Rapid Mixing for Lattice Colorings with Fewer Colors

We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet has a finite correlation length and a unique Gibbs measure at zero temperature. Four and five are now the only remaining values of q for which it is not known whether there exists a rapidly mixing Markov chain for q-colorings of the square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA

The analysis and forecasting of male cycling time trial records established within England and Wales.

The format of cycling time trials in England, Wales and Northern Ireland, involves riders competing individually over several fixed race distances of 10-100 miles in length and using time constrained formats of 12 and 24 h in duration. Drawing on data provided by the national governing body that covers the regions of England and Wales, an analysis of six male competition record progressions was undertaken to illustrate its progression. Future forecasts are then projected through use of the Singular Spectrum Analysis technique. This method has not been applied to sport-based time series data before. All six records have seen a progressive improvement and are non-linear in nature. Five records saw their highest level of record change during the 1950-1969 period. Whilst new record frequency generally has reduced since this period, the magnitude of performance improvement has generally increased. The Singular Spectrum Analysis technique successfully provided forecasted projections in the short to medium term with a high level of fit to the time series data

Ablation debris control by means of closed thick film filtered water immersion

The performance of laser ablation generated debris control by means of open immersion techniques have been shown to be limited by flow surface ripple effects on the beam and the action of ablation plume pressure loss by splashing of the immersion fluid. To eradicate these issues a closed technique has been developed which ensured a controlled geometry for both the optical interfaces of the flowing liquid film. This had the action of preventing splashing, ensuring repeatable machining conditions and allowed for control of liquid flow velocity. To investigate the performance benefits of this closed immersion technique bisphenol A polycarbonate samples have been machined using filtered water at a number of flow velocities. The results demonstrate the efficacy of the closed immersion technique: a 93% decrease in debris is produced when machining under closed filtered water immersion; the average debris particle size becomes larger, with an equal proportion of small and medium sized debris being produced when laser machining under closed flowing filtered water immersion; large debris is shown to be displaced further by a given flow velocity than smaller debris, showing that the action of flow turbulence in the duct has more impact on smaller debris. Low flow velocities were found to be less effective at controlling the positional trend of deposition of laser ablation generated debris than high flow velocities; but, use of excessive flow velocities resulted in turbulence motivated deposition. This work is of interest to the laser micromachining community and may aide in the manufacture of 2.5D laser etched patterns covering large area wafers and could be applied to a range of wavelengths and laser types

POPULATION NUMBERS OF FUR SEALS AT PRINCE EDWARD ISLAND, SOUTHERN OCEAN

During the period 17–22 December 2001, the onshore distribution and the abundance of Antarctic fur seals Arctocephalus gazella and Subantarctic fur seals A. tropicalis were determined for Prince Edward Island. Two breeding colonies of Antarctic fur seals were located on the south-east coast of the island; the first a mixed (with Subantarctic fur seals) breeding colony with an estimated 24 pups on a vegetated promontory on the northern section of Boggel Beach, and the second, a presumably pure Antarctic fur seal breeding colony with an estimated 380 pups, at Penguin Beach. At a mean intrinsic rate of natural increase of 16.2&#37 per year, Antarctic fur seals appear to be in the rapid recolonization phase of population growth. Breeding colonies of Subantarctic fur seals, largely found on the entire east coast, produced an estimated 15 000 pups, and the population had maintained a mean intrinsic rate of natural increase of some 9.5&#37 per year since 1987/88.Afr. J. mar. Sci. 25: 549–55

A change in the NICE guidelines on antibiotic prophylaxis: British Heart Valve Society update

The National Institute for Health and Care Excellence (NICE) has made an important change to Clinical Guideline 64 (CG64)1 adding the word ‘routinely’ to Recommendation 1.1.3: 'Antibiotic prophylaxis against infective endocarditis is not recommended routinely for people undergoing dental procedures.' In a letter about the change to the MP Chris Philp,2 Sir Andrew Dillon, CEO of NICE, confirmed that '… in individual cases, antibiotic prophylaxis may be appropriate.

