메뉴 건너뛰기




Volumn 75, Issue 6, 2013, Pages 967-987

Probabilistic Approach for Predicting Periodic Orbits in Piecewise Affine Differential Models

Author keywords

Genetic networks; Piecewise affine models

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; GENE REGULATORY NETWORK; MATHEMATICAL PHENOMENA; STATISTICAL MODEL; SYSTEMS BIOLOGY;

EID: 84879167862     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-012-9773-6     Document Type: Article
Times cited : (2)

References (25)
  • 2
    • 4243170669 scopus 로고    scopus 로고
    • Exact volume computation for convex polytopes: a practical study
    • G. Ziegler (Ed.), Basel: Birkhäuser
    • Büeler, B., Enge, A., & Fukuda, K. (2000). Exact volume computation for convex polytopes: a practical study. In: G. Ziegler (ed.) Polytopes-combinatorics and computation. Basel: Birkhäuser.
    • (2000) Polytopes-Combinatorics and Computation
    • Büeler, B.1    Enge, A.2    Fukuda, K.3
  • 3
    • 29244452623 scopus 로고    scopus 로고
    • Piecewise-linear models of genetic regulatory networks: equilibria and their stability
    • Casey, R., de Jong, H. & Gouzé, J. (2006). Piecewise-linear models of genetic regulatory networks: equilibria and their stability. J. Math. Biol., 52, 27-56.
    • (2006) J. Math. Biol. , vol.52 , pp. 27-56
    • Casey, R.1    de Jong, H.2    Gouzé, J.3
  • 4
    • 79956219214 scopus 로고    scopus 로고
    • Exact control of genetic networks in a qualitative framework: the bistable switch example
    • Chaves, M. & Gouzé, J. (2011). Exact control of genetic networks in a qualitative framework: the bistable switch example. Automatica, 47, 1105-1112.
    • (2011) Automatica , vol.47 , pp. 1105-1112
    • Chaves, M.1    Gouzé, J.2
  • 5
    • 77955854468 scopus 로고    scopus 로고
    • Comparing Boolean and piecewise affine differential models for genetic networks
    • Chaves, M., Tournier, L., & Gouzé, J. L. (2010). Comparing Boolean and piecewise affine differential models for genetic networks. Acta Biotheor., 58(2), 217-232.
    • (2010) Acta Biotheor. , vol.58 , Issue.2 , pp. 217-232
    • Chaves, M.1    Tournier, L.2    Gouzé, J.L.3
  • 6
    • 0034315476 scopus 로고    scopus 로고
    • Analysis of continuous-time switching networks
    • Edwards, R. (2000). Analysis of continuous-time switching networks. Physica D, 146, 165-199.
    • (2000) Physica D , vol.146 , pp. 165-199
    • Edwards, R.1
  • 7
    • 32544456601 scopus 로고    scopus 로고
    • Geometric properties of a class of piecewise affine biological network models
    • Farcot, E. (2006). Geometric properties of a class of piecewise affine biological network models. J. Math. Biol., 52(3), 373-418.
    • (2006) J. Math. Biol. , vol.52 , Issue.3 , pp. 373-418
    • Farcot, E.1
  • 8
    • 50049108362 scopus 로고    scopus 로고
    • A mathematical framework for the control of piecewise-affine models of gene networks
    • Farcot, E., & Gouzé, J. L. (2008). A mathematical framework for the control of piecewise-affine models of gene networks. Automatica, 44(9), 2326-2332.
    • (2008) Automatica , vol.44 , Issue.9 , pp. 2326-2332
    • Farcot, E.1    Gouzé, J.L.2
  • 9
    • 77949885161 scopus 로고    scopus 로고
    • Periodic solutions of piecewise affine gene network models with non uniform decay rates: the case of a negative feedback loop
    • Farcot, E., & Gouzé, J. L. (2009). Periodic solutions of piecewise affine gene network models with non uniform decay rates: the case of a negative feedback loop. Acta Biotheor., 57, 429-455.
    • (2009) Acta Biotheor. , vol.57 , pp. 429-455
    • Farcot, E.1    Gouzé, J.L.2
  • 10
    • 0842288337 scopus 로고    scopus 로고
    • Inferring cellular networks using probabilistic graphical models
    • Friedman, N. (2004). Inferring cellular networks using probabilistic graphical models. Science, 303(5659), 799-805.
    • (2004) Science , vol.303 , Issue.5659 , pp. 799-805
    • Friedman, N.1
  • 11
    • 0035511560 scopus 로고    scopus 로고
    • Planar systems of piecewise linear differential equations with a line of discontinuity
    • Giannakopoulos, F., & Pliete, K. (2001). Planar systems of piecewise linear differential equations with a line of discontinuity. Nonlinearity, 14, 1611-1632.
    • (2001) Nonlinearity , vol.14 , pp. 1611-1632
    • Giannakopoulos, F.1    Pliete, K.2
  • 12
    • 33749553474 scopus 로고
    • Combinatorial and topological methods in nonlinear chemical kinetics
    • Glass, L. (1975). Combinatorial and topological methods in nonlinear chemical kinetics. J. Chem. Phys., 63, 1325-1335.
    • (1975) J. Chem. Phys. , vol.63 , pp. 1325-1335
    • Glass, L.1
  • 13
    • 0015609281 scopus 로고
    • The logical analysis of continuous, nonlinear biochemical control networks
