Fixed points, stability, and harmless perturbations

Much has been written about systems in which each constant is a solution and each solution approaches a constant. It is a small step to conjecture that functions promoting such behavior constitute harmless perturbations of stable equations. That idea leads to a new way of avoiding delay terms in a functional-differential equation. In this paper we use fixed point theory to show that such a conjecture is valid for a set of classical equations

Public preferences for multiple dimensions of bird biodiversity at the coast: insights for the cultural ecosystem services framework

This work was funded by the NERC Research project Coastal Biodiversity and Ecosystem Services (CBESS) project Grant NE/J015644/1 with support from the Biodiversity and Ecosystem Service Sustainability (BESS) programme. BESS is a six-year programme (2011–2017) funded by the UK Natural Environment Research Council (NERC) and the Biotechnology and Biological Sciences Research Council (BBSRC) as part of the UK's Living with Environmental Change (LWEC) programme.Biodiversity is valuable to society, including through its contribution to cultural benefits: “the non-material benefits people obtain from biodiversity and ecosystem services through spiritual enrichment, cognitive development, reflection, recreation, and aesthetic experiences”. Biodiversity encompasses numerous measures, but the distinct values of these measures have been little studied. We conducted a discrete choice experiment to elicit respondents’ (n = 3,000) willingness to pay for increases in four measures of bird diversity in UK coastal ecosystems: number of bird species (species richness), number of individual birds (abundance), probability of seeing rare or unusual bird species, and probability of seeing large flocks of birds (wildlife spectacles). Respondents had a positive willingness to pay (through one-time voluntary donations) for increases in all four measures (mean £3 to £5 per household). However, using latent class analysis we found considerable heterogeneity of preferences, identifying four classes of respondents with strikingly different levels of marginal willingness to pay for the four measures. Income, age, environmental activity, visits to environmental settings, and gender were important determinants of class membership. While focusing on birds, our results demonstrate the importance of a multi-dimensional conceptualisation of biodiversity in broader ecosystem management, rather than focussing on a single aspect such as species richness or abundance. Our findings also highlight the implications of heterogeneous public preferences for biodiversity for conservationists, planners, shoreline managers and developers. These need to be considered in the development of new frameworks for ecosystem services, and when planning and funding conservation actions so that the cultural benefits will accrue across a range of social groups.PostprintPeer reviewe

Flip the Clinic: A Digital Health Approach to Youth Mental Health Service Delivery During the COVID-19 Pandemic and Beyond.

The demand for mental health services is projected to rapidly increase as a direct and indirect result of the COVID-19 pandemic. Given that young people are disproportionately disadvantaged by mental illness and will face further challenges related to the COVID-19 pandemic, it is crucial to deliver appropriate mental health care to young people as early as possible. Integrating digital health solutions into mental health service delivery pathways has the potential to greatly increase efficiencies, enabling the provision of "right care, first time." We propose an innovative digital health solution for demand management intended for use by primary youth mental health services, comprised of (1) a youth mental health model of care (ie, the Brain and Mind Centre Youth Model) and (2) a health information technology specifically designed to deliver this model of care (eg, the InnoWell Platform). We also propose an operational protocol of how this solution could be applied to primary youth mental health service delivery processes. By "flipping" the conventional service delivery models of majority in-clinic and minority web-delivered care to a model where web-delivered care is the default, this digital health solution offers a scalable way of delivering quality youth mental health care both in response to public health crises (such as the COVID-19 pandemic) and on an ongoing basis in the future

InterFace : A software package for face image warping, averaging, and principal components analysis

We describe InterFace, a software package for research in face recognition. The package supports image warping, reshaping, averaging of multiple face images, and morphing between faces. It also supports principal components analysis (PCA) of face images, along with tools for exploring the “face space” produced by PCA. The package uses a simple graphical user interface, allowing users to perform these sophisticated image manipulations without any need for programming knowledge. The program is available for download in the form of an app, which requires that users also have access to the (freely available) MATLAB Runtime environment

