Program Veri¿cation in the presence of complex numbers, functions with branch cuts etc

Abstract-In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as "does the lowlevel arithmetic implement the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more dif¿cult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simpli¿cation rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities

A “piano movers” problem reformulated

Abstract-It has long been known that cylindrical algebraic decompositions (CADs) can in theory be used for robot motion planning. However, in practice even the simplest examples can be too complicated to tackle. We consider in detail a "Piano Mover's Problem" which considers moving an infinitesimally thin piano (or ladder) through a right-angled corridor. Producing a CAD for the original formulation of this problem is still infeasible after 25 years of improvements in both CAD theory and computer hardware. We review some alternative formulations in the literature which use differing levels of geometric analysis before input to a CAD algorithm. Simpler formulations allow CAD to easily address the question of the existence of a path. We provide a new formulation for which both a CAD can be constructed and from which an actual path could be determined if one exists, and analyse the CADs produced using this approach for variations of the problem. This emphasises the importance of the precise formulation of such problems for CAD. We analyse the formulations and their CADs considering a variety of heuristics and general criteria, leading to conclusions about tackling other problems of this form

Two-dimensional elastoplastic analysis of cylindrical cavity problems in Tresca materials

This paper presents analytical elastic-plastic solutions for static stress loading analysis and quasi-static expansion analysis of a cylindrical cavity in Tresca materials, considering biaxial far-field stresses and shear stresses along the inner cavity wall. The two-dimensional static stress solution is obtained by assuming that the plastic zone is statically determinate and using the complex variable theory in the elastic analysis. A rigorous conformal mapping function is constructed, which predicts that the elastic-plastic boundary is in an elliptic shape under biaxial in situ stresses, and the range of the plastic zone extends with increasing internal shear stresses. The major axis of the elliptical elastic-plastic boundary coincides with the direction of the maximum far-field compression stress. Furthermore, considering the internal shear stresses, an analytical large-strain displacement solution is derived for continuous cavity expansion analysis in a hydrostatic initial stress filed. Based on the derived analytical stress and displacement solutions, the influence of the internal shear stresses on the quasi-static cavity expansion process is studied. It is shown that additional shear stresses could reduce the required normal expansion pressure to a certain degree, which partly explains the great reduction of the axial soil resistance due to rotations in rotating cone penetration tests. In addition, through additionally considering the potential influences of biaxial in situ stresses and shear stresses generated around the borehole during drillings, an improved cavity expansion approach for estimating the maximum allowable mud pressure of horizontal directional drillings (HDDs) in undrained clays is proposed and validated

How are falls and fear of falling associated with objectively measured physical activity in a cohort of community-dwelling older men?

BACKGROUND: Falls affect approximately one third of community-dwelling older adults each year and have serious health and social consequences. Fear of falling (FOF) (lack of confidence in maintaining balance during normal activities) affects many older adults, irrespective of whether they have actually experienced falls. Both falls and fear of falls may result in restrictions of physical activity, which in turn have health consequences. To date the relation between (i) falls and (ii) fear of falling with physical activity have not been investigated using objectively measured activity data which permits examination of different intensities of activity and sedentary behaviour. METHODS: Cross-sectional study of 1680 men aged 71-92 years recruited from primary care practices who were part of an on-going population-based cohort. Men reported falls history in previous 12 months, FOF, health status and demographic characteristics. Men wore a GT3x accelerometer over the hip for 7 days. RESULTS: Among the 12% of men who had recurrent falls, daily activity levels were lower than among non-fallers; 942 (95% CI 503, 1381) fewer steps/day, 12(95% CI 2, 22) minutes less in light activity, 10(95% CI 5, 15) minutes less in moderate to vigorous PA [MVPA] and 22(95% CI 9, 35) minutes more in sedentary behaviour. 16% (n = 254) of men reported FOF, of whom 52% (n = 133) had fallen in the past year. Physical activity deficits were even greater in the men who reported that they were fearful of falling than in men who had fallen. Men who were fearful of falling took 1766(95% CI 1391, 2142) fewer steps/day than men who were not fearful, and spent 27(95% CI 18, 36) minutes less in light PA, 18(95% CI 13, 22) minutes less in MVPA, and 45(95% CI 34, 56) minutes more in sedentary behaviour. The significant differences in activity levels between (i) fallers and non-fallers and (ii) men who were fearful of falling or not fearful, were mediated by similar variables; lower exercise self-efficacy, fewer excursions from home and more mobility difficulties. CONCLUSIONS: Falls and in particular fear of falling are important barriers to older people gaining health benefits of walking and MVPA. Future studies should assess the longitudinal associations between falls and physical activity

Emergency medical service provider decision-making in out of hospital cardiac arrest: An exploratory study

© 2017 The Author(s). Background: There are approximately 60,000 out-of-hospital cardiac arrests (OHCA) in the United Kingdom (UK) each year. Within the UK there are well-established clinical practice guidelines that define when resuscitation should be commenced in OHCA, and when resuscitation should cease. Background literature indicates that decision-making in the commencement and cessation of resuscitation efforts in OHCA is complex, and not comprehensively understood. No relevant research from the UK has been published to date and this research study seeks to explore the influences on UK Emergency Medical Service (EMS) provider decision-making when commencing and ceasing resuscitation attempts in OHCA. The aim of this research to explore the influences on UK Emergency Medical Services provider decision-making when commencing and ceasing resuscitation attempts in OHCA. Methods: Four focus groups were convened with 16 clinically active EMS providers. Four case vignettes were discussed to explore decision-making within the focus groups. Thematic analysis was used to analyse transcripts. Results: This research found that there are three stages in the decision-making process when EMS providers consider whether to commence or cease resuscitation attempts in OHCA. These stages are: the call; arrival on scene; the protocol. Influential factors present at each of the three stages can lead to different decisions and variability in practice. These influences are: factual information available to the EMS provider; structural factors such as protocol, guidance and research; cultural beliefs and values; interpersonal factors; risk factors; personal values and beliefs. Conclusions: An improved understanding of the circumstantial, individual and interpersonal factors that mediate the decision-making process in clinical practice could inform the development of more effective clinical guidelines, education and clinical decision support in OHCA. These changes have the potential to lead to greater consistency. and EMS provider confidence, with the potential for improved patient outcome from OHCA

