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Hamiltonian Monte Carlo explained
Understanding an effective way of sampling from complex distributions with 3d-demonstrations
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Graphical Introduction to Dynamic Programming
I’ve been helping a friend understand dynamic programming (DP for short), so I’ve been on the lookout for good resources. The topic is covered all across the web, but I found many of them focused on the code, and not enough on the beautiful visualizations that shed light into how DP works.
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Quantum mechanics as a generalization of probability (2007)
There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you…
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Why I am learning category theory
Category theory is a domain of mathematics that exerts a strange influence over programmers. One thing that can be said for sure about category theory is tha...
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How random is xkcd? (2015)
Apparently Randall Munroe gets a lot of messages saying that the “random” button on xkcd is biased.
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How Lewis Carroll computed determinants (2023)
Charles Dodgson (a.k.a. Lewis Carroll) developed a method of computing determinants which has some practical advantages.
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Mona Lisa in 50 polygons, using a genetic algorithm (2008)
This weekend I decided to play around a bit with genetic programming and put evolution to the test, the test of fine art 🙂
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Are deep neural networks dramatically overfitted? (2019)
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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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How Advanced Is the NSA's Cryptanalysis, and Can We Resist It?
The latest Snowden document is the US intelligence ‘black budget.’ There’s a lot of information in the few pages the Washington Post decided to publish, including an introduction by Director of National Intelligence James Clapper. In it, he drops a tantalizing hint: ‘Also, we are investing in groundbreaking…
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Music and Geometry: Intervals and Scales
An article about music and geometry, in particular about musical intervals and scales and their geometric equivalent ...
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Why Multi-armed Bandit algorithms are superior to A/B testing (with Math)
In a recent post, a company selling A/B testing services made the claim that A/B testing is superior to bandit algorithms. They do make a compelling case that A/B testing is superior to one particular not very good bandit algorithm, because that particular algorithm does not take …
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The Mathematics of 2048: Optimal Play with Markov Decision Processes (2018)
Finding provably optimal strategies for 2048 using Markov Decision Processes
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I simulated California housing and learned about simulators
Back in the early 2000s, XML was all the rage. An unusual evolution from HTML, which itself was an evolution (devolution?) from SGML, XML w...
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Understanding Quaternions
Quaternions are used to represent an orientation in 3D space. This article attempts to demystify the complexities of quaternions.
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Teaching Linear Algebra
In a recent Hacker News post I made reference to an interesting teaching experience I had in the mid-90s. This is a longer explanation of ...
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Damn Cool Algorithms: Levenshtein Automata
Posted by Nick Johnson | Filed under python , tech , coding , damn-cool-algorithms
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Think in math, write in code (2019)
Programmers love to discuss programming languages. We not only debate their technical merits and aesthetic qualities, but they become integrated into our personal identities, along with the values and traits that we associate with them. Some even defend a form of Linguistic Determinism that thinking is confined to…
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Using Fourier Transforms to Multiply Numbers
The purpose of this article is to show you step-by-step examples of how to use the Fourier transform algorithm to multiply two numbers. The primary advantage of using fourier transforms to multiply numbers is that you can use the asymptotically much faster 'Fast Fourier Transform algorithm', to achieve better…
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Best algorithms book I ever read
Best algorithms book I ever read I took a fair amount of time looking at data structures and algorithms while I was st...
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Glow: Better Reversible Generative Models
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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A Visual Exploration of Gaussian Processes
Consulting software engineer and research scientist. I build visualization systems for complex data and machine learning models.
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The Sell ∀ ∃ as ∃ ∀ Scam
Artificial intelligence, like machine learning before it, is making big money off what I call the “sell ∀ ∃ as ∃ ∀ scam.” The scam works as follows. Build a sy…
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What Is Spacetime, Really?
On the 100th anniversary of Einstein’s Theory of Relativity, Stephen Wolfram discusses the nature of space and time, and fundamental theory of physics.
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