Stability analysis of spatially discretized approximations to invariant circle solutions to a noninvertible map is shown to produce seemingly spurious eigenvalues, found to exist for all truncation numbers. Numerical analysis of the spectral Galerkin projection procedure used to compute the solutions and the eigenvalues of the linearization shows that the set of discrete eigenvalues converges i...

We introduce the use of DCTNet, an efficient approximation and alternative to PCANet, for acoustic signal classification. In PCANet, the eigenfunctions of the local sample covariance matrix (PCA) are used as filterbanks for convolution and feature extraction. When the eigenfunctions are well approximated by the Discrete Cosine Transform (DCT) functions, each layer of of PCANet and DCTNet is ess...

We develop a spectrally accurate numerical method to compute solutions of a model PDE used in plasma physics to describe diffusion in velocity space due to Fokker–Planck collisions. The solution is represented as a discrete and continuous superposition of normalizable and nonnormalizable eigenfunctions via the spectral transform associated with a singular Sturm–Liouville operator. We present a ...

We present a novel hierarchical framework for solving Markov decision processes (MDPs) using a multiscale method called diffusion wavelets. Diffusion wavelet bases significantly differ from the Laplacian eigenfunctions studied in the companion paper (Mahadevan and Maggioni, 2006): the basis functions have compact support, and are inherently multi-scale both spectrally and spatially, and capture...

This paper examines a dataset which is modeled well by the Poisson-Log Normal process and by this process mixed with Log Normal data, which are both turned into compositions. This generates compositional data that has zeros without any need for conditional models or assuming that there is missing or censored data that needs adjustment. It also enables us to model dependence on covariates and wi...

in previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. then we extendedthis research to the simulation of continuous fuzzy systems models. in this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. consider a crisp continuous system whose evolution depends ondifferential equations. such a ...