Algebraic and combinatorial aspects of sandpile monoids on directed graphs

The sandpile group of a graph is a well-studied object that combines ideas from algebraic graph theory, group theory, dynamical systems, and statistical physics. A graph's sandpile group is part of a larger algebraic structure on the graph, known as its sandpile monoid. Most of the work on sandpiles so far has focused on the sandpile group rather than the sandpile monoid of a graph, and has also assumed the underlying graph to be undirected. A notable exception is the recent work of Babai and Toumpakari, which builds up the theory of sandpile monoids on directed graphs from scratch and provides many connections between the combinatorics of a graph and the algebraic aspects of its sandpile monoid. In this paper we primarily consider sandpile monoids on directed graphs, and we extend the existing theory in four main ways. First, we give a combinatorial classification of the maximal subgroups of a sandpile monoid on a directed graph in terms of the sandpile groups of certain easily-identifiable subgraphs. Second, we point out certain sandpile results for undirected graphs that are really results for sandpile monoids on directed graphs that contain exactly two idempotents. Third, we give a new algebraic constraint that sandpile monoids must satisfy and exhibit two infinite families of monoids that cannot be realized as sandpile monoids on any graph. Finally, we give an explicit combinatorial description of the sandpile group identity for every graph in a family of directed graphs which generalizes the family of (undirected) distance-regular graphs. This family includes many other graphs of interest, including iterated wheels, regular trees, and regular tournaments.Comment: v2: Cleaner presentation, new results in final section. Accepted for publication in J. Combin. Theory Ser. A. 21 pages, 5 figure

A Comparative Analysis of Post-Traumatic Stress Syndrome among Individuals Exposed to Different Stressor Events

The purpose of the present study was to compare post-traumatic stress syndrome among persons involved in nine different stressor events: combat in the Vietnam War; rape; serious life-threatening events; divorce; the death of a significant other; critical, near fatal illness of a significant other; family trauma; multiple traumatic events; and no stressful event. To assess the severity of the symptoms which define post-traumatic stress disorder (PTSD), the Impact of Event Scale, the Beck Depression Inventory, the Stress Assessment Scale for PTSD from the Vietnam Era Stress Inventory (Wilson & Krauss, 1980) and the Sensation Seeking Scale were administered to the participants (N=409). A person by situation conceptual model of PTSD was presented from which two major hypotheses were tested. As predicted from the model, the degree of loss of a significant other and life-threat were predictive of syndromespecific symptoms of PTSD. The results of the study strongly support the heuristic value of an interactionist model of PTSD

A computer controlled power tool for the servicing of the Hubble Space Telescope

The Hubble Space Telescope (HST) Pistol Grip Tool (PGT) is a self-contained, microprocessor controlled, battery-powered, 3/8-inch-drive hand-held tool. The PGT is also a non-powered ratchet wrench. This tool will be used by astronauts during Extravehicular Activity (EVA) to apply torque to the HST and HST Servicing Support Equipment mechanical interfaces and fasteners. Numerous torque, speed, and turn or angle limits are programmed into the PGT for use during various missions. Batteries are replaceable during ground operations, Intravehicular Activities, and EVA's

High-sensitivity cardiac troponin concentrations at presentation in patients with ST-segment elevation myocardial infarction

No abstract available

A First Catalog of Variable Stars Measured by the Asteroid Terrestrial-impact Last Alert System (ATLAS)

The Asteroid Terrestrial-impact Last Alert System (ATLAS) carries out its primary planetary defense mission by surveying about 13000 deg^2 at least four times per night. The resulting data set is useful for the discovery of variable stars to a magnitude limit fainter than r~18, with amplitudes down to 0.01 mag for bright objects. Here we present a Data Release One catalog of variable stars based on analyzing 142 million stars measured at least 100 times in the first two years of ATLAS operations. Using a Lomb-Scargle periodogram and other variability metrics, we identify 4.7 million candidate variables which we analyze in detail. Through Space Telescope Science Institute, we publicly release lightcurves for all of them, together with a vector of 169 classification features for each star. We do this at the level of unconfirmed candidate variables in order to provide the community with a large set of homogeneously analyzed photometry and avoid pre-judging which types of objects others may find most interesting. We use machine learning to classify the candidates into fifteen different broad categories based on lightcurve morphology. About 10% (430,000 stars) pass extensive tests designed to screen out spurious variability detections: we label these as `probable' variables. Of these, 230,000 receive specific classifications as eclipsing binaries, pulsating, Mira-type, or sinusoidal variables: these are the `classified' variables. New discoveries among the probable variables number more than 300,000, while 150,000 of the classified variables are new, including about 10,000 pulsating variables, 2,000 Mira stars, and 70,000 eclipsing binaries.Comment: Accepted by AJ; gives instructions for querying ATLAS variable star database; this new version has nicer lightcurve figure

