Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation

A contraction metric for an autonomous ordinary differential equation is a Riemannian metric such that the distance between adjacent solutions contracts over time. A contraction metric can be used to determine the basin of attraction of a periodic orbit without requiring information about its position or stability. Moreover, it is robust to small perturbations of the system. In two-dimensional systems, a contraction metric can be characterised by a scalar-valued function. In [9], the function was constructed as solution of a first-order linear Partial Differential Equation (PDE), and numerically constructed using meshless collocation. However, information about the periodic orbit was required, which needed to be approximated. In this paper, we overcome this requirement by studying a second-order PDE, which does not require any information about the periodic orbit. We show that the second-order PDE has a solution, which defines a contraction metric. We use meshless collocation to approximate the solution and prove error estimates. In particular, we show that the approximation itself is a contraction metric, if the collocation points are dense enough. The method is applied to two examples

Safety and efficacy of antenatal milk expressing for women with diabetes in pregnancy: protocol for a randomised controlled trial

Many maternity providers recommend that women with diabetes in pregnancy express and store breast milk in late pregnancy so breast milk is available after birth, given (1) infants of these women are at increased risk of hypoglycaemia in the first 24 h of life; and (2) the delay in lactogenesis II compared with women without diabetes that increases their infant\u27s risk of receiving infant formula. The Diabetes and Antenatal Milk Expressing (DAME) trial will establish whether advising women with diabetes in pregnancy (pre-existing or gestational) to express breast milk from 36 weeks gestation increases the proportion of infants who require admission to special or neonatal intensive care units (SCN/NICU) compared with infants of women receiving standard care. Secondary outcomes include birth gestation, breastfeeding outcomes and economic impact

Automatic anomaly detection in fuel grab load trace data using a knowledge-based system vs. multiple deep autoencoders

Of the seven Advanced Gas-cooled Reactor nuclear power stations in the UK, the majority are approaching their planned closure date. As the graphite core of these type of reactors cannot be repaired or replaced, this is one of the main life-limiting factors. The refuelling of a nuclear power station is an ongoing process and refuelling of the reactor occurs typically every 6 to 8 weeks. During this process, data relating to the weight of the fuel assembly is recorded: this data is called fuel grab load trace data and the major contributing factor to this are the frictional forces, with a magnitude related to the channel bore diameter. Through an understanding of this data, it is possible to manually interpret whether there are any defects in the individual brick layers that make up the graphite core but doing so requires significant expertise, experience and understanding. In this paper, we present a knowledge-based system to automatically detect defects in individual brick layers in the fuel grab load trace data. This is accomplished using a set of rules defined by specialist engineers. Secondly, by splitting up the trace into overlapping regions, the use of multiple deep autoencoders is explored to produce a generative model for a normal response. Using this model, it is possible to detect responses that do not generalise and identify anomalies such as defects in the individual brick layers. Finally, the two approaches are compared, and conclusions are drawn about the applications of these techniques into industry

Reviews

The following publications have been reviewed by the mentioned authors;Windsor Chairmaking by Thos Moser, reviewed by Bernard AylwardRelief Woodcarving by E. J. Tangerman, reviewed by Bernard AylwardWorking Green Wood with PEG by Patrick Spielman, reviewed by J. W. ThompsonWork Experience in Secondary Schools edited by John Eggleston, reviewed by Charles PeaceScale Model Cannon by Richard Stewart and Donald Heyes, reviewed by John EgglestonHow to Make Your Own Picture Frames by Hal Rogers and Ed Reinhardt, reviewed by John EgglestonThe Story of Craft by Edward Lucie Smith, reviewed by John EgglestonThe Landsdowne Book of Handcrafts reviewed by Roger BensonUnderstanding Design in the Home by Margaret Picton, reviewed by John EgglestonWoodturning Projects for Dining by John Sainsbury, reviewed by M. P. BourneCrafts Conference for Teachers - April 1982 published by Crafts Council, reviewed by Bernard L. MyersCraft Design Technology reviewed by M. JohnArt and Imaginations: A Study in the Philosophy of Mind by Roger Scruton, reviewed by G. H. Bantock'Forget all the rules you ever learned about Graphic Design including the ones in this Book by Bob Gill, reviewed by Cal SwannProfessional Smithing by Donald Streeter, reviewed by J. N. AtkinsGraphic Communication by John Twyford, reviewed by Cal Swan

Baseline Q-Wave Surpasses Time From Symptom Onset as a Prognostic Marker in ST-Segment Elevation Myocardial Infarction Patients Treated With Primary Percutaneous Coronary Intervention

