Statistically independent features can be extracted by nding a factorial representation of a signal distribution. Principal Component Analysis (PCA) accomplishes this for linear correlated and Gaussian distributed signals. Independent Component Analysis (ICA), formalized by Comon (1994), extracts features in the case of linear statistical dependent but not necessarily Gaussian distributed signa...

The non-linear wave equation is taken as a model problem for the investigation. Different multisymplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses...

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these extended-linear symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forwar...

The Faddeev-Jackiw Hamiltonian Reduction approach to constrained dynamics is applied to the collective coordinates analysis of non-linear waves, and compared with the alternative procedure known as symplectic formalism. SWAT-147 January 1997 hep-th/9702040

In this series of papers, we study some Hamiltonian structures of Painlevé systems (HJ ), J = V I, V, IV, III, II, I, namely, symplectic structures of the spaces for Painlevé systems constructed by K. Okamoto([7]), and a characterization of Painlevé systems by their spaces. As is well known, P. Painlevé and B. Gambier discovered, at the beginning of this century, six nonlinear second order diff...

This paper investigates a fixed-time convergence issue using the sliding mode observer-based controller for class of uncertain nonlinear double integrator systems. is designed assuming that only first state measurement available and there no information about external disturbances modeling uncertainties. A new form observer in combination with to estimate unmeasured unknown uncertainties as wel...

Abstract We propose and analyse a numerical integrator that computes low-rank approximation to large time-dependent matrices are either given explicitly via their increments or the unknown solution matrix differential equation. Furthermore, is extended of tensors by Tucker fixed multilinear rank. The proposed different from known projector-splitting for dynamical approximation, but it retains i...

Abstract We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe coupling and dynamics in bulk- surface-spaces, treats nonlinear terms similarly an exponential integrator. convergence proof is estimates for recursive formulation of error, using smoothing property analytic semig...

We explore the nonlinear dynamics of a forced core-mantle system. We show that the free axisymmetric motion of a uniform-vorticity Ñuid core coupled to a rigid mantle (the model) is Poincare -Hough integrable. We derive an approximate Hamiltonian for the core tilt mode that includes the leading nonlinear contribution. We then include gravitational perturbations in the analysis. We identify the...

The nonlinear properties of the dendrites in prepositus hypoglossi neurons are involved in maintenance of eye position. The biophysical properties of these neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel method named QSA (quadratic sinusoidal analysis) for voltage clamped neurons was used...