Pattern avoidance classes and subpermutations

Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers a structure theorem is given. The structure theorem shows that the class is almost closed under direct sums or has a rational generating function.Comment: 18 pages, 4 figures (all in-line

A new camera for high-resolution infrared imaging of works of art

A new camera – SIRIS (scanning infrared imaging system) – developed at the National Gallery in London allows high-resolution images to be made in the near infrared region (900–1700 nm). The camera is based on a commercially available 320 × 256 pixel indium gallium arsenide area array sensor. This relatively small sensor is moved across the focal plane of the camera using two orthogonal translation stages to give images of c. 5000 × 5000 pixels. The main advantages of the SIRIS camera over scanning infrared devices or sequential image capture and mosaic assembly are its comparative portability and rapid image acquisition – making a 5000 × 5000 pixel image takes less than 20 minutes. The SIRIS camera can operate at a range of resolutions; from around 2.5 pixels per millimetre over an area of up to 2 × 2 m to 10 pixels per millimetre when examining an area measuring 0.5 × 0.5 m. The development of the mechanical, optical and electronic components of the camera, including the design of a new lens, is described. The software used to control image capture and to assemble the individual frames into a seamless mosaic image is mentioned. The camera was designed primarily to examine underdrawings in paintings; preliminary results from test targets and paintings imaged in situ are presented and the quality of the images compared with those from other cameras currently used for this application

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.Comment: 17 pages; minor corrections, comparison to lattice results added; accepted for publication in Phys. Rev.

SIRIS: a high resolution scanning infrared camera for examining paintings

The new SIRIS (Scanning InfraRed Imaging System) camera developed at the National Gallery in London allows highresolution images of paintings to be made in the near infrared region (900–1700 nm). Images of 5000 × 5000 pixels are made by moving a 320 × 256 pixel InGaAs array across the focal plane of the camera using two orthogonal translation stages. The great advantages of this camera over scanning infrared devices are its relative portability and that image acquisition is comparatively rapid – a full 5000 × 5000 pixel image can be made in around 20 minutes. The paper describes the development of the mechanical, optical and electronic components of the camera, including the design of a new lens. The software routines used to control image capture and to assemble the individual 320 × 256 pixel frames into a seamless mosaic image are also mentioned. The optics of the SIRIS camera have been designed so that the camera can operate at a range of resolutions; from around 2.5 pixels per millimetre on large paintings of up to 2000 × 2000 mm to 10 pixels per millimetre on smaller paintings or details of paintings measuring 500 × 500 mm. The camera is primarily designed to examine underdrawings in paintings; preliminary results from test targets and paintings are presented and the quality of the images compared with those from other cameras currently used in this field

Hematodinium sp. infection in Norway lobster Nephrops norvegicus and its effects on meat quality

Hematodinium and Hematodinium-like species have emerged in the last 3 decades as important parasitic pathogens of crustaceans worldwide, causing a significant economic loss to fisheries and related markets. In some species (notably the Tanner crab Chionoecetes bairdi), the parasite reportedly causes the cooked meat to taste bitter and aspirin-like. The bitter taste, together with the gross pathology of the infection, renders these crabs unmarketable. Surprisingly, no organoleptic tests have ever been conducted to date, and the cause for the bitter taste is still unknown. Nevertheless, it is generally assumed that the bitter taste occurs widely in cooked meats and products derived from crustaceans infected with Hematodinium. In the present study, we analysed the meat quality and organoleptic attributes after capture and during storage of Norway lobsters Nephrops norvegicus from Scottish waters that were either asymptomatic or symptomatic of patent Hematodinium infection. Results from the sensory evaluation of the cooked product indicate that tail meat from symptomatic N. norvegicus is bland in flavour and aftertaste, and more friable or sloppier in texture than meat from asymptomatic animals. As a consequence, infected meat tends to be less palatable, although surprisingly no bitter taste is reported. From an analytical point of view, tail meat from patently infected animals is at an advanced stage of auto - lysis, while no difference in microbial load is detected. These results suggest that Norway lobsters heavily infected with Hematodinium are of inferior marketing quality even after the tails have been cooked

Multiplicative renormalizability of gluon and ghost propagators in QCD

We reformulate the coupled set of continuum equations for the renormalized gluon and ghost propagators in QCD, such that the multiplicative renormalizability of the solutions is manifest, independently of the specific form of full vertices and renormalization constants. In the Landau gauge, the equations are free of renormalization constants, and the renormalization point dependence enters only through the renormalized coupling and the renormalized propagator functions. The structure of the equations enables us to devise novel truncations with solutions that are multiplicatively renormalizable and agree with the leading order perturbative results. We show that, for infrared power law behaved propagators, the leading infrared behavior of the gluon equation is not solely determined by the ghost loop, as concluded in previous studies, but that the gluon loop, the three-gluon loop, the four-gluon loop, and even massless quarks also contribute to the infrared analysis. In our new Landau gauge truncation, the combination of gluon and ghost loop contributions seems to reject infrared power law solutions, but massless quark loops illustrate how additional contributions to the gluon vacuum polarization could reinstate these solutions. Moreover, a schematic study of the three-gluon and four-gluon loops shows that they too need to be considered in more detail before a definite conclusion about the existence of infrared power behaved gluon and ghost propagators can be reached.Comment: 13 pages, 1 figure, submitted to Phys. Rev.

Growth rates for subclasses of Av(321)

Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates

Community experiences of organised crime in Scotland

The research explored community experiences of serious organised crime in Scotland (SOC). The report provides information on the nature and extent of the impact of SOC on everyday life in the community, as well as offering suggestions for policy development. The study sought to answer the following questions: 1)What are the relationships that exist between SOC and communities in Scotland? 2)What are the experiences and perceptions of residents, stakeholders and organisations of the scope and nature of SOC within their local area? and 3)How does SOC impact on community wellbeing, and to what extent can the harms associated with SOC be mitigated

Disorder and chain superconductivity in YBa_2Cu_3O_{7-\delta}

The effects of chain disorder on superconductivity in YBa_2Cu_3O_{7-\delta} are discussed within the context of a proximity model. Chain disorder causes both pair-breaking and localization. The hybridization of chain and plane wavefunctions reduces the importance of localization, so that the transport anisotropy remains large in the presence of a finite fraction $\delta$ of oxygen vacancies. Penetration depth and specific heat measurements probe the pair-breaking effects of chain disorder, and are discussed in detail at the level of the self-consistent T-matrix approximation. Quantitative agreement with these experiments is found when chain disorder is present.Comment: 4 pages, 2 figures, submitted to PRB rapid communication