Longitudinal wave instability in magnetized high correlation dusty plasma

Low frequency longitudinal wave instability in magnetized high correlation dusty plasmas is investigated. The dust charging relaxation is taken into account. It is found that the instablity of wave is determined significantly by the frequency of wave, the dust charging relaxation, the shear viscosity and viscoelastic relaxation time, the coupling parameter of high correlation of dust as well the strength of magnetic field.Comment: 10 pages, No figure

Analysis of Sequential Quadratic Programming through the Lens of Riemannian Optimization

We prove that a "first-order" Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/\kappa_R)^k$, where $\kappa_R$ is the condition number of the Riemannian Hessian, and global convergence with rate $k^{-1/4}$. Our analysis builds on insights from Riemannian optimization -- we show that the SQP and Riemannian gradient methods have nearly identical behavior near the constraint manifold, which could be of broader interest for understanding constrained optimization

Thomson backscattering in combined uniform magnetic and envelope modulating circularly-polarized laser fields

The Thomson backscattering spectra in combined uniform magnetic and cosine-envelope circularly-polarized laser fields are studied in detail. With an introduction of the envelope modulation, the radiation spectra exhibit high complexity attributed to the strong nonlinear interactions. On the other hand, four fundamental laws related to the scale invariance of the radiation spectra are analytically revealed and numerically validated. They are the laws for the radiation energy as the $6$th power of the motion constant exactly, also as the approximate negative $6$th power with respect to the initial axial momentum and laser intensity in a certain of conditions, respectively, and finally an important self-similar law, i.e., when the circular laser frequency, the envelope modulation frequency, and the modified cyclotron frequency are simultaneously increased by a factor, the radiation energy will be increased by the second power of that factor without changing the shape of the spectrum. With the application of these laws, especially the last one, a much higher radiation energy can be obtained and the harmonic at which the maximum radiation occurs can be precisely tuned without changing its amplitude. These findings provide a possible way to advance radiation technology in many fields such as medicine, communications, astrophysics, and security.Comment: 29 pages, 8 figure

Proximal algorithms for constrained composite optimization, with applications to solving low-rank SDPs

We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of such problems exhibit local linear convergence under a quadratic growth condition, which the compositional structure we consider ensures. The main application of our results is to low-rank semidefinite optimization with Burer-Monteiro factorizations. We precisely identify the conditions for quadratic growth in the factorized problem via structures in the semidefinite problem, which could be of independent interest for understanding matrix factorization

Gaia Calibrated UV Luminous Stars in LAMOST

We take advantage of the Gaia data release 2 to present 275 and 1,774 ultraviolet luminous stars in the FUV and the NUV. These stars are 5$\sigma$ exceeding the centers of the reference frame that is built with over one million UV stars in the log $g$ vs $T_\textrm{eff}$ diagram. The Galactic extinction is corrected with the 3D dusty map. In order to limit the Lutz-Kelker effect to an insignificant level, we select the stars with the relative uncertainties of the luminosity less than 40% and the trigonometric parallaxes less than 20%. We cross-identified our sample with the catalogs of RR Lyr stars and possible white dwarf main-sequence binaries, and find they compose $\sim$ 62% and $\sim$ 16% of our sample in the FUV and NUV, respectively. This catalog provides a unique sample to study stellar activity, spectrally unresolved compact main-sequence binaries and variable stars

The Classification of n-Lie Algebras

This paper proves the isomorphic criterion theorem for (n+2)-dimensional n-Lie algebras, and gives a complete classification of (n+1)-dimensional n-Lie algebras and (n+2)-dimensional n-Lie algebras over an algebraically closed field of characteristic zero

Energy-momentum tensor is nonsymmetric for spin-polarized photons

It has been assumed for a century that the energy-momentum tensor of the photon takes a symmetric form, with the renowned Poynting vector assigned as the same density for momentum and energy flow. Here we show that the symmetry of the photon energy-momentum tensor can actually be inferred from the known difference between the diffraction patterns of light with spin and orbital angular momentum, respectively. The conclusion is that the symmetric expression of energy-momentum tensor is denied, and the nonsymmetric canonical expression is favored.Comment: 3 pages, 1 figur

The Landscape of Empirical Risk for Non-convex Losses

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is practically important but still poorly understood. Classical empirical process theory implies uniform convergence of the empirical risk to the population risk. While uniform convergence implies consistency of the resulting M-estimator, it does not ensure that the latter can be computed efficiently. In order to capture the complexity of computing M-estimators, we propose to study the landscape of the empirical risk, namely its stationary points and their properties. We establish uniform convergence of the gradient and Hessian of the empirical risk to their population counterparts, as soon as the number of samples becomes larger than the number of unknown parameters (modulo logarithmic factors). Consequently, good properties of the population risk can be carried to the empirical risk, and we can establish one-to-one correspondence of their stationary points. We demonstrate that in several problems such as non-convex binary classification, robust regression, and Gaussian mixture model, this result implies a complete characterization of the landscape of the empirical risk, and of the convergence properties of descent algorithms. We extend our analysis to the very high-dimensional setting in which the number of parameters exceeds the number of samples, and provide a characterization of the empirical risk landscape under a nearly information-theoretically minimal condition. Namely, if the number of samples exceeds the sparsity of the unknown parameters vector (modulo logarithmic factors), then a suitable uniform convergence result takes place. We apply this result to non-convex binary classification and robust regression in very high-dimension.Comment: This version presents a general framework, and applies it to several statistical learning problem

GIFT: A Real-time and Scalable 3D Shape Search Engine

Projective analysis is an important solution for 3D shape retrieval, since human visual perceptions of 3D shapes rely on various 2D observations from different view points. Although multiple informative and discriminative views are utilized, most projection-based retrieval systems suffer from heavy computational cost, thus cannot satisfy the basic requirement of scalability for search engines. In this paper, we present a real-time 3D shape search engine based on the projective images of 3D shapes. The real-time property of our search engine results from the following aspects: (1) efficient projection and view feature extraction using GPU acceleration; (2) the first inverted file, referred as F-IF, is utilized to speed up the procedure of multi-view matching; (3) the second inverted file (S-IF), which captures a local distribution of 3D shapes in the feature manifold, is adopted for efficient context-based re-ranking. As a result, for each query the retrieval task can be finished within one second despite the necessary cost of IO overhead. We name the proposed 3D shape search engine, which combines GPU acceleration and Inverted File Twice, as GIFT. Besides its high efficiency, GIFT also outperforms the state-of-the-art methods significantly in retrieval accuracy on various shape benchmarks and competitions.Comment: accepted by CVPR16, achieved the first place in Shrec2016 competition: Large-Scale 3D Shape Retrieval under the perturbed cas

Effects of finite spatial extent on Schwinger pair production

Electron-positron pair production from vacuum in external electric fields with space and time dependencies is studied numerically using real time Dirac-Heisenberg-Wigner formalism. The influence of spatial focusing scale of the electric field on momentum distribution and the total yield of the particles is examined by considering standing wave mode of the electric field with different temporal configurations. With the decrease of spatial extent of the external field, signatures of the temporal field are weaken in the momentum spectrum. Moreover, in the extremely small spatial extent, novel features emerge due to the combined effects of both temporal and spatial variations. We also find that for dynamically assisted particle production, while the total particle yield drops significantly in small spatial extents, the assistance mechanism tends to increase in these highly inhomogeneous regimes, where the slow and fast pulses are affected differently by the overall spatial inhomogeneity.Comment: 18 pages, 6 fugure