Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

“Thanks for letting us all share your mammogram experience virtually” : developing an online hub for cancer screening

Background: The decision around whether to attend breast screening can often involve making sense of confusing and contradictory information on risks and benefits. The Word of Mouth Mammogram e-Network (WoMMeN) project was established to create an online resource to support decision making around breast screening. This paper presents data from our user-centred approach to engaging stakeholders (both health professionals and service-users) in the design of this online resource. Our novel approach involved creating a user-design group within Facebook to allow access to ongoing discussion between researchers, radiographers and existing and potential service-users. Objective: The current study had two objectives. The first was to examine the utility of an online user-design group for generating insight for the creation of online health resources. We sought to explore the advantages and limitations of this approach. The second objective was to analyse what women want from an online resource for breast screening information. Methods: We recruited a user-design group in Facebook, and also posted a survey within the group asking questions around design considerations for an online breast screening hub. Although the membership of the Facebook group varied over time, there were 71 members in the Facebook group at the end point of analysis. We next conducted framework analysis on 70 threads from Facebook and thematic analysis on the 23 survey responses. We focused additional analysis on how the themes were discussed by the different stakeholders within the context of the design group. Results: Two major themes were found across both the Facebook discussion and the survey data: ‘The power of information’, and ‘The hub as a place for communication and support’. Information was discussed as empowering, but also recognised as threatening. Communication and the sharing of experiences were deemed important but there was also recognition of potential miscommunication within online discussion. Health professionals and service-users expressed the same broad concerns, but also showed subtle differences. Importantly, the themes were triangulated between the Facebook discussions and the survey data, supporting the validity of an online user-design group. Conclusions: Online user-design groups afford a useful method for understanding stakeholder needs. In contrast to focus groups, they afford access to users from diverse geographical locations, and traverse time constraints allowing more considered follow-ups to responses. The use of Facebook provides a familiar and naturalistic setting for discussion. Whilst also acknowledging limitations in the sample, this approach has allowed us to understand the views of stakeholders in the user-centred design of the WoMMeN hub for breast screening

The holistic phase model of early adult crisis

The objective of the current study was to explore the structural, temporal and experiential manifestations of crisis episodes in early adulthood, using a holistic-systemic theoretical framework. Based on an analysis of 50 interviews with individuals about a crisis episode between the ages of 25 and 35, a holistic model was developed. The model comprises four phases: (1) Locked-in, (2) Separation/Time-out, (3) Exploration and (4) Rebuilding, which in turn have characteristic features at four levels—person-in-environment, identity, motivation and affect-cognition. A crisis starts out with a commitment at work or home that has been made but is no longer desired, and this is followed by an emotionally volatile period of change as that commitment is terminated. The positive trajectory of crisis involves movement through an exploratory period towards active rebuilding of a new commitment, but ‘fast-forward’ and ‘relapse’ loops can interrupt Phases 3 and 4 and make a positive resolution of the episode less likely. The model shows conceptual links with life stage theories of emerging adulthood and early adulthood, and it extends current understandings of the transitional developmental challenges that young adults encounter

Identification of signaling pathways in early mammary gland development by mouse genetics

The mammary gland develops as an appendage of the ectoderm. The prenatal stage of mammary development is hormone independent and is regulated by sequential and reciprocal signaling between the epithelium and the mesenchyme. A number of recent studies using human and mouse genetics, in particular targeted gene deletion and transgenic expression, have identified some of the signals that control specific steps in development. This process involves cell specification and proliferation, reciprocal tissue interactions and cell migration. Since some of these events are recapitulated during tumorigenesis, an understanding of these signaling pathways may contribute to the development of targeted therapies and novel drugs

Birth data accessibility via primary care health records to classify health status in a multi-ethnic population of children: an observational study

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Challenges of liver cancer: Future emerging tools in imaging and urinary biomarkers.

© The Author(s) 2015. Published by Baishideng Publishing Group Inc. All rights reserved.Chronic liver disease has become a global health problem as a result of the increasing incidence of viral hepatitis, obesity and alcohol misuse. Over the past three decades, in the United Kingdom alone, deaths from chronic liver disease have increased both in men and in women. Currently, 2.5% of deaths worldwide are attributed to liver disease and projected figures suggest a doubling in hospitalisation and associated mortality by 2020. Chronic liver diseases vary for clinical manifestations and natural history, with some individuals having relatively indolent disease and others with a rapidly progressive course. About 30% of patients affected by hepatitis C has a progressive disease and develop cirrhosis over a 20 years period from the infection, usually 5-10 years after initial medical presentation. The aim of the current therapeutic strategies is preventing the progression from hepatitis to fibrosis and subsequently, cirrhosis. Hepatic steatosis is a risk factor for chronic liver disease and is affecting about the half of patients who abuse alcohol. Moreover non-alcoholic fatty liver disease is part of the metabolic syndrome, associated with obesity, hypertension, type ? diabetes mellitus and dyslipidaemia, and a subgroup of patients develops non-alcoholic steatohepatitis and fibrosis with subsequent cirrhosis. The strengths and pitfalls of liver biopsy are discussed and a variety of new techniques to assess liver damage from transient elastography to experimental techniques, such as in vitro urinary nuclear magnetic resonance spectroscopy. Some of the techniques and tests described are already suitable for more widespread clinical application, as is the case with ultrasound-based liver diagnostics, but others, such as urinary metabonomics, requires a period of critical evaluation or development to take them from the research arena to clinical practice

Urban centre green metrics in Great Britain: a geospatial and socioecological study

