Tag Archives: software

Scientific software workflow

We know the big differences between trying out a calculation on a back of an envelope and writing a rigorous proof. Likewise, there are differences between prototyping in a Matlab script and writing a reliable pre that supports a reproducible research project. In a 15-minute presentation for a introductory workshop on scientific software at UW Madison math department, I showcased my own workflow on a simple example of plotting several solutions to an ODE in Matlab.

Repository for the workshop can be obtained by

git clone https://bitbucket.org/mbudisic/workshopworkflow.git

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Finite-Time Braiding Exponents

Jean-Luc Thiffeault and I have just uploaded our paper on Finite-Time Braiding Exponents (FTBE) to arXiv. In the paper we study how closely topological entropy of a mixing dynamical system can be approximated by sampling only finitely many trajectories from the flow.

Based on numerical results (obtained using braidlab 3.1), we find that FTBEs of finitely-many trajectories converge to topological entropy as number of trajectories is increased. The paper further explores robustness and dependence of  FTBEs on time step, number of trajectories, and their length.

braidlab 3.0 is out!

The latest full release of braidlab is out! Braidlab is a MATLAB toolbox which incorporates algorithms for analyzing braid groups of punctured disks in both theoretical and applied contexts. It was primarily written by Jean-Luc Thiffeault, but Michael Allshouse and I have contributed code to it as well. Feel free to direct your questions either at JLT or at me.

You can find a good summary of release updates on the main release-3.0 announcement, but here’s my list of favorites:

  • We moved the repository to GitHub. This means that you can (and should) use our Issue Tracker to let us know what went wrong or what you would like to see included in future releases. We are also present on MATLAB Central.
  • Installation from source should now work on Matlab 2014b without any special configuration. There are two known installation issues which are out of our reach: conflict of “mex” command with a LaTeX command, and lack of GMP libraries on your system. Make sure you read the installation guidelines in the manual first to see how to resolve these (and other) known problems.
  • “Data braids” now have a broader support. This type of braids is useful if you are trying to represent physical trajectories, which have an independent variable, e.g., time, attached to them.
  • More functions are implemented as MEX C++ code, which means that they ultimately run faster (some of them have even been parallelized!)

To install, go to the release page, scroll down, download the pre-packaged binaries. If you want to build from source, you can either download the source or even clone our git repository to stay up to date with the latest developments.

In all cases: let us know if braidlab works on your end and if you find it useful.

Madison Math Circle: Mathematics of epidemics

Last night I had an amazing time at Madison Math Circle, hanging out with a bunch of bright school kids, who were undaunted by either diseases or mathematics. Since I had quite a few questions after the lecture, I decided to post an overview so anyone interested can go over it themselves. For those of you who attended and have further questions, or even wish to explore mathematical dynamics on your own, feel free to leave a comment below or e-mail me at marko@math.wisc.edu and I’ll try to answer all your questions and provide some guidance for future.
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Ergodic quotient in a finite-time, expanding context

I am currently attending 10th AIMS Conference on dynamics in Madrid, where I participated in the session on transport barriers in unsteady fluid flows. One of the talks in the session suggested that the ergodic quotient techniques for detecting coherent sets would not apply to finite-time setting, i.e., when ergodic averages are replaced by finite-time averages. This is, of course, of interest in cases when ergodic averages do not exist, so finite-time average is a potential resolution of this problem. I decided to investigate the potentially-problematic example given (2d linear saddle) using the code I made available at [github]. I found that in that case, ergodic quotient algorithm still works, even away from the asymptotic averaging limit.
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