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Faster than radix sort: Kirkpatrick-Reisch sorting
Radix sort sorts n w-bit integers by splitting them up into chunks of logn\log nlogn bits each, and sorting each chunk in linear time. Thus it achieves O(nw/logn)O(nw/\log n)O(nw/logn) time.
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The 2,500 year old history of why Python’s all([]) returns True
How a Python function relates to a two thousand year old debate in philosophy
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Introduction to Clifford Algebra (2006)
Clifford algebra gives a unified view of many things that otherwise would need to be understood separately.
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Algorithm for Drawing Trees
I recently wanted to take a hierarchy of items and draw them in a nice tree structure. For example, a Family Tree. At the time, I thought “This will be easy, I’ll just Google for an alg…
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Dissecting Lemire's nearly divisionless random number generator
A very late blog post announcing the readability contest winners, a new (very) annotated implementation, and a surprising sort-of security issue found along the way.
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Reverse-engineering the problematic tail behavior of Fivethirtyeight forecast
We’ve been writing a bit about some odd tail behavior in the Fivethirtyeight election forecast, for example that it was giving Joe Biden a 3% chance of winning Alabama (which seemed high), it was displaying Trump winning California as in “the range of scenarios our model thinks is possible” (which didn’t seem right)…
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Why Bayesian Stats Needs Monte-Carlo Methods
Bayesian statistics rely heavily on Monte-Carlo methods. A common question that arises is “isn’t there an easier, analytical solution?” This post explores a bit more why this is by breaking down the analysis of a Bayesian A/B test and showing how tricky the analytical path is and exploring more of t
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Roman Finger Counting
I recently wrote a final paper on the history of written numerals. In the process, I discovered this fascinating tidbit that didn’t really fit in my paper, but I wanted to put it somewhere. So I’m writing about it here.
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A Software Engineer’s Guide to Cybernetics
Before ‘cyber’ was a prefix for everything internet and computers, it was how mathematicians were going to conquer the world.
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What are Differential Equations and how do they work?
Science News, Physics, Science, Philosophy, Philosophy of Science
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Hindley-Milner Type Inference (2012)
Robin Milner's type system with parametric polymorphism was a significant advance over the systems of Russell and Church. Arguably it is the ability to use type-variables that makes higher order logic a practical vehicle for proving non-trivial theorems. The Hindley-Milner algorithm is used to automatically infer…
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Lambda Calculus Diagrams (2015)
The following table shows diagrams of identity, the booleans, some standard combinators, some Church numerals, the predecessor function on Church numerals, and Omega. term definition diagram alternative I/1 λx.x K/true λx.λy.x false/0 λx.λy.y S λx.λy.λz.(x z)(y z) Y λf.(λx.x x)(λx.f(x x)) 2 λf.λx.f(f x) 3 λf.λx.f(f(f…
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Weighing a Car with Tire Pressures
The first thing I wanted to do with my Saab 96 was to establish a baseline weight.
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Toward an API for the Real Numbers
Towards an API for the real numbers, Boehm, PLDI’20 Last time out we saw that even in scientific computing applications built by experts, problems with floating point numbers are commonplace. …
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A brief introduction to the beauty of Information Theory
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
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Basic skeletal animation with geometric algebra
Klein - Realtime Projective Geometric Algebra
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A Pretty Good Mathematical Model of Perfectionism
I struggle with perfectionism. Well, not so much “struggle with” — I’m f*cking great at it. It comes naturally. There are some upsides, but perfectionism is also associated …
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Chesterton’s Fence: A Lesson in Second Order Thinking
A core component of making great decisions is understanding previous decisions. If we don’t understand how we got “here,” we run the risk of making things much worse.
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Finding Mona Lisa in the Game of Life
Using a SAT solver to find Game of Life states that turn into pictures.
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Cofactor Explained: Clearing Elliptic Curves' dirty little secret
Efficient elliptic curves tend not to have a prime order. This discusses the problems this causes, and the solutions.
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Elo sucks – better multiplayer rating systems for smaller games (2019)
Elo does not work when different skill levels must play against each other. Can we make a better system?
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Better Geometry Through Graph Theory (2018)
A few months ago, I decided to implement set operations on curved regions. I had the the canonical textbook on computational geometry , which described approaches for polygons comprised of straight lines, and it seemed like other projects had extended these techniques to parametric curves . I figured it would take a…
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GNU GCC does not round floating-point divisions to the nearest value
I know that floating-point arithmetic is a bit crazy on modern computers. For example, floating-point numbers are not associative: 0.1+(0.2+0.3) == 0.599999999999999978 (0.1+0.2)+0.3 == 0.600000000000000089 But, at least, this is fairly consistent in my experience. You should simply not assume fancy properties like…
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Summary of all the MIT Introduction to Algorithms lectures (2009)
As you all may know, I watched and posted my lecture notes of the whole MIT Introduction to Algorithms course. In this post I want to summarize all the topics that were covered in the lectures and point out some of the most interesting things in them. Actually, before I wrote this article, I had started writing an...
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Logistic regression from scratch
Deep dives into Cryptography and Privacy.
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Plotting patterns in music with a fantasy record player
A blog about signals, programming, music, and other stuff.