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

Symmetric spaces of higher rank do not admit differentiable compactifications

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.Comment: 13 pages, to appear in Mathematische Annale

Assessing the impact of silicon nanowires on bacterial transformation and viability of Escherichia coli

We investigated the biomaterial interface between the bacteria Escherichia coli DH5α and silicon nanowire patterned surfaces. We optimised the engineering of silicon nanowire coated surfaces using metal-assisted chemical etching. Using a combination of focussed ion beam scanning electron microscopy, and cell viability and transformation assays, we found that with increasing interfacing force, cell viability decreases, as a result of increasing cell rupture. However, despite this aggressive interfacing regime, a proportion of the bacterial cell population remains viable. We found that the silicon nanowires neither resulted in complete loss of cell viability nor partial membrane disruption and corresponding DNA plasmid transformation. Critically, assay choice was observed to be important, as a reduction-based metabolic reagent was found to yield false-positive results on the silicon nanowire substrate. We discuss the implications of these results for the future design and assessment of bacteria–nanostructure interfacing experiments

Bacterial toxin-triggered release of antibiotics from capsosomes protects a fly model from lethal methicillin-resistant Staphylococcus aureus (MRSA) infection

Antibiotic resistance is a severe global health threat and hence demands rapid action to develop novel therapies, including microscale drug delivery systems. Herein, a hierarchical microparticle system is developed to achieve bacteria-activated single- and dual-antibiotic drug delivery for preventing methicillin-resistant Staphylococcus aureus (MRSA) bacterial infections. The designed system is based on a capsosome structure, which consists of a mesoporous silica microparticle coated in alternating layers of oppositely charged polymers and antibiotic-loaded liposomes. The capsosomes are engineered and shown to release their drug payloads in the presence of MRSA toxins controlled by the Agr quorum sensing system. MRSA-activated single drug delivery of vancomycin and synergistic dual delivery of vancomycin together with an antibacterial peptide successfully kills MRSA in vitro. The capability of capsosomes to selectively deliver their cargo in the presence of bacteria, producing a bactericidal effect to protect the host organism, is confirmed in vivo using a Drosophila melanogaster MRSA infection model. Thus, the capsosomes serve as a versatile multidrug, subcompartmentalized microparticle system for preventing antibiotic-resistant bacterial infections, with potential applications to protect wounds or medical device implants from infections

Nodal discontinuous Galerkin methods on graphics processors

Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy without compromising simulation stability. Lately, another property of DG has been growing in importance: The majority of a DG operator is applied in an element-local way, with weak penalty-based element-to-element coupling. The resulting locality in memory access is one of the factors that enables DG to run on off-the-shelf, massively parallel graphics processors (GPUs). In addition, DG's high-order nature lets it require fewer data points per represented wavelength and hence fewer memory accesses, in exchange for higher arithmetic intensity. Both of these factors work significantly in favor of a GPU implementation of DG. Using a single US$400 Nvidia GTX 280 GPU, we accelerate a solver for Maxwell's equations on a general 3D unstructured grid by a factor of around 50 relative to a serial computation on a current-generation CPU. In many cases, our algorithms exhibit full use of the device's available memory bandwidth. Example computations achieve and surpass 200 gigaflops/s of net application-level floating point work. In this article, we describe and derive the techniques used to reach this level of performance. In addition, we present comprehensive data on the accuracy and runtime behavior of the method. (C) 2009 Elsevier Inc. All rights reserved

A population of high-redshift type-2 quasars-II. Radio Properties

We present multi-frequency radio observations of a sample of z~2 obscured (type-2) quasars in the Spitzer extragalactic First Look Survey area. We combine the public data at 1.4 GHz, used in the selection of these sources, with new observations at 610 MHz (GMRT) and at 4.9 GHz (VLA). We find the sample includes sources with steep, flat and gigahertz-peaked spectra. There are no strong correlations between the presence or absence of emission lines in the optical spectra and the radio spectral properties of the sample. However, there are no secure flat-spectrum type-2 quasars with narrow emission lines which would be problematic for unified schemes. Most of the population have straight radio spectra with spectral index alpha~1 as is expected for developed, potentially FRI-like, jets in which continous injection of relativistic electrons is accompanied by inverse-Compton losses against the cosmic microwave background.Comment: 6 pages, 2 colour figures, submitted to MNRA

