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Deterministic thinking: a problem in how we think, not just in how we act
– Basketball Stats: Don’t model the probability of win, model the expected score differential.
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The latest blog posts to take off on Hacker News. 216 posts.
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Algorithm No One Knows About (2016)
Here’s a program roughly 0% of programmers know how to write: generate a list of random tweets, without duplication. You may think you know how to do this, but you almost assuredly don’…
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Time to Abolish "Statistical Significance"?
The idea of "statistical significance" has been a basic concept in introductory statistics courses for decades. If you spend any time lookin...
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The exponential function is a miracle
From the highly eclectic blog of Mark Dominus
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A Million Digits of Pi in 9 Lines of JavaScript
"Big integers" have landed in Javascript, at least in Firefox and Chrome. One of my favorite things to do with high precision arithmetic is to calculate digits of π. From scratch, that is, using only addition, subtraction, multiplication, and division.
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The Riemann Hypothesis (Part 2)
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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It’s not just p=0.048 vs. p=0.052
Peter Dorman points to this post on statistical significance and p-values by Timothy Taylor, editor of the Journal of Economic Perspectives, a highly influential publication of the American Economic Association.
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The Riemann Hypothesis
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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Solving Every Sudoku Puzzle (2006)
Every square has exactly 3 units and 20 peers. For example, here are the units and peers for the square C2 :
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RSA: Theory and Implementation
RSA has been a staple of public key cryptography for over 40 years, and is still being used today for some tasks in the newest TLS 1.3 standard. This post describes the theory behind RSA - the math that makes it work, as well as some practical considerations; it also presents a complete implementation of RSA key…
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Shenanigans With Hash Tables
One reason to know how your data structures work is so that when your problem has unusual constraints you can tweak how they work to fit the problem better or work faster. In this article I’ll talk about four different fun tweaks to the concept of a hash table that I made in the process of using hash tables to…
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Tree traversal without recursion: the tree as a state machine (2007)
I am currently working my way through Higher-Order Perl , a highly recommended tome on effective and practical use of functional programming techniques in Perl. As you’d expect from a book that spends a lot of time discussing such concepts as function composition and recursion, the subject of tree traversal makes a…
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Escher-Like Spiral Tilings
The artist M.C. Escher drew many lovely tilings, which he called “regular divisions of the plane”. He worked hard to ensure that his tilings were of lifelike animal forms such as birds and fish. He filled notebooks with hand-drawn sketches of tilings, many of which later found their way into his woodcuts. If you’d…
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The Paxos Algorithm, or How to Win a Turing Award
The lectures assume no prior knowledge of the Paxos consensus algorithm or of TLA+, the language in which the specifications are written. In fact, the lectures constitute a crash course on TLA+. If you're interested just in the algorithm, you will probably find the specs annoying and will try to read only the…
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Understanding SAT by Implementing a Simple SAT Solver in Python (2014)
SAT is often described as the "mother of all NP-complete problems." This post goes over what SAT is and why it is considered to be so important. A simple SAT solver is implemented using Python in the process.
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A Molecular Near Miss
I’m thrilled to report that I’m a co-author of the article “ An ultra-stable gold-coordinated protein cage displaying reversible assembly “, which was recently published in Nature . This work is the result of an exciting collaboration between biochemists, physicists, structural biologists, mathematicians, and others…
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Words that do Handstands
The other day I ordered a book on art history from Amazon… which reminded me of the movie Angels and Demons , which reminded me of ambigrams. Ambigrams are those stylized words that look the same when you turn them upside down. Here is the classic, by John Langdon .
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Exploring Weight Agnostic Neural Networks
Posted by Adam Gaier, Student Researcher and David Ha, Staff Research Scientist, Google Research, Tokyo When training a neural network to accompl...
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A book from Alan Turing and a mysterious piece of paper
Sleuthing into the history of a 1930 book on quantum mechanics previously owned by Alan Turing and a lambda calculus note tucked inside.
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Gamedev Tutorial: Trigonometry Basics – Sine and Cosine
[latexpage] 本文之中文翻譯在此 Overview Trigonometry is a very essential building block to a huge portion of game math. That's why I've chosen this topic for the first tutorial of my new Gamedev Tutorials series. Having a solid understanding of basic of trigonometry can go a long way for game development. It is used…
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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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Calculus Is Deeply Irrational
You’re lying on a beautiful beach when you feel a tap on your shoulder, and suddenly you’re not at the beach at all — you’re in a classroom. The student who woke you looks apologe…
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Math in Data Science
Find out how much math is involved in data science and what math you need to know to get started in a data science role.
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The lat/lon floating point delusion
This morning I had a shower for 6.11686718 minutes. For breakfast I had 189.41576911 ml of fruit juice, followed by 75.24902503 g of muesli topped with 36.55668786 ml of milk and 15.44171338 g of yogurt.
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What’s the difference between statistics and machine learning?
I had an interesting discussion at work today (among people I think would all call themselves statisticians!) about the distinction(s) between statistics and machine learning. It is something I am …
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Curve fitting A: Linear Least Squares
The graph on the left shows a third example, taken from analytical chemistry: a straight-line calibration data set where X = concentration and Y = instrument reading (Y = a + b X). Click to download that data . The blue dots are the data points. They don't all fall in a perfect straight line because of random noise…
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Exploring Mathematics with Matplotlib and Python
Data Visualization can be a great tool for mathematical exploration and experimentation. In this article, I show you an example using Matplotlib and Python.
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Knuth on Huang's Sensitivity Proof: “I've got the proof down to one page” [pdf]
The Sensitivity Conjecture, which I blogged about here, says that, for every Boolean function f:{0,1}n→{0,1}, the sensitivity of f—that is, the maximum, over all 2n input strings x∈{0,1}n, of…
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A Brief Guide to a Few Algebraic Structures
Occasional writings about Haskell.