- Previous Article
- DCDS-S Home
- This Issue
-
Next Article
Turing instability in a coupled predator-prey model with different Holling type functional responses
Dynamics of boolean networks
1. | Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, United States |
References:
[1] |
R. Albert and H. Othmer, The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster, J. Theor. Biol., 223 (2003), 1-18.
doi: 10.1016/S0022-5193(03)00035-3. |
[2] |
C. L. Barrett, W. Y. C. Chen and M. J. Zheng, Discrete dynamical systems on graphs and boolean functions, Math. Comput. Simul., 66 (2004), 487-497.
doi: 10.1016/j.matcom.2004.03.003. |
[3] |
D. Bollman, O. Coló-Reyes and E. Orozco, Fixed points in discrete models for regulatory genetic networks, EURASIP Journal on Bioinformatics and System Biology, (2007), On-line ID97356. |
[4] |
G. Boole, "The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning," Macmillan, Barclay and Macmillan, Cambridge; George Bell, London, 1847. Reprints (1948, 1951), Basil Blackwell, Oxford. |
[5] |
G. Boole, "An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities," Macmillan, Barclay and Macmillan, Cambridge; Walton and Maberly, London, 1854. Reprint (1960), Dover, New York. |
[6] |
M. Brickenstein and A. Dreyer, PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials, J. Symbolic Comput., 44 (2009), 1326-1345
doi: 10.1016/j.jsc.2008.02.017. |
[7] |
M. Brickenstein, A. Dreyer, G-M. Greuel, M. Wedler and O. Wienand, New developments in the theory of Gröbner bases and applications to formal verification, J. Pure Appl. Algebra, 213 (2009), 1612-1635. arXiv:0801.1177. |
[8] |
O. Colón-Reyes, R. Laubenbacher and B. Pareigis, Boolean monomial dynamical systems, Annals of Combinatorics, 8 (2004), 425-439. arXiv:math/0403166v1. |
[9] |
M. I. Davidich and S. Bornholdt, Boolean network model predicts cell cycle sequence of fission yeast, PLoS ONE, 3 (2008), e1672. |
[10] |
E. Dubrova, M. Teslenko and A. Martinelli, Kauffman networks: Analysis and applications, Computer-Aided Design, IEEE/ACM International Conference (2005), 479-484,
doi: 10.1109/ICCAD.2005.1560115. |
[11] |
E. D. Fabricius, "Modern Digital Design and Switching Theory," CRC Press 1992. |
[12] |
J. F. Groote and M. Keinänen, A sub-quadratic algorithm for conjunctive and disjunctive BESs, Theoretical aspects of computing-ICTAC 2005, 532-545, Lecture Notes in Comput. Sci., 3722, Springer, Berlin 2005. |
[13] |
R. A. Hernádez-Toledo, Linear finite dynamical systems, Communications in Algebra, 33 (2005), 2977-2989.
doi: 10.1081/AGB-200066211. |
[14] |
A. Ilichinsky, "Cellular Automata: A Discrete Universe," World Scientific Publishing Company, 2001. |
[15] |
A. Jarrah, R. Laubenbacher, B. Stigler and M. Stillman, Reverse-engineering of polynomial dynamical systems, Adv. in Appl. Math., 39 (2007), 477-489. arXiv:q-bio/0605032v1. |
[16] |
A. Jarrah, B. Raposa and R. Laubenbacher, Nested canalyzing, unate cascade, and polynomial functions, Physica D, 233 (2007), 167-174. arXiv:q-bio/0606013v3. |
[17] |
A. Jarrah, R. Laubenbacher and A. Veliz-Cuba, The dynamics of conjunctive and disjunctive Boolean networks,, preprint available at: \arXiv{0805.0275v1}., ().
|
[18] |
W. Just, The steady state system problem is NP-hard even for monotone quadratic Boolean dynamical systems,, preprint available at: \url{http://www.math.ohiou.edu/ just/publ.html}., ().
|
[19] |
S. Kauffman, C. Peterson, B. Samuelsson and C. Troein, Genetic networks with canalyzing Boolean rules are always stable, PNAS, 101 (2004), 17102-17107.
