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

Bone morphogenetic proteins, breast cancer, and bone metastases: striking the right balance

Bone morphogenetic proteins (BMPs) belong to the TGF-β super family, and are essential for regulation of foetal development, tissue differentiation and homeostasis, and a multitude of cellular functions. Naturally, this has led to the exploration of aberrance in this highly regulated system as a key factor in tumourigenesis. Originally identified for their role in osteogenesis and bone turnover, attention has been turned to the potential role of BMPs in tumour metastases to, and progression within, the bone niche. This is particularly pertinent to breast cancer, which commonly metastasises to bone, and in which studies have revealed aberrations of both BMP expression and signalling which correlate clinically with breast cancer progression. Ultimately a BMP profile could provide new prognostic disease markers. As the evidence suggests a role for BMPs in regulating breast tumour cellular function, in particular interactions with tumour stroma and the bone metastatic microenvironment, there may be novel therapeutic potential in targeting BMP signalling in breast cancer. This review provides an update on the current knowledge of BMP abnormalities and their implication in the development and progression of breast cancer, particularly in the disease specific bone metastasis