Description: International Chair in Mathematical Physics and Applications, University of Abomey-Calavi, Cotonou, Benin. Principal Component Analysis (PCA) is one of the popular statistical methods for feature extraction. The neural network model has been performed on the PCA to obtain nonlinear principal component analysis (NLPCA), which allows the extraction of nonlinear features in the dataset missed by the PCA. NLPCA is applied to the monthly Sea Surface Temperatu...

Hagos, S. M. and Cook, K. H.: Development of a coupled regional model and its application to the study of interactions between the West African monsoon and the eastern tropical Atlantic ocean, J. Climate, 18, 4993–5010, 2008.; Hastenrath, S. and Lamb, P. J.: Climatic Atlas of the Tropical Atlantic and Eastern Pacific Oceans, The University of Wisconsin Press, Madison, 112 pp., 1977.; Hastie, T. and Stuetzle, W.: Principal curves, J. Am. Stat. Assoc., 84, 502–516, 1989.; ...

Description: Los Alamos National Laboratory, Los Alamos, New Mexiko. The velocity of sound in rock is a strong function of pressure, indicating that wave propagation in rocks is very nonlinear. The quasistatic elastic properties of rocks axe hysteretic, possessing discrete memory. In this paper a new theory is developed, placing all of these properties (nonlinearity, hysteresis, and memory) on equal footing. The starting point of the n...

Description: Institute of Geophysics and Planetary Physics, University of California Riverside, Riverside CA 92521, USA. A Hamiltonian description of oblique travelling waves in a two-fluid, charge-neutral, electron-proton plasma reveals that the transverse momentum equations for the electron and proton fluids are exactly integrable in cases where the total transverse momentum flux integrals, P_y^(d) and P_z

Abramowitz, M. and Stegun, I. A.: Handbook of Mathematical Functions, (Dover: New York), 589 pp., 1965.; Bridges, T. J.: Spatial Hamiltonian structure, energy flux and the water wave problem, Proc. Roy. Soc. Lond. A, 439, 297–315, 1992.; Bridges, T. J.: Multi-symplectic structures and wave propagation, Math. Proc. Camb. Philos. Soc., 121, 147–190, 1997a.; Magri, F.: A simple model of the integrable Hamiltonian equation, J. Math. Phys., 19, 5, 1156–1162, 1978.; Bridges, T...

Description: Indian Institute of Astrophysics, Bangalore 560 034, India. The solar wind serves as a laboratory for investigating magnetohydrodynamic turbulence under conditions irreproducible on the terra firma. Here we show that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of th...

Description: Space Science Center, University of New Hampshire, Durham, New Hampshire, 03824, USA. Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law to incompressible MHD, makes it possible to measure the energy cascade rate in incompressible MHD turbulence by means of third-order moments. In hydrodynamics, accurate measurement of third-order moments requires large amounts of data because the probability distributions of velocity-difference...

Balogh, A., Beek, T J., Forsyth, R J., Hedgecock, P C., Marquedant, R J., Smith, E J., Southwood, D J., and Tsurutani, B T.: The magnetic field investigation on the ULYSSES mission - Instrumentation and preliminary scientific results, Astron. Astrophys.\ Suppl. Ser., 92, 221–236, 1992.; Belcher, J W. and Davis, L.: Large-amplitude Alfvén waves in the interplanetary medium, 2., J Geophys. Res., 76, 3534–3563, 1971.; Dudok de Wit, T.: Can high-order moments be meaningfully...