Green infrastructure plays a vital role in urban ecosystems. This includes sustaining biodiversity and human health. Despite a large number of studies investigating greenspace disparities in suburban areas, no known studies have compared the green attributes (e.g., trees, greenness, and greenspaces) of urban centres. Consequently, there may be uncharacterised socioecological disparities between the cores of urban areas (e.g., city centres). This is important because people spend considerable time in urban centres due to employment, retail and leisure opportunities. Therefore, the availability of––and disparities in––green infrastructure in urban centres can affect many lives and potentially underscore a socio-ecological justice issue. To facilitate comparisons between urban centres in Great Britain, we analysed open data of urban centre boundaries with a central business district and population of ≥100,000 (n = 68). Given the various elements that contribute to ‘greenness’, we combine a range of different measurements (trees, greenness, and accessible greenspaces) into a single indicator. We applied the normalised difference vegetation index (NDVI) to estimate the mean greenness of urban centres and the wider urban area (using a 1 km buffer) and determined the proportion of publicly accessible greenspace within each urban centre with Ordnance Survey Open Greenspace data. Finally, we applied a land cover classification algorithm using i-Tree Canopy to estimate tree coverage. This is the first study to define and rank urban centres based on multiple green attributes. The results suggest important differences in the proportion of green attributes between urban centres. For instance, Exeter scored the highest with a mean NDVI of 0.15, a tree coverage of 11.67%, and an OS Greenspace coverage of 0.05%, and Glasgow the lowest with a mean NDVI of 0.02, a tree cover of 1.95% and an OS Greenspace coverage of 0.00%. We also demonstrated that population size negatively associated with greenness and tree coverage, but not greenspaces, and that green attributes negatively associated with deprivation. This is important because it suggests that health-promoting and biodiversity-supporting resources diminish as population and deprivation increase. Disparities in green infrastructure across the country, along with the population and deprivation-associated trends, are important in terms of socioecological and equity justice. This study provides a baseline and stimulus to help local authorities and urban planners create and monitor equitable greening interventions in urban/city centres

A Snapshot of J. L. Synge

A brief description is given of the life and influence on relativity theory of Professor J. L. Synge accompanied by some technical examples to illustrate his style of work

Exponentially Increasing Incidences of Cutaneous Malignant Melanoma in Europe Correlate with Low Personal Annual UV Doses and Suggests 2 Major Risk Factors

For several decades the incidence of cutaneous malignant melanoma (CMM) steadily increased in fair-skinned, indoor-working people around the world. Scientists think poor tanning ability resulting in sunburns initiate CMM, but they do not understand why the incidence continues to increase despite the increased use of sunscreens and formulations offering more protection. This paradox, along with lower incidences of CMM in outdoor workers, although they have significantly higher annual UV doses than indoor workers have, perplexes scientists. We found a temporal exponential increase in the CMM incidence indicating second-order reaction kinetics revealing the existence of 2 major risk factors. From epidemiology studies, we know one major risk factor for getting CMM is poor tanning ability and we now propose the other major risk factor may be the Human Papilloma Virus (HPV) because clinicians find β HPVs in over half the biopsies. Moreover, we uncovered yet another paradox; the increasing CMM incidences significantly correlate with decreasing personal annual UV dose, a proxy for low vitamin D3 levels. We also discovered the incidence of CMM significantly increased with decreasing personal annual UV dose from 1960, when it was almost insignificant, to 2000. UV and other DNA-damaging agents can activate viruses, and UV-induced cytokines can hide HPV from immune surveillance, which may explain why CMM also occurs in anatomical locations where the sun does not shine. Thus, we propose the 2 major risk factors for getting CMM are intermittent UV exposures that result in low cutaneous levels of vitamin D3 and possibly viral infection

Facilitating return to work through early specialist health-based interventions (FRESH): protocol for a feasibility randomised controlled trial

Background Over one million people sustain traumatic brain injury each year in the UK and more than 10 % of these are moderate or severe injuries, resulting in cognitive and psychological problems that affect the ability to work. Returning to work is a primary rehabilitation goal but fewer than half of traumatic brain injury survivors achieve this. Work is a recognised health service outcome, yet UK service provision varies widely and there is little robust evidence to inform rehabilitation practice. A single-centre cohort comparison suggested better work outcomes may be achieved through early occupational therapy targeted at job retention. This study aims to determine whether this intervention can be delivered in three new trauma centres and to conduct a feasibility, randomised controlled trial to determine whether its effects and cost effectiveness can be measured to inform a definitive trial. Methods/design Mixed methods study, including feasibility randomised controlled trial, embedded qualitative studies and feasibility economic evaluation will recruit 102 people with traumatic brain injury and their nominated carers from three English UK National Health Service (NHS) trauma centres. Participants will be randomised to receive either usual NHS rehabilitation or usual rehabilitation plus early specialist traumatic brain injury vocational rehabilitation delivered by an occupational therapist. The primary objective is to assess the feasibility of conducting a definitive trial; secondary objectives include measurement of protocol integrity (inclusion/exclusion criteria, intervention adherence, reasons for non-adherence) recruitment rate, the proportion of eligible patients recruited, reasons for non-recruitment, spectrum of TBI severity, proportion of and reasons for loss to follow-up, completeness of data collection, gains in face-to-face Vs postal data collection and the most appropriate methods of measuring primary outcomes (return to work, retention) to determine the sample size for a larger trial. Discussion To our knowledge, this is the first feasibility randomised controlled trial of a vocational rehabilitation health intervention specific to traumatic brain injury. The results will inform the design of a definitive trial