doi: 10.1073/pnas.0407783101. |
[20] |
R. Laubenbacher and B. Stigler, A computational algebra approach to the reverse engineering of gene regulatory networks, J. Theor. Biol., 229 (2004), 523-537. arXiv:q-bio/0312026. |
[21] |
T. E. Malloy, J. Butner and G. C. Jensen, The emergence of dynamic form through phase relations in dynamic systems, Nonlinear Dynamics, Psychology, and Life Sciences, 12 (2008), 371-395. |
[22] |
R. Pal, I. Ivanov, A. Datta, M. L. Bittner and E. R. Dougherty, Generating Boolean networks with a prescribed attractor structure, Bioinformatics, 21 (2005), 4021-4025.
doi: 10.1093/bioinformatics/bti664. |
[23] |
J. Reger and K. Schmidt, Modeling and analyzing finite state automata in the finite field $F_2$, Mathematics and Computers in Simulation, 66 (2004), 193-206.
doi: 10.1016/j.matcom.2003.11.005. |
[24] |
N. A. W. Riel, Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments, Briefings in Bioinformatics, 7 (2006), 364-374.
doi: 10.1093/bib/bbl040. |
[25] |
S. Rudeanu, "Boolean Functions and Equations," North-Holland, Amsterdam, 1974. |
[26] |
M. H. Stone, The theory of representation for Boolean algebras, Transactions of American Mathematical Society, 40 (1936), 37-111. |
[27] |
T. Tamura and T. Akutsu, Algorithms for singleton attractor detection in planar and nonplanar AND/OR Boolean networks, Math. Comput. Sci., 2 (2009), 401-420.
doi: 10.1007/s11786-008-0063-5. |
[28] |
C. J. Tomlin and J. D. Aelrod, Biology by numbers: Mathematical modelling in developmental biology, Nature Reviews Genetics, 8 (2007), 331-340.
doi: 10.1038/nrg2098. |
[29] |
S-Q. Zhang, M. Hayashida, T. Akutsu, W-K. Ching and M. K. Ng, Algorithms for finding small attractors in Boolean networks, EURASIP Journal on Bioinformatics and Systems Biology (2007).
doi: 10.1155/2007/20180. |
show all references
References:
[1] |
R. Albert and H. Othmer, The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster, J. Theor. Biol., 223 (2003), 1-18.
doi: 10.1016/S0022-5193(03)00035-3. |
[2] |
C. L. Barrett, W. Y. C. Chen and M. J. Zheng, Discrete dynamical systems on graphs and boolean functions, Math. Comput. Simul., 66 (2004), 487-497.
doi: 10.1016/j.matcom.2004.03.003. |
[3] |
D. Bollman, O. Coló-Reyes and E. Orozco, Fixed points in discrete models for regulatory genetic networks, EURASIP Journal on Bioinformatics and System Biology, (2007), On-line ID97356. |
[4] |
G. Boole, "The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning," Macmillan, Barclay and Macmillan, Cambridge; George Bell, London, 1847. Reprints (1948, 1951), Basil Blackwell, Oxford. |
[5] |
G. Boole, "An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities," Macmillan, Barclay and Macmillan, Cambridge; Walton and Maberly, London, 1854. Reprint (1960), Dover, New York. |
[6] |
M. Brickenstein and A. Dreyer, PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials, J. Symbolic Comput., 44 (2009), 1326-1345
doi: 10.1016/j.jsc.2008.02.017. |
[7] |
M. Brickenstein, A. Dreyer, G-M. Greuel, M. Wedler and O. Wienand, New developments in the theory of Gröbner bases and applications to formal verification, J. Pure Appl. Algebra, 213 (2009), 1612-1635. arXiv:0801.1177. |
[8] |
O. Colón-Reyes, R. Laubenbacher and B. Pareigis, Boolean monomial dynamical systems, Annals of Combinatorics, 8 (2004), 425-439. arXiv:math/0403166v1. |
[9] |
M. I. Davidich and S. Bornholdt, Boolean network model predicts cell cycle sequence of fission yeast, PLoS ONE, 3 (2008), e1672. |
[10] |
E. Dubrova, M. Teslenko and A. Martinelli, Kauffman networks: Analysis and applications, Computer-Aided Design, IEEE/ACM International Conference (2005), 479-484,
doi: 10.1109/ICCAD.2005.1560115. |
[11] |
E. D. Fabricius, "Modern Digital Design and Switching Theory," CRC Press 1992. |
[12] |
J. F. Groote and M. Keinänen, A sub-quadratic algorithm for conjunctive and disjunctive BESs, Theoretical aspects of computing-ICTAC 2005, 532-545, Lecture Notes in Comput. Sci., 3722, Springer, Berlin 2005. |
