Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio

Role of the Transporter Regulator Protein (RS1) in the Modulation of Concentrative Nucleoside Transporters (CNTs) in Epithelia

ABSTRACT SLC28 genes encode three plasma membrane transporter proteins, human concentrative nucleoside transporter (CNT)1, CNT2, and CNT3, all of which are implicated in the uptake of natural nucleosides and a variety of nucleoside analogs used in the chemotherapy of cancer and viral and inflammatory diseases. Mechanisms determining their trafficking toward the plasma membrane are not well known, although this might eventually become a target for therapeutic intervention. The transporter regulator RS1, which was initially identified as a short-term, post-transcriptional regulator of the high-affinity, Na ϩ -coupled, glucose transporter sodium-dependent glucose cotransporter 1, was evaluated in this study as a candidate for coordinate regulation of membrane insertion of human CNTtype proteins. With a combination of studies with mammalian cells, Xenopus laevis oocytes, and RS1-null mice, evidence that RS1 down-regulates the localization and activity at the plasma membrane of the three members of this protein family (CNT1, CNT2, and CNT3) is provided, which indicates the biochemical basis for coordinate regulation of nucleoside uptake ability in epithelia and probably in other RS1-expressing cell types