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Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue.
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A. J. Majda, J. Harlim, Information flow between subspaces of complex dynamical systems, Proceedings of the National Academy of Sciences 104 (23) (2007) 9558–9563
T. P. Sapsis, A. J. Majda, Blending modified gaussian closure and non-Gaussian reduced subspace methods for turbulent dynamical systems, Journal of Nonlinear Science 23 (6) (2013) 1039–1071
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T. P. Sapsis, A. J. Majda, Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems, Proceedings of the National Academy of Sciences 110 (34) (2013) 13705–13710
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N. Chen, A. J. Majda, D. Giannakis, Predicting the cloud patterns of the Madden-Julian Oscillation through a low-order nonlinear stochastic model, Geophysical Research Letters 41 (15) (2014) 5612–5619
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2007
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A. J. Majda, C. Franzke, B. Khouider, An applied mathematics perspective on stochastic modelling for climate, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 366 (1875) (2008) 2427–2453
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A. J. Majda, C. Franzke, D. Crommelin, Normal forms for reduced stochastic climate models, Proceedings of the National Academy of Sciences 106 (10) (2009) 3649–3653
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F. Ackerman, E. A. Stanton, R. Bueno, Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE, Ecological Economics 69 (8) (2010) 1657–1665
2010
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A. J. Majda, B. Gershgorin, Y. Yuan, Low-frequency climate response and fluctuation–dissipation theorems: Theory and practice, Journal of the Atmospheric Sciences 67 (4) (2010) 1186–1201
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N. Chen, A. J. Majda, X. T. Tong, Information barriers for noisy Lagrangian tracers in filtering random incompressible flows, Nonlinearity 27 (9) (2014) 2133
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A. J. Majda, I. Grooms, New perspectives on superparameterization for geophysical turbulence, Journal of Computational Physics 271 (2014) 60–77
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J. Harlim, A. Mahdi, A. J. Majda, An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models, Journal of Computational Physics 257 (2014) 782–812
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A. J. Majda, D. Qi, T. P. Sapsis, Blended particle filters for large-dimensional chaotic dynamical systems, Proceedings of the National Academy of Sciences 111 (21) (2014) 7511–7516
2014
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A. J. Majda, Y. Lee, Conceptual dynamical models for turbulence, Proceedings of the National Academy of Sciences 111 (18) (2014) 6548–6553
2014
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M. Branicki, N. Chen, A. J. Majda, Non-Gaussian test models for prediction and state estimation with model errors, in: Partial Differential Equations: Theory, Control and Approximation, Springer, 2014, pp. 99–138
2014
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N. Chen, A. J. Majda, Predicting the real-time multivariate Madden–Julian oscillation index through a low-order nonlinear stochastic model, Monthly Weather Review 143 (6) (2015) 2148–2169
2015
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N. Chen, A. J. Majda, Predicting the cloud patterns for the boreal summer intraseasonal oscillation through a low-order stochastic model, Mathematics of Climate and Weather Forecasting 1 (1) (2015) 1–20
2015
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N. Chen, A. J. Majda, X. T. Tong, Noisy Lagrangian tracers for filtering random rotating compressible flows, Journal of Nonlinear Science 25 (3) (2015) 451–488
2015
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L. Slivinski, E. Spiller, A. Apte, B. Sandstede, A hybrid particle–ensemble Kalman filter for Lagrangian data assimilation, Monthly Weather Review 143 (1) (2015) 195–211
2015
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A. J. Majda, Statistical energy conservation principle for inhomogeneous turbulent dynamical systems, Proceedings of the National Academy of Sciences 112 (29) (2015) 8937–8941
2015
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A. Majda, Introduction to turbulent dynamical systems in complex systems, Frontiers in Applied Dynamical Systems: Reviews and Tutorials 5, Springer, 2016
2016
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M. A. Mohamad, T. P. Sapsis, Probabilistic response and rare events in Mathieu’s equation under correlated parametric excitation, Ocean Engineering 120 (2016) 289–297
2016
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W. Cousins, T. P. Sapsis, Reduced-order precursors of rare events in unidirectional nonlinear water waves, Journal of Fluid Mechanics 790 (2016) 368–388
2016
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S. Thual, A. J. Majda, N. Chen, S. N. Stechmann, Simple stochastic model for El Niño with westerly wind bursts, Proceedings of the National Academy of Sciences (2016) 201612002
2016
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N. Chen, A. J. Majda, Filtering nonlinear turbulent dynamical systems through conditional Gaussian statistics, Monthly Weather Review 144 (12) (2016) 4885–4917
2016
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N. Chen, A. J. Majda, Filtering the stochastic skeleton model for the Madden–Julian oscillation, Monthly Weather Review 144 (2) (2016) 501–527
2016
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N. Chen, A. J. Majda, Model error in filtering random compressible flows utilizing noisy Lagrangian tracers, Monthly Weather Review 144 (11) (2016) 4037–4061
2016
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G. K. Vallis, Atmospheric and oceanic fluid dynamics, Cambridge University Press, 2017
2017
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