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

The radio remnant of SN1993J: an instrumental explanation for the evolving complex structure

We present simulated images of Supernova 1993J at 8.4 GHz using Very Long Baseline Interferometry (VLBI) techniques. A spherically symmetric source model is convolved with realistic uv-plane distributions, together with standard imaging procedures, to assess the extent of instrumental effects on the recovered brightness distribution. In order to facilitate direct comparisons between the simulations and published VLBI images of SN1993J, the observed uv-coverage is determined from actual VLBI observations made in the years following its discovery. The underlying source model only exhibits radial variation in its density profile, with no azimuthal dependence and, even though this model is morphologically simple, the simulated VLBI observations qualitatively reproduce many of the azimuthal features of the reported VLBI observations, such as appearance and evolution of complex azimuthal structure and apparent rotation of the shell. We demonstrate that such features are inexorably coupled to the uv-plane sampling. The brightness contrast between the peaks and the surrounding shell material are not as prominent in the simulations (which of course assume no antenna- or baseline-based amplitude or phase errors, meaning no self-calibration procedures will have incorporated any such features in models). It is conclusive that incomplete uv-plane sampling has a drastic effect on the final images for observations of this nature. Difference imaging reveals residual emission up to the 8 sigma level. Extreme care should be taken when using interferometric observations to directly infer the structure of objects such as supernovae.Comment: 14 pages, 10 figures, 2 tables, accepted for publication in MNRA

Expanding e-MERLIN with the Goonhilly Earth Station

A consortium of universities has recently been formed with the goal of using the decommissioned telecommunications infrastructure at the Goonhilly Earth Station in Cornwall, UK, for astronomical purposes. One particular goal is the introduction of one or more of the ~30-metre parabolic antennas into the existing e-MERLIN radio interferometer. This article introduces this scheme and presents some simulations which quantify the improvements that would be brought to the e-MERLIN system. These include an approximate doubling of the spatial resolution of the array, an increase in its N-S extent with strong implications for imaging the most well-studied equatorial fields, accessible to ESO facilities including ALMA. It also increases the overlap between the e-MERLIN array and the European VLBI Network. We also discuss briefly some niche science areas in which an e-MERLIN array which included a receptor at Goonhilly would be potentially world-leading, in addition to enhancing the existing potential of e-MERLIN in its role as a Square Kilometer Array pathfinder instrument.Comment: 7 pages, 3 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

Goonhilly: a new site for e-MERLIN and the EVN

The benefits for the e-MERLIN and EVN arrays of using antennae at the satellite communication station at Goonhilly in Cornwall are discussed. The location of this site - new to astronomy - will provide an almost equal distribution of long baselines in the east-west- and north-south directions, and opens up the possibility to get significantly improved observations of equatorial fields with e-MERLIN. These additional baselines will improve the sensitivity on a set of critical spatial scales and will increase the angular resolution of e-MERLIN by a factor of two. e-MERLIN observations, including many allocated under the e-MERLIN Legacy programme, will benefit from the enhanced angular resolution and imaging capability especially for sources close to or below the celestial equator (where ESO facilities such as ALMA will operate) of including the Goonhilly telescopes. Furthermore, the baselines formed between Goonhilly and the existing stations will close the gap between the baselines of e-MERLIN and those of the European VLBI Network (EVN) and therefore enhance the legacy value of e-MERLIN datasets.Comment: 10 pages, 2 figue

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

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

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