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The most popular blog posts about math & algorithms on Hacker News. 184 posts.
Once upon a time, my computer architecture professor mentioned that using a random eviction policy for caches really isn't so bad. That random eviction isn't bad can be surprising — if your cache fills up and you have to get rid of something, choosing the least recently used (LRU) is an obvious choice, since you're…
Would you believe me, if I claimed that an algorithm which has been on the books as "optimal" for 46 years, which have been analyzed in excruciating detail by geniuses like Knuth and taught in all CS courses in the world, can be optimized to run ten times faster ?
I. Allen Ginsberg’s famous poem on Moloch:What sphinx of cement and aluminum bashed open their skulls and ate up their brains and imagination? Moloch! Solitude! Filth! Ugliness! Ashcans and u…
From the highly eclectic blog of Mark Dominus
Peter Dorman points to this post on statistical significance and p-values by Timothy Taylor, editor of the Journal of Economic Perspectives, a highly influential publication of the American Economic Association.
In the previous post, I described a simple way to think about matrices, namely as bipartite graphs. Today I'd like to share a different way to picture matrices—one which is used not only in mathematics, but also in physics and machine learning. Here's the basic idea. An $m\times n$ matrix $M$ with real entries…
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
Eller's algorithm creates 'perfect' mazes, having only a single path between any two cells, one row at a time. The algorithm itself is incredibly fast, and far more memory efficient than other popular algorithms (such as Prim's and Kruskal's) requiring storage proportional to only a single row. This makes it possible…
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.
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…
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…
Consulting software engineer and research scientist. I build visualization systems for complex data and machine learning models.
Many times on this blog I've argued that the difference between pure and applied math is motivation. As my graduate advisor used to say, “Applied mathematics is not a subject classification. It's an attitude.” Traditionally there was general agreement regarding what is pure math and what is applied. Number theory and…
How to build a constraint programming solver in Julia. Part 1: Solving Sudoku using backtracking
Every square has exactly 3 units and 20 peers. For example, here are the units and peers for the square C2 :
Many people are surprised to learn that `sed`, a seemingly simple text filtering program, is actually Turing complete. This realization prompts the question: how can a text processing utility achieve such computational power? The answer lies in sed's fundamental operations. Essentially, sed functions as a miniature...
I had an interesting discussion at work today (among people I think would all call themselves statisticians!) about the distinction(s) between statistics and machine learning. It is something I am …
Not all instructions on modern processors cost the same. Additions and subtractions are cheaper than multiplications which are themselves cheaper than divisions. For this reason, compilers frequently replace division instructions by multiplications. Roughly speaking, it works in this manner. Suppose that you want to…
From the highly eclectic blog of Mark Dominus
An automatic system for rolling a polyhedral die and taking photos of the rolls; extracting the image of just the die from those images; clustering the images of the die by which face is shown; and analyzing the results.
The essence of constraint is projection.
Three more fundamental algorithms in the series. Today, recursive permutations, subsets of the given set and variations with repetitions. Th...
In this post we’ll explore how we can derive logistic regression from Bayes’ Theorem. Starting with Bayes’ Theorem we’ll work our way to computing the log odds of our problem and the arrive at the inverse logit function. After reading this post you’ll have a much stronger intuition for how logistic
The code used to generate the plots for this post can be found here.
