Heuristic Coloring Algorithm for the Composite Graph Coloring Problem

A composite graph is a finite undirected graph in which a positive integer known as a chromaticity is associated with each vertex of the graph. The composite graph coloring problem (CGCP) is the problem of finding the chromatic number of a composite graph, i.e., the minimum number of colors (positive integers) required to assign a sequence of consecutive colors to each vertex of the graph in a manner such that adjacent vertices are not assigned sequences with colors in common and the sequence assigned to a vertex has the number of colors indicated by the chromaticity of the vertex. The CGCP problem is an NP-complete problem that has applications to scheduling and resource allocation problems in which the tasks to be scheduled are of unequal durations. The pigeonhole principle gives rise to a problem reduction technique for the CGCP and a vertex ordering used in the vertex-sequentia1-with-interchange (VSI) algorithm. LFPHI. An upper bound on the chromatic number of a composite graph is obtained from the definition of a color-sequential coloring algorithm for the CGCP. The performances of twelve heuristic coloring algorithms are compared on a variety of random composite graphs. Three VSI algorithms (LF1I, LFPHI, and LFCDI) performed superior to the other algorithms on graphs having the lower numbers of vertices and low edge densities while two color-sequential algorithms (RLF1 and RLFD1) were superior on graphs having the higher numbers of vertices and high edge densities

Regionally acquired intestinal failure data suggest an underestimate in national service requirements

Objectives, setting and patients: With complete case referral for prolonged parenteral nutrition (PN) beyond term equivalent, serving a stable population of 1.25 million people, we describe the long-term outcome and survival of patients referred to an intestinal failure (IF) nutrition support team over the first 8 years of existence at a regional paediatric centre, and extrapolate to potential numbers of national home parenteral nutrition (HPN) cases and intestinal transplantation data. Design and outcome measures: Retrospective analysis detailing patient demographics, interventions, use of HPN, occurrence of intestinal failure-associated liver disease (IFALD), and outcomes of enteral adaptation, survival, and referral for and receipt of organ transplantation. Results: 23 patients were referred over 8 years, 20 being PN dependent within the neonatal period. Diagnoses included short bowel syndrome (SBS) (18), neuromuscular abnormalities (4) and congenital enterocyte disorder (1). 12 696 days of PN were delivered with 314 confirmed episodes of sepsis at a median of 12 episodes per patient. 144 central venous catheters (CVCs) were required at a median of four per patient. IFALD occurred in 17 (73%) patients, with 10 (44%) referred for transplant assessment. Thirteen (56%) children received HPN. Overall mortality was 44%. A significant predictor for survival in the SBS group was residual bowel >40 cm (82% vs 28%, p = 0.049). Conclusions: Survival for IF at 56% was lower than reported from non-UK supra-regional centres, and nationally collected data, possibly reflecting pre-selected referral populations. Data from regional centres with complete ascertainment may be important both when counselling parents and when planning regional and national HPN and IF specialist services

Superconductivity up to 29 K in SrFe2As2 and BaFe2As2 at high pressures

We report the discovery of superconductivity at high pressure in SrFe2As2 and BaFe2As2. The superconducting transition temperatures are up to 27 K in SrFe2As2 and 29 K in BaFe2As2, making these the highest pressure-induced superconducting materials discovered thus far.Comment: Accepted in Journal of Physics: Condensed Matte

IMAPS Observations of Interstellar Neutral Argon and the Implications for Partially Ionized Gas

We use the absorption features from neutral argon at 1048 and 1066 A to determine interstellar abundances or their lower limits toward nine early-type stars. These features were observed with the Interstellar Medium Absorption Profile Spectrograph (IMAPS) along sight lines with low reddening and low fractional abundances of molecular hydrogen. We find that the interstellar Ar I is below its solar and B-star abundance with respect to hydrogen toward zeta Pup, gamma2 Vel and beta Cen A with (logarithmic) reduction factors -0.37+/-0.09, -0.18+/-0.10, and -0.61+/-0.12 dex, respectively. While Ar can condense onto the surfaces of dust grains in the interiors of dense clouds, it is unlikely that argon atoms are depleted by this process in the low-density lines of sight considered in this study. Instead, we propose that the relatively large photoionization cross section of Ar makes it much easier to hide in its ionized form than H. In regions that are about half ionized, this effect can lower Ar I/H I by -0.11 to -0.96 dex, depending on the energy of the photoionizing radiation and its intensity divided by the local electron density. We apply this interpretation for the condition of the gas in front of beta Cen A, which shows the largest deficiency of Ar. Also, we determine the expected magnitudes of the differential ionizations for He, N, O, Ne and Ar in the partly ionized, warm gas in the local cloud around our solar system. For the local cloud and others that can be probed by UV studies, the observed Ar I to H I ratio may be a good discriminant between two possible alternatives, collisional ionization or photoionization, for explaining the existence of partly ionized regions.Comment: 36 pages, 3 figure

Determination of the Nature of the Tetragonal to Orthorhombic Phase Transition in SrFe_2As_2 by Measurement of the Local Order Parameter

SrFe2As2 is the end-member for a series of iron-pnictide superconductors and has a tetragonal-to-orthorhombic phase transition near 200 K. Previous macroscopic measurements to determine the nature of the transition gave seemingly inconsistent results so we use electron microscopy to monitor the local order parameter showing that the transformation is first order and that the orthorhombic phase grows as needle domains. This suggests the transition occurs via the passage of transformation dislocations, explaining the apparent inconsistencies. This mechanism may be common to similar transitions.Comment: 4 pages, 4 figures submitted to Physical Review Letters. Supplementary information can be found at http://cook.msm.cam.ac.uk/~supp_info/ An extra sentence in the second last paragraph and reference 16 has been adde