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New
The latest blog posts to take off on Hacker News. 2,391 posts.
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Clojure Numerics: Orthogonalization and Least Squares
How to solve linear systems that have many solutions, or those that have no solutions at all? That's the theme for a thick math textbook, of course, but from...
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One model to learn them all
One model to learn them all Kaiser et al., arXiv 2017 You almost certainly have an abstract conception of a banana in your head. Suppose you ask me if I’d like anything to eat. I can say the word ‘…
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What the Four Color Theorem Can Teach Us About Writing Software
A visual exploration of what The Four Color Theorem can say about software complexity.
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GPU Fluid
Benedikt Bitterli's Portfolio
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Homotopy Type Theory and Higher Inductive Types
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) ci…
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Algorithm efficiency comes from problem information
This is a high level post about algorithms (especially mathematical, scientific, and data analysis algorithms) which I hope can help people who are not researchers or numerical software developers better understand how to choose and evaluate algorithms. When scientists and programmers think about efficiency of…
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A Pragmatic Introduction to Signal Processing
A retirement project created and maintained by Tom O'Haver , Professor Emeritus , Department of Chemistry and Biochemistry
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The scrypt parameters
The recommended scrypt parameters in the Go docs were recently brought up for discussion given they haven’t changed since 2009.
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Learning from Scratch by Thinking Fast and Slow
Reinforcement Learning
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Colorized Math Equations
Years ago, while working on an explanation of the Fourier Transform, I found this diagram: Most ideas aren't inherently confusing, but their technical…
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Algorithmic Solution to My Insomnia
I’ve struggled with insomnia for all of my adult life. It began in college and has waxed and waned in severity ever since, correlating with stress levels…
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The strange story of “Extended Random”
Yesterday, David Benjamin posted a pretty esoteric note on the IETF’s TLS mailing list. At a superficial level, the post describes some seizure-inducingly boring flaws in older Canon printers…
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A Zero-Math Introduction to Markov Chain Monte Carlo Methods
For many of us, Bayesian statistics is voodoo magic at best, or completely subjective nonsense at worst. Among the trademarks of the…
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Simulating Chutes and Ladders in Python
Edit 12/19/2017: added a new subsection on analyzing Chutes & Ladders as an Absorbing Markov Chain.
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The ABC conjecture has still not been proved
Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of the ABC conjecture. I have nothing further to add on the sociological aspects of mathematics discussed in that post, but I just wanted to…
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Stats without Tears (2016)
Printer Friendly: The whole text in one file , all 164,000 words, convenient for printing. (The printed length will vary, depending to your browser settings. For me it’s 401 pages.)
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Gerrymandering with geographically compact districts
The following tweet has been making the rounds on social media: Notice that since the Democrats won overall, it would be impossible for Republicans to win all seven districts, no matter how the map…
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What are the complex numbers, really?
Where did complex numbers come from? You might think that people invented \(i\) just so that they had a solution to the quadratic equat...
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Modes, Medians and Means: A Unifying Perspective
Introduction / Warning Link to heading Any traditional introductory statistics course will teach students the definitions of modes, medians and means. But, because introductory courses can’t assume that students have much mathematical maturity, the close relationship between these three summary statistics can’t be…
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Matrices from a geometric perspective
Graphics is all about geometry. In particular, there are points that have a certain color, and the pattern of colors gives you a certain picture. You can change the way the points are distributed by applying certain transformations like translation (movement), rotation and scaling. While most people familiar with the…
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Understanding LSTM Networks (2015)
Humans don’t start their thinking from scratch every second. As you read this essay, you understand each word based on your understanding of previous words. You don’t throw everything away and start thinking from scratch again. Your thoughts have persistence.
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Statistics, we have a problem
Recently, while browsing Twitter, I saw a few machine learning researchers post about an incident at one of their big conferences (NIPS) in…
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Three-Valued Logic
Making decision despite missing SQL data (NULL): How to avoid OR…IS NULL in the WHERE clause.
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Using loaded dice to cheat at Settlers of Catan, and p-values to avoid suspicion
My copy of Settlers of Catan came with two normal wooden dice. To load these dice, I placed them in a small plate of water overnight, leaving the 6 side exposed.
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How to Read Mathematics
Ranked a top 100 research university, VCU is a place where discovery and creativity go hand in hand. Located in downtown Richmond, Virginia, its more than 200 programs emphasize hands-on learning, creativity and engaging in the world around us.