Accurate macroscale modelling of spatial dynamics in multiple dimensions

Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid microscale dynamics the dynamical systems approach constructs accurate closures of macroscale discretisations of the microscale system. Here we specifically explore reaction-diffusion problems in two spatial dimensions as a prototype of generic systems in multiple dimensions. Our approach unifies into one the modelling of systems by a type of finite elements, and the `equation free' macroscale modelling of microscale simulators efficiently executing only on small patches of the spatial domain. Centre manifold theory ensures that a closed model exist on the macroscale grid, is emergent, and is systematically approximated. Dividing space either into overlapping finite elements or into spatially separated small patches, the specially crafted inter-element/patch coupling also ensures that the constructed discretisations are consistent with the microscale system/PDE to as high an order as desired. Computer algebra handles the considerable algebraic details as seen in the specific application to the Ginzburg--Landau PDE. However, higher order models in multiple dimensions require a mixed numerical and algebraic approach that is also developed. The modelling here may be straightforwardly adapted to a wide class of reaction-diffusion PDEs and lattice equations in multiple space dimensions. When applied to patches of microscopic simulations our coupling conditions promise efficient macroscale simulation.Comment: some figures with 3D interaction when viewed in Acrobat Reader. arXiv admin note: substantial text overlap with arXiv:0904.085

Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions

Developments in dynamical systems theory provides new support for the discretisation of pdes and other microscale systems. Here we explore the methodology applied to the gap-tooth scheme in the equation-free approach of Kevrekidis in two spatial dimensions. The algebraic detail is enormous so we detail computer algebra procedures to handle the enormity. However, modelling the dynamics on 2D spatial patches appears to require a mixed numerical and algebraic approach that is detailed in this report. Being based upon the computation of residuals, the procedures here may be simply adapted to a wide class of reaction-diffusion equations

Senior management perspectives of mathematics and statistics support in higher education: moving to an ‘ecological’ approach

© 2016 Association for Tertiary Education Management and the LH Martin Institute for Tertiary Education Leadership and ManagementThis article explores the perspectives of three senior managers in higher education institutions in England regarding their mathematics and statistics support provision. It does so by means of a qualitative case study that draws upon the writing of Ronald Barnett about the identity of an ‘ecological’ university, along with metaphors associated with the notion of organisations as living ‘organisms’, suggested by Gareth Morgan. Using these ideas as a heuristic sheds light upon the view that whilst outwardly universities appear to represent a uniform landscape, mathematics and statistics support alternatively, can be seen as different ‘species’ within the higher education system. The study illustrates how three universities occupying contrasting ecological ‘niches’ are responding to the challenges they face by providing and planning different forms of learning support for mathematics and statistics. In conclusion, it is recommended that senior managers reflect upon the possibilities offered by the idea of ‘ecological’ identities in order to explore how they might respond strategically to a rapidly changing environment. This includes adapting various solutions and the further development of innovative ways of supporting students’ transitions throughout the academic lifecycle. In addition, an ecological approach could also aid the formation of the co-creational relationships and networks required for the future success of those developments

Striving for sustainable global democracy through a group decision-making process: a critical review of an online course to model transformative praxis

The Journal is an open access journal. All articles are made freely available to readers.Our open access policy is in in accordance with the Budapest Open Access Initiative (BOAI) definition - it means that articles have free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself.Sustainability is not simply about changing practices but more centrally about agreeing to change practices together’ (Flanagan et al. 2011). To achieve such ends, groups need to improve processes for making complex decisions together. The challenge faced recently in Copenhagen (including a large number of diverse participants in policy discussions) indicates the need for new ways to mprove discursive democracy. Poverty and climate change are ‘wicked’ problems (Rittel and Webber 1984) that comprise many diverse interrelated variables and that have a strong value and emotional dimension. The shortcomings of many approaches to these problems is that they are expert driven, do not involve the public in decision making, and have a narrow focus on technical issues. They do not consider issues in terms of their interrelated complexity with human cultural issues and values. This paper addresses the transboundary conundrum of how to address complex social and environmental challenges while engaging with people's diverse values and emotion

Effects of Harmful Algal Blooms on Fish and Shellfish Species: A Case Study of New Zealand in a Changing Environment

Harmful algal blooms (HABs) have wide-ranging environmental impacts, including on aquatic species of social and commercial importance. In New Zealand (NZ), strategic growth of the aquaculture industry could be adversely affected by the occurrence of HABs. This review examines HAB species which are known to bloom both globally and in NZ and their effects on commercially important shellfish and fish species. Blooms of Karenia spp. have frequently been associated with mortalities of both fish and shellfish in NZ and the sub-lethal effects of other genera, notably Alexandrium spp., on shellfish (which includes paralysis, a lack of byssus production, and reduced growth) are also of concern. Climate change and anthropogenic impacts may alter HAB population structure and dynamics, as well as the physiological responses of fish and shellfish, potentially further compromising aquatic species. Those HAB species which have been detected in NZ and have the potential to bloom and harm marine life in the future are also discussed. The use of environmental DNA (eDNA) and relevant bioassays are practical tools which enable early detection of novel, problem HAB species and rapid toxin/HAB screening, and new data from HAB monitoring of aquaculture production sites using eDNA are presented. As aquaculture grows to supply a sizable proportion of the world’s protein, the effects of HABs in reducing productivity is of increasing significance. Research into the multiple stressor effects of climate change and HABs on cultured species and using local, recent, HAB strains is needed to accurately assess effects and inform stock management strategies

