Bounds on \"{U}bercrossing and Petal Numbers for Knots

An $n$-crossing is a point in the projection of a knot where $n$ strands cross so that each strand bisects the crossing. An \"ubercrossing projection has a single $n$-crossing and a petal projection has a single $n$-crossing such that there are no loops nested within others. The \"ubercrossing number, $\text{\"u}(K)$, is the smallest $n$ for which we can represent a knot $K$ with a single $n$-crossing. The petal number is the number of loops in the minimal petal projection. In this paper, we relate the \"{u}bercrossing number and petal number to well-known invariants such as crossing number, bridge number, and unknotting number. We find that the bounds we have constructed are tight for $(r, r+1)$-torus knots. We also explore the behavior of \"{u}bercrossing number under composition.Comment: 13 pages, 8 figure

Investigation into background levels of small organic samples at the NERC Radiocarbon Laboratory

Recent progress in preparation/combustion of submilligram organic samples at our laboratories is presented. Routine methods had to be modified/refined to achieve acceptable and consistent procedural blanks for organic samples smaller than 1000 g C. A description of the process leading to a modified combustion method for smaller organic samples is given in detail. In addition to analyzing different background materials, the influence of different chemical reagents on the overall radiocarbon background level was investigated, such as carbon contamination arising from copper oxide of different purities and from different suppliers. Using the modified combustion method, small amounts of background materials and known-age standard IAEA-C5 were individually combusted to CO2. Below 1000 g C, organic background levels follow an inverse mass dependency when combusted with the modified method, increasing from 0.13 0.05 pMC up to 1.20 0.04 pMC for 80 g C. Results for a given carbon mass were lower for combustion of etched Iceland spar calcite mineral, indicating that part of the observed background of bituminous coal was probably introduced by handling the material in atmosphere prior to combustion. Using the modified combustion method, the background-corrected activity of IAEA-C5 agreed to within 2 s of the consensus value of 23.05 pMC down to a sample mass of 55 g C

Progress in AMS target production in sub-milligram samples at the NERC Radiocarbon Laboratory

. Recent progress in graphite target production for sub-milligram environmental samples in our facility is presented. We describe an optimized hydrolysis procedure now routinely used for the preparation of CO2 from inorganic samples, a new high-vacuum line dedicated to small sample processing (combining sample distillation and graphitization units), as well as a modified graphitization procedure. Although measurements of graphite targets as small as 35 µg C have been achieved, system background and measurement uncertainties increase significantly below 150 µg C. As target lifetime can become critically short for targets <150 µg C, the facility currently only processes inorganic samples down to 150 µg C. All radiocarbon measurements are made at the Scottish Universities Environmental Research Centre (SUERC) accelerator mass spectrometry (AMS) facility. Sample processing and analysis are labor-intensive, taking approximately 3 times longer than samples ≥500 µg C. The technical details of the new system, graphitization yield, fractionation introduced during the process, and the system blank are discussed in detail

A self-management programme to reduce falls and improve safe mobility in people with secondary progressive MS: the BRiMS feasibility RCT

This is the final version, also available from NIHR journals library via the DOI in this record.Abstract Background Balance, mobility impairments and falls are common problems for people with multiple sclerosis (MS). Our ongoing research has led to the development of Balance Right in MS (BRiMS), a 13-week home- and group-based exercise and education programme intended to improve balance and encourage safer mobility. Objective This feasibility trial aimed to obtain the necessary data and operational experience to finalise the planning of a future definitive multicentre randomised controlled trial. Design Randomised controlled feasibility trial. Participants were block randomised 1 : 1. Researcher-blinded assessments were scheduled at baseline and at 15 and 27 weeks post randomisation. As is appropriate in a feasibility trial, statistical analyses were descriptive rather than involving formal/inferential comparisons. The qualitative elements utilised template analysis as the chosen analytical framework. Setting Four sites across the UK. Participants Eligibility criteria included having a diagnosis of secondary progressive MS, an Expanded Disability Status Scale (EDSS) score of between ≥ 4.0 and ≤ 7.0 points and a self-report of two or more falls in the preceding 6 months. Interventions Intervention – manualised 13-week education and exercise programme (BRiMS) plus usual care. Comparator – usual care alone. Main outcome measures Trial feasibility, proposed outcomes for the definitive trial (including impact of MS, mobility, quality of life and falls), feasibility of the BRiMS programme (via process evaluation) and economic data. Results A total of 56 participants (mean age 59.7 years, standard deviation 9.7 years; 66% female; median EDSS score of 6.0 points, interquartile range 6.0–6.5 points) were recruited in 5 months; 30 were block randomised to the intervention group. The demographic and clinical data were broadly comparable at baseline; however, the intervention group scored worse on the majority of baseline outcome measures. Eleven participants (19.6%) withdrew or were lost to follow-up. Worsening of MS-related symptoms unrelated to the trial was the most common reason (n = 5) for withdrawal. Potential primary and secondary outcomes and economic data had completion rates of > 98% for all those assessed. However, the overall return rate for the patient-reported falls diary was 62%. After adjusting for baseline score, the differences between the groups (intervention compared with usual care) at week 27 for the potential primary outcomes were MS Walking Scale (12-item) version 2 –7.7 [95% confidence interval (CI) –17.2 to 1.8], MS Impact Scale (29-item) version 2 (MSIS-29vs2) physical 0.6 (95% CI –7.8 to 9) and MSIS-29vs2 psychological –0.4 (95% CI –9.9 to 9) (negative score indicates improvement). After the removal of one outlier, a total of 715 falls were self-reported over the 27-week trial period, with substantial variation between individuals (range 0–93 falls). Of these 715 falls, 101 (14%) were reported as injurious. Qualitative feedback indicated that trial processes and participant burden were acceptable, and participants highlighted physical and behavioural changes that they perceived to result from undertaking BRiMS. Engagement varied, influenced by a range of condition- and context-related factors. Suggestions to improve the utility and accessibility of BRiMS were highlighted. Conclusions The results suggest that the trial procedures are feasible and acceptable, and retention, programme engagement and outcome completion rates were sufficient to satisfy the a priori progression criteria. Challenges were experienced in some areas of data collection, such as completion of daily diaries.National Institute for Health Research (NIHR

