I will try to cover two topics: multithreading with Matlab on HPC and new numeric methods for the density forward propagation.
In the first part (~15-20min), I'll briefly present Matlab code which allows easy and flexible multithreading for the loops which have independent internal blocks with different values of loop-variables. It should be useful in many computationally expensive optimization problems. The main problem here was to devise a method for locking a JobSubmit file which is used for communication between the main programs and the threads. Unfortunately, I have just discovered that the method I implemented does not give 100% result. At the same time, the code works in most of the cases and simply leads to duplicate computations in the rare situations when the file-locking method failures.
The second part will be on numeric methods for the forward propagation. In recent years a number of articles has been published which focused on the methods for the solution of the Fokker-Planck equation for the associated stochastic integrate-and-fire model. We develop a new method for the numerical estimation of the forward propagation density by computing it via direct quadratic convolution on a dynamic adaptive grid. This method allows us to significantly improve the accuracy of the computations, avoid treating the extreme cases as such and to improve (or, at least, preserve) the speed of the computation in comparison to other methods. We also found that below some value of the time step of the numeric propagation the solution becomes unstable. By considering the density being not centered in the bins centers, but distributed across the bins, we derive a simple condition for the stability of the method. Interestingly, the condition we derive binds linearly the temporal and spatial resolutions - contrary to the well-known Courant stability condition for the Fokker-Planck equation. We further improve the speed of the method by combining it with the fast gauss transform.