Random Number Generator and Monte Carlo type Simulations on the CNN-UM

The computational paradigm represented by cellular neural networks (CNN) gives new perspectives also for computational physics. Here we study the possibility of performing stochastic simulations on the CNN universal machine (CNN-UM). First by using a chaotic cellular automaton perturbed with the natural noise of the CNN-UM chip, a realistic binary random number generator (RNG) is built. Using this RNG the site-percolation problem and the two-dimensional Ising model is studied by Monte Carlo type simulations. The results obtained on an ACE16K chip are in good agreement with the results obtained on digital computers. Computational time measurements suggest that the developing trend of the CNN-UM chips could assure an important advantage for the CNN-UM in the near future

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

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

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

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

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

[6]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

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

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

[9]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[10]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

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

[12]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[13]  I. Szatmari,et al.  Image processing library for the Aladdin Visual Computer , 2002, Proceedings of the 2002 7th IEEE International Workshop on Cellular Neural Networks and Their Applications.

[14]  J. W. Essam,et al.  Percolation theory , 1980 .

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

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