197851275320 59910735745658243457138160802170063601085186072703319516241231606…
237
Visual Sum of Cubes
This article discusses a ‘visual’ derivation of the formula for 1³+2³+…+n³.
238
You can beat the binary search
We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values We sometimes have to look for a value in a sorted array. The simplest algorithm consists in just going through the values one by one, until we encounter the value, or exhaust the … Continue reading…
239
Biggest image in the smallest space
What’s the biggest pixel size of a PNG image in the smallest number of bytes? I wanted to try to create an image that could be downloaded but whose pixel buffer would be too big to store in the RAM of a PC. Here is a PNG image of 6,132,534 bytes (5.8 MB) and 225,000 × 225,000 pixels (50.625 gigapixels), which, if…
240