MESMER: MeerKAT Search for Molecules in the Epoch of Reionization

[Abridged] Observations of molecular gas at all redshifts are critical for measuring the cosmic evolution in molecular gas density and understanding the star-formation history of the Universe. The 12CO molecule (J=1-0 transition = 115.27 GHz) is the best proxy for extragalactic H2, which is the gas reservoir from which star formation occurs, and has been detected out to z~6. Typically, redshifted high-J lines are observed at mm-wavelengths, the most commonly targeted systems exhibiting high SFRs (e.g. submm galaxies), and far-IR-bright QSOs. While the most luminous objects are the most readily observed, detections of more typical galaxies with modest SFRs are essential for completing the picture. ALMA will be revolutionary in terms of increasing the detection rate and pushing the sensitivity limit down to include such galaxies, however the limited FoV when observing at such high frequencies makes it difficult to use ALMA for studies of the large-scale structure traced out by molecular gas in galaxies. This article introduces a strategy for a systematic search for molecular gas during the EoR (z~7 and above), capitalizing on the fact that the J=1-0 transition of 12CO enters the upper bands of cm-wave instruments at high-z. The FoV advantage gained by observing at such frequencies, coupled with modern broadband correlators allows significant cosmological volumes to be probed on reasonable timescales. In this article we present an overview of our future observing programme which has been awarded 6,500 hours as one of the Large Survey Projects for MeerKAT, the forthcoming South African SKA pathfinder instrument. Its large FoV and correlator bandwidth, and high-sensitivity provide unprecedented survey speed for such work. An existing astrophysical simulation is coupled with instrumental considerations to demonstrate the feasibility of such observations and predict detection rates.Comment: 7 pages, 4 figures, to appear in the proceedings of "Astronomy with megastructures: Joint science with the E-ELT and SKA", 10-14 May 2010, Crete, Greece (Eds: Isobel Hook, Dimitra Rigopoulou, Steve Rawlings and Aris Karastergiou

Controlled dendrimersome nanoreactor system for localised hypochlorite-induced killing of bacteria

Antibiotic resistance is a serious global health problem necessitating new bactericidal approaches such as nanomedicines. Dendrimersomes (DSs) have recently become a valuable alternative nanocarrier to polymersomes and liposomes due to their molecular definition and synthetic versatility. Despite this, their biomedical application is still in its infancy. Inspired by the localized antimicrobial function of neutrophil phagosomes and the versatility of DSs, a simple three-component DS-based nanoreactor with broad-spectrum bactericidal activity is presented. This was achieved by encapsulation of glucose oxidase (GOX) and myeloperoxidase (MPO) within DSs (GOX-MPO-DSs), self-assembled from an amphiphilic Janus dendrimer, that possesses a semipermeable membrane. By external addition of glucose to GOX-MPO-DS, the production of hypochlorite (−OCl), a highly potent antimicrobial, by the enzymatic cascade was demonstrated. This cascade nanoreactor yielded a potent bactericidal effect against two important multidrug resistant pathogens, Staphylococcus aureus (S. aureus) and Pseudomonas aeruginosa (P. aeruginosa), not observed for H2O2 producing nanoreactors, GOX-DS. The production of highly reactive species such as –OCl represents a harsh bactericidal approach that could also be cytotoxic to mammalian cells. This necessitates the development of strategies for activating –OCl production in a localized manner in response to a bacterial stimulus. One option of locally releasing sufficient amounts of substrate using a bacterial trigger (released toxins) was demonstrated with lipidic glucose-loaded giant unilamellar vesicles (GUVs), envisioning, e.g., implant surface modification with nanoreactors and GUVs for localized production of bactericidal agents in the presence of bacterial growth

Epidermal Growth Factor–PEG Functionalized PAMAM-Pentaethylenehexamine Dendron for Targeted Gene Delivery Produced by Click Chemistry

Aim of this study was the site-specific conjugation of an epidermal growth factor (EGF)-polyethylene glycol (PEG) chain by click chemistry onto a poly(amido amine) (PAMAM) dendron, as a key step toward defined multifunctional carriers for targeted gene delivery. For this purpose, at first propargyl amine cored PAMAM dendrons with ester ends were synthesized. The chain terminal ester groups were then modified by oligoamines with different secondary amino densities. The oligoamine-modified PAMAM dendrons were well biocompatible, as demonstrated in cytotoxicity assays. Among the different oligoamine-modified dendrons, PAMAM-pentaethylenehexamine (PEHA) dendron polyplexes displayed the best gene transfer ability. Conjugation of PAMAM-PEHA dendron with PEG spacer was conducted via click reaction, which was performed before amidation with PEHA. The resultant PEG-PAMAM-PEHA copolymer was then coupled with EGF ligand. pDNA transfections in HuH-7 hepatocellular carcinoma cells showed a 10-fold higher efficiency with the polyplexes containing conjugated EGF as compared to the ligand-free ones, demonstrating the concept of ligand targeting. Overall gene transfer efficiencies, however, were moderate, suggesting that additional measures for overcoming subsequent intracellular bottlenecks in delivery have to be taken