Checking the validity of truncating the cumulant hierarchy description of a small system

We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and derived an infinite hierarchy of differential equations for the cumulant moments. They focused on the behavior of infinite size systems using a strategy based on truncating the hierarchy. In this work we explore the reliability of such an approach to describe systems with a small number of elements. We carry out an extensive numerical analysis of the truncated hierarchy as well as numerical simulations of the full set of Langevin equations governing the dynamics. We find that the results provided by the truncated hierarchy for finite systems are at variance with those of the Langevin simulations for large regions of parameter space. The truncation of the hierarchy leads to a dependence on initial conditions and to the coexistence of states which are not consistent with the theoretical expectations based on the multidimensional linear Fokker-Planck equation for finite arrays

Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

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

Temperature-driven single-valley Dirac fermions in HgTe quantum wells

We report on temperature-dependent magnetospectroscopy of two HgTe/CdHgTe quantum wells below and above the critical well thickness $d_c$. Our results, obtained in magnetic fields up to 16 T and temperature range from 2 K to 150 K, clearly indicate a change of the band-gap energy with temperature. The quantum well wider than $d_c$ evidences a temperature-driven transition from topological insulator to semiconductor phases. At the critical temperature of 90 K, the merging of inter- and intra-band transitions in weak magnetic fields clearly specifies the formation of gapless state, revealing the appearance of single-valley massless Dirac fermions with velocity of $5.6\times10^5$ m$\times$s$^{-1}$. For both quantum wells, the energies extracted from experimental data are in good agreement with calculations on the basis of the 8-band Kane Hamiltonian with temperature-dependent parameters.Comment: 5 pages, 3 figures and Supplemental Materials (4 pages

Vaccination Targeting a Surface Sialidase of P. acnes: Implication for New Treatment of Acne Vulgaris

BACKGROUND: Acne vulgaris afflicts more than fifty million people in the United State and the severity of this disorder is associated with the immune response to Propionibacterium acnes (P. acnes). Systemic therapies for acne target P. acnes using antibiotics, or target the follicle with retinoids such as isotretinoin. The latter systemic treatment is highly effective but also carries a risk of side effects including immune imbalance, hyperlipidemia, and teratogenicity. Despite substantial research into potential new therapies for this common disease, vaccines against acne vulgaris are not yet available. METHODS AND FINDINGS: Here we create an acne vaccine targeting a cell wall-anchored sialidase of P. acnes. The importance of sialidase to disease pathogenesis is shown by treatment of a human sebocyte cell line with recombinant sialidase that increased susceptibility to P. acnes cytotoxicity and adhesion. Mice immunized with sialidase elicit a detectable antibody; the anti-sialidase serum effectively neutralized the cytotoxicity of P. acnes in vitro and P. acnes-induced interleukin-8 (IL-8) production in human sebocytes. Furthermore, the sialidase-immunized mice provided protective immunity against P. acnes in vivo as this treatment blocked an increase in ear thickness and release of pro-inflammatory macrophage inflammatory protein (MIP-2) cytokine. CONCLUSIONS: Results indicated that acne vaccines open novel therapeutic avenues for acne vulgaris and other P. acnes-associated diseases

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

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