1. Method of Particles as a Universal Solver Witold Dzwinel AGH - Department of Computer Science Dzwinel W, Alda W, Kitowski J, Yuen DA, Molecular Simulation, 20/6, 361-384 2000 Dzwinel W, Future Generation Computer Systems, 12, 371-389, 1997 Dzwinel W, Yuen DA, Boryczko K, Chemical Engineering Sci., 61, 2169-2185, 2006.

2. Universal solver = automata or a formalism having universal computational capabilities (equivalent to TM, or lambda calculus or 110 Wolfram rule) = paradigm, which can be a common platform of an offspring of algorithms designated for solving a broad class of seemingly unrelated problems from e.g.  modeling and simulation (PM, CA, ANN, MA …)  optimization (GA, SA, ANN, PM, MA …)  learning theory and systems (ANN, GA …)  etc.

3. Method of particles – in simulation and modeling The algorithms employing moving and interacting particles as primitives. Taxonomy due to  definition of particle (quark, atom, molecule, granule, cluster, chunk of something, item, many items, galaxies etc)  definition of interactions (hard, soft: pair, manybody, multipole)  moving scheme (deterministic, stochastic)  granularity (?) of space and time continuous/continuous (MD, DPD, FPM, SC-DPD, SPH) continuous/discrete (hard spheres, DSMC) discrete/continuous (lattice dynamical systems) discrete/discrete (LG, LBG, percolation, DLA etc.) http://www.amara.com/papers/nbody.html#p3m

4. Method of particles – in simulation and modeling Boryczko K, Dzwinel W, Yuen DA, J Mol. Modeling,8,33-45,2002

5. Method of particles – in simulation and modeling Dzwinel W, Boryczko K, Yuen DA, Finely Dispersed Particles: Micro-, Nano-, and Atto-Engineering A.M. Spasic & J.P. Hsu eds., Taylor&Francis, CRC Press, 715-778, 2006

6. Fluid Particles Flekkoy and Coveney, 1999 Serrano and Espanol, 2002

7. Method of particles – in simulation and modeling Boryczko K, Dzwinel W, Yuen DA, J Mol. Modeling,9,16-33,2003 Dzwinel W, Boryczko K, Yuen DA, J Colloid Int Sci, 258/1, 163-173, 2003

8. Method of particles – in graphics www.graphics.stanford.edu/.../vortex_particle-sig05/

9. Method of particles – crowding Helbing D., Farkas I., Vicsek T., Nature, Vol. 407, pp. 487-490. 2000

10. Method of particles – crowding

12. Two groups of people running from opposite directions

13. Optimization - L-J cluster http://www.uniovi.es/qcg/d-MolSym/LJ1/

15. Global minimum search http://www.mat.univie.ac.at/~neum/glopt.html

16. Global minimum search - particles

17. GA vs. MD - global minimum of N-D function (N~10) Many interacting solutions (particles)  the lowest can attract stronger the higher  others Clustering around wells Bad derivatives approach (mimics annealing process)

18. Bad derivative method

19. GA vs. MD - global minimum of N-D function parents domain searched final cluster of particles in minimum well Jasińska-Suwada, A., Dzwinel, W., Rozmus, K., Sołtysiak, J., Computer Science, 2, 13-51, 2000

20. … more dimensions?? More advanced version of coordinate decent scheme Problems when  irregular and x i have very different domains  Needs regularization and normalization procedures  Additional difficulties with gradient calculations Best fit:  is the sum of simple functions, like in MD, the total force acting on a single particle

21. Multi-dimensional scaling – not a trivial example The MDS mapping from D-dimensional space to d- dimensional (D>>d) consists in minimization of the quadratic loss function, called “the stress function”: where C N and w ij are free parameters, which depend on the MDS goals. Smaller values of the “stress function“ mean better correspondence between source and target data structures.

22. Multi-dimensional scaling – not a trivial example 1.Dzwinel W, Blasiak J, Future Generation Computers Systems, 15, 365-379, 1999

23. Examples – periodic boundary conditions Arodz, Boryczko, Dzwinel, Kurdziel, Yuen: IEEE Visualization 2005: 90

24. Examples - mammograms

25. Examples - earthquakes Yuen, W. Dzwinel, Yehuda Ben-Zion, B.Kadlec, Encyclopedia of Complexity and System Science, Springer Verlag, 2007