Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Deriving bases for Abelian functions

We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstrass identities for the case of the trigonal curve of genus four.Comment: 35page

Re-evaluating the Relevance of Vegetation Trimlines in the Canadian Arctic as an Indicator of Little Ice Age Paleoenvironments

The origin of trimlines associated with the so-called “lichen-free” areas in the Canadian Arctic has been attributed both to perennial snowfield expansion during the Little Ice Age (LIA) and to seasonally persistent snow cover in more recent times. Because of the disparate hypotheses (ecological versus paleoclimatic) regarding the formation of these trimlines, their use as a paleoclimatic indicator has been abandoned for more than two decades. We re-examine this debate and the validity of the opposing hypotheses in the light of new regional mapping of trimlines across the Queen Elizabeth Islands (QEI). The ecological hypothesis—insufficient duration of the growing season resulting from seasonally persistent snow cover—fails to account for the poikilohydric nature of lichens and their ability to endure short growing seasons. It cannot adequately explain the existence of sharp trimlines or account for the occurrence of those trimlines on sparsely vegetated carbonate terrain. Furthermore, trimlines outlining the former extent of thin plateau ice caps are accordant with trimlines associated with former perennial snowfields, indicating that these trimlines record snow and ice expansion during the LIA rather than the seasonal persistence of more recent snow cover. We suggest that these features represent an important LIA climate indicator and should therefore be used for paleoclimatic reconstruction.L’origine des épaulements propres aux zones dites sans lichen de l’Arctique canadien a été attribuée tant à l’expansion des champs de neige pérenne pendant le petit âge glaciaire qu’à la couverture de neige longévive d’époques plus récentes. Puisqu’il existe des hypothèses disparates (écologiques par opposition à paléoclimatiques) quant à la formation de ces épaulements, on a arrêté de s’en servir à titre d’indicateur paléoclimatique depuis plus d’une vingtaine d’années. Ici, ce débat fait l’objet d’un nouvel examen où l’on se penche sur la validité des hypothèses divergentes à la lumière du nouveau mappage régional des épaulements des îles de la Reine-Élisabeth. L’hypothèse d’ordre écologique —durée insuffisante de la saison de croissance découlant de la couverture de neige longévive en saison —omet de tenir compte de la nature poecilitique du lichen et de son aptitude à endurer de courtes saisons de croissance. Cette hypothèse ne permet pas d’expliquer adéquatement l’existence d’épaulements précis ou de tenir compte de la présence de ces épaulements en terrain carbonaté à végétation éparse. Par ailleurs, les épaulements qui délimitent l’ancienne étendue des minces calottes glaciaires des plateaux correspondent aux épaulements associés aux anciens champs de neige pérenne, ce qui indique que ces épaulements dénotent les expansions de neige et de glace du petit âge glaciaire et non pas de la couverture de neige longévive saisonnière plus récente. On suggère que ces caractéristiques représentent un important indicateur climatique du petit âge glaciaire et par conséquent, qu’on devrait s’en servir à des fins de reconstruction paléoclimatique

Veterinary practitioners’ selection of diagnostic tests for the primary evaluation of colic in the horse

The aim of this study was to survey veterinary practitioners’ selection of diagnostic tests for horses with clinical signs of abdominal pain. A questionnaire was distributed to veterinary surgeons involved in the primary evaluation of horses with abdominal pain, including the respondent's demographics, selection of diagnostic tests and factors affecting decision-making. Data analysis included descriptive analysis, categorisation of free text and simple univariable correlations to explore the relationships between independent variables and the relative self-estimated frequency that diagnostic tests were performed. A total of 228 responses were analysed. Participants worked in mixed practice (55.7 per cent), first opinion equine (22.8 per cent), first and second opinion equine (17.9 per cent) and referral practice (3.1 per cent). The majority (48.2 per cent, 105/218) were very confident managing a colic case (confidence level 4/5). The most frequently used diagnostic tests were ‘response to analgesia’ (87.2±24.0 per cent cases), rectal examination (75.9±21.2 per cent) and nasogastric intubation (43.8±27.6 per cent). Approach varied between practitioners, and for all diagnostic tests with frequency of use ranging from 0 to 100 per cent of cases. ‘Risk to personal safety’ was the most common reason for not using rectal examination. Practitioner's opinion of their confidence level in managing a colic case was associated with how frequently they used different diagnostic tests. There was marked variation in practitioners’ approaches, highlighting the need for further evidence to support decision-making

Reviewing research evidence and the case of participation in sport and physical recreation by black and minority ethnic communities

The paper addresses the implications of using the process of systematic review in the many areas of leisure where there is a dearth of material that would be admitted into conventional Cochrane Reviews. This raises important questions about what constitutes legitimate knowledge, questions that are of critical import not just to leisure scholars, but to the formulation of policy. The search for certainty in an area that lacks conceptual consensus results in an epistemological imperialism that takes a geocentric form. While clearly, there is a need for good research design whatever the style of research, we contend that the wholesale rejection of insightful research is profligate and foolhardy. A mechanism has to be found to capitalise on good quality research of whatever form. In that search, we draw upon our experience of conducting a review of the material available on participation in sport and physical recreation by people from Black and minority ethnic groups. The paper concludes with a proposal for a more productive review process that makes better use of the full panoply of good quality research available. © 2012 © 2012 Taylor & Francis

Abelian functions associated with a cyclic tetragonal curve of genus six

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y^4 = x^5 + λ[4]x^4 + λ[3]x^3 + λ[2]x^2 + λ[1]x + λ[0]. We construct Abelian functions using the multivariate sigma-function associated with the curve, generalizing the theory of theWeierstrass℘-function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi inversion problem, a power series expansion for σ(u) and a new addition formula

