A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

Combined antiapoptotic and antioxidant approach to acute neuroprotection for stroke in hypertensive rats

We hypothesized that targeting key points in the ischemic cascade with combined neuroglobin (Ngb) overexpression and c-jun N-terminal kinase (JNK) inhibition (SP600125) would offer greater neuroprotection than single treatment after in vitro hypoxia/reoxygenation and in a randomized, blinded in vivo experimental stroke study using a clinically relevant rat strain. Male spontaneously hypertensive stroke-prone rats underwent transient middle cerebral artery occlusion (tMCAO) and were divided into the following groups: tMCAO; tMCAO+control GFP-expressing canine adenovirus-2, CAVGFP; tMCAO+Ngb-expressing CAV-2, CAVNgb; tMCAO+SP600125; tMCAO+CAVNgb+SP600125; or sham procedure. Rats were assessed till day 14 for neurologic outcome before infarct determination. In vitro, combined lentivirus-mediated Ngb overexpression+SP600125 significantly reduced oxidative stress and apoptosis compared with single treatment(s) after hypoxia/reoxygenation in B50 cells. In vivo, infarct volume was significantly reduced by CAVNgb, SP600125, and further by CAVNgb+SP600125. The number of Ngb-positive cells in the peri-infarct cortex and striatum was significantly increased 14 days after tMCAO in animals receiving CAVNgb. Neurologic outcome, measured using a 32-point neurologic score, significantly improved with CAVNgb+SP600125 compared with single treatments at 14 days after tMCAO. Combined Ngb overexpression with JNK inhibition reduced hypoxia/reoxygenation-induced oxidative stress and apoptosis in cultured neurons and reduced infarct and improved neurologic outcome more than single therapy after in vivo experimental stroke in hypertensive rats

Rational Prediction Of Future Pension Expense: A Simulation Approach

Because future pension expense can have a material influence on a firm’s future earnings, financial analysts are faced with the difficult task of forecasting its impact.  The purpose of this paper is to demonstrate a model that can be used with a simulation approach to predict future pension expense and its associated uncertainties.  Because of the importance and complexity of the pension expense component in the estimate of future earnings, a simulation model acts as a powerful analytical tool that can give the analyst greater confidence as to the magnitude and variability of future pension expense

The VLA Galactic Plane Survey

The VLA Galactic Plane Survey (VGPS) is a survey of HI and 21-cm continuum emission in the Galactic plane between longitude 18 degrees 67 degr. with latitude coverage from |b| < 1.3 degr. to |b| < 2.3 degr. The survey area was observed with the Very Large Array (VLA) in 990 pointings. Short-spacing information for the HI line emission was obtained by additional observations with the Green Bank Telescope (GBT). HI spectral line images are presented with a resolution of 1 arcmin x 1 arcmin x 1.56 km/s (FWHM) and rms noise of 2 K per 0.824 km/s channel. Continuum images made from channels without HI line emission have 1 arcmin (FWHM) resolution. VGPS images are compared with images from the Canadian Galactic Plane Survey (CGPS) and the Southern Galactic Plane Survey (SGPS). In general, the agreement between these surveys is impressive, considering the differences in instrumentation and image processing techniques used for each survey. The differences between VGPS and CGPS images are small, < 6 K (rms) in channels where the mean HI brightness temperature in the field exceeds 80 K. A similar degree of consistency is found between the VGPS and SGPS. The agreement we find between arcminute resolution surveys of the Galactic plane is a crucial step towards combining these surveys into a single uniform dataset which covers 90% of the Galactic disk: the International Galactic Plane Survey (IGPS). The VGPS data will be made available on the World Wide Web through the Canadian Astronomy Data Centre (CADC).Comment: Accepted for publication in The Astronomical Journal. 41 pages, 13 figures. For information on data release, colour images etc. see http://www.ras.ucalgary.ca/VGP

A genome-wide association study for genetic susceptibility to Mycobacterium bovis infection in dairy cattle identifies a susceptibility QTL on chromosome 23

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.BACKGROUND: Bovine tuberculosis (bTB) infection in cattle is a significant economic concern in many countries, with annual costs to the UK and Irish governments of approximately €190 million and €63 million, respectively, for bTB control. The existence of host additive and non-additive genetic components to bTB susceptibility has been established. METHODS: Two approaches i.e. single-SNP (single nucleotide polymorphism) regression and a Bayesian method were applied to genome-wide association studies (GWAS) using high-density SNP genotypes (n = 597,144 SNPs) from 841 dairy artificial insemination (AI) sires. Deregressed estimated breeding values for bTB susceptibility were used as the quantitative dependent variable. Network analysis was performed using the quantitative trait loci (QTL) that were identified as significant in the single-SNP regression and Bayesian analyses separately. In addition, an identity-by-descent analysis was performed on a subset of the most prolific sires in the dataset that showed contrasting prevalences of bTB infection in daughters. RESULTS: A significant QTL region was identified on BTA23 (P value >1 × 10(-5), Bayes factor >10) across all analyses. Sires with the minor allele (minor allele frequency = 0.136) for this QTL on BTA23 had estimated breeding values that conferred a greater susceptibility to bTB infection than those that were homozygous for the major allele. Imputation of the regions that flank this QTL on BTA23 to full sequence indicated that the most significant associations were located within introns of the FKBP5 gene. CONCLUSIONS: A genomic region on BTA23 that is strongly associated with host susceptibility to bTB infection was identified. This region contained FKBP5, a gene involved in the TNFα/NFκ-B signalling pathway, which is a major biological pathway associated with immune response. Although there is no study that validates this region in the literature, our approach represents one of the most powerful studies for the analysis of bTB susceptibility to date