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Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 179 posts.
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Prospecting for Hash Functions
Update 2022 : TheIronBorn has found even better permutations using a smarter technique. That thread completely eclipses my efforts in this article.
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How to Be Wrong (2016)
“To be wrong, or not to be wrong?” That is the wrong question. You are going to spend a lot of your time being wrong, especially if you become a scientist or mathematician. The question…
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When the bubble bursts
We are clearly not in a steady-state situation. Is this a bubble or a revolution? The answer surely includes a bit of revolution—the fields of vision and speech recognition have been turned over by great empirical successes created by deep neural architectures and more generally machine learning has found plentiful…
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Optimizing a breadth-first search
Optimizing a breadth-first search of an implicit graph for secondary storage, and memory use in general.
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Connected Components – The one Graph Algorithm you need to know
Graphs provide us with a very useful data structure.
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Losing the Nobel Prize
There’s a fascinating new book just now appearing in book stores, Losing the Nobel Prize, by astronomer Brian Keating. An excerpt from the book is available at Nautilus, with the title How My…
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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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Empiricism and the limits of gradient descent
This post is actually about artificial intelligence, and argues a position that many AI researchers will disagree with. Specifically, it arg...
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Using Self-Organizing Maps to Solve the Traveling Salesman Problem
Using Self-Organizing Maps to solve the Traveling Salesman Problem The Traveling Salesman Problem is a well known challenge in Computer Science: it consists on finding the shortest route possible that traverses all cities in a given map only once. Although its simple explanation, this problem is, indeed, NP-Complete…
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A Gentle Introduction to Markov Chain Monte Carlo (2012)
Applying probabilistic models to data usually involves integrating a complex, multi-dimensional probability distribution. For example, calculating the expectation/mean of a model distribution invol…
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How to design co-programs
I recently attended the Matthias Felleisen Half-Time Show, a symposium held in Boston on 3rd November in celebration of Matthias’s 60th birthday. I was honoured to be able to give a talk ther…
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Why are amplitudes complex?
[By prior agreement, this post will be cross-posted on Microsoft’s Q# blog, even though it has nothing to do with the Q# programming language. It does, however, contain many examples th…
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Life lessons from differential equations (2015)
Some problems simply have no solution. Some problems have no simple solution. Some problems have many solutions. ...
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A whirlwind introduction to dataflow graphs
While in the middle of writing “Reading bits in far too many ways, part 3”, I realized that I had written a lot of background material that had absolutely nothing to do with bit I/O and…
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How thick is the atmosphere? A derivation of the Boltzmann distribution
Let’s talk about a small question as a way of introducing a big question. How thick is the atmosphere? How far does Earth’s atmosphere extend into space? In other words, how high can y…
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Supertasks
Background Reading: Earman and Norton, Infinite Pains: The Trouble with Supertasks and Comments on Laraudogoita's Supertask
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The Categories Were Made for Man, Not Man for the Categories (2014)
I. “Silliest internet atheist argument” is a hotly contested title, but I have a special place in my heart for the people who occasionally try to prove Biblical fallibility by pointing …
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Why FTL implies time travel
In science fiction, it is pretty standard fare to introduce some form of faster-than-light communication or travel. After all, space is big, and you can't write your swashbuckling Hornblower-in-space novel if you have to wait for a generation ship to crawl painfully slowly between the nearest stars,