-
1
-
-
69949088984
-
Early-warning signals for critical transitions
-
Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53-59 (2009).
-
(2009)
Nature
, vol.461
, pp. 53-59
-
-
Scheffer, M.1
-
2
-
-
84859741480
-
Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers
-
Chen, L., Liu, R., Liu, Z., Li, M. & Aihara, K. Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Sci. Rep. 2, 342 (2012).
-
(2012)
Sci. Rep.
, vol.2
, pp. 342
-
-
Chen, L.1
Liu, R.2
Liu, Z.3
Li, M.4
Aihara, K.5
-
3
-
-
84897433296
-
Early diagnosis of complex diseases by molecular biomarkers, network biomarkers, and dynamical network biomarkers
-
Liu, R., Wang, X., Aihara, K. & Chen, L. Early diagnosis of complex diseases by molecular biomarkers, network biomarkers, and dynamical network biomarkers. Med. Res. Rev. 34, 455-478 (2014).
-
(2014)
Med. Res. Rev.
, vol.34
, pp. 455-478
-
-
Liu, R.1
Wang, X.2
Aihara, K.3
Chen, L.4
-
4
-
-
84949554340
-
-
Ch. 3, Westview Press
-
Strogatz, S. H. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Ch. 3, 56-84 (Westview Press, 2014).
-
(2014)
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering
, pp. 56-84
-
-
Strogatz, S.H.1
-
5
-
-
0035846180
-
Catastrophic shifts in ecosystems
-
Scheffer, M., Carpenter, S., Foley, J. A., Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591-596 (2001).
-
(2001)
Nature
, vol.413
, pp. 591-596
-
-
Scheffer, M.1
Carpenter, S.2
Foley, J.A.3
Folke, C.4
Walker, B.5
-
6
-
-
79957619918
-
Early-warnings of regime shifts: A whole-ecosystem experiment
-
Carpenter, S. R. et al. Early-warnings of regime shifts: a whole-ecosystem experiment. Science 332, 1079-1082 (2011).
-
(2011)
Science
, vol.332
, pp. 1079-1082
-
-
Carpenter, S.R.1
-
7
-
-
33644933342
-
Rising variance: A leading indicator of ecological transition
-
Carpenter, S. R. & Brock, W. A. Rising variance: a leading indicator of ecological transition. Ecol. Lett. 9, 311-318 (2006).
-
(2006)
Ecol. Lett.
, vol.9
, pp. 311-318
-
-
Carpenter, S.R.1
Brock, W.A.2
-
8
-
-
22544432515
-
Eutrophication of aquatic ecosystems: Bistability and soil phosphorus
-
Carpenter, S. R. Eutrophication of aquatic ecosystems: bistability and soil phosphorus. Proc. Natl. Acad. Sci. USA 102, 10002-10005 (2005).
-
(2005)
Proc. Natl. Acad. Sci. USA
, vol.102
, pp. 10002-10005
-
-
Carpenter, S.R.1
-
9
-
-
77957147507
-
Early-warning signals of extinction in deteriorating environments
-
Drake, M. J. & Griffen, D. B. Early-warning signals of extinction in deteriorating environments. Nature 467, 456-459 (2010).
-
(2010)
Nature
, vol.467
, pp. 456-459
-
-
Drake, M.J.1
Griffen, D.B.2
-
10
-
-
55749083715
-
Slowing down as an early-warning signal for abrupt climate change
-
Dakos, V. et al. Slowing down as an early-warning signal for abrupt climate change. Proc. Natl. Acad. Sci. USA 105, 14308-14312 (2008).
-
(2008)
Proc. Natl. Acad. Sci. USA
, vol.105
, pp. 14308-14312
-
-
Dakos, V.1
-
11
-
-
41149154410
-
Tipping elements in the earth's climate system
-
Lenton, T. M. et al. Tipping elements in the earth's climate system. Proc. Natl. Acad. Sci. USA 105, 1786-1793 (2008).
