Constructing cell data for diagram algebras

We show how the treatment of cellularity in families of algebras arising from diagram calculi, such as Jones' Temperley--Lieb wreaths, variants on Brauer's centralizer algebras, and the contour algebras of Cox et al (of which many algebras are special cases), may be unified using the theory of tabular algebras. This improves an earlier result of the first author (whose hypotheses covered only the Brauer algebra from among these families).Comment: Approximately 38 pages, AMSTeX. Revised in light of referee comments. To appear in the Journal of Pure and Applied Algebr

Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond

The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers by inclusion, such as symplectic blob algebras (diagram algebra quotients of the type-\hati{C} Hecke algebras). By carefully reviewing the diagram algebra construction, we find a new set of functors interrelating module categories of ordinary blob algebras (diagram algebra quotients of the type-${B}$ Hecke algebras) at {\em different} values of the algebra parameters. We show that these functors generalise to determine the structure of symplectic blob algebras, and hence of certain two-boundary Temperley-Lieb algebras arising in Statistical Mechanics. We identify the diagram basis with a cellular basis for each symplectic blob algebra, and prove that these algebras are quasihereditary over a field for almost all parameter choices, and generically semisimple. (That is, we give bases for all cell and standard modules.)Comment: 61 page

Quantum Gravity and Higher Curvature Actions

Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.Comment: 28 pages, based on a lecture course at the 42nd Karpacz Winter School of Theoretical Physics ``Current Mathematical Topics in Gravitation and Cosmology,'' Ladek, Poland, February 6-11, 200

The provision of education and training for healthcare professionals through the medium of the internet

This paper describes a new initiative to provide Internet based courses to student and professional occupational therapists in four centres in the UK, Belgium the Netherlands and Sweden. The basis of this collaborative Occupational Therapy Internet School (OTIS) is the concept of the “Virtual College”. This comprises the design and implementation of a sophisticated Internet-based system through which courses can be managed, prepared and delivered online in an effective fashion, and where students can communicate both with the staff and their peers. The aim is to support and facilitate the whole range of educational activities within a remote electronic environment. A major feature of the course organisation is the adoption of a problem-based approach in which students will collaborate internationally to propose effective intervention in given case study scenarios. The paper outlines the rationale for OTIS, the content and structure of the courseware, the technical specification of the system and evaluation criteria. In addition to the more conventional web-based learning facilities generally offered, a number of agent-based approaches are being adopted to assist in the management of the course by ensuring the proper delivery of course materials and to assist the functioning of project groups. </p

On the "Causality Argument" in Bouncing Cosmologies

We exhibit a situation in which cosmological perturbations of astrophysical relevance propagating through a bounce are affected in a scale-dependent way. Involving only the evolution of a scalar field in a closed universe described by general relativity, the model is consistent with causality. Such a specific counter-example leads to the conclusion that imposing causality is not sufficient to determine the spectrum of perturbations after a bounce provided it is known before. We discuss consequences of this result for string motivated scenarios.Comment: 4 pages, 1 figure, ReVTeX, to appear in Phys. Rev. Let

Interband, intraband and excited-state direct photon absorption of silicon and germanium nanocrystals embedded in a wide band-gap lattice

Embedded Si and Ge nanocrystals (NCs) in wide band-gap matrices are studied theoretically using an atomistic pseudopotential approach. From small clusters to large NCs containing on the order of several thousand atoms are considered. Effective band-gap values as a function of NC diameter reproduce very well the available experimental and theoretical data. It is observed that the highest occupied molecular orbital for both Si and Ge NCs and the lowest unoccupied molecular orbital for Si NCs display oscillations with respect to size among the different irreducible representations of the $C_{3v}$ point group to which these spherical NCs belong. Based on this electronic structure, first the interband absorption is thoroughly studied which shows the importance of surface polarization effects that significantly reduce the absorption when included. This reduction is found to increase with decreasing NC size or with increasing permittivity mismatch between the NC core and the host matrix. Reasonable agreement is observed with the experimental absorption spectra where available. The deformation of spherical NCs into prolate or oblate ellipsoids are seen to introduce no pronounced effects for the absorption spectra. Next, intraconduction and intravalence band absorption coefficients are obtained in the wavelength range from far-infrared to visible region. These results can be valuable for the infrared photodetection prospects of these NC arrays. Finally, excited-state absorption at three different optical pump wavelengths, 532 nm, 355 nm and 266 nm are studied for 3- and 4 nm-diameter NCs. This reveals strong absorption windows in the case of holes and a broad spectrum in the case of electrons which can especially be relevant for the discussions on achieving gain in these structures.Comment: Published version, 13 pages, 15 figures, local field effects include

