The latest blog posts to take off on Hacker News. 2,391 posts.
Timsort: A very fast , O(n log n), stable sorting algorithm built for the real world — not constructed in academia. Timsort is a sorting algorithm that is efficient for real-world data and not created in an academic laboratory. Tim Peters created Timsort for the Python programming language in 2001.
Exploring the relationship between Kalman filtering and optimal frequency domain filtering.
Start with any triangulation of a convex polygon, and then repeatedly choose a random diagonal and flip it, replacing the two triangles it borders with two d...
The images described here are generated by analysing the following series for each point (c x ,c y ) on the plane.
[ An updated treatment of this material appears in Chapter 1 of the Energy and Human Ambitions on a Finite Planet (free) textbook , and also appears as part of an article in Nature Physics in 2022.]
Looking at Taylor series as streams of real numbers, solving differential equations becomes as easy as writing them.
Description of the film grain synthesis algorithm in AV1. This page provides information on the film grain synthesis algorithm and links for further study
(Or, “regularized greedy algorithms and their applications.”) James Gilles “Algorithm” is one of those words that sounds fancier than it really deserves. We hear all the time about the “facebook algorithm”, the “youtube algorithm”, “high frequency trading algorithms”, “artificial intelligence algorithms”, and so on…
It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.
In Steven Pinker’s guest post from last week, there’s one bit to which I never replied. Steve wrote: After all, in many areas Einstein was no Einstein. You [Scott] above all could speak…
Where do you stand in order to minimize the expected distance to walk to catch the first elevator that arrives? Maybe not where you think.
About six weeks ago, on May 19, 2022, GitHub released Math support on Markdown. At the time of the release, it received criticism for being ill-designed and buggy. I, too, wrote a blog post about it.
W hat happens, if 100 persons in a room are given $100 each and give away a Dollar to one randomly chosen person in this room each tick of the clock? How is wealth distributed over time by pure chance?
Whenever a student wonders why linear algebra, matrices, and vectors are important, the response from teachers usually sounds like this:
Why some systems -- as a consequence of their intrinsic dynamics -- require a control action that first pushes them the wrong way and makes things worse before it gets better.
However, no experiment with actual coin-tosses has been done to investigate whether the predicted effect is empirically observed. Diaconis et al noted, correctly, that to estimate the probability with a S.E. of 0.1% would require 250,000 tosses, but this seems unnecessarily precise. Let's work with numbers of tosses…
Audio Link With the arrival of summer weather in many parts of the U.S., it’s time to think again about various outdoor activities. Wat...
Finally! On May 19, 2022, GitHub released one of its most requested features: Math support on Markdown! Many had been anticipating this for years, including myself, so much in fact that I wrote a browser extension to get there early. (xhub, it can do a few other things so check it out.)
Six matrix factorizations dominate in numerical linear algebra and matrix analysis: for most purposes one of them is sufficient for the task at hand. We summarize them here. For each factorization …
Gerrymandering distorts the will of the people, but the basic math of geographic representation makes it difficult to get rid of, unless we get rid of representation for geographic districts.
I saw a math puzzle the other day on Hacker News. It reads as follows: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don’t know the numbers…
I am very happy to say that I have recently received a generous grant from the Astera Institute to set up a small group to work on automatic theorem proving, in the first instance for about three y…
Update (April 27): Boaz Barak—Harvard CS professor, longtime friend-of-the-blog, and coauthor of my previous guest post on this topic—has just written an awesome FAQ, providing his pers…
Bayesianism, the doctrine that it's always rational to represent our beliefs in terms of probabilities, dominates the intellectual world, from decision theory to the philosophy of science. But does it make sense to quantify our beliefs about such ineffable things as scientific theories or the future? And what separates
How does set theory help to understand type assignability and resolution in TypeScript?