-
(2008)
Proc. Natl. Acad. Sci. USA
, vol.105
, pp. 1786-1793
-
-
Lenton, T.M.1
-
12
-
-
16644399750
-
Detection of climate system bifurcations by degenerate fingerprinting
-
Held, H. & Kleinen, T. Detection of climate system bifurcations by degenerate fingerprinting. Geophys. Res. Lett. 31, L23207 (2004).
-
(2004)
Geophys. Res. Lett.
, vol.31
, pp. L23207
-
-
Held, H.1
Kleinen, T.2
-
13
-
-
0242482780
-
The potential role of spectral properties in detecting thresholds in the earth system: Application to the thermohaline circulation
-
Kleinen, T., Held, H. & Petschel-Held, G. The potential role of spectral properties in detecting thresholds in the earth system: application to the thermohaline circulation. Ocean Dyn. 53, 53-63 (2003).
-
(2003)
Ocean Dyn.
, vol.53
, pp. 53-63
-
-
Kleinen, T.1
Held, H.2
Petschel-Held, G.3
-
14
-
-
84901315597
-
Identifying critical transitions of complex diseases based on a single sample
-
Liu, R. et al. Identifying critical transitions of complex diseases based on a single sample. Bioinformatics 30, 1579-1586 (2014).
-
(2014)
Bioinformatics
, vol.30
, pp. 1579-1586
-
-
Liu, R.1
-
15
-
-
84897674607
-
International transmission of shocks and fragility of a bank network
-
Feng, X., Jo, W. S. & Kim, B. J. International transmission of shocks and fragility of a bank network. Physica A 403, 120-129 (2014).
-
(2014)
Physica A
, vol.403
, pp. 120-129
-
-
Feng, X.1
Jo, W.S.2
Kim, B.J.3
-
16
-
-
39749111958
-
Ecology for bankers
-
May, R. M., Levin, S. A. & Sugihara, G. Ecology for bankers. Nature 451, 893-895 (2008).
-
(2008)
Nature
, vol.451
, pp. 893-895
-
-
May, R.M.1
Levin, S.A.2
Sugihara, G.3
-
17
-
-
0031238062
-
Pseudospectra of linear operators
-
Trefethen, L. N. Pseudospectra of linear operators. SIAM Rev. 39, 383-406 (1997).
-
(1997)
SIAM Rev.
, vol.39
, pp. 383-406
-
-
Trefethen, L.N.1
-
18
-
-
0027628642
-
Hydrodynamic stability without eigenvalues
-
Trefethen, L., Trefethen, A., Reddy, S. & Driscoll, T. Hydrodynamic stability without eigenvalues. Science 261, 578-584 (1993).
-
(1993)
Science
, vol.261
, pp. 578-584
-
-
Trefethen, L.1
Trefethen, A.2
Reddy, S.3
Driscoll, T.4
-
19
-
-
1342310021
-
Optimization and pseudospectra, with applications to robust stability
-
Burke, J. V., Lewis, A. S. & Overton, M. L. Optimization and pseudospectra, with applications to robust stability. SIAM J. Matrix Anal. Appl. 25, 80-104 (2003).
-
(2003)
SIAM J. Matrix Anal. Appl.
, vol.25
, pp. 80-104
-
-
Burke, J.V.1
Lewis, A.S.2
Overton, M.L.3
-
20
-
-
0001930649
-
Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability
-
Springer Netherlands
-
Bulgak, H. Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability. In Error control and adaptivity in scientific computing 95-124 (Springer Netherlands, 1999).
-
(1999)
Error Control and Adaptivity in Scientific Computing
, pp. 95-124
-
-
Bulgak, H.1
-
21
-
-
0029933942
-
A model for evolution and extinction
-
Roberts, B. W. & Newman, M. J. A model for evolution and extinction. J. Theor. Biol. 180, 39-54 (1996).
-
(1996)
J. Theor. Biol.
, vol.180
, pp. 39-54
-
-
Roberts, B.W.1
Newman, M.J.2
-
22
-
-
33646744156
-
Statistical methods for analysis of seasonal modifications in the salt marshes of the Venice lagoon
-
Camuffo, M., Benvenuto, F., Marani Abbadessa, M., Modenese, L. & Marani, A. Statistical methods for analysis of seasonal modifications in the salt marshes of the Venice lagoon. Management of Environmental Quality 17, 323-338 (2003).
