Research PapersNo Access

Classes of states of discrete systems

Malgorzata J. Krawczyk

Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland

Search for more papers by this author

https://doi.org/10.1142/S0129183115501260Cited by:2 (Source: Crossref)

Abstract

We present a method which allows for a reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of the system to another. The method is based on the system symmetry; we get classes of states, which can be used instead of states. A detailed procedure is presented for undirected/directed and/or unweighted/weighted graphs. Several applications of the method are shown for different types of systems. In particular, new results are presented for the random Boolean networks.

Keywords:

PACS: 89.75.-k, 05.10.-a

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

S. Kripke , Acta Philosophica Fennica 16 , 83 ( 1963 ) . Google Scholar
S. P. Borgatti and M. G. Everett , Social Netw. 11 , 65 ( 1989 ) . Crossref, Web of Science, Google Scholar
N. G. van Kampen , Stochastic Processes in Physics and Chemistry ( Elsevier Science Publisher B.V. , 1981 ) . Google Scholar
S. Wolfram , A New Kind of Science ( Wolfram Media , 2002 ) . Google Scholar
M. J. Krawczyk , Phys. Lett. A 374 , 2510 ( 2010 ) . Crossref, Web of Science, ADS, Google Scholar
M. Shiga , Physica B 49 , 293 ( 1988 ) . Crossref, Web of Science, Google Scholar
M. J. Krawczyk , Physica A 390 , 2181 ( 2011 ) . Crossref, Web of Science, ADS, Google Scholar
M. J. Krawczyk , European Phys. J. B 86 , 246 ( 2013 ) . Crossref, Web of Science, ADS, Google Scholar
P.-G. de Gennes , Scaling Concepts in Polymer Physics ( Cornell University Press , 1996 ) . Google Scholar
M. E. J. Newman and G. T. Barkema , Monte Carlo Methods in Statistical Physics ( Clarendon Press , Oxford , 1999 ) . Crossref, Google Scholar
J. L. Viovy , Rev. Mod. Phys. 72 , 813 ( 2000 ) . Crossref, Web of Science, ADS, Google Scholar
G. W. Slater et al. , Electrophoresis 23 , 3791 ( 2002 ) . Crossref, Web of Science, Google Scholar
M. J. Krawczyk, New aspects of symmetry of elementary cellular automata, submitted , arXiv:1304.5771 . Google Scholar
S. Wolfram , Theory and Applications of Cellular Automata ( World Scientific Publishing Co. Ltd. , 1986 ) . Google Scholar
M. J. Krawczyk , J. Magn. Magn. Mater. 349 , 63 ( 2014 ) . Crossref, Web of Science, ADS, Google Scholar
R. M. White , Quantum Theory of Magnetism ( McGraw-Hill , New York , 1970 ) . Google Scholar
A. V. Khaetskii and Y. V. Nazarov , Phys. Rev. B 61 , 12639 ( 2000 ) . Crossref, Web of Science, ADS, Google Scholar
B. Drossel , Reviews of Nonlinear Dynamics and Complexity 1 , ed. H. G. Schuster ( Viley-VCH , Weinheim , 2008 ) . Google Scholar
S. A. Kauffman , The Origins of Order ( Oxford University Press , 1993 ) . Crossref, Google Scholar
S. Bornholdt , Science 310 , 449 ( 2005 ) . Crossref, Web of Science, Google Scholar