Identifying the magnetotail lobes with Cluster magnetometer data

We describe a novel method for identifying times when a spacecraft is in Earth’s magnetotail lobes solely using magnetometer data. We propose that lobe intervals can be well identified as times when the magnetic field is strong and relatively invariant, defined using thresholds in the magnitude of BX and the standard deviation σ of the magnetic field magnitude. Using data from the Cluster spacecraft at downtail distances greater than 8 RE during 2001–2009, we find that thresholds of 30 nT and 3.5 nT, respectively, optimize agreement with a previous, independently derived lobe identification method that used both magnetic and plasma data over the same interval. Specifically, our method has a moderately high accuracy (66%) and a low probability of false detection (11%) in comparison to the other method. Furthermore, our method identifies the lobe on many other occasions when the previous method was unable to make any identification and yields longer continuous intervals in the lobe than the previous method, with intervals at the 90th percentile being triple the length. Our method also allows for analyses of the lobes outside the time span of the previous method

The Recent Star Formation History of NGC 5102

We present Hubble Space Telescope photometry of young stars in NGC 5102, a nearby gas-rich post-starburst S0 galaxy with a bright young stellar nucleus. We use the IAC-pop/MinnIAC algorithm to derive the recent star formation history in three fields in the bulge and disk of NGC 5102. In the disk fields, the recent star formation rate has declined monotonically and is now barely detectable, but a starburst is still in progress in the bulge and has added about 2 percent to the mass of the bulge over the last 200 Myr. Other studies of star formation in NGC 5102 indicate that about 20 percent of its stellar mass was added over the past Gyr. If this is correct, then much of the stellar mass of the bulge may have formed over this period. It seems likely that this star formation was fueled by the accretion of a gas-rich system with HI mass of about 2 x 10^9 Msol which has now been almost completely converted into stars. The large mass of recently formed stars and the blue colours of the bulge suggest that the current starburst, which is now fading, may have made a significant contribution to build the bulge of NGC 5102.Comment: 36 pages, 16 figures, accepted in A

Burden of disease from inadequate water, sanitation and hygiene in low- and middle-income settings: a retrospective analysis of data from 145 countries

objective To estimate the burden of diarrhoeal diseases from exposure to inadequate water, sanitation and hand hygiene in low- and middle-income settings and provide an overview of the impact on other diseases. methods For estimating the impact of water, sanitation and hygiene on diarrhoea, we selected exposure levels with both sufficient global exposure data and a matching exposure-risk relationship. Global exposure data were estimated for the year 2012, and risk estimates were taken from the most recent systematic analyses. We estimated attributable deaths and disability-adjusted life years (DALYs) by country, age and sex for inadequate water, sanitation and hand hygiene separately, and as a cluster of risk factors. Uncertainty estimates were computed on the basis of uncertainty surrounding exposure estimates and relative risks. results In 2012, 502 000 diarrhoea deaths were estimated to be caused by inadequate drinking water and 280 000 deaths by inadequate sanitation. The most likely estimate of disease burden from inadequate hand hygiene amounts to 297 000 deaths. In total, 842 000 diarrhoea deaths are estimated to be caused by this cluster of risk factors, which amounts to 1.5% of the total disease burden and 58% of diarrhoeal diseases. In children under 5 years old, 361 000 deaths could be prevented, representing 5.5% of deaths in that age group. conclusions This estimate confirms the importance of improving water and sanitation in low- and middle-income settings for the prevention of diarrhoeal disease burden. It also underscores the need for better data on exposure and risk reductions that can be achieved with provision of reliable piped water, community sewage with treatment and hand hygiene