Continuous and discontinuous phase transitions in hypergraph processes

Let V denote a set of N vertices. To construct a "hypergraph process", create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with arbitrary probability generating function r(x), except that we assume P(K=1) +P(K=2) > 0. Given K=k, the k vertices appearing in the new hyperedge are selected uniformly at random from V. Hyperedges of cardinality 1 are called patches, and serve as a way of selecting root vertices. Identifiable vertices are those which are reachable from these root vertices, in a strong sense which generalizes the notion of graph component. Hyperedges are also called identifiable if all of their vertices are identifiable. We use "fluid limit" scaling: hyperedges arrive at rate N, and we study structures of size O(1) and O(N). After division by N, numbers of identifiable vertices and reducible hyperedges exhibit phase transitions, which may be continuous or discontinuous depending on the shape of the structure function -log(1 - x)/r'(x), for x in (0,1). Both the case P(K=1) > 0 and the case P(K=1) = 0 < P(K=2) are considered; for the latter, a single extraneous patch is added to mark the root vertex.Comment: 25 pages, 2 figures. Revised version. To appear in Random Structures & Algorithm

HI and OH absorption in the lensing galaxy of MG J0414+0534

We report the detection of \HI 21-cm absorption in the $z=0.96$ early-type lensing galaxy towards MG J0414+0534 with the Green Bank Telescope. The absorption, with total $N_{\rm HI}=1.6 \times 10^{18} (T_{\rm s}/f) {\rm cm}^{-2}$, is resolved into two strong components, probably due to the two strongest lens components, which are separated by 0.4\arcsec. Unlike the other three lenses which have been detected in \HI, J0414+0534 does not exhibit strong OH absorption, giving a OH/\HI column density ratio of N_{\rm OH}/N_{\rm HI}\lapp10^{-6} (for $T_{\rm s}=100$ K, $T_{\rm x}=10$ K and $f_{\rm HI}=f_{\rm OH}=1$). This underabundance of molecular gas may indicate that the extreme optical--near-IR colour ($V-K=10.26$) along the line-of-sight is not due to the lens. We therefore suggest that despite the strong upper limits on molecular absorption at the quasar redshift, as traced by millimetre lines, the extinction occurs primarily in the quasar host galaxy.Comment: Accepted by MNRAS Letters, 5 (and a bit) pages, 5 figure

Cosmological Bounds on Spatial Variations of Physical Constants

We derive strong observational limits on any possible large-scale spatial variation in the values of physical 'constants' whose space-time evolution is driven by a scalar field. The limits are imposed by the isotropy of the microwave background on large angular scales in theories which describe space and time variations in the fine structure constant, the electron-proton mass ratio, and the Newtonian gravitational constant, G. Large-scale spatial fluctuations in the fine structure constant are bounded by 2x10^-9 and 1.2x10^-8 in the BSBM and VSL theories respectively, fluctuations in the electron-proton mass ratio by 9x10^-5 in the BM theory and fluctuations in G by 3.6x10^-10 in Brans-Dicke theory. These derived bounds are significantly stronger than any obtainable by direct observations of astrophysical objects at the present time.Comment: 13 pages, 1 table, typos corrected, refs added. Published versio

Relaxation at late stages in an entropy barrier model for glassy systems

The ground state dynamics of an entropy barrier model proposed recently for describing relaxation of glassy systems is considered. At stages of evolution the dynamics can be described by a simple variant of the Ehrenfest urn model. Analytical expression for the relaxation times from an arbitrary state to the ground state is derived. Upper and lower bounds for the relaxation times as a function of system size are obtained.Comment: 9 pages no figures. to appear in J.Phys. A: Math. and Ge

Calcium isotopic composition of high-latitude proxy carrier Neogloboquadrina pachyderma (sin.)

International audienceThe accurate reconstruction of sea surface temperature (SST) history in climate-sensitive regions (e.g. tropical and polar oceans) became a challenging task in palaeoceanographic research. However, biogenic shell carbonate SST proxies successfully developed for tropical regions often fail in cool water environments. Their major regional shortcomings and the cryptic diversity now found within the major high latitude proxy carrier Neogloboquadrina pachyderma (sin.) highlight an urgent need to develop complementary SST proxies for these cool water regions. Here we incorporate the genetic component into a calibration study of a new SST proxy for the high latitudes. We found that the calcium isotopic composition (?44/40Ca) of calcite from genotyped net catches and core-top samples of the planktonic foraminifera Neogloboquadrina pachyderma (sin) is strongly related to temperature and unaffected by genetic variations. The temperature sensitivity has been found to be 0.17 (±0.04)? per 1°C highlighting its potential for downcore applications in open marine cool-water environments. Our results further indicate that however in extreme polar environments, below a critical threshold temperature of 2.0 (±0.5)°C and salinity of 33.0 (±0.5)? a prominent shift in biomineralization affect the Ca isotope composition of N. pachyderma (sin.) becoming insensitive to temperature. These findings highlight the need of systematic calibration studies to unravel the influencing factors on Ca isotope fractionation and to validate the proxies' applicability

