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In (2), Tutte has shown that the number, Bn, of rooted non-separable planar maps having n edges is [2(3n — 3)!]/[n! (2n — 1)!]. Rooting was accomplished by designating one edge as the root, orienting it, and distinguishing between its sides as left and right. We shall here compute the number, Bn,m, of rooted non-separable planar maps having n edges and such that the face to the left of the root is incident with exactly m edges, which maps will be said to be of type [n, m].
ƒ(k, 5) is defined to be the smallest integer n for which there exists a regular graph of valency k and girth 5, having n vertices. In (3) it was shown that
Hoffman and Singleton proved in (4) that equality holds in the lower bound of (1.1) only for k = 2, 3, 7, and possibly 57. Robertson showed in (6) that ƒ(4, 5) = 19 and constructed the unique minimal graph.
The discovery of the first electromagnetic counterpart to a gravitational wave signal has generated follow-up observations by over 50 facilities world-wide, ushering in the new era of multi-messenger astronomy. In this paper, we present follow-up observations of the gravitational wave event GW170817 and its electromagnetic counterpart SSS17a/DLT17ck (IAU label AT2017gfo) by 14 Australian telescopes and partner observatories as part of Australian-based and Australian-led research programs. We report early- to late-time multi-wavelength observations, including optical imaging and spectroscopy, mid-infrared imaging, radio imaging, and searches for fast radio bursts. Our optical spectra reveal that the transient source emission cooled from approximately 6 400 K to 2 100 K over a 7-d period and produced no significant optical emission lines. The spectral profiles, cooling rate, and photometric light curves are consistent with the expected outburst and subsequent processes of a binary neutron star merger. Star formation in the host galaxy probably ceased at least a Gyr ago, although there is evidence for a galaxy merger. Binary pulsars with short (100 Myr) decay times are therefore unlikely progenitors, but pulsars like PSR B1534+12 with its 2.7 Gyr coalescence time could produce such a merger. The displacement (~2.2 kpc) of the binary star system from the centre of the main galaxy is not unusual for stars in the host galaxy or stars originating in the merging galaxy, and therefore any constraints on the kick velocity imparted to the progenitor are poor.
Light curve analysis by MDW of the photometry and RV data accumulated to date on HD 209458 has made use of a simulations database created for an 8-day HST observing project led by RLG to look for transits in 47 Tuc. We report progress in developing a consistent set of parameters obtained with our versions of the Wilson-Devinney program, WD98 and wd98k93, specially modified to treat large grid sizes, corresponding to objects with radii exceeding 0.7RJ and masses greater than 0.1 MJ.
This work is supported in part by grants to EFM by Canadian NSERC and by the Univ. of Calgary Research Grants Committee.
The public health burden of alcohol is unevenly distributed across the life course, with levels of use, abuse, and dependence increasing across adolescence and peaking in early adulthood. Here, we leverage this temporal patterning to search for common genetic variants predicting developmental trajectories of alcohol consumption. Comparable psychiatric evaluations measuring alcohol consumption were collected in three longitudinal community samples (N = 2,126, obs = 12,166). Consumption-repeated measurements spanning adolescence and early adulthood were analyzed using linear mixed models, estimating individual consumption trajectories, which were then tested for association with Illumina 660W-Quad genotype data (866,099 SNPs after imputation and QC). Association results were combined across samples using standard meta-analysis methods. Four meta-analysis associations satisfied our pre-determined genome-wide significance criterion (FDR < 0.1) and six others met our ‘suggestive’ criterion (FDR <0.2). Genome-wide significant associations were highly biological plausible, including associations within GABA transporter 1, SLC6A1 (solute carrier family 6, member 1), and exonic hits in LOC100129340 (mitofusin-1-like). Pathway analyses elaborated single marker results, indicating significant enriched associations to intuitive biological mechanisms, including neurotransmission, xenobiotic pharmacodynamics, and nuclear hormone receptors (NHR). These findings underscore the value of combining longitudinal behavioral data and genome-wide genotype information in order to study developmental patterns and improve statistical power in genomic studies.
