A survey for planetary transits in the field of NGC 7789

We present results from 30 nights of observations of the open cluster NGC 7789 with the Wide Field Camera on the Isaac Newton Telescope, La Palma. From ~900 epochs, we obtained light curves and Sloan r'-i' colours for ~33000 stars, with ~2400 stars having better than 1 per cent precision. We expected to detect ~2 transiting hot Jupiter planets if 1 per cent of stars host such a companion and a typical hot Jupiter radius is ~1.2R_J. We find 24 transit candidates, 14 of which we can assign a period. We rule out the transiting planet model for 21 of these candidates using various robust arguments. For two candidates, we are unable to decide on their nature, although it seems most likely that they are eclipsing binaries as well. We have one candidate exhibiting a single eclipse, for which we derive a radius of 1.81+0.09-0.00R_J. Three candidates remain that require follow-up observations in order to determine their nature.

Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Ecophysiology of seed dormancy and the control of germination in early spring-flowering Galanthus nivalis and Narcissus pseudonarcissus (Amaryllidaceae)

Seed dormancy induction and alleviation in the winter-flowering moist temperate woodland species Galanthus nivalis and Narcissus pseudonarcissus are complex and poorly understood. Temperature, light and desiccation were investigated to elucidate their role in the germination ecophysiology of these species. Outdoor and laboratory experiments simulating different seasonal temperatures, seasonal durations, and temperature fluctuations; the presence of light during different seasons; and intermittent drying (during the summer period) over several ‘years’ investigated the importance of these factors in germination. Warm summer-like temperatures (20°C) were necessary for germination at subsequent cooler autumn-like temperatures (greatest at 15°C in G. nivalis and 10°C in N. pseudonarcissus). As the warm temperature duration increased so did germination at subsequent cooler temperatures; further germination occurred in subsequent ‘years’ at cooler temperatures following a second, and also third, warm period. Germination was significantly greater in darkness, particularly in G. nivalis. Dormancy increased with seed maturation period in G. nivalis, because seeds extracted from green capsules germinated more readily than those from yellow. Desiccation increased dormancy in an increasing proportion of N. pseudonarcissus seeds the later they were dried in ‘summer’. Seed viability was only slightly reduced by desiccation in N. pseudonarcissus but was poor and variable in G. nivalis. Shoot formation occurred both at the temperature at which germination was greatest and also if 5°C cooler. In summary, continuous hydration of seeds of both species during warm summer-like temperatures results in the gradual release of seed dormancy; thereafter, darkness and cooler temperatures promote germination. Cold temperatures, increased seed maturity (G. nivalis), and desiccation (N. pseudonarcissus) increase dormancy while light inhibits germination.

Faces and awareness: low-level, not emotional factors determine perceptual dominance

Threat-relevant stimuli such as fear faces are prioritized by the human visual system. Recent research suggests that this prioritization begins during unconscious processing: A specialized (possibly subcortical) pathway evaluates the threat relevance of visual input, resulting in preferential access to awareness for threat stimuli. Our data challenge this claim. We used a continuous flash suppression (CFS) paradigm to present emotional face stimuli outside of awareness. It has been shown using CFS that salient (e.g., high contrast) and recognizable stimuli (faces, words) become visible more quickly than less salient or less recognizable stimuli. We found that although fearful faces emerge from suppression faster than other faces, this was wholly explained by their low-level visual properties, rather than their emotional content. We conclude that, in the competition for visual awareness, the visual system prefers and promotes unconscious stimuli that are more “face-like,” but the emotional content of a face has no effect on stimulus salience.

'Nature concocts & expels': the agents and processes of recovery from disease in Early Modern England

The ‘golden saying’ in early modern medicine was ‘Nature is the healer of disease’. This article uncovers the meaning and significance of this forgotten axiom by investigating perceptions of the agents and physiological processes of recovery from illness in England, c.1580-1720. Drawing on sources such as medical texts and diaries, it shows that doctors and laypeople attributed recovery to three agents – God, Nature, and the practitioner. While scholars are familiar with the roles of providence and medicine, the vital agency of Nature has been overlooked. In theory, the agents operated in a hierarchy: Nature was ‘God’s instrument’, and the physician, ‘Nature’s servant’; but in practice the power balance was more ambivalent. Nature was depicted both as a housewife who cooked and cleaned the humours, and as a warrior, who defeated the disease. Through exploring these complex dynamics, the article sheds fresh light on concepts of gender, disease, and bodies.

