Objective functions with redundant domains

Let (E,A) be a set system consisting of a finite collection A of subsets of a ground set E, and suppose that we have a function ϕ which maps A into some set S. Now removing a subset K from E gives a restriction A(K¯) to those sets of A disjoint from K, and we have a corresponding restriction ϕ|A(K¯) of our function ϕ. If the removal of K does not affect the image set of ϕ, that is Im(ϕ|A(X¯))=Im(ϕ), then we will say that K is a kernel set of A with respect to ϕ. Such sets are potentially useful in optimisation problems defined in terms of ϕ. We will call the set of all subsets of E that are kernel sets with respect to ϕ a kernel system and denote it by Kerϕ(A). Motivated by the optimisation theme, we ask which kernel systems are matroids. For instance, if A is the collection of forests in a graph G with coloured edges and ϕ counts how many edges of each colour occurs in a forest then Kerϕ(A) is isomorphic to the disjoint sum of the cocycle matroids of the differently coloured subgraphs; on the other hand, if A is the power set of a set of positive integers, and ϕ is the function which takes the values 1 and 0 on subsets according to whether they are sum-free or not, then we show that Kerϕ(A) is essentially never a matroid

Valuing initial teacher education at Master's level

The future of Master’s-level work in initial teacher education (ITE) in England seems uncertain. Whilst the coalition government has expressed support for Master’s-level work, its recent White Paper focuses on teaching skills as the dominant form of professional development. This training discourse is in tension with the view of professional learning advocated by ITE courses that offer Master’s credits. Following a survey of the changing perceptions of Master’s-level study during a Post Graduate Certificate in Education course by student teachers in four subject groups, this paper highlights how the process of professional learning can have the most impact on how they value studying at a higher level during their early professional development

Pancyclicity when each cycle must pass exactly k Hamilton cycle chords.

It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required. A possibly ‘intermediate’ variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length each of which passes exactly k chords? For fixed k, we establish a lower bound of Ω n 1/k� on the growth rate

Computational Non-Newtonian Hemodynamics of Small Vessels

The significance of non-Newtonian hemodynamics of small blood vessels is addressed via the description and critical discussion of cogent models within Computational Fluid Dynamics (CFD) software, in this case ANSYS-CFX. Several applicable hemodynamical shear-thinning models are presented and the relevance with respect to prediction of Shear Strain Rate (SSR) rigorously examined, in order to critically evaluate salient literature. It is found that the small vessels explored, in line with the aforementioned literature, that non-Newtionian evaluation of the fluid behavior is indeed negligible. The work presented herein is a precursor to investigation of more complex geometries and hemodynamic simulations, which are being actively researched. This is a technical note which attempts to address the significance of Newtonian/non-Newtonian flows in small blood vessels

Explaining the effects of an intervention designed to promote evidence-based diabetes care : a theory-based process evaluation of a pragmatic cluster randomised controlled trial

Background The results of randomised controlled trials can be usefully illuminated by studies of the processes by which they achieve their effects. The Theory of Planned Behaviour (TPB) offers a framework for conducting such studies. This study used TPB to explore the observed effects in a pragmatic cluster randomised controlled trial of a structured recall and prompting intervention to increase evidence-based diabetes care that was conducted in three Primary Care Trusts in England. Methods All general practitioners and nurses in practices involved in the trial were sent a postal questionnaire at the end of the intervention period, based on the TPB (predictor variables: attitude; subjective norm; perceived behavioural control, or PBC). It focussed on three clinical behaviours recommended in diabetes care: measuring blood pressure; inspecting feet; and prescribing statins. Multivariate analyses of variance and multiple regression analyses were used to explore changes in cognitions and thereby better understand trial effects. Results Fifty-nine general medical practitioners and 53 practice nurses (intervention: n = 55, 41.98% of trial participants; control: n = 57, 38.26% of trial participants) completed the questionnaire. There were no differences between groups in mean scores for attitudes, subjective norms, PBC or intentions. Control group clinicians had 'normatively-driven' intentions (i.e., related to subjective norm scores), whereas intervention group clinicians had 'attitudinally-driven' intentions (i.e., related to attitude scores) for foot inspection and statin prescription. After controlling for effects of the three predictor variables, this group difference was significant for foot inspection behaviour (trial group × attitude interaction, beta = 0.72, p < 0.05; trial group × subjective norm interaction, beta = -0.65, p < 0.05). Conclusion Attitudinally-driven intentions are proposed to be more consistently translated into action than normatively-driven intentions. This proposition was supported by the findings, thus offering an interpretation of the trial effects. This analytic approach demonstrates the potential of the TPB to explain trial effects in terms of different relationships between variables rather than differences in mean scores. This study illustrates the use of theory-based process evaluation to uncover processes underlying change in implementation trials.European Union ReBEQI projec