Previous research suggests that many people receiving mental health
treatment do not meet criteria for a mental disorder but are rather ‘the
To examine the association of past-year mental health treatment with
The World Health Organization's World Mental Health (WMH) Surveys
interviewed community samples of adults in 23 countries
(n = 62 305) about DSM-IV disorders and treatment in
the past 12 months for problems with emotions, alcohol or drugs.
Roughly half (52%) of people who received treatment met criteria for a
past-year DSM-IV disorder, an additional 18% for a lifetime disorder and
an additional 13% for other indicators of need (multiple subthreshold
disorders, recent stressors or suicidal behaviours). Dose–response
associations were found between number of indicators of need and
The vast majority of treatment in the WMH countries goes to patients with
mental disorders or other problems expected to benefit from
Restoration in Mediterranean-climate grasslands is strongly impeded by lack of native propagules and competition with exotic grasses and forbs. We report on a study testing several methods for exotic plant control combined with planting native grasses to restore prairies in former agricultural land in coastal California. Specifically we compared tarping (shading out recently germinated seedlings with black plastic) once, tarping twice, topsoil removal, herbicide (glyphosate), and a control treatment in factorial combinations with or without wood mulch. Into each treatment we planted three native grass species (Elymus glaucus, Hordeum brachyantherum, and Stipa pulchra) and monitored plant survival and cover for three growing seasons. Survival of native grass species was high in all treatments, but was slightly lower in unmulched soil removal and control treatments in the first 2 yr. Mulching, tarping, and herbicide were all effective in reducing exotic grass cover and enhancing native grass cover for the first 2 yr, but by the third growing season cover of the plant guilds and bare ground had mostly converged, primarily because of the declining effects of the initial treatments. Mulching and tarping were both considerably more expensive than herbicide treatment. Topsoil removal was less effective in increasing native grass cover likely because soil removal altered the surface hydrology in this system. Our results show that several treatments were effective in enhancing native grass establishment, but that longer term monitoring is needed to evaluate the efficacy of restoration efforts. The most appropriate approach to controlling exotics to restore specific grassland sites will depend not only on the effectiveness, but also on relative costs and site constraints.
Significant new opportunities for astrophysics and cosmology have been identified at low radio frequencies. The Murchison Widefield Array is the first telescope in the southern hemisphere designed specifically to explore the low-frequency astronomical sky between 80 and 300 MHz with arcminute angular resolution and high survey efficiency. The telescope will enable new advances along four key science themes, including searching for redshifted 21-cm emission from the EoR in the early Universe; Galactic and extragalactic all-sky southern hemisphere surveys; time-domain astrophysics; and solar, heliospheric, and ionospheric science and space weather. The Murchison Widefield Array is located in Western Australia at the site of the planned Square Kilometre Array (SKA) low-band telescope and is the only low-frequency SKA precursor facility. In this paper, we review the performance properties of the Murchison Widefield Array and describe its primary scientific objectives.
The aim of this study was to estimate the amount of childhood hepatitis B virus transmission in children born in the UK, a very low-prevalence country, that is preventable only by universal hepatitis B immunization of infants. Oral fluid specimens were collected from schoolchildren aged 7–11 years in four inner city multi-ethnic areas and tested for the presence of antibody to hepatitis B core antigen (anti-HBc). Those found positive or indeterminate were followed up with testing on serum to confirm their hepatitis B status. The overall prevalence of anti-HBc in children was low [0·26%, 95% confidence interval (CI) 0·14–0·44]. The estimated average annual incidence of hepatitis B was estimated to be 29·26/100 000 children (95% CI 16·00–49·08). The total incidence that is preventable only by a universal infant immunization programme in the UK was estimated to be between 5·00 and 12·49/100 000. The study demonstrates that the extent of horizontal childhood hepatitis B virus transmission is low in children born in the UK and suggests that schools in the UK are an uncommon setting for the transmission of the virus. Targeted hepatitis B testing and immunization of migrants from intermediate- and high-prevalence countries is likely to be a more effective measure to reduce childhood transmission than a universal infant immunization programme.