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The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
papad Hard to believe Sanjeev Arora and his coauthors consider it “a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling.” Christos Papadimitriou calls it “so hard to believe that it has been discovered five times and forgotten.” It…
Concise summary of the Hilbert transform: mathematics, effects on signals, and applications in telecommunications.
When I first learned about Fourier series and integrals, I hated it because it seemed like a collection of many ad-hoc definitions, formally related but very different.
In fact, only of the lower house, the Sejm. During its current term, 460 deputies voted 5545 times since the 8th of November 2011. The Sejm website publishes the individual results of the votes as …
If I were to design a computer algebra system (CAS) from scratch today, I would try to achieve the following goals. Several ideas have already been implemented in one system or another, but certainly not all at once. Some ideas could be adopted by existing CASes; others would require fundamentally different designs or…
Please click or tap in the gray square below. It will fill with a jolly tableau of colored disks—first big blue ones, then somewhat smaller purple ones, and eventually lots of tiny red dots.
Towards deep symbolic reinforcement learning Garnelo et al, 2016 Every now and then I read a paper that makes a really strong connection with me, one where I can’t stop thinking about the imp…
TLA, the Temporal Logic of Actions is the core of TLA+. It is a temporal logic that minimizes the use of temporal reasoning in favor of more ordinary mathematics. It is a general mathematical framework for describing and reasoning about algorithms and systems.
A possibly new algorithm for LLM Inference. Adjust smoothly - and in real time - how many calculations you'd like to do during inference.
It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.
The Dow Jones Industrial Average (or 'the Dow', ^DJI, DJIA), is a stock market index created back in 1896 by Charles Dow, a journalist. The goal of the index is provide a view of the stock market's health. The Dow is an index of just 30 (arbitrarily chosen) stocks, weighted by the stock prices of its component…
Any Boolean function can be computed with Tofolli gates, and Tofolli gates are reversible, and so any Boolean function can be computed reversibly.
This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectan…
Here is my (extended) family tree: Everyone in the tree shares at least one common ancestor and at least one common descendant. This ...
We build complex mathematical formulas bottom-up using pure lambda calculus. Includes instructions of how to translate Taylor series and other approximations to lambda terms.
Just announced $latex {\dots}&fg=000000$ Oded Goldreich is one of the top researchers in cryptography, randomness, and complexity theory. Today Ken and I wish to thank the Knuth Prize Committee…
neural networks , convolutional neural networks , convolution , math , probability
Background Backpropagation is a common method for training a neural network. There is no shortage of papers online that attempt to explain how backpropagation works, but few that include an example…
This article is one chapter of my master thesis entitled “Design and implementation of a graphical user interface for git”. It describes the algorithm I designed to draw the commit graph in my own prototype git client called gitamine. I have adapted the content so that it fits better with this blog. Drawing graphs is…
There are hundreds of gas stations around San Francisco in the California Bay area. One might think that gas stations would spread out to serve local neighborhoods. But this idea is contradicted by a common observation. Whenever you visit a gas station, there is almost always another in the vicinity, often just across…
Douglas G. Steigerwald joined the faculty of the Department of Economics at the University of California, Santa Barbara after completing an M.A. in Statistics and a Ph.D. in Economics at the University of California, Berkeley. His research and teaching focus on frontier econometric methods at the intersection of…
Chess puzzles, but you are what you eat.
I like to think there are some solid foundations to my life. I will be able to do the Monday New York Times crossword and I will not be able to do the Thursday version. My dental hygienist will not be satisfied with the amount of flossing I do. I will get my favorite spaghetti meal served on my birthday.
When NP-hardness pops up on the internet, say because some silly blogger wants to write about video games, it’s often tempting to conclude that the problem being proved NP-hard is actually very hard! “Scientists proved Super Mario is NP-hard? I always knew there was a reason I wasn’t very good at it!” Sorry, these two…
