A symbolic computation approach to a problem involving multivariate Poisson distributions

Advances in Applied Mathematics

Volumn 44, Issue 4, 2010, Pages 359-377

  Sontag, Eduardo D ^a   Zeilberger, Doron ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPLICATION AREA; BIO-MOLECULAR; CONDITIONAL STATISTICS; INTEGER CONSTRAINTS; POISSON RANDOM VARIABLES; SYMBOLIC COMPUTATION;

POISSON EQUATION; RANDOM PROCESSES; RANDOM VARIABLES;

POISSON DISTRIBUTION;

EID: 77249109274     PISSN: 01968858     EISSN: 10902074     Source Type: Journal    
DOI: 10.1016/j.aam.2009.08.002     Document Type: Article

References (17)

1. Almkvist G., and Zeilberger D. The method of differentiating under the integral sign. J. Symbolic Comput. 10 (1990) 571-591
2. Anderson D.F., Craciun G., and Kurtz T.G. Product-form stationary distributions for deficiency zero chemical reaction networks (2008). arXiv.org:0803.3042
3. Apagodu M., and Zeilberger D. Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. Adv. in Appl. Math. 37 (2006) 139-152
4. Batchelor E., and Goulian M. Robustness and the cycle of phosphorylation and dephosphorylation in a two-component regulatory system. Proc. Natl. Acad. Sci. USA 100 (2003) 691-696
5. Chaves M., Sontag E.D., and Dinerstein R.J. Steady-states of receptor-ligand dynamics: A theoretical framework. J. Theoret. Biol. 227 (2004) 413-428
6. Conradi C., Saez-Rodriguez J., Gilles E.-D., and Raisch J. Using chemical reaction network theory to discard a kinetic mechanism hypothesis. IET Syst. Biol. 152 (2005) 243-248
7. Feinberg M. Chemical reaction network structure and the stability of complex isothermal reactors - I. The deficiency zero and deficiency one theorems. Chem. Engr. Sci. 42 (1987) 2229-2268
8. Feinberg M. The existence and uniqueness of steady states for a class of chemical reaction networks. Arch. Rational Mech. Anal. 132 (1995) 311-370
9. Gillespie D.T. The chemical Langevin equation. J. Chem. Phys. 113 (2000) 297-306
10. Gnacadja G., Shoshitaishvili A., Gresser M.J., Varnum B., Balaban D., Durst M., Vezina C., and Li Y. Monotonicity of interleukin-1 receptor-ligand binding with respect to antagonist in the presence of decoy receptor. J. Theoret. Biol. 244 (2007) 478-488
11. Kelly F. Reversibility and Stochastic Networks (1979), Wiley, New York
12. Mairesse J., and Nguyen H.-T. Deficiency zero Petri nets and product form. arXiv:0905.3158
13. Petkovsek M., Wilf H.S., and Zeilberger D. A = B (1996), AK Peters, Wellesley [available on-line from the authors' websites]
14. Sontag E.D. Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction. IEEE Trans. Automat. Control 46 (2001) 1028-1047
15. Wang L., and Sontag E.D. Singularly perturbed monotone systems and an application to double phosphorylation cycles. J. Nonlinear Sci. 18 (2008) 527-550
16. Wilf H.S., and Zeilberger D. An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities. Invent. Math. 108 (1992) 575-633
17. Zeilberger D. The method of creative telescoping. J. Symbolic Comput. 11 (1991) 195-204