Bio-based smart materials for fish product packaging: a review

Conventional packaging offers protection, containment, communication, and convenience to packaged food. The most commonly used packaging materials are petrochemical-based plastics which generate massive wastes that persist for a long time in the environment after their use. Bio-based materials are the best option to replace this synthetic plastic. This review presents the importance of packaging fish products using polysaccharides, proteins, polyhydroxyalkanoates, polylactic acids, pullulan, and xanthan gums loaded with different nanofillers and bioactive molecules. Bio-based smart materials easily decompose into carbon dioxide, methane, water, and inorganic compounds. Biopolymers can be produced from natural biomass, bio-monomers, and microorganisms. These biopolymers demonstrate excellent physiochemical, thermal, and mechanical properties when mixed or alone as fish packaging materials. Integration of nanofillers and bioactive molecules improves mechanical, gas barrier, antioxidant and antimicrobial properties of bio-based materials. Bioactive molecules like anthocyanins, betalains, curcumin, and clove oil are sensitive to pH, temperature, light, and time. Bioactive molecules can be loaded into bio-based packaging materials to monitor the real-time freshness of fish products during storage. It is concluded that bio-based smart materials have the potential for fish packaging, do not harm the environment, and easily interact with nanofillers and bioactive molecules

Using item response theory to explore the psychometric properties of extended matching questions examination in undergraduate medical education

BACKGROUND: As assessment has been shown to direct learning, it is critical that the examinations developed to test clinical competence in medical undergraduates are valid and reliable. The use of extended matching questions (EMQ) has been advocated to overcome some of the criticisms of using multiple-choice questions to test factual and applied knowledge. METHODS: We analysed the results from the Extended Matching Questions Examination taken by 4th year undergraduate medical students in the academic year 2001 to 2002. Rasch analysis was used to examine whether the set of questions used in the examination mapped on to a unidimensional scale, the degree of difficulty of questions within and between the various medical and surgical specialties and the pattern of responses within individual questions to assess the impact of the distractor options. RESULTS: Analysis of a subset of items and of the full examination demonstrated internal construct validity and the absence of bias on the majority of questions. Three main patterns of response selection were identified. CONCLUSION: Modern psychometric methods based upon the work of Rasch provide a useful approach to the calibration and analysis of EMQ undergraduate medical assessments. The approach allows for a formal test of the unidimensionality of the questions and thus the validity of the summed score. Given the metric calibration which follows fit to the model, it also allows for the establishment of items banks to facilitate continuity and equity in exam standards

A mathematical model for the onset of avascular tumor growth in response to the loss of p53 function

We present a mathematical model for the formation of an avascular tumor based on the loss by gene mutation of the tumor suppressor function of p53. The wild type p53 protein regulates apoptosis, cell expression of growth factor and matrix metalloproteinase, which are regulatory functions that many mutant p53 proteins do not possess. The focus is on a description of cell movement as the transport of cell population density rather than as the movement of individual cells. In contrast to earlier works on solid tumor growth, a model is proposed for the initiation of tumor growth. The central idea, taken from the mathematical theory of dynamical systems, is to view the loss of p53 function in a few cells as a small instability in a rest state for an appropriate system of differential equations describing cell movement. This instability is shown (numerically) to lead to a second, spatially inhomogeneous, solution that can be thought of as a solid tumor whose growth is nutrient diffusion limited. In this formulation, one is led to a system of nine partial differential equations. We show computationally that there can be tumor states that coexist with benign states and that are highly unstable in the sense that a slight increase in tumor size results in the tumor occupying the sample region while a slight decrease in tumor size results in its ultimate disappearance

New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

Surgery versus epilation for the treatment of minor trichiasis in Ethiopia: a randomised controlled noninferiority trial.

Trachomatous trichiasis can cause corneal damage and visual impairment. WHO recommends surgery for all cases. However, in many regions surgical provision is inadequate and patients frequently decline. Self-epilation is common and was associated with comparable outcomes to surgery in nonrandomised studies for minor trichiasis (<six lashes touching eye). This trial investigated whether epilation is noninferior to surgery for managing minor trichiasis

Longer fixation duration while viewing face images

The spatio-temporal properties of saccadic eye movements can be influenced by the cognitive demand and the characteristics of the observed scene. Probably due to its crucial role in social communication, it is argued that face perception may involve different cognitive processes compared with non-face object or scene perception. In this study, we investigated whether and how face and natural scene images can influence the patterns of visuomotor activity. We recorded monkeys’ saccadic eye movements as they freely viewed monkey face and natural scene images. The face and natural scene images attracted similar number of fixations, but viewing of faces was accompanied by longer fixations compared with natural scenes. These longer fixations were dependent on the context of facial features. The duration of fixations directed at facial contours decreased when the face images were scrambled, and increased at the later stage of normal face viewing. The results suggest that face and natural scene images can generate different patterns of visuomotor activity. The extra fixation duration on faces may be correlated with the detailed analysis of facial features