A random hierarchical lattice: the series-parallel graph and its properties

We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability $p$ and $1-p$ respectively. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at $p=1/2$

Central limit theorems for the spectra of classes of random fractals

We discuss the spectral asymptotics of some open subsets of the real line with random fractal boundary and of a random fractal, the continuum random tree. In the case of open subsets with random fractal boundary we establish the existence of the second order term in the asymptotics almost surely and then determine when there will be a central limit theorem which captures the fluctuations around this limit. We will show examples from a class of random fractals generated from Dirichlet distributions as this is a relatively simple setting in which there are sets where there will and will not be a central limit theorem. The Brownian continuum random tree can also be viewed as a random fractal generated by a Dirichlet distribution. The first order term in the spectral asymptotics is known almost surely and here we show that there is a central limit theorem describing the fluctuations about this, though the positivity of the variance arising in the central limit theorem is left open. In both cases these fractals can be described through a general Crump-Mode-Jagers branching process and we exploit this connection to establish our central limit theorems for the higher order terms in the spectral asymptotics. Our main tool is a central limit theorem for such general branching processes which we prove under conditions which are weaker than those previously known

The Solar Neighborhood XV: Discovery of New High Proper Motion Stars with mu >= 0.4"/yr between Declinations -47 degrees and 00 degrees

We report the discovery of 152 new high proper motion systems (mu >= 0.4"/yr) in the southern sky (Declination = -47 degrees to 00 degrees) brighter than UKST plate R_{59F} =16.5 via our SuperCOSMOS-RECONS (SCR) search. This paper complements Paper XII in The Solar Neighborhood series, which covered the region from Declination = -90 degrees to -47 degrees and discussed all 147 new systems from the southernmost phase of the search. Among the total of 299 systems from both papers, there are 148 (71 in Paper XII, 77 in this paper) new systems moving faster than 0.5"/yr that are additions to the classic ``LHS'' (Luyten Half Second) sample. These constitute an 8% increase in the sample of all stellar systems with mu >= 0.5"/yr in the southern sky. As in Paper XII, distance estimates are provided for the systems reported here based upon a combination of photographic plate magnitudes and 2MASS photometry, assuming all stars are on the main sequence. Two SCR systems from the portion of the sky included in this paper are anticipated to be within 10 pc, and an additional 23 are within 25 pc. In total, the results presented in Paper XII and here for this SCR sweep of the entire southern sky include five new systems within 10 pc and 38 more between 10 and 25 pc. The largest number of nearby systems have been found in the slowest proper motion bin, 0.6"/yr > mu >= 0.4"/yr, indicating that there may be a large population of low proper motion systems very near the Sun.Comment: 36 pages, 5 figures, accepted for publication in Astronomical Journa

Evaluating the impact of the graduate fellowship programme of the International Livestock Research Institute. A tools and process report

Post graduate research projects are an effective method for building new research capacity in sub-Saharan Africa. The International Livestock Research Institute (ILRI) offers a graduate fellowship programme for scientists from developing and developed countries. This is done in partnership with universities in African and Asian countries, Europe, Australia and North America. To date such programmes have not been adequately assessed to find the impact on national research capacity, the graduate fellows and the partner institutions. To assess the value of this training, ILRI conducted an impact study of its graduate fellows in Kenya and Ethiopia between 1978 and 1997. This report presents the tools and methods used in this study. Others may use these freely, but appropriate acknowledgement of the source will be appreciated. Future users may modify these instruments for their own impact studies; and indeed are encouraged to do so. We recognise that many improvements could be made and request feedback from others on how they have accomplished this. This report also presents part of the results to enable those interested in future impact studies in Ethiopia or Kenya to use the data as a benchmark

FUSE Observations of the Magellanic Bridge Gas toward Two Early-Type Stars: Molecules, Physical Conditions, and Relative Abundance

We discuss FUSE observations of two early-type stars, DI1388 and DGIK975, in the low density and low metallicity gas of Magellanic Bridge (MB). Toward DI1388, the FUSE observations show molecular hydrogen, O VI, and numerous other atomic or ionic transitions in absorption, implying the presence of multiple gas phases in a complex arrangement. The relative abundance pattern in the MB is attributed to varying degrees of depletion onto dust similar to that of halo clouds. The N/O ratio is near solar, much higher than N/O in damped Ly-alpha systems, implying subsequent stellar processing to explain the origin of nitrogen in the MB. The diffuse molecular cloud in this direction has a low column density and low molecular fraction. H2 is observed in both the Magellanic Stream and the MB, yet massive stars form only in the MB, implying significantly different physical processes between them. In the MB some of the H2 could have been pulled out from the SMC via tidal interaction, but some also could have formed in situ in dense clouds where star formation might have taken place. Toward DGIK975, the presence of neutral, weakly and highly ionized species suggest that this sight line has also several complex gas phases. The highly ionized species of O VI, C IV, and Si IV toward both stars have very broad features, indicating that multiple components of hot gas at different velocities are present. Several sources (a combination of turbulent mixing layer, conductive heating, and cooling flows) may be contributing to the production of the highly ionized gas in the MB. Finally, this study has confirmed previous results that the high-velocity cloud HVC 291.5-41.2+80 is mainly ionized composed of weakly and highly ions. The high ion ratios are consistent with a radiatively cooling gas in a fountain flow model.Comment: Accepted for publication in the ApJ (October 10, 2002). Added reference (Gibson et al. 2000