-
(2003)
Management of Environmental Quality
, vol.17
, pp. 323-338
-
-
Camuffo, M.1
Benvenuto, F.2
Marani Abbadessa, M.3
Modenese, L.4
Marani, A.5
-
23
-
-
34548039747
-
Robust RLS methods for online estimation of power system electromechanical modes
-
Zhou, N., Pierre, J. W., Trudnowski, D. J. & Guttromson, R. T. Robust RLS methods for online estimation of power system electromechanical modes. IEEE Trans. Power Syst. 22, 1240-1249 (2007).
-
(2007)
IEEE Trans. Power Syst.
, vol.22
, pp. 1240-1249
-
-
Zhou, N.1
Pierre, J.W.2
Trudnowski, D.J.3
Guttromson, R.T.4
-
24
-
-
33646337424
-
Imaging gene expression: Tiny signals make a big noise
-
Longo, D. & Hasty, J. Imaging gene expression: tiny signals make a big noise. Nat. Chem. Biol. 2, 181-182 (2006).
-
(2006)
Nat. Chem. Biol.
, vol.2
, pp. 181-182
-
-
Longo, D.1
Hasty, J.2
-
25
-
-
31544481170
-
Small signal, big noise: Performance of the CIDI depression module
-
Kurdyak, P. A. & Gnam, W. H. Small signal, big noise: performance of the CIDI depression module. Can. J. Psychiatry 50, 851 (2005).
-
(2005)
Can. J. Psychiatry
, vol.50
, pp. 851
-
-
Kurdyak, P.A.1
Gnam, W.H.2
-
26
-
-
84884882107
-
Information dissipation as an early-warning signal for the Lehman Brothers collapse in financial time series
-
Quax, R., Kandhai, D. & Sloot, P. Information dissipation as an early-warning signal for the Lehman Brothers collapse in financial time series. Sci. Rep. 3, 1898 (2013).
-
(2013)
Sci. Rep.
, vol.3
, pp. 1898
-
-
Quax, R.1
Kandhai, D.2
Sloot, P.3
-
27
-
-
84887816730
-
Dynamical network biomarkers for identifying critical transitions and their driving networks of biologic processes
-
Liu, R., Aihara, K. & Chen, L. Dynamical network biomarkers for identifying critical transitions and their driving networks of biologic processes. Quant. Biol. 1, 105-114 (2013).
-
(2013)
Quant. Biol.
, vol.1
, pp. 105-114
-
-
Liu, R.1
Aihara, K.2
Chen, L.3
-
28
-
-
84871750865
-
Identifying critical transitions and their leading networks for complex diseases
-
Liu, R. et al. Identifying critical transitions and their leading networks for complex diseases. Sci. Rep. 2, 813 (2012).
-
(2012)
Sci. Rep.
, vol.2
, pp. 813
-
-
Liu, R.1
-
29
-
-
84877337118
-
Detecting early-warning signals of type 1 diabetes and its leading biomolecular networks by dynamical network biomarkers
-
Liu, X. P., Liu, R., Zhao, X.-M. & Chen, L. Detecting early-warning signals of type 1 diabetes and its leading biomolecular networks by dynamical network biomarkers. BMC Med. Genomics 6, S8 (2013).
-
(2013)
BMC Med. Genomics
, vol.6
, pp. S8
-
-
Liu, X.P.1
Liu, R.2
Zhao, X.-M.3
Chen, L.4
-
30
-
-
84896468768
-
Detecting tissue-specific early-warning signals for complex diseases based on dynamical network biomarkers: Study of type-2 diabetes by cross-tissue analysis
-
Li, M., Zeng, T., Liu, R. & Chen, L. Detecting tissue-specific early-warning signals for complex diseases based on dynamical network biomarkers: study of type-2 diabetes by cross-tissue analysis. Brief. Bioinform. 15, 229-243 (2013).