Elastic and thermodynamic properties of the shape-memory alloy AuZn

The current work reports on the elastic shear moduli, internal friction, and the specific heat of the B2 cubic ordered alloy AuZn as a function of temperature. Measurements were made on single-crystal and polycrystalline samples using Resonant Ultrasound Spectroscopy (RUS), semi-adiabatic calorimetry and stress-strain measurements. Our results confirm that this alloy exhibits the shape-memory effect and a phase transition at 64.75 K that appears to be continuous (second-order) from the specific heat data. It is argued that the combination of equiatomic composition and a low transformation temperature constrain the chemical potential and its derivatives to exhibit behavior that lies at the borderline between that of a first-order (discontinuous) and a continuous phase transition. The acoustic dissipation does not peak at the transtion temperature as expected, but shows a maximum well into the low-temperature phase. The Debye temeprature value of 219 K, obtained from the low-temperature specific heat data is in favorable agreement with that determined from the acoustic data (207 K) above the transition.Comment: 25 pages, 6 figures, submitted to Phys. Rev.

Hidden breakpoints in genome alignments

During the course of evolution, an organism's genome can undergo changes that affect the large-scale structure of the genome. These changes include gene gain, loss, duplication, chromosome fusion, fission, and rearrangement. When gene gain and loss occurs in addition to other types of rearrangement, breakpoints of rearrangement can exist that are only detectable by comparison of three or more genomes. An arbitrarily large number of these "hidden" breakpoints can exist among genomes that exhibit no rearrangements in pairwise comparisons. We present an extension of the multichromosomal breakpoint median problem to genomes that have undergone gene gain and loss. We then demonstrate that the median distance among three genomes can be used to calculate a lower bound on the number of hidden breakpoints present. We provide an implementation of this calculation including the median distance, along with some practical improvements on the time complexity of the underlying algorithm. We apply our approach to measure the abundance of hidden breakpoints in simulated data sets under a wide range of evolutionary scenarios. We demonstrate that in simulations the hidden breakpoint counts depend strongly on relative rates of inversion and gene gain/loss. Finally we apply current multiple genome aligners to the simulated genomes, and show that all aligners introduce a high degree of error in hidden breakpoint counts, and that this error grows with evolutionary distance in the simulation. Our results suggest that hidden breakpoint error may be pervasive in genome alignments.Comment: 13 pages, 4 figure

High-dimensional quantum dynamics of adsorption and desorption of H2_2 at Cu(111)

We performed high-dimensional quantum dynamical calculations of the dissociative adsorption and associative desorption of hydrogen on Cu(111). The potential energy surface (PES) is obtained from density functional theory calculations. Two regimes of dynamics are found, at low energies sticking is determined by the minimum energy barrier, at high energies by the distribution of barrier heights. Experimental results are well-reproduced qualitatively, but some quantitative discrepancies are identified as well.Comment: 4 two column pages, revtex, 4 figures, to appear in Phys. Rev. Let

ALMA Observations of Circumnuclear Disks in Early Type Galaxies: 12CO(2-1) and Continuum Properties

We present results from an Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 2 program to map CO(2-1) emission in nearby early-type galaxies (ETGs) that host circumnuclear gas disks. We obtained $\sim0.3''-$resolution Band 6 observations of seven ETGs selected on the basis of dust disks in Hubble Space Telescope images. We detect CO emission in five at high signal-to-noise ratio with the remaining two only faintly detected. All CO emission is coincident with the dust and is in dynamically cold rotation. Four ETGs show evidence of rapid central rotation; these are prime candidates for higher-resolution ALMA observations to measure the black hole masses. In this paper we focus on the molecular gas and continuum properties. Total gas masses and H$_2$ column densities for our five CO-bright galaxies are on average $\sim10^8$ $M_\odot$ and $\sim10^{22.5}$ cm$^{-2}$ over the $\sim$kpc-scale disks, and analysis suggests that these disks are stabilized against gravitational fragmentation. The continuum emission of all seven galaxies is dominated by a central, unresolved source, and in five we also detect a spatially extended component. The $\sim$230 GHz nuclear continua are modeled as power laws ranging from $S_\nu \sim \nu^{-0.4}$ to $\nu^{1.6}$ within the observed frequency band. The extended continuum profiles of the two radio-bright (and CO-faint) galaxies are roughly aligned with their radio jet and suggests resolved synchrotron jets. The extended continua of the CO-bright disks are coincident with optically thick dust absorption and have spectral slopes that are consistent with thermal dust emission.Comment: 20 pages, 10 figures; accepted for publication in Ap

Studying changes in the practice of two teachers developing assessment for learning

This paper describes changes in the practice of two teachers, observed over an eighteen month period, who were participating in a study intended to support teachers in developing their use of assessment in support of learning. The design of the intervention allowed each teacher to choose for themselves which aspects of their practice to develop. Analysis of lesson observations, journal entries and interviews indicate that both teachers were keen to change their practice, but were concerned about the disruption to their established routines, and in particular about the potential for loss of control of their classes. Both teachers did effect significant changes in their classrooms, but these tended to be developments of existing preferred ways of working, rather than radical innovations. In conclusion, it is suggested that to be most effective, teacher professional development needs to be structured strongly enough to afford teacher growth, but flexible enough to allow different teachers to take their practice in different ways