Two new pulsating hot subdwarf stars from the Edinburgh-Cape survey

We report the discovery of very rapid pulsations in two hot subdwarf stars from the Edinburgh- Cape blue object survey. The short periods, small amplitudes and multiperiodicity establish these stars as members of the class of rapidly-pulsating sdB stars. The spectrograms of both stars, however, show relatively strong He II 4686 and they are therefore more properly classified as sdOB. The light curve of EC 01541?1409 is dominated by two strong (?1 per cent) variations with frequencies near 7114 and 7870 ?Hz (periods near 140.6 and 127.1 s), though at least five frequencies are present with amplitudes above about 0.002 mag. The light curve of EC 22221?3152 appears to be generated by at least 10 frequencies in the range 5670-11850 ?Hz (about 175-85 s) with amplitudes between about 0.01 and 0.001 mag, including the first overtone of the strongest variation. Somewhat surprisingly, this number of frequencies is detectable in observing runs as short as 3 h, probably due to the fact that the detected frequencies are well-separated.IS

The Edinburgh-Cape Blue Object Survey - III. Zone 2; galactic latitudes -30? > b > -40?

The Edinburgh–Cape Blue Object Survey seeks to identify point sources with an ultraviolet excess. Results for zone 2 of the survey are presented here, covering that part of the South Galactic Cap between 30◦ and 40◦ from the Galactic plane and south of about −12. ◦ 3 of declination. Edinburgh–Cape zone 2 comprises 66 UK Schmidt Telescope fields covering about 1730 deg2, in which we find some 892 blue objects, including 423 hot subdwarfs (∼47 per cent); 128 white dwarfs (∼14 per cent); 25 cataclysmic variables (∼3 per cent); 119 binaries (∼13 per cent), mostly composed of a hot subdwarf and a main-sequence F or G star; 66 horizontal branch stars (∼7 per cent) and 48 ‘star-like’ extragalactic objects (∼5 per cent). A further 362 stars observed in the survey, mainly low-metallicity F- and G-type stars, are also listed. Both low-dispersion spectroscopic classification and UBV photometry are presented for almost all of the hot objects and either spectroscopy or photometry (or both) for the cooler ones.Department of HE and Training approved lis

A Search for Photometric Rotation Periods in Low-Mass Stars and Brown Dwarfs in the Pleiades

We have photometrically monitored (Cousins Ic) eight low mass stars and brown dwarfs which are probable members of the Pleiades. We derived rotation periods for two of the stars - HHJ409 and CFHT-PL8 - to be 0.258 d and 0.401 d, respectively. The masses of these stars are near 0.4 and 0.08 Msun, respectively; the latter is the second such object near the hydrogen-burning boundary for which a rotation period has been measured. We also observed HHJ409 in V; the relative amplitude in the two bands shows that the spots in that star are about 200 K cooler than the stellar effective temperature of 3560 K and have a filling factor on the order of 13%. With one possible exception, the remaining stars in the sample do not show photometric variations larger than the mean error of measurement. We also examined the M9.5V disk star 2MASSJ0149, which had previously exhibited a strong flare event, but did not detect any photometric variation.Comment: 13 pages, four figures. Accepted for publication in A

Quiescent and flaring X-ray emission from the nearby M/T dwarf binary SCR 1845-6357

We investigate an XMM-Newton observation of SCR 1845-6357, a nearby, ultracool M8.5/T5.5 dwarf binary. The binary is unresolved in the XMM detectors, however the X-ray emission is very likely from the M8.5 dwarf. We compare its flaring emission to those of similar very low mass stars and additionally present an XMM observation of the M8 dwarf VB 10. We detect quasi-quiescent X-ray emission from SCR 1845-6357 at soft X-ray energies in the 0.2-2.0 keV band, as well as a strong flare with a count rate increase of a factor of 30 and a duration of only 10 minutes. The quasi-quiescent X-ray luminosity of log L_x = 26.2 erg/s and the corresponding activity level of log L_x/L_bol = -3.8 point to a fairly active star. Coronal temperatures of up to 5 MK and frequent minor variability support this picture. During the flare, that is accompanied by a significant brightening in the near-UV, plasma temperatures of 25-30 MK are observed and an X-ray luminosity of L_x= 8 x 10^27 erg/s is reached. SCR 1845-6357 is a nearby, very low mass star that emits X-rays at detectable levels in quasi-quiescence, implying the existence of a corona. The high activity level, coronal temperatures and the observed large flare point to a rather active star, despite its estimated age of a few Gyr.Comment: Accepted by A&A, 6 pages, 5 figure

A quasi-sure non-degeneracy property for the Brownian rough path

In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in every degree) of Brownian motion is non-selfintersecting. This property relates closely to a non-degeneracy property for the Brownian rough path arising naturally from the uniqueness of signature problem in rough path theory. As an important consequence we conclude that quasi-surely, the Brownian rough path does not have any tree-like pieces and every sample path of Brownian motion is uniquely determined by its signature up to reparametrization