ObjectivesWe assessed the incremental value of baseline Q waves over time from symptom onset as a marker of clinical outcome in ST-segment elevation myocardial infarction (STEMI).BackgroundTime from symptom onset is a central focus in STEMI patients. The presence of Q waves on the baseline electrocardiogram (ECG) has been suggested to be of incremental value to time from symptom onset in evaluating clinical outcomes.MethodsWe evaluated baseline Q waves and ST-segment resolution 30 min after primary percutaneous intervention (PCI) ECGs in 4,530 STEMI patients without prior infarction. Additionally, peak biomarkers; 90-day mortality; and the composite of death, congestive heart failure (CHF), or cardiogenic shock were assessed.ResultsFifty-six percent of patients had baseline Q waves: they were older, more frequently male and diabetic, and had a more advanced Killip class. Patients with baseline Q waves had greater mortality and a higher composite rate of death, CHF, and shock versus patients without baseline Q waves at 90 days (5.3% vs. 2.1% and 12.1% vs. 4.8%, respectively, both p < 0.001). Complete ST-segment resolution was highest, whereas 90-day mortality and the composite outcome were lowest among those randomized ≤3 h without baseline Q waves. After multivariable adjustment, baseline Q-wave but not time from symptom onset was significantly associated with a 78% relative increase in the hazard of 90-day mortality and a 90% relative increase in the hazard of death, shock, and CHF.ConclusionsBaseline Q waves in STEMI patients treated with primary PCI provide an independent prognostic marker of clinical outcome. These data might be useful in designing future clinical trials as well as in evaluating patients for triage and potential transfer for planned primary PCI. (Pexelizumab in Conjunction With Angioplasty in Acute Myocardial Infarction [APEX-AMI]; NCT00091637

Super Earth Explorer: A Coronagraphic Off-Axis Space Telescope

The Super-Earth Explorer is an Off-Axis Space Telescope (SEE-COAST) designed for high contrast imaging. Its scientific objective is to make the physico-chemical characterization of exoplanets possibly down to 2 Earth radii >. For that purpose it will analyze the spectral and polarimetric properties of the parent starlight reflected by the planets, in the wavelength range 400-1250 nmComment: Accepted in Experimental Astronom

Correlations of Behavioral Deficits with Brain Pathology Assessed through Longitudinal MRI and Histopathology in the R6/2 Mouse Model of HD

Huntington's disease (HD) is caused by the expansion of a CAG repeat in the huntingtin (HTT) gene. The R6/2 mouse model of HD expresses a mutant version of exon 1 HTT and develops motor and cognitive impairments, a widespread huntingtin (HTT) aggregate pathology and brain atrophy. Despite the vast number of studies that have been performed on this model, the association between the molecular and cellular neuropathology with brain atrophy, and with the development of behavioral phenotypes remains poorly understood. In an attempt to link these factors, we have performed longitudinal assessments of behavior (rotarod, open field, passive avoidance) and of regional brain abnormalities determined through magnetic resonance imaging (MRI) (whole brain, striatum, cortex, hippocampus, corpus callosum), as well as an end-stage histological assessment. Detailed correlative analyses of these three measures were then performed. We found a gender-dependent emergence of motor impairments that was associated with an age-related loss of regional brain volumes. MRI measurements further indicated that there was no striatal atrophy, but rather a lack of striatal growth beyond 8 weeks of age. T2 relaxivity further indicated tissue-level changes within brain regions. Despite these dramatic motor and neuroanatomical abnormalities, R6/2 mice did not exhibit neuronal loss in the striatum or motor cortex, although there was a significant increase in neuronal density due to tissue atrophy. The deposition of the mutant HTT (mHTT) protein, the hallmark of HD molecular pathology, was widely distributed throughout the brain. End-stage histopathological assessments were not found to be as robustly correlated with the longitudinal measures of brain atrophy or motor impairments. In conclusion, modeling pre-manifest and early progression of the disease in more slowly progressing animal models will be key to establishing which changes are causally related. © 2013 Rattray et al

Methane in the atmosphere of the transiting hot Neptune GJ436b?

We present an analysis of seven primary transit observations of the hot Neptune GJ436b at 3.6, 4.5 and $8~\mu$m obtained with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. After correcting for systematic effects, we fitted the light curves using the Markov Chain Monte Carlo technique. Combining these new data with the EPOXI, HST and ground-based $V, I, H$ and $K_s$ published observations, the range $0.5-10~\mu$m can be covered. Due to the low level of activity of GJ436, the effect of starspots on the combination of transits at different epochs is negligible at the accuracy of the dataset. Representative climate models were calculated by using a three-dimensional, pseudo-spectral general circulation model with idealised thermal forcing. Simulated transit spectra of GJ436b were generated using line-by-line radiative transfer models including the opacities of the molecular species expected to be present in such a planetary atmosphere. A new, ab-initio calculated, linelist for hot ammonia has been used for the first time. The photometric data observed at multiple wavelengths can be interpreted with methane being the dominant absorption after molecular hydrogen, possibly with minor contributions from ammonia, water and other molecules. No clear evidence of carbon monoxide and dioxide is found from transit photometry. We discuss this result in the light of a recent paper where photochemical disequilibrium is hypothesised to interpret secondary transit photometric data. We show that the emission photometric data are not incompatible with the presence of abundant methane, but further spectroscopic data are desirable to confirm this scenario.Comment: 19 pages, 10 figures, 1 table, Astrophysical Journal in pres