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Parallel Parentheses Matching
The parallel parentheses matching problem can be parallelized in different manners depending on the use case and is a good example of how stacks map to parallel hardware.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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Why does Heap's algorithm work? (2016)
Heap's algorithm for constructing all permutations is efficient and simple but not easy to understand. This article explains Heap's algorithm by example.
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The Math Inside the US Highway System
At first glance, the US highway seems like a jumble of roads: However, the numbers follow a grid, with rules nobody told me (image source, click to enlarge):
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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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Understanding the Y Combinator
This article is about the Y combinator, a fixed-point combinator that provides a way of using recursion in scenarios and programming languages where symbols are not available. The concept of the Y combinator itself is closely related to lambda calculus (λ-calculus) and functional programming languages. More…
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Degenerate matter: How reality deals with uncertainty
Casual introduction to the uncertainty principle from quantum mechanics and how it leads to neutron stars and superfluids
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Need Something Sorted? Sleep on It
An unexpected paradigm journey into sleep sort
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Math on GitHub: Following Up
About six weeks ago, on May 19, 2022, GitHub released Math support on Markdown. At the time of the release, it received criticism for being ill-designed and buggy. I, too, wrote a blog post about it.
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A Perl Regular Expression That Matches Prime Numbers
Take a look at this Perl regular expression: perl -lne '(1x$_) =~ /^(11+?)\1+$/ && print "$_ is composite"' This regular expression matches only the composite numbers (and doesn't match prime numbers). Can you figure out how it works? I'll give the explanation below but try to figure it…
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Understanding Convolutions in Probability
In this post we take a look a how the mathematical idea of a convolution is used in probability. In probability a convolution is a way to add two random variables. Using a slightly ridiculous, mad-science, example we walk through multiple way to compute a convolution and ultimate arrive at the formu
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The Math Required for Machine Learning
For the past year, I’ve been working on implementing well known model architectures and building web applications, so I have a fair amount…
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100 years of Zermelo's axiom of choice: What was the problem with it? (2006)
Cantor conceived set theory in a sequence of six papers published in the Mathematische Annalen during the five year period 1879–1884. In the fifth of these papers, published in 1883, 1 he stated as a law of thought ( Denkgesetz ) that every set can be well-ordered or, more precisely, that it is always possible to…
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Case study: Creative math – How AI fakes proofs
Many AI enthusiasts debate whether Large Language Models actually "reason." My research indicates that a reasoning process does indeed occur, but its goal is different than we assume.
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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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P < 0.05 Considered Harmful
The unreasonable persistence of an old standard
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The Tetris Effect
Minimalist 3D Tetris.
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Breaking Bell's Inequality with Monte Carlo Simulations in Python
The article explains the Bell inequality using Monte Carlo simulations in Python, and shows how non-local action-at-a-distance can be used to break it with entangled qubits.
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Doing First Grade Math in Rust's Type System
MIT student who enjoys performance engineering, compilers, and creating unconventional code
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Backpropogation Is Just Steepest Descent with Automatic Differentiation (2013)
Preface The intended audience of this article is someone who knows something about Machine Learning and Artifical Neural Networks (ANNs) in particular and who recalls that fitting an ANN required a…
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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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