Lagrangian Multiform Structures, Discrete Systems and Quantisation

Lagrangian multiforms are an important recent development in the study of integrable variational problems. In this thesis, we develop two simple examples of the discrete Lagrangian one-form and two-form structures. These linear models still display all the features of the discrete Lagrangian multiform; in particular, the property of Lagrangian closure. That is, the sum of Lagrangians around a closed loop or surface, on solutions, is zero. We study the behaviour of these Lagrangian multiform structures under path integral quantisation and uncover a quantum analogue to the Lagrangian closure property. For the one-form, the quantum mechanical propagator in multiple times is found to be independent of the time-path, depending only on the endpoints. Similarly, for the two-form we define a propagator over a surface in discrete space-time and show that this is independent of the surface geometry, depending only on the boundary. It is not yet clear how to extend these quantised Lagrangian multiforms to non-linear or continuous time models, but by examining two such examples, the generalised McMillan maps and the Degasperis-Ruijsenaars model, we are able to make some steps towards that goal. For the generalised McMillan maps we find a novel formulation of the r-matrix for the dual Lax pair as a normally ordered fraction in elementary shift matrices, which offers a new perspective on the structure. The dual Lax pair may ultimately lead to commuting flows and a one-form structure. We establish the relation between the Degasperis-Ruijsenaars model and the integrable Ruijsenaars-Schneider model, leading to a Lax pair and two particle Lagrangian, as well as finding the quantum mechanical propagator. The link between these results is still needed. A quantum theory of Lagrangian multiforms offers a new paradigm for path integral quantisation of integrable systems; this thesis offers some first steps towards this theory

Interaction of C-60 molecules on Si(100)

The interactions between pairs of C60 molecules adsorbed upon the Si(1 0 0) surface have been studied via a series of DFT calculations. Configurations which have the fullerene cage located within the dimer trench bonded to four dimers (t4) have been investigated, as these have previously been found to be among the most stable for the C60 molecule. These t4 configurations are explored with all possible pairs of fullerene configuration combinations considered. We have looked at two distinct groups of separation distances between the two C60 molecules. These have the fullerene bonding sites as either adjacent to one another or separated by one Si surface dimer. Comparisons between the two groups confirm the trend of the combinations becoming more favourable at a greater fullerene separation. In the systems with adjacent bonding sites the combined pair of fullerenes were in general less favourable than the two isolated cases. At the longer fullerene separation distance this trend was reversed. The longer fullerene separation distance reflects the experimental separation observed by Moriarty et al. [P. Moriarty, Y.R. Ma, M.D. Upward, P.H. Beton, Surf. Sci. 407 (1998) 27]

MAPK-dependent regulation of IL-1- and β-adrenoreceptor-induced inflammatory cytokine production from mast cells: Implications for the stress response

BACKGROUND: Catecholamines, such as epinephrine, are elaborated in stress responses, and mediate vasoconstriction to cause elevation in systemic vascular resistance and blood pressure. Our previous study has shown that IL-1 can induce mast cells to produce proinflammatory cytokines which are involved in atherogenesis. The aim of this study was to determine the effects of epinephrine on IL-1-induced proatherogenic cytokine production from mast cells. RESULTS: Two ml of HMC-1 (0.75 × 10(6 )cells/ml) were cultured with epinephrine (1 × 10(-5 )M) in the presence or absence of IL-1β (10 ng/ml) for 24 hrs. HMC-1 cultured alone produced none to trace amounts of IL-6, IL-8, and IL-13. IL-1β significantly induced production of these cytokines in HMC-1, while epinephrine alone did not. However, IL-6, IL-8, and IL-13 production induced by IL-1β were significantly enhanced by addition of epinephrine. The enhancing effect appears to involve NF-κB and p38 MAPK pathways. Flow cytometry showed the presence of β(1 )and β(2 )adrenoreceptors on resting mast cells. The enhancing effect of proatherogenic cytokine production by epinephrine was down regulated by the β(1 )and β(2 )adrenoceptor antagonist, propranolol, but not by the β(1 )adrenoceptor antagonist, atenolol, suggesting the effect involved β(2 )adrenoceptors. The enhancing effect of epinephrine on proatherogenic cytokine production was also down regulated by the immunosuppressive drug, dexamethasone. CONCLUSIONS: These results not only confirm that an acute phase cytokine, IL-1β, regulates mast cell function, but also show that epinephrine up regulates the IL-1β induction of proatherogenic cytokines in mast cells. These data provide a novel role for epinephrine, a stress hormone, in inflammation and atherogenesis

The ACS Survey of Galactic Globular Clusters: M54 and Young Populations in the Sagittarius Dwarf Spheroidal Galaxy