POPULATION OF THE MACARONI PENGUIN EUDYPTES CHRYSOLOPHUS AT MARION ISLAND, 1994/95–2002/03, WITH INFORMATION ON BREEDING AND DIET

There is indication that numbers of macaroni penguins Eudyptes chrysolophus at subantarctic Marion Island have decreased since the early 1980s. Estimates of the population at the island fell from about 405 000 pairs in 1983/84 and 434 000 pairs in 1994/95 to about 356 000 pairs in 2002/03. Two large colonies, at Bullard Beach and Kildalkey Bay, account for about 85&#37 of the overall population. At both these colonies, the area occupied by breeders showed no trend between 1983/84 and 2002/03, but the mean density of nests decreased. However, error on estimates of abundance at these colonies precludes demonstration of a significant decrease in the overall population. Numbers of occupied nests at other colonies decreased from 79 000 in 1994/95 to 31 000 in 2002/03. At three small colonies there was a significant decrease of 88&#37 between 1982/83 and 2002/03. At Marion Island, macaroni penguins usually breed for the first time when aged about three years. From 1994/95 to 2002/03, pairs fledged an average of 0.46 chicks per year, a number considered insufficient to maintain the population. However, during that period there was a significant increase in reproductive success with time. In the same period, the masses of males and females on arrival at breeding colonies were significantly correlated. Both showed a marked decrease in 1998/99, after the El Niño of 1997/98. In most seasons from 1994/95 to 2001/02 crustaceans dominated the food, but the mass of chicks at fledging was significantly related to the contribution of fish to the diet.Afr. J. mar. Sci. 25: 475–48

Local Nodes in Global Networks: The Geography of Knowledge Flows in Biotechnology Innovation

The literature on innovation and interactive learning has tended to emphasize the importance of local networks, inter-firm collaboration and knowledge flows as the principal source of technological dynamism. More recently, however, this view has come to be challenged by other perspectives that argue for the importance of non-local knowledge flows. According to this alternative approach, truly dynamic economic regions are characterized both by dense local social interaction and knowledge circulation, as well as strong inter-regional and international connections to outside knowledge sources and partners. This paper offers an empirical examination of these issues by examining the geography of knowledge flows associated with innovation in biotechnology. We begin by reviewing the growing literature on the nature and geography of innovation in biotechnology research and the commercialization process. Then, focusing on the Canadian biotech industry, we examine the determinants of innovation (measured through patenting activity), paying particular attention to internal resources and capabilities of the firm, as well as local and global flows of knowledge and capital. Our study is based on the analysis of Statistics Canada’s 1999 Survey of Biotechnology Use and Development, which covers 358 core biotechnology firms. Our findings highlight the importance of in-house technological capability and absorptive capacity as determinants of successful innovation in biotechnology firms. Furthermore, our results document the precise ways in which knowledge circulates, in both embodied and disembodied forms, both locally and globally. We also highlight the role of formal intellectual property transactions (domestic and international) in promoting knowledge flows. Although we document the importance of global networks in our findings, our results also reveal the value of local networks and specific forms of embedding. Local relational linkages are especially important when raising capital—and the expertise that comes with it—to support innovation. Nevertheless, our empirical results raise some troubling questions about the alleged pre-eminence of the local in fostering innovation

Counting approximately-shortest paths in directed acyclic graphs

Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights L_1 and L_2, we show how to approximately count the s-t paths that have length at most L_1 in the first graph and length at most L_2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph

Symmetry-preserving matchings

In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely speaking, the matching hypersurface is restricted to be tangent to the orbits of a desired local group of symmetries admitted at both sides of the matching and thus admitted by the whole matched spacetime. This general definition is shown to lead to conditions on the properties of the preserved groups. First, the algebraic type of the preserved group must be kept at both sides of the matching hypersurface. Secondly, the orthogonal transivity of two-dimensional conformal (in particular isometry) groups is shown to be preserved (in a way made precise below) on the matching hypersurface. This result has in particular direct implications on the studies of axially symmetric isolated bodies in equilibrium in General Relativity, by making up the first condition that determines the suitability of convective interiors to be matched to vacuum exteriors. The definition and most of the results presented in this paper do not depend on the dimension of the manifolds involved nor the signature of the metric, and their applicability to other situations and other higher dimensional theories is manifest.Comment: LaTeX, 19 page

Multi-Modal Courtship in the Peacock Spider, Maratus volans (O.P.-Cambridge, 1874)

The peacock spider, Maratus volans, has one of the most elaborate courtship displays in arthropods. Using regular and high-speed video segments captured in the lab, we provide detailed descriptions of complete male courtship dances. As research on jumping spiders has demonstrated that males of some species produce vibrations concurrently with visual displays, we also used laser vibrometry to uncover such elements for this species. Our recordings reveal and describe for the first time, that M. volans males use vibratory signals in addition to complex body ornaments and motion displays. The peacock spider and other closely related species are outstanding study organisms for testing hypotheses about the evolution and functional significance of complex displays, thus, this descriptive study establishes a new model system for behavioral ecology, one that certainly stands to make important contributions to the field