    • Glass, L., & Kauffman, S. (1973). The logical analysis of continuous, nonlinear biochemical control networks. J. Theor. Biol., 39, 103-129.
    • (1973) J. Theor. Biol. , vol.39 , pp. 103-129
    • Glass, L.1    Kauffman, S.2
  • 14
    • 0018168876 scopus 로고
    • Stable oscillations in mathematical models of biological control systems
    • Glass, L., & Pasternak, J. (1978). Stable oscillations in mathematical models of biological control systems. J. Math. Biol., 6, 207-223.
    • (1978) J. Math. Biol. , vol.6 , pp. 207-223
    • Glass, L.1    Pasternak, J.2
  • 15
    • 77958183488 scopus 로고    scopus 로고
    • Piecewise affine models of regulatory genetic networks: review and probabilistic interpretation
    • Lecture notes in control and information sciences, J. Lévine, P. Müllhaupt (Eds.), Berlin: Springer
    • Gouzé, J., & Chaves, M. (2010). Piecewise affine models of regulatory genetic networks: review and probabilistic interpretation. In: J. Lévine & P. Müllhaupt (Eds.), Lecture notes in control and information sciences: Vol. 470. Advances in the theory of control, signals and systems, with physical modelling (pp. 241-253). Berlin: Springer.
    • (2010) Advances in the Theory of Control, Signals and Systems, with Physical Modelling , vol.470 , pp. 241-253
    • Gouzé, J.1    Chaves, M.2
  • 16
    • 0036938728 scopus 로고    scopus 로고
    • A class of piecewise linear differential equations arising in biological models
    • Gouzé, J., & Sari, T. (2002). A class of piecewise linear differential equations arising in biological models. Dyn. Syst., 17(4), 299-316.
    • (2002) Dyn. Syst. , vol.17 , Issue.4 , pp. 299-316
    • Gouzé, J.1    Sari, T.2
  • 17
    • 0242523712 scopus 로고    scopus 로고
    • A control problem for affine dynamical systems on a full-dimensional polytope
    • Habets, L., & Schuppen, J. V. (2004). A control problem for affine dynamical systems on a full-dimensional polytope. Automatica, 40, 21-35.
    • (2004) Automatica , vol.40 , pp. 21-35
    • Habets, L.1    Schuppen, J.V.2
  • 18
    • 0037044575 scopus 로고    scopus 로고
    • The IkB-NFkB signaling module: temporal control and selective gene activation
    • Hoffmann, A., Levchenko, A., Scott, M., & Baltimore, D. (2002). The IkB-NFkB signaling module: temporal control and selective gene activation. Science, 298, 1241-1245.
    • (2002) Science , vol.298 , pp. 1241-1245
    • Hoffmann, A.1    Levchenko, A.2    Scott, M.3    Baltimore, D.4
  • 19
    • 9444239213 scopus 로고    scopus 로고
    • A probabilistic functional network of yeast genes
    • Lee, I., Date, S., Adai, A., & Marcotte, E. (2004). A probabilistic functional network of yeast genes. Science, 306(5701), 1555-1558.
    • (2004) Science , vol.306 , Issue.5701 , pp. 1555-1558
    • Lee, I.1    Date, S.2    Adai, A.3    Marcotte, E.4
  • 20
    • 0002501173 scopus 로고    scopus 로고
    • Chaos in high-dimensional neural and gene networks
    • Mestl, T., Lemay, C., & Glass, L. (1996). Chaos in high-dimensional neural and gene networks. Physica D, 98, 33-52.
    • (1996) Physica D , vol.98 , pp. 33-52
    • Mestl, T.1    Lemay, C.2    Glass, L.3
  • 21
    • 0036184629 scopus 로고    scopus 로고
    • Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks
    • Shmulevich, I., Dougherty, E., Kim, S., & Zhang, W. (2002). Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 18(2), 261-274.
    • (2002) Bioinformatics , vol.18 , Issue.2 , pp. 261-274
    • Shmulevich, I.1    Dougherty, E.2    Kim, S.3    Zhang, W.4
  • 22
    • 0024916497 scopus 로고
    • Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach
    • Snoussi, E. (1989). Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach. Dyn. Stab. Syst., 4(3-4), 189-207.
    • (1989) Dyn. Stab. Syst. , vol.4 , Issue.3-4 , pp. 189-207
    • Snoussi, E.1
  • 24
    • 68949178676 scopus 로고    scopus 로고
    • Uncovering operational interactions in genetic networks using asynchronous boolean dynamics
    • Tournier, L., & Chaves, M. (2009). Uncovering operational interactions in genetic networks using asynchronous boolean dynamics. J. Theor. Biol., 260(2), 196-209.
    • (2009) J. Theor. Biol. , vol.260 , Issue.2 , pp. 196-209
    • Tournier, L.1    Chaves, M.2
  • 25
    • 2642513030 scopus 로고    scopus 로고
    • Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space
    • Wiback, S., Famili, I., Greenberg, H., & Palsson, B. (2004). Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space. J. Theor. Biol., 228(4), 437-447.
    • (2004) J. Theor. Biol. , vol.228 , Issue.4 , pp. 437-447
    • Wiback, S.1    Famili, I.2    Greenberg, H.3    Palsson, B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.