A note on bounds for the cop number using tree decompositions

In this short note, we supply a new upper bound on the cop number in terms of tree decompositions. Our results in some cases extend a previously derived bound on the cop number using treewidth

Low Frequency VLA Observations of Abell 754: Evidence for a Cluster Radio Halo and Possible Radio Relics

We present 74 MHz and 330 MHz VLA observations of Abell 754. Diffuse, halo-like emission is detected from the center of the cluster at both frequencies. At 330 MHz the resolution of 90'' distinguishes this extended emission from previously known point sources. In addition to the halo and at a much lower level, outlying steep-spectrum emission regions straddle the cluster center and are seen only at 74 MHz. The location, morphology and spectrum of this emission are all highly suggestive of at least one, and possibly two cluster radio relics. Easily obtained higher resolution, higher sensitivity VLA observations at both frequencies are required to confirm the extended nature of the halo-like emission and the 74 MHz relic detections. However, since there is prior evidence that this cluster is or has recently been in the process of a major merger event, the possible discovery of relics in this system is of great interest in light of recent observational and theoretical evidence in favor of a merger-relic connection. We discuss the possible role the merger shock waves, which are seen in the X-ray emission, may have played in the formation of the halo and radio relics in A754.Comment: 15 pages including 4 figures. Accepted for publication by Ap

Hyperopic Cops and Robbers

We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the usual cop number, the hyperopic cop number is at most 3. The hyperopic cop number is considered for countable graphs, and it is shown that for connected chains of graphs, the hyperopic cop density can be any real number in $[0,1/2].

Pisces IV submersible observations in the epicentral region of the 1929 Grand Banks earthquake

The PISCES IVsubmersible was used to investigate the upper continental slope around 44 ON, 56 W, near the epicentre of the 1929 Grand Banks earthquake. Four dives in water depths of 800-2000 m were undertaken to observe speci3c features identijied with the SeaMARC I sidescan system in 1983. Two dives were made in the head of Eastern Valley where pebbly mudstones ofprobable Pleistocene age were recognized outcropping on the seafloor. Constructional features of cobbles and boulders, derived by exhumation and reworking of the pebbly mudstone, were also observed. These include gravel/sand bedforms (transverse waves) on the valley floor. Slope failure features in semiconsolidated mudstone were recognized on two dives onto the St. Pierre slope. Exposures in these mudstones are rapidly eroded by intense burrowing by benthic organisms

The Origin of Episodic Accretion Bursts in the Early Stages of Star Formation

We study numerically the evolution of rotating cloud cores, from the collapse of a magnetically supercritical core to the formation of a protostar and the development of a protostellar disk during the main accretion phase. We find that the disk quickly becomes unstable to the development of a spiral structure similar to that observed recently in AB Aurigae. A continuous infall of matter from the protostellar envelope makes the protostellar disk unstable, leading to spiral arms and the formation of dense protostellar/protoplanetary clumps within them. The growing strength of spiral arms and ensuing redistribution of mass and angular momentum creates a strong centrifugal disbalance in the disk and triggers bursts of mass accretion during which the dense protostellar/protoplanetary clumps fall onto the central protostar. These episodes of clump infall may manifest themselves as episodes of vigorous accretion rate (\ge 10^{-4} M_sun/yr) as is observed in FU Orionis variables. Between these accretion bursts, the protostar is characterized by a low accretion rate (< 10^{-6} M_sun/yr). During the phase of episodic accretion, the mass of the protostellar disk remains less than or comparable to the mass of the protostar.Comment: 5 pages, 2 figures, accepted for publication in ApJ

The invertebrate Caenorhabditis elegans biosynthesizes ascorbate.

l-Ascorbate, commonly known as vitamin C, serves as an antioxidant and cofactor essential for many biological processes. Distinct ascorbate biosynthetic pathways have been established for animals and plants, but little is known about the presence or synthesis of this molecule in invertebrate species. We have investigated ascorbate metabolism in the nematode Caenorhabditis elegans, where this molecule would be expected to play roles in oxidative stress resistance and as cofactor in collagen and neurotransmitter synthesis. Using high-performance liquid chromatography and gas-chromatography mass spectrometry, we determined that ascorbate is present at low amounts in the egg stage, L1 larvae, and mixed animal populations, with the egg stage containing the highest concentrations. Incubating C. elegans with precursor molecules necessary for ascorbate synthesis in plants and animals did not significantly alter ascorbate levels. Furthermore, bioinformatic analyses did not support the presence in C. elegans of either the plant or the animal biosynthetic pathway. However, we observed the complete (13)C-labeling of ascorbate when C. elegans was grown with (13)C-labeled Escherichia coli as a food source. These results support the hypothesis that ascorbate biosynthesis in invertebrates may proceed by a novel pathway and lay the foundation for a broader understanding of its biological role

Modelling concentration fluctuation moments for spherically symmetric mean concentration

Clarke and Mole (Environmetrics, 6 (1995) 607-617) presented a model for concentration fluctuation moments of a passive scalar dispersing in a turbulent flow. This followed Sullivan and Moseley’s work in making use of the equation for the evolution of the concentration moments integrated over all space, together with Chatwin and Sullivan’s (J. Fluid Mech., 212 (1990) 533-556) description relating higher moments to the mean concentration. The model incorporated a simple closure to express the concentration gradient in terms of the concentration. Numerical results were presented for 1, 2 and 3 spatial dimensions under the assumption that the spatial distribution of the mean concentration was spherically symmetric and Gaussian. Two simple functional forms were used for the spreading rate of the mean cloud. Here those results are briefly summarised. Some asymptotic large time results are also given for spherically symmetric mean concentration of general functional form, and numerical results are obtained for a number of different functional forms