[13] |
R. A. Hernádez-Toledo, Linear finite dynamical systems, Communications in Algebra, 33 (2005), 2977-2989.
doi: 10.1081/AGB-200066211. |
[14] |
A. Ilichinsky, "Cellular Automata: A Discrete Universe," World Scientific Publishing Company, 2001. |
[15] |
A. Jarrah, R. Laubenbacher, B. Stigler and M. Stillman, Reverse-engineering of polynomial dynamical systems, Adv. in Appl. Math., 39 (2007), 477-489. arXiv:q-bio/0605032v1. |
[16] |
A. Jarrah, B. Raposa and R. Laubenbacher, Nested canalyzing, unate cascade, and polynomial functions, Physica D, 233 (2007), 167-174. arXiv:q-bio/0606013v3. |
[17] |
A. Jarrah, R. Laubenbacher and A. Veliz-Cuba, The dynamics of conjunctive and disjunctive Boolean networks,, preprint available at: \arXiv{0805.0275v1}., ().
|
[18] |
W. Just, The steady state system problem is NP-hard even for monotone quadratic Boolean dynamical systems,, preprint available at: \url{http://www.math.ohiou.edu/ just/publ.html}., ().
|
[19] |
S. Kauffman, C. Peterson, B. Samuelsson and C. Troein, Genetic networks with canalyzing Boolean rules are always stable, PNAS, 101 (2004), 17102-17107.
doi: 10.1073/pnas.0407783101. |
[20] |
R. Laubenbacher and B. Stigler, A computational algebra approach to the reverse engineering of gene regulatory networks, J. Theor. Biol., 229 (2004), 523-537. arXiv:q-bio/0312026. |
[21] |
T. E. Malloy, J. Butner and G. C. Jensen, The emergence of dynamic form through phase relations in dynamic systems, Nonlinear Dynamics, Psychology, and Life Sciences, 12 (2008), 371-395. |
[22] |
R. Pal, I. Ivanov, A. Datta, M. L. Bittner and E. R. Dougherty, Generating Boolean networks with a prescribed attractor structure, Bioinformatics, 21 (2005), 4021-4025.
doi: 10.1093/bioinformatics/bti664. |
[23] |
J. Reger and K. Schmidt, Modeling and analyzing finite state automata in the finite field $F_2$, Mathematics and Computers in Simulation, 66 (2004), 193-206.
doi: 10.1016/j.matcom.2003.11.005. |
[24] |
N. A. W. Riel, Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments, Briefings in Bioinformatics, 7 (2006), 364-374.
doi: 10.1093/bib/bbl040. |
[25] |
S. Rudeanu, "Boolean Functions and Equations," North-Holland, Amsterdam, 1974. |
[26] |
M. H. Stone, The theory of representation for Boolean algebras, Transactions of American Mathematical Society, 40 (1936), 37-111. |
[27] |
T. Tamura and T. Akutsu, Algorithms for singleton attractor detection in planar and nonplanar AND/OR Boolean networks, Math. Comput. Sci., 2 (2009), 401-420.
doi: 10.1007/s11786-008-0063-5. |
[28] |
C. J. Tomlin and J. D. Aelrod, Biology by numbers: Mathematical modelling in developmental biology, Nature Reviews Genetics, 8 (2007), 331-340.
doi: 10.1038/nrg2098. |
[29] |
S-Q. Zhang, M. Hayashida, T. Akutsu, W-K. Ching and M. K. Ng, Algorithms for finding small attractors in Boolean networks, EURASIP Journal on Bioinformatics and Systems Biology (2007).
