December  2016, 21(10): 3391-3405. doi: 10.3934/dcdsb.2016103

Computational methods for asynchronous basins

1. 

Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, 724 SW Harrison Street, Portland, OR 97201, United States

Received  December 2015 Revised  March 2016 Published  November 2016

For a Boolean network we consider asynchronous updates and define the exclusive asynchronous basin of attraction for any steady state or cyclic attractor. An algorithm based on commutative algebra is presented to compute the exclusive basin. Finally its use for targeting desirable attractors by selective intervention on network nodes is illustrated with two examples, one cell signalling network and one sensor network measuring human mobility.
Citation: Ian H. Dinwoodie. Computational methods for asynchronous basins. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3391-3405. doi: 10.3934/dcdsb.2016103
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show all references

References:
[1]

J. Abbott and A. M. Bigatti, CoCoALib: A C++ library for doing Computations in Commutative Algebra, 2014., Available from: , ().   Google Scholar

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PLoS One, 9 (2014), e90256. doi: 10.1371/journal.pone.0090256.  Google Scholar

[3]

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[4]

Aging, 6 (2014), 707-717. doi: 10.18632/aging.100690.  Google Scholar

[5]

Arch. Neurol., 67 (2010), 980-986. Google Scholar

[6]

Jour. Theoret. Biol., 235 (2005), 431-449. doi: 10.1016/j.jtbi.2005.01.023.  Google Scholar

[7]

Springer, New York, 1997.  Google Scholar

[8]

W. Decker, G.-M. Greuel, G. Pfister and H. Schönemann, Singular 4-0-2 - A Computer Algebra System for Polynomial Computations, 2015., Available from: , ().   Google Scholar

[9]

Brain Res. Rev., 33 (2000), 1-12. Google Scholar

[10]

Methodol. Comput. Appl. Probab., 16 (2014), 161-168. doi: 10.1007/s11009-012-9304-9.  Google Scholar

[11]

Proc. Amer. Math. Soc., 142 (2014), 2991-3002. doi: 10.1090/S0002-9939-2014-12044-2.  Google Scholar

[12]

Stat. Methods Appt., 19 (2009), 171-192. doi: 10.1007/s10260-009-0123-2.  Google Scholar

[13]

Ann. Inst. Statist. Math. 67 (2015), 687-706. doi: 10.1007/s10463-014-0472-y.  Google Scholar

[14]

D. R. Grayson and M. E. Stillman, Macaulay2, A Software System for Research in Algebraic Geometry, 2014., Available from: , ().   Google Scholar

[15]

Bioinformatics, 28 (2012), 557-663. Google Scholar

[16]

Springer, New York, 2009. doi: 10.1007/978-0-387-21606-5.  Google Scholar

[17]

Conf. Proc. IEEE Eng. Med. Biol. Soc., 2010 (2010), 2147-2150. doi: 10.1109/IEMBS.2010.5628022.  Google Scholar

[18]

J. Cell. Mol. Med., 14 (2009), 30-41. doi: 10.1111/j.1582-4934.2009.00976.x.  Google Scholar

[19]

BMC Bioinformatics, 12 (2011), p295. doi: 10.1186/1471-2105-12-295.  Google Scholar

[20]

Bull. Math. Biol. 73 (2011), 1583-1602. doi: 10.1007/s11538-010-9582-8.  Google Scholar

[21]

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[22]

BMC Bioinformatics, 7 (2006), 1471-2105. Google Scholar

[23]

Springer, New York, 2000. doi: 10.1007/978-3-540-70628-1.  Google Scholar

[24]

Amer. Math. Monthly, 116 (2009), 882-891. doi: 10.4169/000298909X477005.  Google Scholar

[25]

Molecular BioSystems, 7 (2011), 843-851. doi: 10.1109/CDC.2010.5716936.  Google Scholar

[26]

Bioinformatics, 27 (2011), 548-555. doi: 10.1093/bioinformatics/btq703.  Google Scholar

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[28]

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[29]

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[30]

EURASIP J. Bioinform. and Syst. Biol., 2012 (2012), p5. doi: 10.1186/1687-4153-2012-5.  Google Scholar

[31]

Bioinformatics, 26 (2010), 1378-1380. Google Scholar

[32]

IEEE J. Biomed. Health Inform., 18 (2014), 1590-1596. doi: 10.1109/JBHI.2013.2294276.  Google Scholar

[33]

J. Intern. Med., 256 (2004), 183-194. doi: 10.1111/j.1365-2796.2004.01388.x.  Google Scholar

[34]

Chapman and Hall, Boca Raton Florida, 2001.  Google Scholar

[35]

BMC Syst. Biol., 6 (2012), p125. Google Scholar

[36]

PLoS Comp. Biol. 7 (2011), e1002267. Google Scholar

[37]

J. Theor. Biol., 266 (2010), 641-656. doi: 10.1016/j.jtbi.2010.07.022.  Google Scholar

[38]

PLoS Comput. Biol., 5 (2009), e1000595. doi: 10.1371/journal.pcbi.1000595.  Google Scholar

[39]

Bioinformatics, 18 (2002), 261-274. doi: 10.1093/bioinformatics/18.2.261.  Google Scholar

[40]

AMS 2006 Proceedings of Symposia in Applied Mathematics, 64 (2007), 53-84. doi: 10.1090/psapm/064/2359649.  Google Scholar

[41]

T. Therneau, B. Atkinson and B. Ripley, Rpart: Recursive Partitioning and Regression Trees, 2015., Available from: , ().   Google Scholar

[42]

J. Theoret. Biol., 42 (1973), 563-585. Google Scholar

[43]

SIAM Jour. Appl. Dyn. Systems, 11 (2012), 31-48. doi: 10.1137/110828794.  Google Scholar

[44]

Acta Physica Polonica B, 3 (2010), 463-478. Google Scholar

[45]

Proc. Natl. Acad. Sci. USA, 105 (2008), 16308-16313. Google Scholar

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