Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

How do field of view and resolution affect the information content of panoramic scenes for visual navigation? A computational investigation

The visual systems of animals have to provide information to guide behaviour and the informational requirements of an animal’s behavioural repertoire are often reflected in its sensory system. For insects, this is often evident in the optical array of the compound eye. One behaviour that insects share with many animals is the use of learnt visual information for navigation. As ants are expert visual navigators it may be that their vision is optimised for navigation. Here we take a computational approach in asking how the details of the optical array influence the informational content of scenes used in simple view matching strategies for orientation. We find that robust orientation is best achieved with low-resolution visual information and a large field of view, similar to the optical properties seen for many ant species. A lower resolution allows for a trade-off between specificity and generalisation for stored views. Additionally, our simulations show that orientation performance increases if different portions of the visual field are considered as discrete visual sensors, each giving an independent directional estimate. This suggests that ants might benefit by processing information from their two eyes independently

Cladding mode coupling in highly localized fiber Bragg gratings: modal properties and transmission spectra

The spectral characteristics of a fiber Bragg grating (FBG) with a transversely inhomogeneous refractive index profile, differs con- siderably from that of a transversely uniform one. Transmission spectra of inhomogeneous and asymmetric FBGs that have been inscribed with focused ultrashort pulses with the so-called point-by-point technique are investigated. The cladding mode resonances of such FBGs can span a full octave in the spectrum and are very pronounced (deeper than 20dB). Using a coupled-mode approach, we compute the strength of resonant coupling and find that coupling into cladding modes of higher azimuthal order is very sensitive to the position of the modification in the core. Exploiting these properties allows precise control of such reflections and may lead to many new sensing applications.Comment: Submission to OE, 16 pages, 6 figure

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

Noncommutative Quantum Cosmology

We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace. For the Kantowski-Sachs metric we are able to find the exact wave function. We construct wave packets and show that new quantum states that ``compete'' to be the most probable state appear, in clear contrast with the commutative case. A tunneling process could be possible among these states.Comment: 5 pages, 5 figures, revtex4 file, major style changes, to be published in PR

Influence of operating parameters on the biodegradation of steroid estrogens and nonylphenolic compounds during biological wastewater treatment processes

This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Environmental Science & Technology, copyright © American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/es901612v.This study investigated operational factors influencing the removal of steroid estrogens and nonylphenolic compounds in two sewage treatment works, one a nitrifying/denitrifying activated sludge plant and the other a nitrifying/denitrifying activated sludge plant with phosphorus removal. Removal efficiencies of >90% for steroid estrogens and for longer chain nonylphenol ethoxylates (NP4−12EO) were observed at both works, which had equal sludge ages of 13 days. However, the biological activity in terms of milligrams of estrogen removed per day per tonne of biomass was found to be 50−60% more efficient in the nitrifying/denitrifying activated sludge works compared to the works which additionally incorporated phosphorus removal. A temperature reduction of 6 °C had no impact on the removal of free estrogens, but removal of the conjugated estrone-3-sulfate was reduced by 20%. The apparent biomass sorption (LogKp) values were greater in the nitrifying/denitrifying works than those in the nitrifying/denitrifying works with phosphorus removal for both steroid estrogens and nonylphenolic compounds possibly indicating a different cell surface structure and therefore microbial population. The difference in biological activity (mg tonne−1 d−1) identified in this study, of up to seven times, suggests that there is the potential for enhancing the removal of estrogens and nonylphenols if more detailed knowledge of the factors responsible for these differences can be identified and maximized, thus potentially improving the quality of receiving waters.Public Utilities Board (Singapore), Anglian Water Ltd, Severn Trent Water Ltd, Thames Water Utilities Ltd, United Utilities 393 Plc and Yorkshire Water Services

Shining Light on Merging Galaxies I: The Ongoing Merger of a Quasar with a `Green Valley' Galaxy

