Adam H. Monahan

TL;DR: In this paper, a review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) would not correspond well to individual kinematic degrees of freedom, and (iii) will be statistically independent of other EOF models.

TL;DR: A novel probabilistic methodology based upon transfer operators that automatically detect maximally coherent sets that is very simple to implement, requiring only singular vector computations of a matrix of transitions induced by the dynamics.

TL;DR: In this paper, the authors considered the probability distribution of sea surface wind speeds, w, and derived empirical expressions for the probability density function of w in terms of the mean and standard deviation of the vector wind.

TL;DR: In this paper, a review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) would not correspond with individual kinematic degrees of freedom, (iii) will be statistically independent of other EOF models, and (iv) would be strongly influenced by the nonlocal requirement that modesmaximize variance over the target domain.

TL;DR: A nonlinear generalization of principal component analysis (PCA) is implemented in a variational framework using a five-layer autoassociative feed-forward neural network and it is found that as noise is added to the Lorenz attractor, the NLPCA approximation remain superior to the PCA approximations until the noise level is so great that the lowerdimensional nonlinear structure of the data is no longer manifest to the eye.