An Efficient Algorithm by Kurtosis Maximization in Reference-Based Framework

This paper deals with the optimization of kurtosis for complex-valued signals in the independent component analysis (ICA) framework, where source signals are linearly and instantaneously mixed. Inspired by the recently proposed reference-based contrast schemes, a similar contrast function is put forward, based on which a new fast fixed-point (FastICA) algorithm is proposed. The new optimization method is similar in spirit to the former classical kurtosis-based FastICA algorithm but differs in the fact that it is much more efficient than the latter in terms of computational speed, which is significantly striking with large number of samples. The performance of this new algorithm is confirmed through computer simulations

Generalized r-matrix structure and algebro-geometric solution for integrable systems

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure. All these nonlinear systems have {\it r}-matrices, and are completely integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure

Calibration of LAMOST Stellar Surface Gravities Using the Kepler Asteroseismic Data

Asteroseismology is a powerful tool to precisely determine the evolutionary status and fundamental properties of stars. With the unprecedented precision and nearly continuous photometric data acquired by the NASA Kepler mission, parameters of more than 10$^4$ stars have been determined nearly consistently. However, most studies still use photometric effective temperatures (Teff) and metallicities ([Fe/H]) as inputs, which are not sufficiently accurate as suggested by previous studies. We adopted the spectroscopic Teff and [Fe/H] values based on the LAMOST low-resolution spectra (R~1,800), and combined them with the global oscillation parameters to derive the physical parameters of a large sample of stars. Clear trends were found between {\Delta}logg(LAMOST - seismic) and spectroscopic Teff as well as logg, which may result in an overestimation of up to 0.5 dex for the logg of giants in the LAMOST catalog. We established empirical calibration relations for the logg values of dwarfs and giants. These results can be used for determining the precise distances to these stars based on their spectroscopic parameters.Comment: 22 pages, 13 figures and 3 tables, accepted for publication in Astronomical Journal. Table 3 is available at http://lwang.info/research/kepler_lamost

Spectral scaling of the Leray-α\alpha model for two-dimensional turbulence

We present data from high-resolution numerical simulations of the Navier-Stokes-$\alpha$ and the Leray-$\alpha$ models for two-dimensional turbulence. It was shown previously (Lunasin et al., J. Turbulence, 8, (2007), 751-778), that for wavenumbers $k$ such that $k\alpha\gg 1$, the energy spectrum of the smoothed velocity field for the two-dimensional Navier-Stokes-$\alpha$ (NS-$\alpha$) model scales as $k^{-7}$. This result is in agreement with the scaling deduced by dimensional analysis of the flux of the conserved enstrophy using its characteristic time scale. We therefore hypothesize that the spectral scaling of any $\alpha$-model in the sub-$\alpha$ spatial scales must depend only on the characteristic time scale and dynamics of the dominant cascading quantity in that regime of scales. The data presented here, from simulations of the two-dimensional Leray-$\alpha$ model, confirm our hypothesis. We show that for $k\alpha\gg 1$, the energy spectrum for the two-dimensional Leray-$\alpha$ scales as $k^{-5}$, as expected by the characteristic time scale for the flux of the conserved enstrophy of the Leray-$\alpha$ model. These results lead to our conclusion that the dominant directly cascading quantity of the model equations must determine the scaling of the energy spectrum.Comment: 11 pages, 4 figure

Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001

Аналіз особливостей носіїв маркетингових комунікацій на підприємствах послуг мобільного зв’язку України

У статті проаналізовано інструментарій маркетингових комунікацій, що застосовують підприємства послуг мобільного зв’язку України. Розглянуто не традиційні носії інструментів інтегрованих маркетингових комунікацій.The tool of marketing communications that apply the enterprises of services of mobile communication of Ukraine is analysed in the article. The not traditional carriers of instruments of the integrated marketing communications are considered