I've used programming in MATLAB for countless things. Some highlights:
- bioinformatics: besides testing published algorithms, I also developed algorithms for producing surrogate *NAs with completely specified short-range subsequences and biologically plausible codon structure, for molecular phylogeny, and a toy model of *NAs with specified nearest-neighbor thermodynamical properties. In related work I used a numerical calculation to rule out a class of hypotheses about the binding kinetics of oligomers;
- networks: modeling queueing networks and prototyping network monitoring data structures, visualizations and algorithms involving generalized statistical physics and continuous-time martingales and change detection techniques, as well as post-processing outputs from multiple prototype network monitoring systems. Besides prototyping, I've also used MATLAB for QA purposes in my company;
- I outlined some combinatorial calculations about necklaces in MATLAB and C for porting to a reconfigurable computer;
- I elucidated the structure of the Lie algebra of the stochastic group, particularly completely explicit Levi decompositions (this is no trivial feat in a numerical language)--someday I'll clean this up and put it on the arXiv;
- I produced periodic lattices with permutohedral boundary conditions (used so far to validate a 2D lattice Boltzmann model by approximating the initial decay of a Taylor-Green vortex);
- I enumerated the minimal periodic colorings of the root lattice $A_N$ for $N$ small by means of permutation matrices;
- I've analyzed detailed behavior of Anosov systems (e.g., the cat map and a map topologically conjugate to the cross section of the geodesic flow on a surface of negative curvature).
I'm sure I could think of other stuff that has been especially useful to my work. I use MATLAB more days than not.