OJDM  Vol.3 No.3 , July 2013
The Number of Canalyzing Functions over Any Finite Set
ABSTRACT

In this paper, we extend the definition of Boolean canalyzing functions to the canalyzing functions of multi-state case. Namely, f:QnQ , where Q={a1,a2,...,aq} . We obtain its cardinality and the cardinalities of its various subsets (They may not be disjoint). When q=2, we obtain a combinatorial identity by equating our result to the formula in [1]. For a better understanding to the magnitude, we obtain the asymptotes for all the cardinalities as either n or q.


Cite this paper
Y. Li, D. Murrugarra, J. Adeyeye and R. Laubenbacher, "The Number of Canalyzing Functions over Any Finite Set," Open Journal of Discrete Mathematics, Vol. 3 No. 3, 2013, pp. 130-136. doi: 10.4236/ojdm.2013.33024.
References
[1]   W. Just, I. Shmulevich and J. Konvalina, “The Number and Probability of Canalyzing Functions,” Physica D, Vol. 197, No. 3-4, 2004, pp. 211-221. doi:10.1016/j.physd.2004.07.002

[2]   C. H. Waddington, “The Strategy of the Genes,” George Allen and Unwin, London, 1957.

[3]   R. Thomas and R. D’Ari, “Biological Feedback,” CRC Press, Boca Raton, 1989.

[4]   L. Steggles, et al., “Qualitatively Modelling and Analyzing Genetic Regulatory Networks: A Petri Net Approach,” Bioinformatics, Vol. 23, No. 3, 2007, pp. 336-343. doi:10.1093/bioinformatics/btl596

[5]   M. Pogson, et al., “Formal Agent-Based Modelling of Intracellular Chemical Interactions,” Biosystems, Vol. 85, No. 1, 2006, pp. 37-45. doi:10.1016/j.biosystems.2006.02.004

 
 
Top