Lens or Binary? Chandra Observations of the Wide Separation Broad Absorption Line Quasar Pair UM425

We have obtained a 110 ksec Chandra ACIS-S exposure of UM425, a pair of QSOs at z=1.47 separated by 6.5 arcsec, which show remarkably similar emission and broad absorption line (BAL) profiles in the optical/UV. Our 5000 count X-ray spectrum of UM425A (the brighter component) is well-fit with a power law (photon spectral index Gamma=2.0) partially covered by a hydrogen column of 3.8x10^22 cm^-2. The underlying power-law slope for this object and for other recent samples of BALQSOs is typical of radio-quiet quasars, lending credence to the hypothesis that BALs exist in every quasar. Assuming the same Gamma for the much fainter image of UM425B, we detect an obscuring column 5 times larger. We search for evidence of an appropriately large lensing mass in our Chandra image and find weak diffuse emission near the quasar pair, with an X-ray flux typical of a group of galaxies at redshift z ~ 0.6. From our analysis of archival HST WFPC2 and NICMOS images, we find no evidence for a luminous lensing galaxy, but note a 3-sigma excess of galaxies in the UM425 field with plausible magnitudes for a z=0.6 galaxy group. However, the associated X-ray emission does not imply sufficient mass to produce the observed image splitting. The lens scenario thus requires a dark (high M/L ratio) lens, or a fortuitous configuration of masses along the line of sight. UM425 may instead be a close binary pair of BALQSOs, which would boost arguments that interactions and mergers increase nuclear activity and outflows.Comment: 13 pages, 9 figures, Accepted for publication in the Astrophysical Journa

Dark-bellied Brent Geese Branta bernicla bernicla, as recorded by satellite telemetry, do not minimize flight distance during spring migration

Nine Dark-bellied Brent Geese Branta bernicla bernicla were equipped with satellite transmitters during spring staging in the Dutch Wadden Sea in 1998 and 1999. The transmitters (in all cases less than 3% of body mass) were attached to the back by a flexible elastic harness. One juvenile female was tracked to the Yamal peninsula in 1998. Eight adult males were selected from a single catch of 75 to span the range of body mass observed on the date of capture (11 May 1999) and all but the lightest individual completed the first lap of the migratory flight to the White Sea, Russia, according to the time schedule normal for this species. Six birds were successfully tracked to Taymyr for a total distance averaging 5004 km (range 4577-5164) but judging from later movements none bred (although 1999 was breeding year). Although the routes chosen during spring migration were closely similar; none of the tagged birds migrated together. On average the geese used 16 flights to reach their summer destinations on Taymyr. The longest uninterrupted flights during the first half of the journey (Wadden Sea to Kanin) covered 1056 km (mean of seven adult males, range 768-1331), while the corresponding value for the second half of the migration (Kanin-Taymyr) was only 555 km (mean of six adult males). Only 7% of total time during spring migration was spent in active flight, as contrasted to c. 80% at long-term stopovers. Overall average travelling speed was 118 km/day (range 97-148). Including fattening prior to departure the rate of travel falls to 62 km/day (range 49-70), in keeping with theoretical predictions. Routes followed deviated from the great circle route, adding at least 700 km (16%) to the journey from Wadden Sea to Taymyr, and we conclude that the coastal route is chosen to facilitate feeding, drinking and resting en route instead of minimizing total flight distance