Low-distortion Subspace Embeddings in Input-sparsity Time and Applications to Robust Linear Regression

Low-distortion embeddings are critical building blocks for developing random sampling and random projection algorithms for linear algebra problems. We show that, given a matrix $A \in \R^{n \times d}$ with $n \gg d$ and a $p \in [1, 2)$, with a constant probability, we can construct a low-distortion embedding matrix \Pi \in \R^{O(\poly(d)) \times n} that embeds \A_p, the $\ell_p$ subspace spanned by $A$'s columns, into (\R^{O(\poly(d))}, \| \cdot \|_p); the distortion of our embeddings is only O(\poly(d)), and we can compute $\Pi A$ in O(\nnz(A)) time, i.e., input-sparsity time. Our result generalizes the input-sparsity time $\ell_2$ subspace embedding by Clarkson and Woodruff [STOC'13]; and for completeness, we present a simpler and improved analysis of their construction for $\ell_2$. These input-sparsity time $\ell_p$ embeddings are optimal, up to constants, in terms of their running time; and the improved running time propagates to applications such as $(1\pm \epsilon)$-distortion $\ell_p$ subspace embedding and relative-error $\ell_p$ regression. For $\ell_2$, we show that a $(1+\epsilon)$-approximate solution to the $\ell_2$ regression problem specified by the matrix $A$ and a vector $b \in \R^n$ can be computed in O(\nnz(A) + d^3 \log(d/\epsilon) /\epsilon^2) time; and for $\ell_p$, via a subspace-preserving sampling procedure, we show that a $(1\pm \epsilon)$-distortion embedding of \A_p into \R^{O(\poly(d))} can be computed in O(\nnz(A) \cdot \log n) time, and we also show that a $(1+\epsilon)$-approximate solution to the $\ell_p$ regression problem $\min_{x \in \R^d} \|A x - b\|_p$ can be computed in O(\nnz(A) \cdot \log n + \poly(d) \log(1/\epsilon)/\epsilon^2) time. Moreover, we can improve the embedding dimension or equivalently the sample size to $O(d^{3+p/2} \log(1/\epsilon) / \epsilon^2)$ without increasing the complexity.Comment: 22 page

A recombinant Fasciola gigantica 14-3-3 epsilon protein (rFg14-3-3e) modulates various functions of goat peripheral blood mononuclear cells

Background The molecular structure of Fasciola gigantica 14-3-3 protein has been characterized. However, the involvement of this protein in parasite pathogenesis remains elusive and its effect on the functions of innate immune cells is unknown. We report on the cloning and expression of a recombinant F. gigantica 14-3-3 epsilon protein (rFg14-3-3e), and testing its effects on specific functions of goat peripheral blood mononuclear cells (PBMCs). Methods rFg14-3-3e protein was expressed in Pichia pastoris. Western blot and immunofluorescence assay (IFA) were used to examine the reactivity of rFg14-3-3e protein to anti-F. gigantica and anti-rFg14-3-3e antibodies, respectively. Various assays were used to investigate the stimulatory effects of the purified rFg14-3-3e protein on specific functions of goat PBMCs, including cytokine secretion, proliferation, migration, nitric oxide (NO) production, phagocytosis, and apoptotic capabilities. Potential protein interactors of rFg14-3-3e were identified by querying the databases Intact, String, BioPlex and BioGrid. A Total Energy analysis of each of the identified interaction was performed. Gene Ontology (GO) enrichment analysis was conducted using Funcassociate 3.0. Results Sequence analysis revealed that rFg14-3-3e protein had 100% identity to 14-3-3 protein from Fasciola hepatica. Western blot analysis showed that rFg14-3-3e protein is recognized by sera from goats experimentally infected with F. gigantica and immunofluorescence staining using rat anti-rFg14-3-3e antibodies demonstrated the specific binding of rFg14-3-3e protein to the surface of goat PBMCs. rFg14-3-3e protein stimulated goat PBMCs to produce interleukin-10 (IL-10) and transforming growth factor beta (TGF-β), corresponding with low levels of IL-4 and interferon gamma (IFN-γ). Also, this recombinant protein promoted the release of NO and cell apoptosis, and inhibited the proliferation and migration of goat PBMCs and suppressed monocyte phagocytosis. Homology modelling revealed 65% identity between rFg14-3-3e and human 14-3-3 protein YWHAE. GO enrichment analysis of the interacting proteins identified terms related to apoptosis, protein binding, locomotion, hippo signalling and leukocyte and lymphocyte differentiation, supporting the experimental findings. Conclusions Our data suggest that rFg14-3-3e protein can influence various cellular and immunological functions of goat PBMCs in vitro and may be involved in mediating F. gigantica pathogenesis. Because of its involvement in F. gigantica recognition by innate immune cells, rFg14-3-3e protein may have applications for development of diagnostics and therapeutic interventions

The pervasive effects of recombinant Fasciola gigantica Ras-related protein Rab10 on the functions of goat peripheral blood mononuclear cells

Background: Fasciola gigantica-induced immunomodulation is a major hurdle faced by the host for controlling infection. Here, we elucidated the role of F. gigantica Ras-related protein Rab10 (FgRab10) in the modulation of key functions of peripheral blood mononuclear cells (PBMCs) of goats.Methods: We cloned and expressed recombinant FgRab10 (rFgRab10) protein and examined its effects on several functions of goat PBMCs. Protein interactors of rFgRab10 were predicted in silico by querying the databases Intact, String, BioPlex and BioGrid. In addition, a total energy analysis of each of the identified interactions was also conducted. Gene Ontology (GO) enrichment analysis was carried out using FuncAssociate 3.0.Results: The FgRab10 gene (618 bp), encodes 205-amino-acid residues with a molecular mass of ~23 kDa, had complete nucleotide sequence homology with F. hepatica Ras family protein gene (PIS87503.1). The rFgRab10 protein specifically cross-reacted with anti-Fasciola antibodies as shown by Western blot and immunofluorescence analysis. This protein exhibited multiple effects on goat PBMCs, including increased production of cytokines [interleukin-2 (IL-2), IL-4, IL-10, transforming growth factor beta (TGF-β) and interferon gamma (IFN-γ)] and total nitric oxide (NO), enhancing apoptosis and migration of PBMCs, and promoting the phagocytic ability of monocytes. However, it significantly inhibited cell proliferation. Homology modelling revealed 63% identity between rFgRab10 and human Rab10 protein (Uniprot ID: P61026). Protein interaction network analysis revealed more stabilizing interactions between Rab proteins geranylgeranyltransferase component A 1 (CHM) and Rab proteins geranylgeranyltransferase component A 2 (CHML) and rFgRab10 protein. Gene Ontology analysis identified RabGTPase mediated signaling as the most represented pathway.Conclusions: rFgRab10 protein exerts profound influences on various functions of goat PBMCs. This finding may help explain why F. gigantica is capable of provoking recognition by host immune cells, less capable of destroying this successful parasite

The past, present, and future of the Brain Imaging Data Structure (BIDS)

The Brain Imaging Data Structure (BIDS) is a community-driven standard for the organization of data and metadata from a growing range of neuroscience modalities. This paper is meant as a history of how the standard has developed and grown over time. We outline the principles behind the project, the mechanisms by which it has been extended, and some of the challenges being addressed as it evolves. We also discuss the lessons learned through the project, with the aim of enabling researchers in other domains to learn from the success of BIDS