Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Kernel Approximation on Manifolds II: The L∞L_{\infty}-norm of the L2L_2-projector

This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the "de Boor conjecture". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\in L_p, 1\le p\le \infty.Comment: 25 pages; minor revision; new proof of Lemma 3.9; accepted for publication in SIAM J. on Math. Ana

Pharmacological Aspects of Vipera xantina palestinae Venom

In Israel, Vipera xantina palestinae (V.x.p.) is the most common venomous snake, accounting for several hundred cases of envenomation in humans and domestic animals every year, with a mortality rate of 0.5 to 2%. In this review we will briefly address the research developments relevant to our present understanding of the structure and function of V.x.p. venom with emphasis on venom disintegrins. Venom proteomics indicated the presence of four families of pharmacologically active compounds: (i) neurotoxins; (ii) hemorrhagins; (iii) angioneurin growth factors; and (iv) different types of integrin inhibitors. Viperistatin, a α1β1selective KTS disintegrin and VP12, a α2β1 selective C-type lectin were discovered. These snake venom proteins represent promising tools for research and development of novel collagen receptor selective drugs. These discoveries are also relevant for future improvement of antivenom therapy towards V.x.p. envenomation

On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems

Imaging Immune and Metabolic Cells of Visceral Adipose Tissues with Multimodal Nonlinear Optical Microscopy

Visceral adipose tissue (VAT) inflammation is recognized as a mechanism by which obesity is associated with metabolic diseases. The communication between adipose tissue macrophages (ATMs) and adipocytes is important to understanding the interaction between immunity and energy metabolism and its roles in obesity-induced diseases. Yet visualizing adipocytes and macrophages in complex tissues is challenging to standard imaging methods. Here, we describe the use of a multimodal nonlinear optical (NLO) microscope to characterize the composition of VATs of lean and obese mice including adipocytes, macrophages, and collagen fibrils in a label-free manner. We show that lipid metabolism processes such as lipid droplet formation, lipid droplet microvesiculation, and free fatty acids trafficking can be dynamically monitored in macrophages and adipocytes. With its versatility, NLO microscopy should be a powerful imaging tool to complement molecular characterization of the immunity-metabolism interface

Motor Vehicle Crashes in Diabetic Patients with Tight Glycemic Control: A Population-based Case Control Analysis

Using a population-based case control analysis, Donald Redelmeier and colleagues found that tighter glycemic control, as measured by the HbA1c, is associated with an increased risk of a motor vehicle crash

ADAM2 Interactions with Mouse Eggs and Cell Lines Expressing α4/α9 (ITGA4/ITGA9) Integrins: Implications for Integrin-Based Adhesion and Fertilization

Integrins are heterodimeric cell adhesion molecules, with 18 α (ITGA) and eight β (ITGB) subunits forming 24 heterodimers classified into five families. Certain integrins, especially the α(4)/α(9) (ITGA4/ITGA9) family, interact with members of the ADAM (a disintegrin and metalloprotease) family. ADAM2 is among the better characterized and also of interest because of its role in sperm function. Having shown that ITGA9 on mouse eggs participates in mouse sperm-egg interactions, we sought to characterize ITGA4/ITGA9-ADAM2 interactions.An anti-β(1)/ITGB1 function-blocking antibody that reduces sperm-egg binding significantly inhibited ADAM2 binding to mouse eggs. Analysis of integrin subunit expression indicates that mouse eggs could express at least ten different integrins, five in the RGD-binding family, two in the laminin-binding family, two in the collagen-binding family, and ITGA9-ITGB1. Adhesion assays to characterize ADAM2 interactions with ITGA4/ITGA9 family members produced the surprising result that RPMI 8866 cell adhesion to ADAM2 was inhibited by an anti-ITGA9 antibody, noteworthy because ITGA9 has only been reported to dimerize with ITGB1, and RPMI 8866 cells lack detectable ITGB1. Antibody and siRNA studies demonstrate that ITGB7 is the β subunit contributing to RPMI 8866 adhesion to ADAM2.These data indicate that a novel integrin α-β combination, ITGA9-ITGB7 (α(9)β(7)), in RPMI 8866 cells functions as a binding partner for ADAM2. ITGA9 had previously only been reported to dimerize with ITGB1. Although ITGA9-ITGB7 is unlikely to be a widely expressed integrin and appears to be the result of "compensatory dimerization" occurring in the context of little/no ITGB1 expression, the data indicate that ITGA9-ITGB7 functions as an ADAM binding partner in certain cellular contexts, with implications for mammalian fertilization and integrin function

Migration-promoting role of VEGF-C and VEGF-C binding receptors in human breast cancer cells

Vascular endothelial growth factor C (VEGF-C) is a lymphangiogenic factor over-expressed in highly metastatic, cyclooxygenase (COX)-2 expressing breast cancer cells. We tested the hypothesis that tumour-derived VEGF-C may play an autocrine role in metastasis by promoting cellular motility through one or more VEGF-C-binding receptors VEGFR-2, VEGFR-3, neuropilin (NRP)-1, NRP-2, and integrin α9β1. We investigated the expression of these receptors in several breast cancer cell lines (MDA-MB-231, Hs578T, SK-BR-3, T-47D, and MCF7) and their possible requirement in migration of two VEGF-C-secreting, highly metastatic lines MDA-MB-231 and Hs578T. While cell lines varied significantly in their expression of above VEGF-C receptors, migratory activity of MDA-MB-231 and Hs578T cells was linked to one or more of these receptors. Depletion of endogenous VEGF-C by treatments with a neutralising antibody, VEGF-C siRNA or inhibitors of Src, EGFR/Her2/neu and p38 MAP kinases which inhibited VEGF-C production, inhibited cellular migration, indicating the requirement of VEGF-C for migratory function. Migration was differentially attenuated by blocking or downregulation of different VEGF-C receptors, for example treatment with a VEGFR-2 tyrosine kinase inhibitor, NRP-1 and NRP-2 siRNA or α9β1 integrin antibody, indicating the participation of one or more of the receptors in cell motility. This novel role of tumour-derived VEGF-C indicates that breast cancer metastasis can be promoted by coordinated stimulation of lymphangiogenesis and enhanced migratory activity of breast cancer cells