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Reservoir Sampling
Choosing fairly when you don't know how many you're choosing from.
New
The latest blog posts to take off on Hacker News. 2,391 posts.
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Geometrically understanding calculus of inverse functions (2023)
The Legendre transformation tells you how the inverse map acts on integrals
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Unparalleled Misalignments
This is a list of Unparalleled Misalignments, pairs of non-synonymous phrases where the words in one phrase are each synonyms of the words in the other. I've maintained this list since 2018; attributions (when known) can be seen on hover.
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Bloom Filters
The original motivation for the creation of Bloom filters is efficient set membership, using a probabilistic approach to significantly reduce the time and space required to reject items that are not members in a certain set.
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Derivation and Intuition behind Poisson distribution
Made in Notion, the connected workspace where AI agents and teams organize docs, projects and knowledge together.
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Reversible computing with mechanical links and pivots
With the concern that “Moore’s Law is dead,” new interest has grown for unconventional forms of computing. This includes:
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Collatz's Ant
This is a brief continuation of a previous post ( Repo ), which introduced such visualization for collatz sequences based on Langton’s Ant .
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Are polynomial features the root of all evil? (2024)
High-degree polynomial features aren’t inherently unstable: the power basis and unscaled inputs are. This post shows how regularization and Bernstein polynomials make polynomial regression behave.
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100 Years to Solve an Integral (2020)
The integral of sec(x) is well known to any beginners calculus student. Yet this integral was once a major outstanding maths problem. It was first introduced...
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Dumb statistical models, always making people look bad
This is Jessica. In my Prediction for Decision-making class last quarter we talked about human predictions and decisions relative to algorithmic ones. This led to a discussion about why it’s often hard to demonstrate the value of human knowledge once you have a decent statistical model.
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A cute proof that makes e natural
Po-Shen Loh explains why Euler's number e is natural using only precalculus: one exponential curve has tangent slope 1 at the y-axis, which leads to the compound interest limit.
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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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An Introduction to Stochastic Calculus (2022)
Through a couple of different avenues I wandered, yet again, down a rabbit hole leading to the topic of this post. The first avenue was through my main focus on a particular machine learning topic th
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What Is Entropy?
People say many things about entropy: entropy increases with time, entropy is disorder, entropy increases with energy, entropy determines the arrow of time, etc.. But I have no idea what entropy is, and from what I find, neither do most other people. This is the introduction I wish I had when first told about entropy…
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Monte Carlo Crash Course: Sampling
In the previous chapter, we assumed that we can uniformly randomly sample our domain. However, it’s not obvious how to actually do so—in fact, how can a deterministic computer even generate random numbers? 1
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Writing my own dithering algorithm in Racket
My journey implementing a new dithering algorithm in the Racket programming language.
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How much oranger do red orange bags make oranges look?
Look at this orange: Now look at this orange: It’s the same orange. But, look how much more orange it looks with the red mesh on top of it: If you buy bags of oranges (at least at many places in the US), they frequently come in this red mesh bag. This bag makes the oranges look more orange. Oranger. Here’s what that…
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The Bitter Prediction
The Ivory Tower is a blog about software engineering and development philosophy by Anders Sundman.
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Parser Combinators Beat Regexes
Someone online was solving Advent of Code problems, and had a question about last years’ day 3 . They had a working solution using regular expressions (regexes) on String values, but they wanted to use ByteString values instead for performance reasons. They were surprised, however, that there seems to be a lack of…
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Solving a “Layton Puzzle” with Prolog
I have a lot in the works for the this month's Logic for Programmers release. Among other things, I'm completely rewriting the chapter on Logic Programming...
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Analytic Combinatorics – A Worked Example
Chris Grossack's math blog and professional website.
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The Mathematics of Crochet
I remember thinking at school when will I ever in my “real life” use maths. Well much to my utter surprise I’ve come to the stark realisation that there is a link between mathematics and crochet. …
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Animals Made from 13 Circles (2016)
Dori | Art Director, Designer, Artist
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Accessible open textbooks in math-heavy disciplines
The challenge The authoring platform of choice in many math-heavy disciplines is LaTeX. It produces typeset documents of excellent quality and handles formulas and mathematical diagrams extremely w…
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Decomposing a Factorial into Large Factors
I’ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors”. This paper studies the quantity $latex {t(N)}&fg=000000$, defined as the largest quanti…
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Entropy Attacks
The conventional wisdom is that hashing more entropy sources can't hurt: if H is any modern cryptographic hash function then H(x,y,z) is at least as good a random number as H(x,y), no matter how awful z is. So we pile one source on top of another, hashing them all together and hoping that at least one of them is good.
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A (Long) Peek into Reinforcement Learning
[Updated on 2020-09-03: Updated the algorithm of SARSA and Q-learning so that the difference is more pronounced. [Updated on 2021-09-19: Thanks to 爱吃猫的鱼, we have this post in Chinese].
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Numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us