Using spectral submanifolds for optimal mode selection in nonlinear model reduction

Exact Nonlinear Model Reduction for a von Karman beam: Slow-Fast Decomposition and Spectral Submanifolds

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Kármán beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a li...

Complexity reduction for intra mode selection in HEVC using OpenMP

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding...

Optimal Wavelength Selection in Ultraviolet Spectroscopy for the Estimation of Toxin Reduction Ratio during Hemodialysis

Introduction The concentration of substances, including urea, creatinine, and uric acid, can be used as an index to measure toxic uremic solutes in the blood during dialysis and interdialytic intervals. The on-line monitoring of toxin concentration allows for the clearance measurement of some low-molecular-weight solutes at any time during hemodialysis.The aim of this study was to determine the...

Exploring model selection techniques for nonlinear dimensionality reduction

Nonlinear dimensionality reduction (NLDR) methods have become useful tools for practitioners who are faced with the analysis of high-dimensional data. Of course, not all NLDR methods are equally applicable to a particular dataset at hand. Thus it would be useful to come up with model selection criteria that help to choose among different NLDR algorithms. This paper explores various approaches t...