Noncommutative Geometry: Fuzzy Spaces, the Groenewold-Moyal Plane

In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenwald-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and discuss some important results in these fields. In the end we outline some recent developments in the field.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Inter-observer variability for cardiac ultrasound measurements in cats repeated at different time points in early adult life

Abstract A high degree of accuracy is required when using echocardiography to diagnose hypertrophic cardiomyopathy (HCM) in cats, as variation in measurements of 0.5 mm may affect classification of individuals as ‘abnormal’. This study in adult cats examined at different time points inter-observer variability between two Board certified echocardiographers in veterinary cardiology. Twenty-four female European shorthair cats were examined at 12, 18 and 24 months of age by observer 1. Two dimensional (2D) echocardiographic images were collected in conscious cats to measure left ventricular, aortic and left atrial dimensions. Measurements were repeated by observer 2 on stored images, and analyzed for effect of time, observer and time-observer interaction. Based on end-diastolic left ventricular wall thickness, cats were diagnosed as ‘normal’ or 'abnormal'. Linear mixed models (generalized when appropriate) were performed. A significant difference between observers was found for all septal (IVSd) and free wall (LVFWd) thickness measurements and left ventricular internal diameters but not for aortic or left atrial measurements. All measurement coefficients of variation (CV) were 5 mm in cats >6 kg bodyweight) was significantly different between observers for IVSd but not LVFWd. Caution is warranted when diagnosing as ‘abnormal’ or interpreting small changes based on IVSd, due to significant inter-observer differences in this measurement

Autoxidation of lipids in parchment

Historic parchment is a macromolecular material, which is complex due to its natural origin, inhomogeneity of the skin structure, unknown environmental history and potential localised degradation. Most research into its stability has so far focussed on thermal and structural methods of analyses. Using gas chromatographic analysis of the atmosphere surrounding parchment during oxidation, we provide the experimental evidence on the production of volatile aldehydes, which can be the products of lipid autoxidation. Oxidation of parchment with different aldehyde emissions was additionally followed in situ using chemiluminometry and the same techniques were used to evaluate the oxidation of differently delipidised parchment. It was shown that the production of peroxides and the emission of aldehydes from the material decrease with lower lipid content. Building on this evidence, we can conclude that the presence of lipids (either initially present in the skin or resulting from conservation intervention) leads to oxidative degradation of collagen and that the non-destructive analysis of the emission of volatiles could be used as a quick tool for evaluation of parchment stability

Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings

The fusion ring for $\widehat{\mathfrak{su}}(n)_m$ Wess-Zumino-Witten conformal field theories is known to be isomorphic to a factor ring of the ring of symmetric polynomials presented by Schur polynomials. We introduce a deformation of this factor ring associated with eigenpolynomials for the elliptic Ruijsenaars difference operators. The corresponding Littlewood-Richardson coefficients are governed by a Pieri rule stemming from the eigenvalue equation. The orthogonality of the eigenbasis gives rise to an analog of the Verlinde formula. In the trigonometric limit, our construction recovers the refined $\widehat{\mathfrak{su}}(n)_m$ Wess-Zumino-Witten fusion ring associated with the Macdonald polynomials.Comment: 21 page

Hamiltonian Reduction and Classical Extended Superconformal Algebras

We present a systematic construction of classical extended superconformal algebras from the hamiltonian reduction of a class of affine Lie superalgebras, which include an even subalgebra $sl(2)$. In particular, we obtain the doubly extended $N=4$ superconformal algebra $\tilde{A}_{\gamma}$ from the hamiltonian reduction of the exceptional Lie superalgebra $D(2|1;\gamma/(1-\gamma))$. We also find the Miura transformation for these algebras and give the free field representation. A $W$-algebraic generalization is discussed.Comment: 13 page

Towards experience management for Search Engine Optimisation

Websites of Small and Medium-sized Enterprises (SMEs) can gain an added advantage by getting listed in the search engine’s results page during the search sessions of the searchers. The Search Engine Optimisation (SEO) enables websites to become visible in search engines during search sessions for its featured products or services. It generates additional revenue for the websites. SEO is a complex technique. Its knowledge and experience gained from optimising websites in the past is highly valuable and applicable to optimise websites. This paper dis- cusses the problem of optimisation of websites based on the experience gained by the authors from optimisation of several case study websites. Process models have been generated in order to capture experience of implementing essential elements of SEO and to explain the procedure of implementation of the fundamental on-page SEO techniques that yielded results for the case study websites

Covariant Harmonic Supergraphity for N = 2 Super Yang--Mills Theories

We review the background field method for general N = 2 super Yang-Mills theories formulated in the N = 2 harmonic superspace. The covariant harmonic supergraph technique is then applied to rigorously prove the N=2 non-renormalization theorem as well as to compute the holomorphic low-energy action for the N = 2 SU(2) pure super Yang-Mills theory and the leading non-holomorphic low-energy correction for N = 4 SU(2) super Yang-Mills theory.Comment: 17 pages, LAMUPHYS LaTeX, no figures; based on talks given by I. Buchbinder and S. Kuzenko at the International Seminar ``Supersymmetries and Quantum Symmetries'', July 1997, Dubna; to be published in the proceeding