Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

Soft-bed experiments beneath Engabreen, Norway: regelation infiltration, basal slip and bed deformation

To avoid some of the limitations of studying soft-bed processes through boreholes, a prism of simulated till (1.8 m × 1.6 m × 0.45 m) with extensive instrumentation was constructed in a trough blasted in the rock bed of Engabreen, a temperate glacier in Norway. Tunnels there provide access to the bed beneath 213 m of ice. Pore-water pressure was regulated in the prism by pumping water to it. During experiments lasting 7–12 days, the glacier regelated downward into the prism to depths of 50– 80 mm, accreting ice-infiltrated till at rates predicted by theory. During periods of sustained high pore water pressure (70–100% of overburden), ice commonly slipped over the prism, due to a water layer at the prism surface. Deformation of the prism was activated when this layer thinned to a sub-millimeter thickness. Shear strain in the till was pervasive and decreased with depth. A model of slip by ploughing of ice-infiltrated till across the prism surface accounts for the slip that occurred when effective pressure was sufficiently low or high. Slip at low effective pressures resulted from water-layer thickening that increased non-linearly with decreasing effective pressure. If sufficiently widespread, such slip over soft glacier beds, which involves no viscous deformation resistance, may instigate abrupt increases in glacier velocity

On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure

Multi-modalities in classroom learning environments

This paper will present initial findings from the second phase of a Horizon 2020 funded project, Managing Affective-learning Through Intelligent Atoms and Smart Interactions (MaTHiSiS). The project focusses on the use of different multi-modalities used as part of the project in classrooms across Europe. The MaTHiSiS learning vision is to develop an integrated learning platform, with re-usable learning components which will respond to the needs of future education in primary, secondary, special education schools, vocational environments and learning beyond the classroom. The system comprises learning graphs which attach individual learning goals to the system. Each learning graph is developed from a set of smart learning atoms designed to support learners to achieve progression. Cutting edge technologies are being used to identify the affect state of learners and ultimately improve engagement of learners. Much research identifies how learners engage with learning platforms (c.f. [1], [2], [3]). Not only do e-learning platforms have the capability to engage learners, they provide a vehicle for authentic classroom and informal learning [4] enabling ubiquitous and seamless learning [5] within a non-linear environment. When experiencing more enjoyable interaction learners become more confident and motivated to learn and become less anxious, especially those with learning disabilities or at risk of social exclusion [6], [13]. [7] identified the importance of understanding the affect state of learners who may experience emotions such as 'confusion, frustration, irritation, anger, rage, or even despair' resulting in disengaging with learning. The MaTHiSiS system will use a range of platform agents such as NAO robots and Kinects to measure multi-modalities that support the affect state: facial expression analysis and gaze estimation [8], mobile device-based emotion recognition [9], skeleton motion using depth sensors and speech recognition. Data has been collected using multimodal learning analytics developed for the project, including annotated multimodal recordings of learners interacting with the system, facial expression data and position of the learner. In addition, interviews with teachers and learners, from mainstream education as well as learners with profound multiple learning difficulties and autism, have been carried out to measure engagement and achievement of learners. Findings from schools based in the United Kingdom, mainstream and special schools will be presented and challenges shared

Follow-up study of sensory-motor polyneuropathy in Type 1 (insulin-dependent) diabetic subjects after simultaneous pancreas and kidney transplantation and after graft rejection

The influence of successful simultaneous pancreas and kidney transplantation on peripheral polyneuropathy was investigated in 53 patients for a mean observation period of 40.3 months. Seventeen patients were followed-up for more than 3 years. Symptoms and signs were assessed every 6 months using a standard questionnaire, neurological examination and measurement of sensory and motor nerve conduction velocities. While symptoms of polyneuropathy improved (pain, paraesthesia, cramps, restless-legs) and nerve conduction velocity increased, there was no change of clinical signs (sensation, muscle-force, tendon-reflexes). Following kidney-graft-rejection there was a slight decrease of nerve conduction verlocity during the first year, which was not statistically significant. Following pancreas-graft rejection there was no change of nerve conduction velocity during the first year. Comparing the maximum nerve conduction velocity of the patients with pancreas-graft-rejection to the nerve conduction velocities of these patients at the end of the study, there was a statistically significant decrease of 6.5 m/s. In conclusion, we believe that strict normalization of glucose metabolism alters the progressive course of diabetic polyneuropathy. It may be stabilized or partly reversed after successful grafting even in long-term diabetic patients

Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

The effects of climatic fluctuations and extreme events on running water ecosystems

Most research on the effects of environmental change in freshwaters has focused on incremental changes in average conditions, rather than fluctuations or extreme events such as heatwaves, cold snaps, droughts, floods or wildfires, which may have even more profound consequences. Such events are commonly predicted to increase in frequency, intensity and duration with global climate change, with many systems being exposed to conditions with no recent historical precedent. We propose a mechanistic framework for predicting potential impacts of environmental fluctuations on running water ecosystems by scaling up effects of fluctuations from individuals to entire ecosystems. This framework requires integration of four key components: effects of the environment on individual metabolism, metabolic and biomechanical constraints on fluctuating species interactions, assembly dynamics of local food webs and mapping the dynamics of the meta-community onto ecosystem function. We illustrate the framework by developing a mathematical model of environmental fluctuations on dynamically assembling food webs. We highlight (currently limited) empirical evidence for emerging insights and theoretical predictions. For example, widely supported predictions about the effects of environmental fluctuations are: high vulnerability of species with high per capita metabolic demands such as large-bodied ones at the top of food webs; simplification of food web network structure and impaired energetic transfer efficiency; reduced resilience and top-down relative to bottom-up regulation of food web and ecosystem processes. We conclude by identifying key questions and challenges that need to be addressed to develop more accurate and predictive bio-assessments of the effects of fluctuations, and implications of fluctuations for management practices in an increasingly uncertain world

General Practitioners' views on the provision of nicotine replacement therapy and bupropion.

BACKGROUND: Nicotine replacement therapies (NRT) and a new drug, bupropion, are licensed in several countries as aids to smoking cessation. General practitioners (GPs) play a crucial role in recommending or prescribing these medications. In the UK there has been discussion about whether the medications should be reimbursable by the National Health Service (NHS). This study assessed English GPs' attitudes towards reimbursement of NRT and bupropion. METHODS: Postal survey of a randomly selected national sample of GPs; 376 GPs completed the questionnaire after one reminder; effective response rate: 53%. There was no difference between the responses of GPs who responded to the initial request and those who responded only after a reminder suggesting minimal bias due to non-response. RESULTS: Attitudes of GPs were remarkably divided on most issues relating to the medications. Forty-three percent thought that bupropion should not be on NHS prescription while 42% thought that it should be (15% did not know); Fifty percent thought that NRT should not be on NHS prescription while 42% thought it should be (8% did not know). Requiring that smokers attend behavioural support programmes to be eligible to receive the medications on NHS prescription made no appreciable difference to the GPs' views. GPs were similarly divided on whether having the medications reimbursable would add unacceptably to their workload or offer a welcome opportunity to discuss smoking with their patients. A principal components analysis of responses to the individual questions on NRT and bupropion revealed that GPs' attitudes could be understood in terms of a single 'pro-con' dimension accounting for 53% of the total variance which made no distinction between the two medications. CONCLUSIONS: GPs in England appear to be divided in their attitudes to medications to aid smoking cessation and appear not to discriminate in their views between different types of medication or different aspects of their use. This suggests that their attitudes are generated by quite fundamental values. Addressing these values may be important in encouraging GPs to adhere more closely to national and international guidelines