Children’s physic: medical perceptions and treatment of sick children in early modern England, c. 1580-1720

Historians of medicine, childhood, and paediatrics, have often assumed that early modern doctors neither treated children, nor adapted their medicines to suit the peculiar temperaments of the young. Through an examination of medical textbooks and doctors’ casebooks, this article refutes these assumptions. It argues that medical authors and practising doctors regularly treated children, and were careful to tailor their remedies to complement the distinctive constitutions of children. Thus, this article proposes that a concept of ‘children’s physic’ existed in early modern England: this term refers to the notion that children were physiologically distinct, requiring special medical care. Children’s physic was rooted in the ancient traditions of Hippocratic and Galenic medicine: it was the child’s humoral makeup that underpinned all medical ideas about children’s bodies, minds, diseases, and treatments. Children abounded in the humour blood, which made them humid and weak, and in need of medicines of a particularly gentle nature.

“Very sore nights and days”: the child’s experience of illness in early modern England, c. 1580-1720

Sick children were ubiquitous in early modern England, and yet they have received very little attention from historians. Taking the elusive perspective of the child, this article explores the physical, emotional, and spiritual experience of illness in England between approximately 1580 and 1720. What was it like being ill and suffering pain? How did the young respond emotionally to the anticipation of death? It is argued that children’s experiences were characterised by profound ambivalence: illness could be terrifying and distressing, but also a source of emotional and spiritual fulfilment and joy. This interpretation challenges the common assumption amongst medical historians that the experiences of early modern patients were utterly miserable. It also sheds light on children’s emotional feelings for their parents, a subject often overlooked in the historiography of childhood. The primary sources used in this article include diaries, autobiographies, letters, the biographies of pious children, printed possession cases, doctors’ casebooks, and theological treatises concerning the afterlife.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Protocol for a feasibility study of a self help cognitive behavioural therapy resource for the reduction of dental anxiety in young people

Background Childhood dental anxiety is very common, with 10–20 % of children and young people reporting high levels of dental anxiety. It is distressing and has a negative impact on the quality of life of young people and their parents as well as being associated with poor oral health. Affected individuals may develop a lifelong reliance on general anaesthetic or sedation for necessary dental treatment thus requiring the support of specialist dental services. Children and young people with dental anxiety therefore require additional clinical time and can be costly to treat in the long term. The reduction of dental anxiety through the use of effective psychological techniques is, therefore, of high importance. However, there is a lack of high-quality research investigating the impact of cognitive behavioural therapy (CBT) approaches when applied to young people’s dental anxiety. Methods/design The first part of the study will develop a profile of dentally anxious young people using a prospective questionnaire sent to a consecutive sample of 100 young people referred to the Paediatric Dentistry Department, Charles Clifford Dental Hospital, in Sheffield. The second part will involve interviewing a purposive sample of 15–20 dental team members on their perceptions of a CBT self-help resource for dental anxiety, their opinions on whether they might use such a resource with patients, and their willingness to recruit participants to a future randomised controlled trial (RCT) to evaluate the resource. The third part of the study will investigate the most appropriate outcome measures to include in a trial, the acceptability of the resource, and retention and completion rates of treatment with a sample of 60 dentally anxious young people using the CBT resource. Discussion This study will provide information on the profile of dentally anxious young people who could potentially be helped by a guided self-help CBT resource. It will gain the perceptions of dental care team members of guided self-help CBT for dental anxiety in young people and their willingness to recruit participants to a trial. Acceptability of the resource to participants and retention and completion rates will also be investigated to inform a future RCT.

The proportion of failures of the Hasse norm principle

For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.