The Number of Canalyzing Functions over Any Finite Set

Affiliation(s)

Department of Mathematics, Winston-Salem State University, Winston-Salem, USA.

School of Mathematics, Georgia Tech, Atlanta, USA.

Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, USA.

Department of Mathematics, Winston-Salem State University, Winston-Salem, USA.

School of Mathematics, Georgia Tech, Atlanta, USA.

Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, USA.

ABSTRACT

In this paper, we extend the
definition of Boolean canalyzing functions to the canalyzing functions of
multi-state case. Namely, *f:Q*^{n}*→**Q* , where *Q={a*_{1}*,a*_{2}*,...,a*_{q}*}* . 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

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.

Y. Li, D. Murrugarra, J. Adeyeye and R. Laubenbacher, "The Number of Canalyzing Functions over Any Finite Set,"

References

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[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