CJCheck Stage 1: development and testing of a checklist for reporting community juries – Delphi process and analysis of studies published in 1996–2015

Background Opportunities for community members to actively participate in policy development are increasing. Community/citizen's juries (CJs) are a deliberative democratic process aimed to illicit informed community perspectives on difficult topics. But how comprehensive these processes are reported in peer-reviewed literature is unknown. Adequate reporting of methodology enables others to judge process quality, compare outcomes, facilitate critical reflection and potentially repeat a process. We aimed to identify important elements for reporting CJs, to develop an initial checklist and to review published health and health policy CJs to examine reporting standards. Design Using the literature and expertise from CJ researchers and policy advisors, a list of important CJ reporting items was suggested and further refined. We then reviewed published CJs within the health literature and used the checklist to assess the comprehensiveness of reporting. Results CJCheck was developed and examined reporting of CJ planning, juror information, procedures and scheduling. We screened 1711 studies and extracted data from 38. No studies fully reported the checklist items. The item most consistently reported was juror numbers (92%, 35/38), while least reported was the availability of expert presentations (5%, 2/38). Recruitment strategies were described in 66% of studies (25/38); however, the frequency and timing of deliberations was inadequately described (29%, 11/38). Conclusions Currently CJ publications in health and health policy literature are inadequately reported, hampering their use in policy making. We propose broadening the CJCheck by creating a reporting standards template in collaboration with international CJ researchers, policy advisors and consumer representatives to ensure standardized, systematic and transparent reporting.RT was supported by a NHMRC Screening and Test Evaluation Program (STEP) Grant (#633033). RS was supported by a Bond University Vice Chancellor’s Research Grant Scheme. CD, SMC and LR received funding support from NHMRC Project Grant (#1023197). CD received funding support from a NHMRC Project Grant (#1083079). SMC is funded through NHMRC Career Development Fellowship (#1032963). JMS was funded by an Australian National Preventive Health Agency Fellowship (20STR2013F) and an NHMRC Capacity Building Grant (565501)

Short-pulse, extreme-ultraviolet continuum emission from a table-top laser plasma light source

We have observed extreme-ultraviolet (XUV) “line-free” continuum emission from laser plasmas of high atomic number elements using targets irradiated with 248 nm laser pulses of 7 ps duration at a power density of ∼ 1013 W/cm2. Using both dispersive spectroscopy and streak camera detection, the spectral and temporal evolution of XUV continuum emission for several target atomic numbers has been measured on a time scale with an upper limit of several hundred picoseconds limited by amplified spontaneous emission

EQ-5D-3L Derived Population Norms for Health Related Quality of Life in Sri Lanka

Background Health Related Quality of Life (HRQoL) is an important outcome measure in health economic evaluation that guides health resource allocations. Population norms for HRQoL are an essential ingredient in health economics and in the evaluation of population health. The aim of this study was to produce EQ-5D-3L-derived population norms for Sri Lanka. Method A population sample (n =  780) was selected from four districts of Sri Lanka. A stratified cluster sampling approach with probability proportionate to size was employed. Twenty six clusters of 30 participants each were selected; each participant completed the EQ-5D-3L in a face-to-face interview. Utility weights for their EQ-5D-3L health states were assigned using the Sri Lankan EQ-5D-3L algorithm. The population norms are reported by age and socio-economic variables. Results The EQ-5D-3L was completed by 736 people, representing a 94% response rate. Sixty per cent of the sample reported being in full health. The percentage of people responding to any problems in the five EQ-5D-3L dimensions increased with age. The mean EQ-5D-3L weight was 0.85 (SD 0.008; 95%CI 0.84-0.87). The mean EQ-5D-3L weight was significantly associated with age, housing type, disease experience and religiosity. People above 70 years of age were 7.5 times more likely to report mobility problems and 3.7 times more likely to report pain/discomfort than those aged 18-29 years. Those with a tertiary education were five times less likely to report any HRQoL problems than those without a tertiary education. A person living in a shanty was 4.3 more likely to have problems in usual activities than a person living in a single house. Conclusion The population norms in Sri Lanka vary with socio-demographic characteristics. The socioeconomically disadvantaged have a lower HRQoL. The trends of population norms observed in this lower middle income country were generally similar to those previously reported in high income countries