Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation

Processing streaming data as they arrive is often necessary for high dimensional data analysis. In this paper, we analyse the convergence of a subspace online PCA iteration, as a followup of the recent work of Li, Wang, Liu, and Zhang [Math. Program., Ser. B, DOI 10.1007/s10107-017-1182-z] who considered the case for the most significant principal component only, i.e., a single vector. Under the sub-Gaussian assumption, we obtain a finite-sample error bound that closely matches the minimax information lower bound of Vu and Lei [Ann. Statist. 41:6 (2013), 2905-2947].Comment: 37 page

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer $k$. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index $k$ of the background black hole metric, which shows that a larger $k$ makes it harder for the condensation to form. We also observe that the index $k$ affects the conductivity and the gap frequency of the holographic superconductors.Comment: 14 pages, 6 figure

Antiretroviral Therapy Initiation Following Policy Changes: Observations From China.

China's HIV/AIDS treatment policies have been evolving over the preceding decade. This study describes patterns of antiretroviral therapy (ART) initiation for a sample of people living with HIV/AIDS (PLHIV) in rural Anhui, China, where most PLHIV were infected via paid plasma donation during the 1990s. A total of 481 PLHIV who were receiving ART were included in our analyses. Times between HIV diagnosis and the initiation of ART were examined relative to the time points when major ART-related policies changed in China. More than half (53%) of PLHIV who had been diagnosed by 2003 received ART within 6 months, whereas 93% of PLHIV who had been diagnosed in 2010 or later received ART within 6 months. The study results provide additional support that the "Four Frees and One Care" policy in 2003 and the relaxation of ART eligibility in 2010 have facilitated the initiation of treatment for PLHIV in China

Designing Digital Games for Reflecting the Performance of Dynamic Balance

Digital games have been applied to study the performance of human dynamic balance. However, how to design the balance games, or how the mechanics of games affect the performance of dynamic balance are still lack of research reports. This study developed a serial of game prototypes to explore the design principles of balance games. The experimental results show that when a balance game is designed, if the moving of object under control is more predictable, the moving of player's weight center is more regular, and the game has suitable challenge designed, the player’s ability of dynamic balance can be more correlated to the game scores

Convex Quadratic Equations and Functions

Three interconnected main results (1)-(3) are presented in closed forms. (1) Regarding the convex quadratic equation (CQE), an analytical equivalent solvability condition and parameterization of all solutions are completely formulated, in a unified framework. The design concept is based on the matrix algebra, while facilitated by a novel equivalence/coordinate transformation. Notably, the parameter-solution bijection is also verified. Two applications are selected as the other two main results. (2) The focus is set on both the infinite and finite-time horizon nonlinear optimal control. By virtue of (1), the CQEs associated with the underlying Hamilton-Jacobi Equation, Hamilton-Jacobi Inequality, and Hamilton-Jacobi-Bellman Equation are algebraically solved, respectively. Each solution set captures the gradient of the associated value function. Moving forward, a preliminary to recover the optimality using the state-dependent (differential) Riccati equation is provided, which can also be used to more efficiently implement the last main result. (3) The nonlinear programming/convex optimization is analyzed via a novel method and perspective. The philosophy is based on the new analysis of CQE in (1), which helps explain the geometric structure of the convex quadratic function (CQF), and the CQE-CQF relation. An impact on the quadratic programming (QP), a basis in the literature, is demonstrated. Specifically, the QPs subject to equality, inequality, equality-and-inequality, and extended constraints are algebraically solved, resp., without knowing a feasible point.Comment: This manuscript is only preliminary and still growing. Therefore, with expectations, we deeply appreciate all kinds of input

First R and I Lights and Their Photometric Analyses of GSC 02393-00680

We obtained complete $R$ and $I$ light curves of GSC 02393-00680 in 2008 and analyzed them with the 2003 version of the W-D code. It is shown that GSC 02393-00680 is a W-type shallow contact binary system with a high mass ratio $q=1.600$ and a degree of contact factor $f=5.0$. It will be a good example to check up on the TRO theory. A period investigation based on all available data suggests that the system has a small-amplitude period oscillation ($A_3=0.^{d}0030$; $T_3=1.92$years). This may indicate it has a moderate mass close third body, which is similar to XY Leo