Serendipitous observations of a pair z = 0.37 interacting galaxies (one hosting a quasar) show a massive gaseous bridge of material connecting the two objects. This bridge is photoionized by the quasar (QSO) revealing gas along the entire projected 38 kpc sightline connecting the two galaxies. The emission lines that result give an unprecedented opportunity to study the merger process at this redshift. We determine the kinematics, ionization parameter (log U ~ -2.5 +- 0.03), column density (N_H ~ 10^{21} cm^{-2}), metallicity ([M/H] ~ -0.20 +- 0.15), and mass (~ 10^8 Msun) of the gaseous bridge. We simultaneously constrain properties of the QSO-host (M_DM>8.8x 10^{11} Msun) and its companion galaxy (M_DM>2.1 x 10^{11} Msun; M_star ~ 2 x 10^{10} Msun; stellar burst age=300-800 Myr; SFR~6 Msun/yr; and metallicity 12+log (O/H)= 8.64 +- 0.2). The general properties of this system match the standard paradigm of a galaxy-galaxy merger caught between first and second passage while one of the galaxies hosts an active quasar. The companion galaxy lies in the so-called `green valley', with a stellar population consistent with a recent starburst triggered during the first passage of the merger and has no detectable AGN activity. In addition to providing case-studies of quasars associated with galaxy mergers, quasar/galaxy pairs with QSO-photoionized tidal bridges such as this one offer unique insights into the galaxy properties while also distinguishing an important and inadequately understood phase of galaxy evolution.Comment: 23 pages, 12 figures, 5 tables, Submitted to ApJ, revised to address referee's comment

Efficacy and safety of autologous whole blood clot in diabetic foot ulcers: a randomised controlled trial

ObjectiveDiabetic foot ulcers (DFUs) present a significant global health challenge, resulting in high morbidity and economic costs. Current available treatments often fail to achieve satisfactory healing rates, highlighting the need for novel therapies. This study evaluated the safety and efficacy of a novel autologous whole blood clot (AWBC)-a blood-based, biodegradable provisional matrix-in conjunction with standard of care (SoC) when compared to SoC alone in the treatment of hard-to-heal DFUs.MethodA multicentre, prospective, blinded assessor, randomised controlled trial was conducted at 16 sites across the US, South Africa and Turkey. A cohort of patients with hard-to-heal DFUs was enrolled and randomised to either the AWBC group or the control group. The primary endpoint was complete wound closure at 12 weeks, while secondary endpoints included time to heal and percentage area reduction (PAR) at four and eight weeks. Data were analysed using both intention-to-treat (ITT) and per-protocol (PP) populations.ResultsThe cohort included 119 patients. AWBC treatment resulted in a significantly higher healing rate compared to the control in both ITT (41% versus 15%, respectively; p=0.002) and PP populations (51% versus 18%, respectively; p=0.0075). AWBC treatment also resulted in a shorter mean time to heal and higher durability of wound closure. Safety analysis showed a similar incidence of adverse events (AEs) between groups, with no device-related AEs.ConclusionThe AWBC system, by modulating the wound microenvironment and providing a functional extracellular matrix, offered a promising new approach to treating hard-to-heal DFUs, demonstrating superior healing outcomes compared to SoC alone in this study

TLR7-mediated skin inflammation remotely triggers chemokine expression and leukocyte accumulation in the brain

Background: The relationship between the brain and the immune system has become increasingly topical as, although it is immune-specialised, the CNS is not free from the influences of the immune system. Recent data indicate that peripheral immune stimulation can significantly affect the CNS. But the mechanisms underpinning this relationship remain unclear. The standard approach to understanding this relationship has relied on systemic immune activation using bacterial components, finding that immune mediators, such as cytokines, can have a significant effect on brain function and behaviour. More rarely have studies used disease models that are representative of human disorders. Methods: Here we use a well-characterised animal model of psoriasis-like skin inflammation—imiquimod—to investigate the effects of tissue-specific peripheral inflammation on the brain. We used full genome array, flow cytometry analysis of immune cell infiltration, doublecortin staining for neural precursor cells and a behavioural read-out exploiting natural burrowing behaviour. Results: We found that a number of genes are upregulated in the brain following treatment, amongst which is a subset of inflammatory chemokines (CCL3, CCL5, CCL9, CXCL10, CXCL13, CXCL16 and CCR5). Strikingly, this model induced the infiltration of a number of immune cell subsets into the brain parenchyma, including T cells, NK cells and myeloid cells, along with a reduction in neurogenesis and a suppression of burrowing activity. Conclusions: These findings demonstrate that cutaneous, peripheral immune stimulation is associated with significant leukocyte infiltration into the brain and suggest that chemokines may be amongst the key mediators driving this response