PERSPECTIVES FOR MONTE CARLO SIMULATIONS ON THE CNN UNIVERSAL MACHINE

Possibilities for performing stochastic simulations on the analog and fully parallelized Cellular Neural Network UniversalMachine (CNN-UM) are investigated. By using a chaotic cellular automaton perturbed with the natural noise of the CNN-UM chip, a realistic binary random number generator is built. As a specific example for Monte Carlo type simulations, we use this random number generator and a CNN template to study the classical site-percolation problem on the ACE16K chip. The study reveals that the analog and parallel architecture of the CNN-UM is very appropriate for stochastic simulations on lattice models. The natural trend for increasing the number of cells and local memories on the CNN-UM chip will definitely favor in the near future the CNN-UM architecture for such problems.

[1]  Tamás Roska,et al.  JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS 12/6 , 2003 .

[2]  Leon O. Chua,et al.  Methods for image processing and pattern formation in Cellular Neural Networks: a tutorial , 1995 .

[3]  Joos Vandewalle,et al.  Watermarking on CNN‐UM for image and video authentication , 2004, Int. J. Circuit Theory Appl..

[4]  Tamás Roska,et al.  The CNN universal machine: an analogic array computer , 1993 .

[5]  Tamás Roska Computational And Computer Complexity Of Analogic Cellular Wave Computers , 2003, J. Circuits Syst. Comput..

[6]  Tamás Roska,et al.  A DOUBLE TIME—SCALE CNN FOR SOLVING TWO‐DIMENSIONAL NAVIER—STOKES EQUATIONS , 1996 .

[7]  A. Zarandy,et al.  Bi-i: a standalone ultra high speed cellular vision system , 2005, IEEE Circuits and Systems Magazine.

[8]  Ángel Rodríguez-Vázquez,et al.  Toward visual microprocessors , 2002, Proc. IEEE.

[9]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[10]  Robert H. Romer American Journal of Physics Goes Online , 1999 .

[11]  L. Chua,et al.  Simulating nonlinear waves and partial differential equations via CNN. I. Basic techniques , 1995 .

[12]  B. A. Minch,et al.  IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing , 1998 .

[13]  Josiane Zerubia,et al.  Markov random field image segmentation using cellular neural network , 1997 .

[14]  Leon O. Chua,et al.  New spatial-temporal patterns and the first programmable on-chip bifurcation test-bed. (Research report of the Analogical and Neural Computing Laboratory DNS-6-2001.) , 2003 .

[15]  D. Stauffer Percolation Clusters as Teaching Aid for Monte Carlo Simulation and Critical Exponents. , 1977 .

[16]  Tamás Roska,et al.  International Journal of Circuit Theory and Applications: Introduction , 2002 .

[17]  L. Chua,et al.  Simulating nonlinear waves and partial differential equations via CNN. II. Typical examples , 1995 .

[18]  M. Sahini,et al.  Applications of Percolation Theory , 2023, Applied Mathematical Sciences.

[19]  Leon O. Chua,et al.  Application of cellular neural networks to model population dynamics , 1995 .

[20]  Klaus Mainzer,et al.  Cellular Neural Networks and Visual Computing , 2003, Int. J. Bifurc. Chaos.

[21]  Lambert Spaanenburg,et al.  1996 FOURTH IEEE INTERNATIONAL WORKSHOP ON CELLULAR NEURAL NETWORKS AND THEIR APPLICATIONS, PROCEEDINGS (CNNA-96) , 1996 .

[22]  Leon O. Chua,et al.  The CNN paradigm , 1993 .

[23]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[24]  Bertram E. Shi,et al.  IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS — I : REGULAR PAPERS , VOL . ? ? , NO . ? ? , ? ? ? ? , 2007 .

[25]  D. Hardin,et al.  Ieee Transactions on Circuits and Systems Ii 1 Multiwavelet Preelters I: Orthogonal Preelters Preserving Approximation Order P 2 , 1997 .

[26]  Á. Rodríguez-Vázquez,et al.  Current-mode techniques for the implementation of continuous- and discrete-time cellular neural networks , 1993 .

[27]  Ákos Zarándy,et al.  CNN universal chips crank up the computing power , 1996 .

[28]  Reports on Progress in Physics , 1934 .