doi: 10.1155/2007/20180. |
[1] |
Roberto Serra, Marco Villani, Alex Graudenzi, Annamaria Colacci, Stuart A. Kauffman. The simulation of gene knock-out in scale-free random Boolean models of genetic networks. Networks and Heterogeneous Media, 2008, 3 (2) : 333-343. doi: 10.3934/nhm.2008.3.333 |
[2] |
Martin Gugat, Falk M. Hante, Markus Hirsch-Dick, Günter Leugering. Stationary states in gas networks. Networks and Heterogeneous Media, 2015, 10 (2) : 295-320. doi: 10.3934/nhm.2015.10.295 |
[3] |
Ö. Uğur, G. W. Weber. Optimization and dynamics of gene-environment networks with intervals. Journal of Industrial and Management Optimization, 2007, 3 (2) : 357-379. doi: 10.3934/jimo.2007.3.357 |
[4] |
Erik Kropat, Gerhard-Wilhelm Weber, Erfan Babaee Tirkolaee. Foundations of semialgebraic gene-environment networks. Journal of Dynamics and Games, 2020, 7 (4) : 253-268. doi: 10.3934/jdg.2020018 |
[5] |
Yongwu Rong, Chen Zeng, Christina Evans, Hao Chen, Guanyu Wang. Topology and dynamics of boolean networks with strong inhibition. Discrete and Continuous Dynamical Systems - S, 2011, 4 (6) : 1565-1575. doi: 10.3934/dcdss.2011.4.1565 |
[6] |
Tiantian Mu, Jun-E Feng, Biao Wang. Pinning detectability of Boolean control networks with injection mode. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022089 |
[7] |
Sujit Nair, Naomi Ehrich Leonard. Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2007, 2 (4) : 597-626. doi: 10.3934/nhm.2007.2.597 |
[8] |
Kunwen Wen, Lifang Huang, Qiuying Li, Qi Wang, Jianshe Yu. The mean and noise of FPT modulated by promoter architecture in gene networks. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2177-2194. doi: 10.3934/dcdss.2019140 |
[9] |
Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344 |
[10] |
Oskar Weinberger, Peter Ashwin. From coupled networks of systems to networks of states in phase space. Discrete and Continuous Dynamical Systems - B, 2018, 23 (5) : 2021-2041. doi: 10.3934/dcdsb.2018193 |
[11] |
Sanmei Zhu, Jun-e Feng, Jianli Zhao. State feedback for set stabilization of Markovian jump Boolean control networks. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1591-1605. doi: 10.3934/dcdss.2020413 |
[12] |
Yvjing Yang, Yang Liu, Jungang Lou, Zhen Wang. Observability of switched Boolean control networks using algebraic forms. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1519-1533. doi: 10.3934/dcdss.2020373 |
[13] |
Jiayuan Yan, Ding-Xue Zhang, Bin Hu, Zhi-Hong Guan, Xin-Ming Cheng. State bounding for time-delay impulsive and switching genetic regulatory networks with exogenous disturbance. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1749-1765. doi: 10.3934/dcdss.2022004 |
[14] |
J. C. Artés, Jaume Llibre, J. C. Medrado. Nonexistence of limit cycles for a class of structurally stable quadratic vector fields. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 259-270. doi: 10.3934/dcds.2007.17.259 |
[15] |
Gershon Wolansky. Limit theorems for optimal mass transportation and applications to networks. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 365-374. doi: 10.3934/dcds.2011.30.365 |
[16] |
William Chad Young, Adrian E. Raftery, Ka Yee Yeung. A posterior probability approach for gene regulatory network inference in genetic perturbation data. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1241-1251. doi: 10.3934/mbe.2016041 |
[17] |
Joo Sang Lee, Takashi Nishikawa, Adilson E. Motter. Why optimal states recruit fewer reactions in metabolic networks. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2937-2950. doi: 10.3934/dcds.2012.32.2937 |
[18] |
Raoul-Martin Memmesheimer, Marc Timme. Stable and unstable periodic orbits in complex networks of spiking neurons with delays. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1555-1588. doi: 10.3934/dcds.2010.28.1555 |
[19] |
Erik Kropat, Silja Meyer-Nieberg, Gerhard-Wilhelm Weber. Computational networks and systems-homogenization of self-adjoint differential operators in variational form on periodic networks and micro-architectured systems. Numerical Algebra, Control and Optimization, 2017, 7 (2) : 139-169. doi: 10.3934/naco.2017010 |
[20] |
Leong-Kwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 193-207. doi: 10.3934/naco.2014.4.193 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]