A Mathematica Package for Computing N=2 Superfield Operator Product Expansions

We describe a general purpose Mathematica package for computing Superfield Operator Product Expansions in meromorphic $N=2$ superconformal field theory. Given the SOPEs for a set of ``basic" superfields, SOPEs of arbitrarily complicated composites can be computed automatically. Normal ordered products are always reduced to a standard form. It is possible to check the Jacobi identities, and to compute Poisson brackets (``classical SOPEs''). We present two explicit examples: a construction of the ``small'' $N=4$ superconformal algebra in terms of $N=2$ superfields, and a realisation of the $N=2$ superconformal algebra in terms of chiral and antichiral fermionic superfields.Comment: 15 pages, LaTeX. Minor corrections, particularly to Mathematica output Out[6],Out[9] in section 4. Available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers

Higher-spin strings and W minimal models

We study the spectrum of physical states for higher-spin generalisations of string theory, based on two-dimensional theories with local spin-2 and spin-$s$ symmetries. We explore the relation of the resulting effective Virasoro string theories to certain $W$ minimal models. In particular, we show how the highest-weight states of the $W$ minimal models decompose into Virasoro primaries.Comment: 13 pages, CTP TAMU-43/93, KUL-TF-93/9

Adaptive adjustment of the number of subsets during iterative image reconstruction

A common strategy to speed-up image reconstruction in tomography is to use subsets, i.e. only part of the data is used to compute the update, as for instance in the OSEM algorithm. However, most subset algorithms do not convergence or have a limit cycle. Different strategies to solve this problem exist, for instance using relaxation. The conceptually easiest mechanism is to reduce the number of subsets gradually during iterations. However, the optimal point to reduce the number of subsets is usually depends on many factors such as initialisation, the object itself, amount of noise etc. In this paper, we propose a simple scheme to automatically compute if the number of subsets is too large (or too small) and adjust the size of the data to consider in the next update automatically. The scheme is based on idea of computing two image updates corresponding to different parts of the data. A comparison of these updates then allows to see if the updates were sufficiently consistent or not. We illustrate this idea using 2 different subset algorithms: OSEM and OSSPS

Advances in Clinical Molecular Imaging Instrumentation

In this article, we describe recent developments in the design of both single-photon emission computed tomography (SPECT) and positron emission tomography (PET) instrumentation that have led to the current range of superior performance instruments. The adoption of solid-state technology for either complete detectors [e.g., cadmium zinc telluride (CZT)] or read-out systems that replace photomultiplier tubes [avalanche photodiodes (APD) or silicon photomultipliers (SiPM)] provide the advantage of compact technology, enabling flexible system design. In SPECT, CZT is well suited to multi-radionuclide and kinetic studies. For PET, SiPM technology provides MR compatibility and superior time-of-flight resolution, resulting in improved signal-to-noise ratio. Similar SiPM technology has also been used in the construction of the first SPECT insert for clinical brain SPECT/MRI

Quantising Higher-spin String Theories

In this paper, we examine the conditions under which a higher-spin string theory can be quantised. The quantisability is crucially dependent on the way in which the matter currents are realised at the classical level. In particular, we construct classical realisations for the $W_{2,s}$ algebra, which is generated by a primary spin-$s$ current in addition to the energy-momentum tensor, and discuss the quantisation for $s\le8$. From these examples we see that quantum BRST operators can exist even when there is no quantum generalisation of the classical $W_{2,s}$ algebra. Moreover, we find that there can be several inequivalent ways of quantising a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already-known $W$ strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalisations lead us to examine the whether classical BRST operators for $W_{2,{n\over 2}}$ ($n$ odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.Comment: CTP TAMU-24/94, KUL-TF-94/11, SISSA-135/94/E

Magnetic coupling with 3D knitted helical coils

Continuous power supply for wearable electronics can be facilitated using wireless power transfer (WPT). We use a 3D knitted helical coil as the receiver coil in the wrist or the waist of a garment. This 3D knitted helical coil is a novel approach to integrate coils in garments that maintains full flexibility of the garment. Measurements and simulations of coil-coil coupling give compelling evidence of the feasibility of this approach for wearable WTP. The coupling factor between a closely wound and knitted coil is found to be ~0.25 and ~0.55 for adjacent coils for a knit in the border of a cuff and waist, respectively. Using a simple circuit, we demonstrate a 30% efficiency between a closely wound transmitter coil worn on the wrist and a 3D knitted helical receiver coil integrated in the cuff of a garment at 6 mm distance

Improved correction for the tissue fraction effect in lung PET/CT imaging

Recently, there has been an increased interest in imaging different pulmonary disorders using PET techniques. Previous work has shown, for static PET/CT, that air content in the lung influences reconstructed image values and that it is vital to correct for this 'tissue fraction effect' (TFE). In this paper, we extend this work to include the blood component and also investigate the TFE in dynamic imaging. CT imaging and PET kinetic modelling are used to determine fractional air and blood voxel volumes in six patients with idiopathic pulmonary fibrosis. These values are used to illustrate best and worst case scenarios when interpreting images without correcting for the TFE. In addition, the fractional volumes were used to determine correction factors for the SUV and the kinetic parameters. These were then applied to the patient images. The kinetic parameters K1 and Ki along with the static parameter SUV were all found to be affected by the TFE with both air and blood providing a significant contribution to the errors. Without corrections, errors range from 34-80% in the best case and 29-96% in the worst case. In the patient data, without correcting for the TFE, regions of high density (fibrosis) appeared to have a higher uptake than lower density (normal appearing tissue), however this was reversed after air and blood correction. The proposed correction methods are vital for quantitative and relative accuracy. Without these corrections, images may be misinterpreted

W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)

We show that that the Jacobi-identities for a W-algebra with primary fields of dimensions 3, 4 and 5 allow two different solutions. The first solution can be identified with WA_4. The second is special in the sense that, even though associative for general value of the central charge, null-fields appear that violate some of the Jacobi-identities, a fact that is usually linked to exceptional W-algebras. In contrast we find for the algebra that has an additional spin 6 field only the solution WA_5.Comment: 17 pages, LaTeX, KCL-TH-92-9, DFFT-70/9

Effect of positron range on PET quantification in diseased and normal lungs

The impact of positron range on PET image reconstruction has often been investigated as a blurring effect that can be partly corrected by adding an element to the PET system matrix in the reconstruction, usually based on a Gaussian kernel constructed from the attenuation values. However, the physics involved in PET is more complex. In regions where density does not vary, positron range indeed involves mainly blurring. However, in more heterogeneous media it can cause other effects. This work focuses on positron range in the lungs and its impact on quantification, especially in the case of pathologies such as cancer or pulmonary fibrosis, for which the lungs have localised varying density. Using Monte Carlo simulations, we evaluate the effects of positron range for multiple radionuclides (18F, 15O, 68Ga, 89Zr, 82Rb, 64Cu and 124I) as, for novel radiotracers, the choice of the labelling radionuclide is important. The results demonstrate quantification biases in highly heterogeneous media, where the measured uptake of high-density regions can be increased by the neighbouring radioactivity from regions of lower density, with the effect more noticeable for radionuclides with highenergy positron emission. When the low-density regions are considered to have less radioactive uptake (e.g. due to the presence of air), the effect is less severe