Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres

Trade dispute settlement mechanisms: the WTO dispute settlement understanding in the wake of the GATT

A critical feature of the GATT Uruguay Round negotiations was the establishment of a new and more effective system of dealing with international trade disputes, known as the WTO Dispute Settlement Understanding (DSU). The original GATT dispute settlement system comprised rudimentary remnants of a more thorough framework contained in the defunct Havana Charter of the International Trade Organization (ITO). By the time of the start of the Uruguay Round negotiations in Punta del Este in 1986, the effectiveness and credibility of the GATT dispute settlement system was being very seriously questioned. The primary reason for the increasing lack of confidence in the system was the propensity of GATT contracting countries to ignore the findings of Panels, resulting in a stalemate in a number of high profile trade disputes. Several trade disputes between the EU and the United States discussed were initiated under the GATT dispute settlement system but remained unresolved. These disputes became increasingly acrimonious as a direct consequence of the failure of the GATT system to enforce a satisfactory resolution. This paper provides an outline of the workings of the GATT and WTO dispute settlement systems underlie several recent trade disputes. The first two sections deal with the GATT system of settling trade disputes. The first details the key elements of the GATT dispute settlement system while the second considers its performance in resolving disputes. Section 3 outlines the origins of the WTO DSU and summarises its principal Articles. The WTO DSU is appraised on the basis of its first nine years of operation in Section 4 followed by a brief discussion of the key issues that have arisen from its operation. The final Section makes some concluding comments on the relative efficacy of the GATT and WTO dispute settlement systems.

Ecology and thermal inactivation of microbes in and on interplanetary space vehicle components Quarterly progress report, 1 Apr. - 30 Jun. 1970

Ecology and thermal inactivation of microbes in and on interplanetary space vehicle component

The XMM-Newton slew survey in the 2-10 keV band

The XMM-Newton Slew Survey (XSS) covers a significant fraction of the sky in a broad X-ray bandpass. Although shallow by contemporary standards, in the `classical' 2-10 keV band of X-ray astronomy, the XSS provides significantly better sensitivity than any currently available all-sky survey. We investigate the source content of the XSS, focussing on detections in the 2-10 keV band down to a very low threshold (> 4 counts net of background). At the faint end, the survey reaches a flux sensitivity of roughly 3e-12 erg/cm2/s (2-10 keV). Our starting point was a sample of 487 sources detected in the XMMSL1d2 XSS at high galactic latitude in the hard band. Through cross-correlation with published source catalogues from surveys spanning the electromagnetic spectrum from radio to gamma-rays, we find that 45% of the sources have likely identifications with normal/active galaxies, 18% are associated with other classes of X-ray object (nearby coronally active stars, accreting binaries, clusters of galaxies), leaving 37% of the XSS sources with no current identification. We go on to define an XSS extragalactic hard band sample comprised of 219 galaxies and active galaxies. We investigate the properties of this extragalactic sample including its X-ray logN-logS distribution. We find that in the low-count limit, the XSS is strongly affected by Eddington bias. There is also a very strong bias in the XSS against the detection of extended sources, most notably clusters of galaxies. A significant fraction of the detections at and around the low-count limit may be spurious. Nevertheless, it is possible to use the XSS to extract a reasonably robust sample of extragalactic sources, excluding galaxy clusters. The differential logN-logS relation of these extragalactic sources matches very well to the HEAO-1 A2 all-sky survey measurements at bright fluxes and to the 2XMM source counts at the faint end.Comment: 16 pages, 13 figures, FITS table of XSS extragalactic sample available from http://www.star.le.ac.uk/~amr30/Slew

Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.Comment: 27 pages, Latex, 17 figs. J. Phys. A, in pres

A pilot inference study for a beta-Bernoulli spatial scan statistic

The Bernoulli spatial scan statistic is used to detect localised clusters in binary labelled point data, such as that used in spatial or spatio-temporal case/control studies. We test the inferential capability of a recently developed beta-Bernoulli spatial scan statistic, which adds a beta prior to the original statistic. This pilot study, which includes two test scenarios with 6,000 data sets each, suggests a marked increase in power for a given false alert rate. We suggest a more extensive study would be worthwhile to corroborate the findings. We also speculate on an explanation for the observed improvement

Mathematical wind profiles

Augmented Fourier polynomials for mathematical representation of vertical profiles for horizontal wind velocitie

Mathematical wind profiles, parts 1, 2, 3, 4

Fourier holograph representation of wind velocity over Cape Kenned