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

Domain wall brane in a reduced Born-Infeld-f(T)f(T) theory

The Born-Infeld $f(T)$ theory is reduced from the Born-Infeld determinantal gravity in Weitzenb\"ock spacetime. We investigate a braneworld scenario in this theory and obtain an analytic domain wall solution by utilizing the first-order formalism. The model is stable against the linear tensor perturbation. It is shown that the massless graviton is localized on the brane, but the continuous massive gravitons are non-localized and will generate a tiny correction with the behavior of ${1}/{(k r)^{3}}$ to the Newtonian potential. The four-dimensional teleparallel gravity is recovered as an effective infrared theory on the brane. As a physical application, we consider the (quasi-)localization property of spin-1/2 Dirac fermion in this model.Comment: 9 pages, 2 figures, published versio

Kidins220 and tumour development: Insights into a complexity of cross-talk among signalling pathways (Review)

The mechanistic complexes of kinase D-interacting substrate of 220 kDa/ankyrin repeat-rich membrane spanning (Kidins220/ARMS) bind and integrate a variety of cellular cues to mediate neuronal activities such as neuronal differentiation, survival, and cytoskeleton remodelling by interacting with a variety of binding partners. Accumulated evidence has also indicated its role in the regulation of vascular development. Mice with Kidins220 knockdown phenotypically present with cardiovascular abnormalities. Kidins220 also contributes to immunomodulation in combination with B cells and T cells. Moreover, emerging evidence has revealed that this protein regulates many crucial cellular processes and thus has been implicated in an increasing number of malignancies. Here, we review recent advances in our understanding of Kidins220 and its role in cancer development. Further investigation is warranted to shed light on the role played by Kidins220 in the dynamic arrangement of the cytoskeleton and epithelial–mesenchymal transition, and its implication in tumourigenesis and cancer progression

Studies on Gas-phase Cyclometalations of [ArNi(PPh3)n]+ (n = 1 or 2) by Electrospray Ionization Tandem Mass Spectrometry

Gas-phase cyclometalation of [ArNi(PPh3)n]+ (n = 1, 2) complexes have been studied by ESI-MS/MS. The electron-donating substituents of aromatic iodides in the para position were found to inhibit the cyclometalation process of losing ArH, while the electron-withdrawing substituents in the para position were found to enhance it. These results indicate that the cyclometalation process of losing ArH is favored by electron-deficient aromatic groups. In addition, the detailed dissociation pathways of the cationic nickel complexes were studied, and among these pathways, the process of aryl-aryl interchange was also found to proceed in ESI-MS/MS

A new modified Newton iteration for computing nonnegative Z-eigenpairs of nonnegative tensors

We propose a new modification of Newton iteration for finding some nonnegative Z-eigenpairs of a nonnegative tensor. The method has local quadratic convergence to a nonnegative eigenpair of a nonnegative tensor, under the usual assumption guaranteeing the local quadratic convergence of the original Newton iteration