Counting Hamilton cycles in sparse random directed graphs

Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically $n!(p(1+o(1)))^{n}$. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically $n!(\log n/n(1+o(1)))^{n}$ directed Hamilton cycles

Structure of Supergiant Shells in the Large Magellanic Cloud

Nine supergiant shells (SGSs) have been identified in the Large Magellanic Cloud (LMC) based on H-alpha images, and twenty-three SGSs have been reported based on HI 21-cm line observations, but these sets do not always identify the same structures. We have examined the physical structure of the optically identified SGSs using HI channel maps and P-V diagrams to analyze the gas kinematics. There is good evidence for seven of the nine optically identified SGSs to be true shells. Of these seven H-alpha SGSs, four are the ionized inner walls of HI SGSs, while three are an ionized portion of a larger and more complex HI structure. All of the H-alpha SGSs are identified as such because they have OB associations along the periphery or in the center, with younger OB associations more often found along the periphery. After roughly 12 Myrs, if no new OB associations have been formed a SGS will cease to be identifiable at visible wavelengths. Thus, the presence and location of ionizing sources is the main distinction between shells seen only in HI and those also seen in H-alpha. Based on our analysis, H-alpha observations alone cannot unambiguously identify SGSs, especially in distant galaxies.Comment: 26 pages, 16 figures, accepted for publication in the Astrophysical Journal Supplemen

Effects of a Supportive Audience on a Handgrip Squeezing Task in Adults

International Journal of Exercise Science 9(1): 4-15, 2016. The role of social facilitation by way of audience effect in select exercise-related variables during an isometric handgrip task was assessed using a mixed design. Fifty three moderately active participants (Mage= 21.76 + 5.27) were recruited from the Midwestern United States. Participants were randomly assigned to one of two groups: supportive audience or control. Audience members provided positive verbal encouragement to participants in the experimental condition throughout the task performance. Participants in the control group performed the task in the absence of an audience and did not receive any verbal encouragement. Participants provided anxiety ratings pre- and post-task using the State-trait anxiety inventory for adults (STAI). Participants’ ratings of perceived exertion (RPE) and heart rate (HR) were monitored and assessed at 30-second intervals. Upon task completion, sustained effort in the form of time on task was recorded in seconds. A repeated measures analysis of variance (RM ANOVA) revealed that there was a time effect within groups of HR = ( F(2.64, 131.85) = 189.3 , p \u3c0.001) and within groups of RPE = (F(2.97, 139.42) = 2189.43 p \u3c0.001). An independent sample T-test revealed significant differences in HR at 0, 30 and 60 seconds between the groups. An independent sample T-test revealed no significant differences in anxiety and RPE between the groups. These results partially support the notion of social facilitation and may have implications for research and practice

Relativistic Hydrodynamics for Heavy--Ion Collisions: Freeze--Out and Particle Spectra

We investigate freeze--out in hydrodynamic models for relativistic heavy--ion collisions. In particular, instantaneous freeze--out across a hypersurface of constant temperature (``isothermal'' freeze--out) is compared with that across a hypersurface at constant time in the center-of-momentum frame (``isochronous'' freeze--out). For one--dimensional (longitudinal) expansion the rapidity distributions are shown to differ significantly in the two scenarios, while the transverse momentum spectra are remarkably similar. We also investigate the rapidity distribution in greater detail and show that the Gaussian-like shape of this distribution commonly associated with the Landau expansion model in general emerges only if one neglects contributions from time-like parts of the isothermal freeze--out hypersurface.Comment: 12 figure

Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory

The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a consistent possibility of coupling them also by axial or chiral type currents. Static self dual vortex solutions together with a vortex-lattice are found with the new couplings.Comment: Plain TEX, 10 page

Silent Transitions in Automata with Storage

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.Comment: 32 pages, submitte

Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets

A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed whithin the anyon theory. Thus, we show that static magnetic vortices correspond to the self-dual Chern - Simons solitons and are described by the Liouville equation. The related magnetic topological charge is associated with the electric charge of anyons. Furthermore, vortex - antivortex configurations are described by the sinh-Gordon equation and its conformally invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199