메뉴 건너뛰기




Volumn 25, Issue 3, 2013, Pages 563-604

Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks

Author keywords

Biological network; Determining node; Differential equations on graphs; Gene regulation; Global attractor; Reaction network; Takens embedding

Indexed keywords


EID: 84883447859     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-013-9312-7     Document Type: Article
Times cited : (134)

References (37)
  • 5
    • 84855221195 scopus 로고    scopus 로고
    • On the global boundedness of the Chen system
    • Barboza, R., Chen, G.: On the global boundedness of the Chen system. Int. J. Bifurcation Chaos 21, 3373-3385 (2011).
    • (2011) Int. J. Bifurcation Chaos , vol.21 , pp. 3373-3385
    • Barboza, R.1    Chen, G.2
  • 6
    • 3042858242 scopus 로고    scopus 로고
    • Connection graph stability method for synchronized coupled chaotic systems
    • Belykh, V. N., Belykh, I. V., Hasler, M.: Connection graph stability method for synchronized coupled chaotic systems. Phys. D 195, 159-187 (2004).
    • (2004) Phys. D , vol.195 , pp. 159-187
    • Belykh, V.N.1    Belykh, I.V.2    Hasler, M.3
  • 7
    • 56349086571 scopus 로고    scopus 로고
    • A fixed-parameter algorithm for the directed feedback vertex set problem
    • Chen, J., Liu, Y., Lu, S., O'Sullivan, B., Razgon, I.: A fixed-parameter algorithm for the directed feedback vertex set problem. J. ACM 55(21), 1-19 (2008).
    • (2008) J. ACM , vol.55 , Issue.21 , pp. 1-19
    • Chen, J.1    Liu, Y.2    Lu, S.3    O'Sullivan, B.4    Razgon, I.5
  • 9
    • 0003241758 scopus 로고
    • Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
    • Springer, New York. AMS Colloquium, Providence (2002)
    • Constantin, P., Foias, C., Nicolaenko, B., Temam, R.: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematics and Sciences, vol. 70. Springer, New York (1989). AMS Colloquium, Providence (2002).
    • (1989) Applied Mathematics and Sciences , vol.70
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 11
    • 84966204481 scopus 로고
    • Determination of the solutions of the Navier-Stokes equations by a set of nodal values
    • Foias, C., Temam, R.: Determination of the solutions of the Navier-Stokes equations by a set of nodal values. Math. Comput. 43, 117-133 (1984).
    • (1984) Math. Comput. , vol.43 , pp. 117-133
    • Foias, C.1    Temam, R.2
  • 12
    • 0000166593 scopus 로고
    • Determining nodes, finite differences schemes and inertial manifolds
    • Foias, C., Titi, E. S.: Determining nodes, finite differences schemes and inertial manifolds. Nonlinearity 4, 135-153 (1991).
    • (1991) Nonlinearity , vol.4 , pp. 135-153
    • Foias, C.1    Titi, E.S.2
  • 13
    • 78650127262 scopus 로고    scopus 로고
    • Network periodic solutions: full oscillation and rigid synchrony
    • Golubitsky, M., Romano, D., Wang, Y.: Network periodic solutions: full oscillation and rigid synchrony. Nonlinearity 23, 3227-3243 (2010).
    • (2010) Nonlinearity , vol.23 , pp. 3227-3243
    • Golubitsky, M.1    Romano, D.2    Wang, Y.3
  • 14
    • 0003293929 scopus 로고
    • Asymptotic Behavior of Dissipative Systems
    • AMS, Providence
    • Hale, J. K.: Asymptotic Behavior of Dissipative Systems. Mathematical Survey 25. AMS, Providence (1988).
    • (1988) Mathematical Survey , vol.25
    • Hale, J.K.1
  • 15
    • 0141459061 scopus 로고    scopus 로고
    • Regularity, determining modes and Galerkin methods
    • Hale, J. K., Raugel, G.: Regularity, determining modes and Galerkin methods. J. Math. Pures Appl., IX 82, 1075-1136 (2003).
    • (2003) J. Math. Pures Appl., IX , vol.82 , pp. 1075-1136
    • Hale, J.K.1    Raugel, G.2
  • 17
    • 33744458441 scopus 로고    scopus 로고
    • Regulatory blueprint for a chordate embryo
    • Imai, K. S., Levine, M., Satoh, N., Satou, Y.: Regulatory blueprint for a chordate embryo. Science 312, 1183-1187 (2006).
    • (2006) Science , vol.312 , pp. 1183-1187
    • Imai, K.S.1    Levine, M.2    Satoh, N.3    Satou, Y.4
  • 18
    • 84857564988 scopus 로고    scopus 로고
    • Observation and inverse problems in coupled cell networks
    • Joly, R.: Observation and inverse problems in coupled cell networks. Nonlinearity 25, 657-676 (2012).
    • (2012) Nonlinearity , vol.25 , pp. 657-676
    • Joly, R.1
  • 19
    • 84883461774 scopus 로고
    • Reducibility among combinatorial problems
    • Karp, R. M.: Reducibility among combinatorial problems. Kibernet Sb. 12, 16-83 (1975).
    • (1975) Kibernet Sb. , vol.12 , pp. 16-83
    • Karp, R.M.1
  • 20
    • 84862988782 scopus 로고    scopus 로고
    • Nonautonomous Dynamical Systems
    • AMS, Providence
    • Kloeden, P. E., Rasmussen, M.: Nonautonomous Dynamical Systems. Mathematical Survey, vol. 176. AMS, Providence (2011).
    • (2011) Mathematical Survey , vol.176
    • Kloeden, P.E.1    Rasmussen, M.2
  • 21
    • 0006444781 scopus 로고
    • Dynamical system generated by the Navier-Stokes equations
    • Translation from. Dokl. Akad. Nauk SSSR 205, 318-320 (1972)
