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.
Tag Archive - mathematics
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…
There’s a new blog aggregator dedicated to Sage, it is called Planet Sage. Enjoy!
cl-buchberger is out!
I’ve just released the first version of cl-buchberger, a Common Lisp
implementation of Buchberger’s algorithm for the computation of
Gröbner bases.
There are many improvements waiting in the pipeline but the basic
functionality is there.
You can read more about cl-buchberger here.
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.
Superficies
I recently came across Superficies, a very nice tool for exploring surfaces and differential geometry concepts that I wanted to share. Here’s a link to its english manual that will give you an idea of the program’s features.
This is GPLed software written in Delphi and although binaries are only available for Windows I had no problem running it under Linux using Wine.
Quick way to use mimetex with SMF
SMF is a nice web forum package but it doesn’t display mathematics by default. If you want it to render LaTeX, one option is to use mimetex. Here is a quick patch to enable [tex]…[/tex] tags in SMF version 1.1. You can get the latest updates to this patch with:
darcs get http://darcs.superadditive.com/smf-mimetex