Last November I wrote a molecular simulator called Go Replicants! that uses Go potentials to simulate protein folding processes and study some of their thermodynamic properties. Its source code and some instructions can be found here.
Archive - mathematics
RSS Feed
Applications of the absolute quadratic complex and the quadric of segments in 3D reconstruction.
The final project in my post-graduate degree in Mathematics explains two approaches for computing a Euclidean upgrading of a projective 3D reconstruction, which has applications in Computer Vision. The slides for a talk I gave a couple of weeks ago explaining the subject matter are also available online.
Continue Reading…
Introductory talk on Geometric Algebra
A few weeks ago I gave at work an introductory talk on Geometric Algebra. In my slides, I mostly followed the exposition in David Hestenes’ New Foundations for Classical Mechanics. And since we’re mostly a MATLAB shop I also used Gable to show how to perform some practical computations.
Continue Reading…
Functional programming in Maple
I have written some notes on functional programming in Maple mainly to help me find my way around it. For the moment these notes are very terse but I find them useful as a cheat sheet and I might expand them in the future.
Mathematics, cryptography, and the real world
Among the many reactions to Neil Koblitz’ article on modern cryptography in the Notices of the AMS the most interesting reply I’ve read is this one by Steven Bellovin:
Mathematicians have known since Euclid that axioms are important. Security, though, is math embedded in the real world, and that matters. Put another way, Euclidean geometry is completely valid as a pure mathematical system. But that doesn’t mean it applies in a relativistic universe. Sure, we live far from any space-warping masses, so we can pretend that the angles in our triangles add up to 180 degrees. In the security world, though, the attacker will toss a black hole at us to warp the space around our provably-secure triangular encryptor. Was that proof of security flawed? Ask Riemann or Lobachevsky.
Short films on topology
Youtube user bothmer has posted a collection of nifty films related to topology and algebraic geometry. As an appetizer, I leave you with this one on Compactness and the Stereographic Projection:
You can find more movies at Advent Calendar 2006 – Geometrical Animations.
Separation axioms and the Topology Database
I recently deemed it convenient to be able to see the relationship between some general topology concepts in just one gaze. That’s why I prepared a graph describing their implications. I have made it available here hoping that it will be of use for someone else. All the definitions come from the book General Topology by Stephen Willard.
I needed to roll my own solution but Ryan Dahl has set up the Topology Database and this website not only publishes more implication graphs like the one above but it also intends to be the online equivalent to Counterexamples in Topology. This is a wiki-like site and the author even publishes the source code licensed under the GNU General Public License.
Introduction to the lambda calculus
A Brave New Hope briefly reviews an interesting text on the lambda calculus. This reminded me of one of the books that got me started in functional programming: An introduction to functional programming through lambda calculus by Greg Michaelson. It is an enjoyable and fast-paced text which I’d recommend if you’re looking for a good introduction to the subject.
Lost integer sequence
4, 8, 15, 16, 23, 42. These numbers are becoming more important in each episode of Lost and Marcus Dicander has submitted them to the On-Line Encyclopedia of Integer Sequences.
I don’t know (yet) what those numbers are supposed to mean in the show but it seems to me that the last two of them are a tribute to William Burrough’s 23 enigma and Douglas Adams’ answer to The Ultimate Question Of Life, the Universe, and Everything respectively.