Constraints on the Progenitor of SN 2016gkg From Its Shock-Cooling Light Curve

SN 2016gkg is a nearby Type IIb supernova discovered shortly after explosion. Like several other Type IIb events with early-time data, SN 2016gkg displays a double-peaked light curve, with the first peak associated with the cooling of a low-mass extended progenitor envelope. We present unprecedented intranight-cadence multi-band photometric coverage of the first light-curve peak of SN 2016gkg obtained from the Las Cumbres Observatory Global Telescope network, the Asteroid Terrestrial-impact Last Alert System, the Swift satellite and various amateur-operated telescopes. Fitting these data to analytical shock-cooling models gives a progenitor radius of ~25-140 solar radii with ~2-30 x 10^-2 solar masses of material in the extended envelope (depending on the model and the assumed host-galaxy extinction). Our radius estimates are broadly consistent with values derived independently (in other works) from HST imaging of the progenitor star. However, the shock-cooling model radii are on the lower end of the values indicated by pre-explosion imaging. Hydrodynamical simulations could refine the progenitor parameters deduced from the shock-cooling emission and test the analytical models.Comment: Accepted by ApJ

The Baryonic Tully Fisher Relation

We validate the baryonic Tully Fisher (BTF) relation by exploring the Tully Fish er (TF) and BTF properties of optically and HI-selected disk galaxies. The data includes galaxies from: Sakai et al. (2000) calibrator sample; McGaugh et al. (2000: MC2000) I-band sample; and 18 newly acquired HI-selected field dwarf galaxies observed with the ANU 2.3m telescope and the ATNF Parkes telescope from Gurovich's thesis sample (2005). As in MC2000, we re-cast the TF and BTF relations as relationships between baryo n mass and W_{20}. First we report some numerical errors in MC2000. Then, we c alculate weighted bi-variate linear fits to the data, and finally we compare the fits of the intrinsically fainter dwarfs with the brighter galaxies of Sakai et al. (2000). With regards to the local calibrator disk galaxies of Sakai et al. (2000), our results suggest that the BTF relation is indeed tighter than the T F relation and that the slopes of the BTF relations are statistically flatter th an the equivalent TF relations. Further, for the fainter galaxies which include the I-band MCG2000 and HI-selected galaxies of Gurovich's thesis sample, we calc ulate a break from a simple power law model because of what appears to be real c osmic scatter. Not withstanding this point, the BTF models are marginally better models than the equivalent TF ones with slightly smaller reduced chi^2.Comment: 3 pages, 3 figs, refereed conference proceeding based on an invited talk at the Structure and Dynamics in the Local Universe, a Sydney workshop to honour Brent Tully's 60th birthday. To appear in Publications of the Astronomical Society of Australia, ed. J. Bland-Hawthor

Measuring nickel masses in Type Ia supernovae using cobalt emission in nebular phase spectra

The light curves of Type Ia supernovae (SNe Ia) are powered by the radioactive decay of $^{56}$Ni to $^{56}$Co at early times, and the decay of $^{56}$Co to $^{56}$Fe from ~60 days after explosion. We examine the evolution of the [Co III] 5892 A emission complex during the nebular phase for SNe Ia with multiple nebular spectra and show that the line flux follows the square of the mass of $^{56}$Co as a function of time. This result indicates both efficient local energy deposition from positrons produced in $^{56}$Co decay, and long-term stability of the ionization state of the nebula. We compile 77 nebular spectra of 25 SN Ia from the literature and present 17 new nebular spectra of 7 SNe Ia, including SN2014J. From these we measure the flux in the [Co III] 5892 A line and remove its well-behaved time dependence to infer the initial mass of $^{56}$Ni ($M_{Ni}$) produced in the explosion. We then examine $^{56}$Ni yields for different SN Ia ejected masses ($M_{ej}$ - calculated using the relation between light curve width and ejected mass) and find the $^{56}$Ni masses of SNe Ia fall into two regimes: for narrow light curves (low stretch s~0.7-0.9), $M_{Ni}$ is clustered near $M_{Ni}$ ~ 0.4$M_\odot$ and shows a shallow increase as $M_{ej}$ increases from ~1-1.4$M_\odot$; at high stretch, $M_{ej}$ clusters at the Chandrasekhar mass (1.4$M_\odot$) while $M_{Ni}$ spans a broad range from 0.6-1.2$M_\odot$. This could constitute evidence for two distinct SN Ia explosion mechanisms.Comment: 16 pages, 12 figures (main text), plus data tables in appendix. Spectra released on WISeREP. Submitted to MNRAS, comments welcom