arXiv subjects
Publications and source records attributed to Ying Tan.
Benchmarking is key for developing and comparing optimization algorithms. In this paper, a CUDA-based real parameter optimization benchmark (cuROB) is introduced. Test functions of diverse properties are included within cuROB and implemented efficiently with CUDA. Speedup of one order of magnitude can be achieved in comparison with CPU-based benchmark of CEC'14.
This paper proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an equilibrium. We extend the methods of constructing of Lyapunov functions for ordinary differential equations on $\mathds{R}^{n}$ to dynamical systems defined on Riemannian manifolds by employing the differential geometry. By employing the derived properties of Lyapunov functions, we obtained the stability of perturbed dynamical systems on Riemannian manifolds. The results are obtained by employing the notions of normal neighborhoods, the injectivity radius on Riemannian manifolds and existence of bump functions on manifolds.
This paper presents an averaging method for nonlinear systems defined on Riemannian manifolds. We extend closeness of solutions results for ordinary differential equations on $R^{n}$ to dynamical systems defined on Riemannian manifolds by employing differential geometry. A generalization of closeness of solutions for periodic dynamical systems on compact time intervals is derived for dynamical systems evolving on compact Riemannian manifolds. Under local asymptotic (exponential) stability of the average vector field, we further relax the compactness of the ambient Riemannian manifold and obtain the closeness of solutions on the infinite time interval by employing the notion of uniform normal neighborhoods of an equilibrium point of a vector field. These results are also presented for time-varying dynamical systems where their averaged systems are almost globally asymptotically or exponentially stable on compact manifolds. The main results of the paper are illustrated by several examples.
We present XMM-Newton spectra of the Seyfert 2 Galaxy IRAS 00521-7054. A strong feature at ~6 keV (observer's frame) can be formally fitted with a strong (EW=1.3+-0.3 keV in the rest frame) and broad Fe Ka line, extending down to 3 keV. The underlying X-ray continuum could be fitted with an absorbed powerlaw (with Gamma = 1.8+-0.2 and N_H = 5.9 x 10^22 cm^-2) plus a soft component. If due to relativistically smeared reflection by an X-ray illuminated accretion disk, the spin of the supermassive black hole is constrained to be 0.97^+0.03_-0.13 (errors at 90% confidence level for one interesting parameter), and the accretion system is viewed at an inclination angle of 37+-4 degree. This would be the first type 2 AGN reported with strong red Fe Ka wing detected which demands a fast rotating SMBH. The unusually large EW would suggest that the light bending effect is strong in this source. Alternatively, the spectra could be fitted by a dual absorber model (though with a global chi^2 higher by ~ 6 for 283 d.o.f) with N_H1 = 7.0 x 10^22 cm^-2 covering 100% of the X-ray source, and N_H2 = 21.7 x 10^22 cm^-2 covering 71%, which does not require an extra broad Fe Ka line.
X-ray unabsorbed Seyfert 2 galaxies appear to have X-ray absorption column densities that are too low (NH < 10^22 cm-2) to explain the absence of broad emission lines in their optical spectra, challenging the standard AGN unification model. In this paper we report Suzaku exposure on the X-ray unabsorbed Seyfert 2 galaxy IRAS F01475-0740, in which a hidden broad line region was detected through spectropolarimetric observation. The X-ray data show rapid and significant variations on time scales down to 5 ks, indicating that we are viewing its central engine directly. A newly obtained optical spectrum and previous optical/X-ray data suggest that state transition is unlikely in this source. These make IRAS F01475-0740 a very peculiar X-ray unabsorbed Seyfert 2 galaxy which can only be explained by absorption from materials with abnormally high dust-to-gas ratio (by a factor of > 4 larger than Galactic). This is in contrast to most AGNs, which typically show dust-to-gas ratios 3 - 100 times lower than the Galactic.