Truth table invariant cylindrical algebraic decomposition

When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This observation motivates our article and definition of a Truth Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors presented an algorithm that can efficiently and directly construct a TTICAD for a list of formulae in which each has an equational constraint. This was achieved by generalising McCallum's theory of reduced projection operators. In this paper we present an extended version of our theory which can be applied to an arbitrary list of formulae, achieving savings if at least one has an equational constraint. We also explain how the theory of reduced projection operators can allow for further improvements to the lifting phase of CAD algorithms, even in the context of a single equational constraint. The algorithm is implemented fully in Maple and we present both promising results from experimentation and a complexity analysis showing the benefits of our contributions.Comment: 40 page

Cannabinoids in experimental stroke: a systematic review and meta-analysis

Cannabinoids (CBs) show promise as neuroprotectants with some agents already licensed in humans for other conditions. We systematically reviewed CBs in preclinical stroke to guide further experimental protocols. We selected controlled studies assessing acute administration of CBs for experimental stroke, identified through systematic searches. Data were extracted on lesion volume, outcome and quality, and analyzed using random effect models. Results are expressed as standardized mean difference (SMD) with 95% confidence intervals (CIs). In all, 144 experiments (34 publications) assessed CBs on infarct volume in 1,473 animals. Cannabinoids reduced infarct volume in transient (SMD −1.41 (95% CI −1.71), −1.11) P<0.00001) and permanent (−1.67 (−2.08, −1.27), P<0.00001) ischemia and in all subclasses: endocannabinoids (−1.72 (−2.62, −0.82), P=0.0002), CB1/CB2 ligands (−1.75 (−2.19, −1.31), P<0.00001), CB2 ligands (−1.65 (−2.09, −1.22), P<0.00001), cannabidiol (−1.20 (−1.63, −0.77), P<0.00001), Δ9-tetrahydrocannabinol (−1.43 (−2.01, −0.86), P<0.00001), and HU-211 (−2.90 (−4.24, −1.56), P<0.0001). Early and late neuroscores significantly improved with CB use (−1.27 (−1.58, −0.95), P<0.00001; −1.63 (−2.64, −0.62), P<0.002 respectively) and there was no effect on survival. Statistical heterogeneity and publication bias was present, median study quality was 4 (range 1 to 6/8). Overall, CBs significantly reduced infarct volume and improve functional outcome in experimental stroke. Further studies in aged, female and larger animals, with other co-morbidities are required

An evaluation of a short course in mindfulness for Health Visitor Practice Teachers

Practice Teachers (PTs) participated in an 8 week course, Mindfulness Based Cognitive for well-being and resilience. The evaluation was undertaken using three (3) evidenced based questionnaires: Perceived stress(PSS) (Cohen et al 1983), Self-Compassion Score SCS (Neff 2003) and Five Facet Mindfulness Questionnaire (FFMQ) (Baer et al 2006) to identify outcomes for the mindfulness training. Findings indicate the impact on personal wellbeing and professional practice with recommendations for retention of students & Health Visitor (HV) workforce. Summary Mindfulness skills to support top performance and good mental health were offered in eight two-hour sessions to 18 Practice Teachers from September- December 2014 and was evaluated. The course drew on the approach of Mindfulness Based Cognitive Therapy, where participants learn to focus their attention and develop the possibility of creating the space for reflection and response rather than reacting to life’s difficulties. Participants had the opportunity to develop self–care and self-compassion in the sessions as well as in between sessions and which research has shown can have a positive effect on others. Compassion is a contemporary theme in the CNO’s strategy to return to the fundamentals of nursing; mindfulness enables the foundation of practising compassion on self and ultimately to practice compassion with others we work and care for. The attendees were encouraged to review and refresh their practice through with the ultimate planned outcome, to reduce student attrition and prevent breakdown of the practice placement. However, this is a the complex area of adult learning and the nature of student attrition from courses as well as from the workforce cannot necessarily be reduced to one factor. The practice of mindfulness can have an influential effect on health, well-being and resilience, as shown by scientific and medical evidence. This experiential course was neither therapy nor religious instruction but an effective means of helping to alleviate stress and promoting well-being, resilience and flourishing. The course was delivered at a time when practitioners, including PTs were experiencing an increase of student numbers and service delivery changes with associated imperative data collection. The perception of practitioners about the declared increase in the HV workforce (DH 2011) to support and implement these changes was not evident and the evaluation indicates the need for self-care and resilience in the workforce which includes students and practitioners. The project outcomes make recommendations based on the impact of this mindfulness training with PTs to inform future developments within the programme and practice education as well as the HV workforce where a number of interventions call for 'mindfulness' with infants, children and families

To be or not to be an auctioneer: Some thoughts on the legal nature of online eBay auctions and the protection of consumers

This paper discusses the legal classification of online “eBay” auctions. The discussion has key implications on the scope of consumer protection law as sale by auctions are, for example, excluded from the scope of the Consumer Protection (Distance Selling) Regulations 2000. The paper uncovers that online “eBay” auctions cannot always be considered as traditional auctions and that eBay, as an intermediary, is not to be considered as an auctioneer. This creates difficulties associated with a distributive application of consumer protection laws such as the Consumer Protection (Distance Selling) Regulations 2000. Another set of difficulties is associated with a lenient legal regime applicable to the liability of eBay under the Electronic Commerce (EC Directive) Regulations 2002 . The paper concludes that there is an urgent need to clarify the legal classification of online auctions and to rethink the liability of online auction sites to better protect consumers