-
(2013)
Brief. Bioinform.
, vol.15
, pp. 229-243
-
-
Li, M.1
Zeng, T.2
Liu, R.3
Chen, L.4
-
31
-
-
32944472413
-
Genomic analysis of murine pulmonary tissue following carbonyl chloride inhalation
-
Sciuto, A. M., Phillips, C. S. & Orzolek, L. D. Genomic analysis of murine pulmonary tissue following carbonyl chloride inhalation. Chem. Res. Toxicol. 18, 1654-1660 (2005).
-
(2005)
Chem. Res. Toxicol.
, vol.18
, pp. 1654-1660
-
-
Sciuto, A.M.1
Phillips, C.S.2
Orzolek, L.D.3
-
32
-
-
84871459120
-
Flickering gives early warning signals of a critical transition to a eutrophic lake state
-
Wang, R. et al. Flickering gives early warning signals of a critical transition to a eutrophic lake state. Nature 492, 419-422 (2012).
-
(2012)
Nature
, vol.492
, pp. 419-422
-
-
Wang, R.1
-
33
-
-
20744444887
-
Noise-induced cooperative behavior in a multicell system
-
Chen, L., Wang, R., Zhou, T. & Aihara, K. Noise-induced cooperative behavior in a multicell system. Bioinformatics 21, 2722-2729 (2005).
-
(2005)
Bioinformatics
, vol.21
, pp. 2722-2729
-
-
Chen, L.1
Wang, R.2
Zhou, T.3
Aihara, K.4
-
34
-
-
58849107628
-
Moment-closure approximations for mass-action models
-
Gillespie, C. S. Moment-closure approximations for mass-action models. IET Syst. Biol. 3, 52C58 (2009).
-
(2009)
IET Syst. Biol.
, vol.3
, pp. 52C58
-
-
Gillespie, C.S.1
-
35
-
-
84859158805
-
Achieving moment closure through cumulant neglect
-
Matis, T. & Guardiola, I. Achieving moment closure through cumulant neglect. Math. J. 12, 1-18 (2010).
-
(2010)
Math. J.
, vol.12
, pp. 1-18
-
-
Matis, T.1
Guardiola, I.2
-
36
-
-
0040706272
-
Edgeworth series for lattice distributions
-
Kolassa, J. E. & McCullagh, P. Edgeworth series for lattice distributions. Ann. Stat. 18, 981-985 (1990).
-
(1990)
Ann. Stat.
, vol.18
, pp. 981-985
-
-
Kolassa, J.E.1
McCullagh, P.2
-
37
-
-
79960630056
-
Binomial moment equations for stochastic reaction systems
-
Barzel, B. & Biham, O. Binomial moment equations for stochastic reaction systems. Phys. Rev. Lett. 106, 150602 (2011).
-
(2011)
Phys. Rev. Lett.
, vol.106
, pp. 150602
-
-
Barzel, B.1
Biham, O.2
-
38
-
-
84948131129
-
Detecting causality from nonlinear dynamics with short-term time series
-
Ma, H., Aihara, K. & Chen, L. Detecting causality from nonlinear dynamics with short-term time series. Sci. Rep. 4, 7464, (2014).
-
(2014)
Sci. Rep.
, vol.4
, pp. 7464
-
-
Ma, H.1
Aihara, K.2
Chen, L.3
-
39
-
-
84922632216
-
Predicting time series from short-term high-dimensional data
-
Ma, H., Aihara, K. & Chen, L. Predicting time series from short-term high-dimensional data. Int. J. Bifurcat. Chaos. 24, 1430033 (2014).
-
(2014)
Int. J. Bifurcat. Chaos.
, vol.24
, pp. 1430033
-
-
Ma, H.1
Aihara, K.2
Chen, L.3
-
40
-
-
0347601794
-
Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena
-
Majda, A. J. & Kramer, P. R. Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena. Phys. Rep. 314, 237-574 (1999).
-
(1999)
Phys. Rep.
, vol.314
, pp. 237-574
-
-
Majda, A.J.1
Kramer, P.R.2
|