1. STDP and Network Architectures Parallel ODE Solver and Event Detector Eugene Lubenov

2. Networks of Neurons GE GI GR

3. Spike-Timing Dependent Plasticity Bi & Poo, J. Neurosci. (1998).

4. Integrate-and-Fire Neuron Model ODE System for the Membrane Potential Special Events V ge gi y = y’ = f (y, t) e (y, t) = V – V_th

5. STDP Model ODE System for the STDP Variables Special Events Weight Matrix Update Rules input (M) output (Pe) GE NE NN input (M) GR NN output (Pr)

6. Project Ingredients Matlab (Mathworks) http://www.mathworks.com/ SUNDIALS (LLNL) http://www.llnl.gov/CASC/sundials/ LAM MPI http://www.lam-mpi.org/ Custom C Code

7. Why Matlab? ode suite event functions knowing what to expect MAT library loading parameters and input saving output BUT: SERIAL ONLY and SLOW

8. Why SUNDIALS SUite of Nonlinear and DIfferential/ALgebraic equation Solvers Adams-Moulton (non-stiff), BDF (stiff) Variable Step, Variable Order (12, 5) Functional Iteration, Linear System Direct (full, banded, diag approx J) Iterative (GMRES) Sclaled Preconditioned (SPGMR) BUT: NO EVENT FUNCTIONS

9. Why LAM MPI? Multiple Processors Solve larger problems Solve problems faster Portable Code BUT:Problem granularity must be suited to underlying architecture: Beowulf cluster coarse granularity

10. Why Custom C Code? Extend CVode with Event Capabilities Problem specific routines: f(.), e(.) Handle I/O and Message Passing Inline Exponential Variables BUT: compatibility: mpicc, mex, gcc memory: Calloc, mxCalloc, CVodeMalloc debugging: parallel code

11. Performance: Serial vs Parallel

12. Performance: Parallel Scalability

13. Problem Stiffness Moderately Stiff?WRONG!Non-Stiff!

14. Correctness: V

15. Correctness: M, Pe, Pr

16. Correctness: GE, GR

17. Network Activity Poisson InhibitionRhythmic Inhibition (10 Hz)

18. Network Activity GE plasticity onlyGR plasticity only

19. Network Weights GE Weight MatrixGE Weight Distribution

20. Network Weights GR tr(GR) = 0 and GR*GR’ = 0

21. Conclusion Serial Code (v 2.3.4) good for real problems. Parallel Code (v 1.1.0) needs work, but speedup might be hard to get. Parallel Code (v 1.2.0) implements asynchronous message passing, but still in alpha. Structure emerges from simulations.

22. Future Directions