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May Bayes Theorem Be with You
The frequentist paradigm enjoys the most widespread acceptance forstatistical analysis. Frequentist concepts such as confidence intervalsand p-values dominat...
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Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Terry Tao on how to compute non-converging infinite sums (2010)
The Riemann zeta function $latex {\zeta(s)}&fg=000000$ is defined in the region $latex {\hbox{Re}(s)>1}&fg=000000$ by the absolutely convergent series $latex \displaystyle \zeta(s) = \su…
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How to build an Anti Aircraft Missile: Bayes’ Theorem and the Kalman Filter
Ever wondered how an Anti Aircraft Missile works? A plane can move at different speeds and altitudes, so how do you know when to fire your missile? Well you need to know two things: where the aircr…
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A Gentle Introduction to Data Compression
Joe Bertolami's portfolio and blog covering artificial intelligence, game development, computer graphics, data compression, and more.
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Climbing the cosmic distance ladder: Terence Tao book announcement
Several years ago, I developed a public lecture on the cosmic distance ladder in astronomy from a historical perspective (and emphasising the role of mathematics in building the ladder). I previous…
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Gaussian Processes Are Not So Fancy
Gaussian Processes have a mystique related to the dense probabilistic terminology that's already evident in their name. But Gaussian Processes are just models, and they're much more like k-nearest neighbors and linear regression than may at first be apparent.
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Tabasco Sort: a super-optimal merge sort
Paul Khuong's personal blog. Some Lisp, some optimisation, mathematical or computer.
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Picturing Mathematics
I’m a great believer in low-tech math. I don’t like to rely on things a computer tells me; what if there’s a bug in the code? I prefer trusting things that I can check for myself. At the same…
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Issues in the Proof that P ≠ NP
Some further comments into the recent claimed proof that P is not equal to NP Yuri Manin is a great mathematician, who has worked in various areas and also is well known for his many excellent expo…
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The Halting Problem is a terrible example of NP-Harder
It's a justifiable copout, but it's still a copout.
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When would you ever want bubblesort? (2023)
There are very few universal rules in software engineering, but there are are a lot of near-universal principles. Things like "prefer composition to...
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The Point of the Banach Tarski Theorem (2015)
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
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The Breeder's Equation
R is the response to selection, S is the selection differential, and h 2 is the narrow-sense heritability. This is the workhorse equation for quantitative genetics. The selective differential S, is the difference between the population average and the average of the parental population (some subset of the total…
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Harvard Railroad Economics Exam (1906)
Final exam from Dr. Stuart Daggett's Harvard economics course on Railroad Practice taught in 1906-07.
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How Correlated Are You?
This post is an offshoot from Chapter 1 of Probably Overthinking It, which is available for pre-order now! Suppose you measure the arm and leg lengths of 4082 people. You would expect those measurements to be correlated, and you would be right. In the ANSUR-II dataset, among male members of the armed forces, this…
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Visually symmetric words
The word "kayak" is a palindrome, but it isn't visually symmetric. The word "bud" is visually symmetric, but not a palindrome.
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Empiricism and the limits of gradient descent
This post is actually about artificial intelligence, and argues a position that many AI researchers will disagree with. Specifically, it arg...
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Stochastic Superoptimization
An “optimizer” should really be called an “improver”, and a “superoptimizer” should be called an “optimizer” 🙂
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The best linear algebra books
If you would follow the road to linear algebra here are some trustworthy signposts.
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Solomon Golomb (1932–2016)
Stephen Wolfram shares a glimpse into his conversations with Solomon Golomb, developments on shift registers, polyominoes, scientific contributions.
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Linguistics Using Category Theory (2018)
Note: These pages make extensive use of the latest XHTML and CSS Standards . They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in…
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Hopefully the last post I'll ever write on Dual EC DRBG
I’ve been working on some other blog posts, including a conclusion of (or at least an installment in) this exciting series on zero knowledge proofs. That’s coming soon, but first I want…
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Introduction to Digital Filters (2024)
INTRODUCTION TO DIGITAL FILTERS WITH AUDIO APPLICATIONS
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The missing digit of Stela C
One bad thing about archeologists is that some of the successful ones get a big head. People used to think the Olmecs, who made these colossal stone heads, were contemporary with the Mayans. But in…
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Parsing Advances
I find myself writing yet another toy parser, as one does during a Christmas break. It roughly follows Resilient LL Parsing Tutorial. Not because I need resilience, but mostly because I find producing a syntax tree and a collection of diagnostics a more natural fit for the problem than bailing out on the first error.