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Patent 5,893,120 reduced to mathematical formulae
I have previously argued that the Bilski ruling renders all software unpatentable in the US because any method of manipulating information ...
A “perfect” voting system
A voting system that sidesteps Arrow's theorem entirely. The scare quotes around
The Prime That Wasn’t
Life, technology, and other good things
Succinct Data Structures: Cramming 80,000 words into a Javascript file
<img src="http://zwibbler.com/shared/1024.png"/> jQuery creator John Resig needs a little help storing lists of words in his side project. Let's go overkill and explore a little known branch of computer science called Succinct Data Structures.
Skip Lists are Fascinating
Skip lists are a fascinating data structure: very simple, and yet have the same asymptotic efficiency as much more complicated AVL trees and red-black trees.
Why Data Structures Matter: left, right folds, btrees
Our experience on Day 0 of JPR11 yielded a nice example of the need to choose an appropriate implementation of an abstract concept. As I mentioned in the previous post, we experimented with Michael…
Visualizing dynamic programming
I’ve always thought dynamic programming was a pretty crummy name for the practice of storing sub-calculations to be used later. Why not call it table-filling algorithms , because indeed, thinking of a dynamic programming algorithm as one that fills in a table is a quite good way of thinking about it.
New string search algorithm
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Maze-generation algorithms, with JS demos
Algorithms, circle mazes, hex grids, masking, weaving, braiding, 3D and 4D grids, spheres, and more!
Java Hangs When Converting 2.2250738585072012e-308
Konstantin Preißer made an interesting discovery , after reading my article “ PHP Hangs On Numeric Value 2.2250738585072011e-308 ”: Java — both its runtime and compiler — go into an infinite loop when converting the decimal number 2.2250738585072012e-308 to double-precision binary floating-point. This number is…
Maze Generation: Wilson's algorithm
Algorithms, circle mazes, hex grids, masking, weaving, braiding, 3D and 4D grids, spheres, and more!
The polynomial algorithm for 3-SAT problem (or P=NP)
Dear Fellow Researchers, Would you kindly pay attention to the article “Non-Orthodox Combinatorial Models Based on Discordant Structures” by the author V. F. Romanov published on arXiv.…
Using Python and heat maps to determine the best place to aim on a dart board
Over break I went out with a buddy of mine and played some darts. This got me to thinking, where exactly should someone aim in order t...
PHP 5.3.3 hangs on numeric value 2.2250738585072011e-308
I stumbled upon a very strange bug in PHP; this statement sends it into an infinite loop:
Maze Generation: Eller's Algorithm
Algorithms, circle mazes, hex grids, masking, weaving, braiding, 3D and 4D grids, spheres, and more!
Yacc is dead: An update
The draft of " Yacc is Dead " that David Darais and I posted on arXiv received some attention, so we'd like to share updates and feedback.
Medical researcher discovers integration, gets 75 citations
(Note: this post is `just for fun;’ no premeds, doctors, researchers, or nobel laureates were meant to be offended in the writing of this post.) The bane of many American physics grad student…
Notation And Thinking
Does notation shape our thinking? Kenneth Iverson was a mathematician who is most famous for designing APL. This was the name of his programming language, and it cleverly stood for “A Program…
Some fun mathematical puzzles
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Proving P!=NP: "...Ryan has taken the first real baby step in decades."
On October 8th, when in my graduate complexity course as we discussed the 1987 Razborov-Smolensky result that one can't compute the Mod p b...
Mathematically correct but psychologically wrong
The snowball strategy says to pay off your smallest debt first, then the next smallest, and so on until you're out of debt. When I first heard of this I thought it was silly. Clearly the optimal strategy is to pay off the debt with the highest interest rate first. That assessment is mathematically correct,