    • Ladyzhenskaya, O. A.: Dynamical system generated by the Navier-Stokes equations. Sov. Phys. Dokl. 17, 647-649 (1972); translation from. Dokl. Akad. Nauk SSSR 205, 318-320 (1972).
    • (1972) Sov. Phys. Dokl. , vol.17 , pp. 647-649
    • Ladyzhenskaya, O.A.1
  • 23
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz, E. N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141 (1963).
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 24
    • 84867995799 scopus 로고
    • The principle of spatial averaging and inertial manifolds for reaction- diffusion equations
    • Proceedings of the Symposium, Washington, DC, Lecture Notes in Mathematics, Springer, Berlin (1987)
    • Mallet-Paret, J., Sell, G. R.: The principle of spatial averaging and inertial manifolds for reaction- diffusion equations. In: Nonlinear Semigroups, Partial Differential Equations and Attractors. Proceedings of the Symposium, Washington, DC (1985). Lecture Notes in Mathematics, vol. 1248, pp. 94-107. Springer, Berlin (1987).
    • (1985) Nonlinear Semigroups, Partial Differential Equations and Attractors , vol.1248 , pp. 94-107
    • Mallet-Paret, J.1    Sell, G.R.2
  • 26
    • 0035216342 scopus 로고    scopus 로고
    • Chaos in the Lorenz equations: a computer assisted proof. III: classical parameter values
    • Mischaikow, K., Mrozek, M., Szymczak, A.: Chaos in the Lorenz equations: a computer assisted proof. III: classical parameter values. J. Differ. Equ. 169, 17-56 (2001).
    • (2001) J. Differ. Equ. , vol.169 , pp. 17-56
    • Mischaikow, K.1    Mrozek, M.2    Szymczak, A.3
  • 27
    • 37349051685 scopus 로고    scopus 로고
    • Structure of regulatory networks and diversity of gene expression patterns
    • Mochizuki, A.: Structure of regulatory networks and diversity of gene expression patterns. J. Theor. Biol. 250, 307-321 (2008).
    • (2008) J. Theor. Biol. , vol.250 , pp. 307-321
    • Mochizuki, A.1
  • 28
    • 77954561302 scopus 로고    scopus 로고
    • Analyzing steady states of dynamics of bio-molecules from the structure of regulatory networks
    • Mochizuki, A., Saito, D.: Analyzing steady states of dynamics of bio-molecules from the structure of regulatory networks. J. Theor. Biol. 266, 323-335 (2010).
    • (2010) J. Theor. Biol. , vol.266 , pp. 323-335
    • Mochizuki, A.1    Saito, D.2
  • 29
    • 84880696206 scopus 로고    scopus 로고
    • Dynamics and control at feedback vertex sets. II: A faithful monitor to determine the diversity of molecular activities in regulatory networks
    • (in press)
    • Mochizuki, A., Fiedler, B., Kurosawa, G., Saito, D.: Dynamics and control at feedback vertex sets. II: A faithful monitor to determine the diversity of molecular activities in regulatory networks. J. Theor. Biol. (2013, in press).
    • (2013) J. Theor. Biol.
    • Mochizuki, A.1    Fiedler, B.2    Kurosawa, G.3    Saito, D.4
  • 30
    • 33746889808 scopus 로고    scopus 로고
    • A comprehensive pathway map of epidermal growth factor receptor signaling
    • Oda, K., Matsuoka, Y., Funahashi, A., Kitano, H.: A comprehensive pathway map of epidermal growth factor receptor signaling. Mol. Syst. Biol. 1, 1-17 (2005).
    • (2005) Mol. Syst. Biol. , vol.1 , pp. 1-17
    • Oda, K.1    Matsuoka, Y.2    Funahashi, A.3    Kitano, H.4
  • 31
    • 4243241129 scopus 로고    scopus 로고
    • Master stability functions for synchronized coupled systems
    • Pecora, L. M., Carroll, T. L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109-2112 (1998).
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 2109-2112
    • Pecora, L.M.1    Carroll, T.L.2
  • 32
    • 0038815248 scopus 로고    scopus 로고
    • Global attractors
    • B. Fiedler (Ed.), Amsterdam: Elsevier
    • Raugel, G.: Global attractors. In: Fiedler, B. (ed.) Handbook of Dynamical Systems, vol. 2, pp. 885-982. Elsevier, Amsterdam (2002).
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 885-982
    • Raugel, G.1
  • 34
    • 0003293377 scopus 로고
    • The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors
    • Springer, Berlin
    • Sparrow, C.: The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Applied Mathematical Sciences, vol. 41. Springer, Berlin (1982).
    • (1982) Applied Mathematical Sciences , vol.41
    • Sparrow, C.1
  • 35
    • 77957135203 scopus 로고    scopus 로고
    • Reconstruction theory and nonlinear time series analysis
    • In: Broer, H., et al. (eds.), Elsevier, Amsterdam
    • Takens, F.: Reconstruction theory and nonlinear time series analysis. In: Broer, H., et al. (eds.) Handbook of Dynamical Systems, vol. 3, pp. 345-377. Elsevier, Amsterdam (2010).
    • (2010) Handbook of Dynamical Systems , vol.3 , pp. 345-377
    • Takens, F.1
  • 37
    • 0002061016 scopus 로고    scopus 로고
    • A rigorous ODE solver and Smale's 14th problem
    • Tucker, W.: A rigorous ODE solver and Smale's 14th problem. Found. Comput. Math. 2(1), 53-117 (2002).
    • (2002) Found. Comput. Math. , vol.2 , Issue.1 , pp. 53-117
    • Tucker, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.