Clinicians' attitude towards a placebo-controlled randomised clinical trial investigating the effect of neuraminidase inhibitors in adults hospitalised with influenza

Background: The value of neuraminidase inhibitors (NAIs) in reducing severe clinical outcomes from influenza is debated. A clinical trial to generate better evidence is desirable. However, it is unknown whether UK clinicians would support a placebo controlled trial. A survey was conducted to determine the attitude of clinicians towards a clinical trial and their current practice in managing adults admitted to hospital with suspected influenza. Methods: Senior clinicians (n=50) across the UK actively involved in the care of patients hospitalised with severe respiratory infections and/or respiratory infection research were invited to participate in an on-line survey. Participants were asked their opinion on the evidence for benefit of NAIs in influenza, their current practice in relation to: a) testing for influenza; b) treating empirically with NAIs; and c) when influenza infection is virolologically confirmed, prescribing NAIs. Results: Thirty-five (70%) of 50 clinicians completed the survey. Respondents were drawn mainly from infectious diseases, intensive care and respiratory medicine. Only 11 (31%) of 35 respondents agreed that NAIs are effective at reducing influenza mortality;14(40%)disagreed, 10 (28.6%) neither agreed nor disagreed. When managing adults admitted to non-ICU wards with a respiratory infection during an influenza season, 15 (51.7%) clinicians indicated they would usually perform a test for influenza in greater than 60% of patients but only 9 (31%) would treat empirically with NAIs in greater than 60% of patients. Few clinicians would either test or empirically treat patients presenting with other (non-respiratory infection related) diagnoses. If influenza infection is confirmed, 17 (64.5%) clinicians would prescribe NAIs in greater than 80% of patients with a respiratory infection treated on non-ICU wards Thirty-one (89%) clinicians agreed that a placebo-controlled clinical trial should be conducted and 29 (85%) would participate in such a trial. Conclusions: There is strong support from UK clinicians for a placebo-controlled trial of NAI treatment in adults hospitalised with suspected influenza. Current variation in medical opinion and clinical practice demonstrates collective equipoise, supporting ethical justification for a trial. Low use of NAIs in the UK suggests randomisation of treatment would not substantially divert patients towards placebo

Elevated <scp>CO₂</scp> interacts with nutrient inputs to restructure plant communities in phosphorus‐limited grasslands

AbstractGlobally pervasive increases in atmospheric CO2 and nitrogen (N) deposition could have substantial effects on plant communities, either directly or mediated by their interactions with soil nutrient limitation. While the direct consequences of N enrichment on plant communities are well documented, potential interactions with rising CO2 and globally widespread phosphorus (P) limitation remain poorly understood. We investigated the consequences of simultaneous elevated CO2 (eCO2) and N and P additions on grassland biodiversity, community and functional composition in P‐limited grasslands. We exposed soil‐turf monoliths from limestone and acidic grasslands that have received &gt;25 years of N additions (3.5 and 14 g m−2 year−1) and 11 (limestone) or 25 (acidic) years of P additions (3.5 g m−2 year−1) to eCO2 (600 ppm) for 3 years. Across both grasslands, eCO2, N and P additions significantly changed community composition. Limestone communities were more responsive to eCO2 and saw significant functional shifts resulting from eCO2–nutrient interactions. Here, legume cover tripled in response to combined eCO2 and P additions, and combined eCO2 and N treatments shifted functional dominance from grasses to sedges. We suggest that eCO2 may disproportionately benefit P acquisition by sedges by subsidising the carbon cost of locally intense root exudation at the expense of co‐occurring grasses. In contrast, the functional composition of the acidic grassland was insensitive to eCO2 and its interactions with nutrient additions. Greater diversity of P‐acquisition strategies in the limestone grassland, combined with a more functionally even and diverse community, may contribute to the stronger responses compared to the acidic grassland. Our work suggests we may see large changes in the composition and biodiversity of P‐limited grasslands in response to eCO2 and its interactions with nutrient loading, particularly where these contain a high diversity of P‐acquisition strategies or developmentally young soils with sufficient bioavailable mineral P.</jats:p

The Dynamics of Democracy, Development and Cultural Values

Over the past decades many countries have experienced rapid changes in their economies, their democratic institutions and the values of their citizens. Comprehensive data measuring these changes across very different countries has recently become openly available. Between country similarities suggest common underlying dynamics in how countries develop in terms of economy, democracy and cultural values. We apply a novel Bayesian dynamical systems approach to identify the model which best captures the complex, mainly non-linear dynamics that underlie these changes. We show that the level of Human Development Index (HDI) in a country drives first democracy and then higher emancipation of citizens. This change occurs once the countries pass a certain threshold in HDI. The data also suggests that there is a limit to the growth of wealth, set by higher emancipation. Having reached a high level of democracy and emancipation, societies tend towards equilibrium that does not support further economic growth. Our findings give strong empirical evidence against a popular political science theory, known as the Human Development Sequence. Contrary to this theory, we find that implementation of human-rights and democratisation precede increases in emancipative values