Fluorescence based Tool to Detect Endogenous Peroxynitrite in M1-Polarized Murine J774.2 Macrophages

Oxidative stress and inflammation are intrinsically linked to each other. In addition, they are implicated in the evolution and progression of noncommunicable diseases (NCDs). Large amounts of reactive oxygen species (ROS) are generated as part of the immune response toward NCDs. Among all of the ROS species, peroxynitrite (ONOO^–) has the shortest half-life with <20 ms under typical physiological conditions. Hence, detecting ONOO^– and studying its generation in vitro allows for a better understanding of inflammatory processes. We demonstrate that peroxyresorufin-1 (PR1) is a selective and sensitive ONOO^– fluorescence-based sensor in J774.2 macrophages. PR1 was able to detect changes in ONOO^– production upon investigation of different factors: enhanced generation of ONOO^– through LPS and IFN-γ as well as diminished ONOO^– production with the introduction of superoxide scavengers and nitric oxide synthase inhibitors. Our study validates PR1 as an effective tool for the detection of ONOO^– in J774.2 murine macrophages and should allow for further elucidation of ROS biology and chemistry

Use of proton pump inhibitors to treat persistent throat symptoms: Multicentre, double blind, randomised, placebo controlled trial

Objective. To assess the use of proton pump inhibitors (PPIs) to treat persistent throat symptoms. Design. Pragmatic, double blind, placebo controlled, randomised trial. Setting. Eight ear, nose, and throat outpatient clinics, United Kingdom. Participants. 346 patients aged 18 years or older with persistent throat symptoms who were randomised according to recruiting centre and baseline severity of symptoms (mild or severe): 172 to lansoprazole and 174 to placebo. Intervention. Random blinded allocation (1:1) to either 30 mg lansoprazole twice daily or matched placebo twice daily for 16 weeks. Main outcome measures. Primary outcome was symptomatic response at 16 weeks measured using the total reflux symptom index (RSI) score. Secondary outcomes included symptom response at 12 months, quality of life, and throat appearances. Results. Of 1427 patients initially screened for eligibility, 346 were recruited. The mean age of the study sample was 52.2 (SD 13.7) years, 196 (57%) were women, and 162 (47%) had severe symptoms at presentation; these characteristics were balanced across treatment arms. The primary analysis was performed on 220 patients who completed the primary outcome measure within a window of 14-20 weeks. Mean RSI scores were similar between treatment arms at baseline: lansoprazole 22.0 (95% confidence interval 20.4 to 23.6) and placebo 21.7 (20.5 to 23.0). Improvements (reduction in RSI score) were observed in both groups—score at 16 weeks: lansoprazole 17.4 (15.5 to19.4) and placebo 15.6 (13.8 to 17.3). No statistically significant difference was found between the treatment arms: estimated difference 1.9 points (95% confidence interval −0.3 to 4.2 points; P=0.096) adjusted for site and baseline symptom severity. Lansoprazole showed no benefits over placebo for any secondary outcome measure, including RSI scores at 12 months: lansoprazole 16.0 (13.6 to 18.4) and placebo 13.6 (11.7 to 15.5): estimated difference 2.4 points (−0.6 to 5.4 points). Conclusions. No evidence was found of benefit from PPI treatment in patients with persistent throat symptoms. RSI scores were similar between the lansoprazole and placebo groups after 16 weeks of treatment and at the 12 month follow-up

Coverage and timing of children's vaccination: an evaluation of the expanded programme on immunisation in The Gambia.

OBJECTIVE: To evaluate the coverage and timeliness of the Expanded Programme on Immunisation (EPI) in The Gambia. METHODS: Vaccination data were obtained between January 2005 and December 2012 from the Farafenni Health and Demographic Surveillance System (FHDSS), the Basse Health and Demographic Surveillance System (BHDSS), the Kiang West Demographic surveillance system (KWDSS), a cluster survey in the more urban Western Health Region (WR) and a cross sectional study in four clinics in the semi-urban Greater Banjul area of WR. Kaplan-Meier survival function was used to estimate the proportion vaccinated by age and to assess timeliness to vaccination. FINDINGS: BCG vaccine uptake was over 95% in all regions. Coverage of DPT1 ranged from 93.2% in BHDSS to 99.8% in the WR. Coverage decreased with increasing number of DPT doses; DPT3 coverage ranged from 81.7% in BHDSS to 99.0% in WR. Measles vaccination coverage ranged from 83.3% in BHDSS to 97.0% in WR. DPT4 booster coverage was low and ranged from 43.9% in the WR to 82.8% in KWDSS. Across all regions, delaying on previous vaccinations increased the likelihood of being delayed for the subsequent vaccination. CONCLUSIONS: The Gambia health system achieves high vaccine coverage in the first year of life. However, there continues to be a delay to vaccination which may impact on the introduction of new vaccines. Examples of effectively functioning EPI programmes such as The Gambia one may well be important models for other low income countries struggling to achieve high routine vaccination coverage