Structure of large random hypergraphs

The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump type Markov processes, established under simple conditions on the Laplace transforms of their Levy kernels. Furthermore, a related Gaussian approximation allows us to describe the randomness which may persist in the limit when certain parameters take critical values. Our method is quite general, but is applied here to vertex identifiability in random hypergraphs. A vertex v is identifiable in n steps if there is a hyperedge containing v all of whose other vertices are identifiable in fewer than n steps. We say that a hyperedge is identifiable if every one of its vertices is identifiable. Our analytic formulae describe the asymptotics of the number of identifiable vertices and the number of identifiable hyperedges for a Poisson random hypergraph on a set of N vertices, in the limit as N goes to infinity.Comment: Revised version with minor conceptual improvements and additional discussion. 32 pages, 5 figure

Differential equation approximations for Markov chains

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is emphasised. The general theory is illustrated in three examples: the classical stochastic epidemic, a population process model with fast and slow variables, and core-finding algorithms for large random hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Proton-Electron Hyperfine Coupling Constants of the Chlorophyll a Cation Radical by ENDOR Spectroscopy

In this paper we describe the assignment of the major coupling constants in monomer chlorophyll a cation free radical by ENDOR spectroscopy. To facilitate chemical manipulation methylpyrochlorophyllide a has been used as a stand-in, and a suite of six selectively deuterated derivatives have been subjected to ENDOR investigation. Details of the synthesis of these compounds are described. To study the effect of structural features on the spin distribution in the free radicals, six additional chlorophyll derivatives have been studied. Five coupling constants have been assigned, which account for about 80% of the observed electron spin resonance line width in the chlorophyll a monomer cation radical. The spin distribution appears to be highly asymmetric

A high pressure, high temperature combustor and turbine-cooling test facility

A new test facility is being constructed for developing turbine-cooling and combustor technology for future generation aircraft gas turbine engines. Prototype engine hardware will be investigated in this new facility at gas stream conditions up to 2480 K average turbine inlet temperature and 4.14 x 10 to the 6th power n sq m turbine inlet pressure. The facility will have the unique feature of fully automated control and data acquisition through the use of an integrated system of mini-computers and programmable controllers which will result in more effective use of operating time, will limit the number of operators required, and will provide built in self protection safety systems. The facility and the planning and design considerations are described

Calibration of Tests for Time Dilation in GRB Pulse Structures

Two tests for cosmological time dilation in $\gamma$-ray bursts -- the peak alignment and auto-correlation statistics -- involve averaging information near the times of peak intensity. Both tests require width corrections, assuming cosmological origin for bursts, since narrower temporal structure from higher energy would be redshifted into the band of observation, and since intervals between pulse structures are included in the averaging procedures. We analyze long ($>$ 2 s) BATSE bursts and estimate total width corrections for trial time-dilation factors (TDF = [1+$z_{\rm dim}$]/[1+$z_{\rm brt}$]) by time-dilating and redshifting bright bursts. Both tests reveal significant trends of increasing TDF with decreasing peak flux, but neither provides sufficient discriminatory power to distinguish between actual TDFs in the range 2--3.Comment: 5 pages in LATeX, REVTEX style, 2 embedded figures. To appear in Third Huntsville GRB Workshop Proceeding

Test for Time Dilation of Intervals Between Pulse Structures in GRBs

If $\gamma$-ray bursts are at cosmological distances, then not only their constituent pulses but also the intervals between pulses should be time-dilated. Unlike time-dilation measures of pulse emission, intervals would appear to require negligible correction for redshift of narrower temporal structure from higher energy into the band of observation. However, stretching of pulse intervals is inherently difficult to measure without incurring a timescale-dependent bias since, as time profiles are stretched, more structure can appear near the limit of resolution. This problem is compounded in dimmer bursts because identification of significant structures becomes more problematic. We attempt to minimize brightness bias by equalizing signal-to-noise (s/n) level of all bursts. We analyze wavelet-denoised burst profiles binned to several resolutions, identifying significant fluctuations between pulse structures and interjacent valleys. When bursts are ranked by peak flux, an interval time-dilation signature is evident, but its magnitude and significance are dependent upon temporal resolution and s/n level.Comment: 5 pages in LATeX, REVTEX style, 2 embedded figures. To appear in Third Huntsville GRB Workshop Proceeding

A Model for Short Gamma-Ray Bursts: Heated Neutron Stars in Close Binary Systems

In this paper we present a model for the short (< second) population of gamma-ray bursts (GRBs). In this model heated neutron stars in a close binary system near their last stable orbit emit neutrinos at large luminosities (~ 10^53 ergs/sec). A fraction of these neutrinos will annihilate to form an electron-positron pair plasma wind which will, in turn, expand and recombine to photons which make the gamma-ray burst. We study neutrino annihilation and show that a substantial fraction (~ 50%) of energy deposited comes from inter-star neutrinos, where each member of the neutrino pair originates from each neutron star. Thus, in addition to the annihilation of neutrinos blowing off of a single star, we have a new source of baryon free energy that is deposited between the stars. To model the pair plasma wind between stars, we do three-dimensional relativistic numerical hydrodynamic calculations. Preliminary results are also presented of new, fully general relativistic calculations of gravitationally attracting stars falling from infinity with no angular momentum. These simulations exhibit a compression effect.Comment: 3 pages, 3 postscript figs (2 color), to appear in "Gamma-Ray Burst and Afterglow Astronomy 2001", Woods Hole; 5-9 Nov, 200