We present new Hubble Space Telescope photometry of the massive globular cluster M54 (NGC 6715) and the superposed core of the tidally disrupted Sagittarius (Sgr) dSph galaxy as part of the ACS Survey of Galactic Globular Clusters. Our deep (F606W~26.5), high-precision photometry yields an unprecedentedly detailed color-magnitude diagram showing the extended blue horizontal branch and multiple main sequences of the M54+Sgr system. The distance and reddening to M54 are revised usingboth isochrone and main-sequence fitting to (m-M)_0=17.27 and E(B-V)=0.15. Preliminary assessment finds the M54+Sgr field to be dominated by the old metal-poor populations of Sgr and the globular cluster. Multiple turnoffs indicate the presence of at least two intermediate-aged star formation epochs with 4 and 6 Gyr ages and [Fe/H]=-0.4 to -0.6. We also clearly show, for the first time, a prominent, 2.3 Gyr old Sgr population of near-solar abundance. A trace population of even younger (0.1-0.8 Gyr old), more metal-rich ([Fe/H]\sim0.6) stars is also indicated. The Sgr age-metallicity relation is consistent with a closed-box model and multiple (4-5) star formation bursts over the entire life of the satellite, including the time since Sgr began disrupting.Comment: Accepted to ApJ Letter; 11 pages, 2 figures; figure 1 uploaded as jpg; paper in ApJ format with full-resolution figures available at: http://www.astro.ufl.edu/~ata/public_hstgc/paperIV/paperIV.p

FEL research and development at STFC Daresbury laboratory

In this paper we present an overview of current and proposed FEL developments at STFC Daresbury Laboratory in the UK. We discuss progress on the ALICE IR-FEL since first lasing in October 2010, covering the optimisation of the FEL performance, progress on the demonstration of a single shot cross correlation experiment and the results obtained so far with a Scanning Near-Field Optical Microscopy beamline. We discuss a proposal for a 250 MeV single pass FEL test facility named CLARA to be built at Daresbury and dedicated to research for future light source applications. Finally we present a brief overview of other recent research highlights

DCE-MRI for pre-treatment prediction and post-treatment assessment of treatment response in sites of squamous cell carcinoma in the head and neck

Background and Purpose It is important to identify patients with head and neck squamous cell carcinoma (SCC) who fail to respond to chemoradiotherapy so that they can undergo post-treatment salvage surgery while the disease is still operable. This study aimed to determine the diagnostic performance of dynamic contrast enhanced (DCE)-MRI using a pharmacokinetic model for pre-treatment predictive imaging, as well as post-treatment diagnosis, of residual SCC at primary and nodal sites in the head and neck. Material and Methods Forty-nine patients with 83 SCC sites (primary and/or nodal) underwent pre-treatment DCEMRI, and 43 patients underwent post-treatment DCE-MRI, of which 33 SCC sites had a residual mass amenable to analysis. Pre-treatment, post-treatment and %change in the mean Ktrans, kep, ve and AUGC were obtained from SCC sites. Logistic regression was used to correlate DCE parameters at each SCC site with treatment response at the same site, based on clinical outcome at that site at a minimum of two years. Results None of the pre-treatment DCE-MRI parameters showed significant correlations with SCC site failure (SF) (29/83 sites) or site control (SC) (54/83 sites). Post-treatment residual masses with SF (14/33) had significantly higher kep (p = 0.05), higher AUGC (p = 0.02), and lower % reduction in AUGC (p = 0.02), than residual masses with SC (19/33), with the% change in AUGC remaining significant on multivariate analysis. Conclusion Pre-treatment DCE-MRI did not predict which SCC sites would fail treatment, but post-treatment DCE-MRI showed potential for identifying residual masses that had failed treatment

DCE-MRI for pre-treatment prediction and post-treatment assessment of treatment response in sites of squamous cell carcinoma in the head and neck

Background and Purpose It is important to identify patients with head and neck squamous cell carcinoma (SCC) who fail to respond to chemoradiotherapy so that they can undergo post-treatment salvage surgery while the disease is still operable. This study aimed to determine the diagnostic performance of dynamic contrast enhanced (DCE)-MRI using a pharmacokinetic model for pre-treatment predictive imaging, as well as post-treatment diagnosis, of residual SCC at primary and nodal sites in the head and neck. Material and Methods Forty-nine patients with 83 SCC sites (primary and/or nodal) underwent pre-treatment DCEMRI, and 43 patients underwent post-treatment DCE-MRI, of which 33 SCC sites had a residual mass amenable to analysis. Pre-treatment, post-treatment and %change in the mean Ktrans, kep, ve and AUGC were obtained from SCC sites. Logistic regression was used to correlate DCE parameters at each SCC site with treatment response at the same site, based on clinical outcome at that site at a minimum of two years. Results None of the pre-treatment DCE-MRI parameters showed significant correlations with SCC site failure (SF) (29/83 sites) or site control (SC) (54/83 sites). Post-treatment residual masses with SF (14/33) had significantly higher kep (p = 0.05), higher AUGC (p = 0.02), and lower % reduction in AUGC (p = 0.02), than residual masses with SC (19/33), with the% change in AUGC remaining significant on multivariate analysis. Conclusion Pre-treatment DCE-MRI did not predict which SCC sites would fail treatment, but post-treatment DCE-MRI showed potential for identifying residual masses that had failed treatment