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This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
The Trypillia megasites of the Ukrainian forest steppe formed the largest fourth-millennium bc sites in Eurasia and possibly the world. Discovered in the 1960s, the megasites have so far resisted all attempts at an understanding of their social structure and dynamics. Multi-disciplinary investigations of the Nebelivka megasite by an Anglo-Ukrainian research project brought a focus on three research questions: (1) what was the essence of megasite lifeways? (2) can we call the megasites early cities? and (3) what were their origins? The first question is approached through a summary of Project findings on Nebelivka and the subsequent modelling of three different scenarios for what transpired to be a different kind of site from our expectations. The second question uses a relational approach to urbanism to show that megasites were so different from other coeval settlements that they could justifiably be termed ‘cities'. The third question turns to the origins of sites that were indeed larger and earlier than the supposed first cities of Mesopotamia and whose development indicates that there were at least two pathways to early urbanism in Eurasia.
A high prevalence of asthma has been documented among the inhabitants of Tristan da Cunha, an isolated island in the South Atlantic. The population derives from just 28 founders. We performed lung function testing, including methacholine inhalation challenge, allergen skin prick testing, and collected DNA from essentially all of the current island population (269 individuals), and genotyped a panel of 43 single-nucleotide polymorphisms (SNPs) reported as associated with asthma and atopy. We carried out a mixed-model association analysis using the known pedigree. There were 96 individuals diagnosed as asthmatic (36%), and heritability estimates were similar to those from nonisolated population samples (multifactorial threshold model, h2 = 48%). The first component from a genetic principal components analysis using the entire SNP panel was nonlinearly associated with asthma, with the maximum risk to those intermediate to reference (Human Genome Diversity Project) European and African samples means. The single most strongly associated SNP was rs2786098 (p = 5.5 × 10−5), known to regulate the gene DENND1B. This explained approximately one-third of the trait heritability, with an allelic odds ratio for the A allele of 2.6. Among A/A carriers, 10 out of 12 individuals were asthmatic. The rs2786098*A variant was initially reported to decrease the risk of childhood (atopic) asthma in European but slightly increase the risk in African-descended populations, and does significantly alter Th2 cell function. Despite an absence of overall association with this variant in recent asthma genome wide association studies meta-analyses, an effect may exist on the particular genetic background of the Tristan da Cunha population.
Patients with essential tremor exhibit heterogeneous cognitive functioning. Although the majority of patients fall under the broad classification of cognitively “normal,” essential tremor is associated with increased risk for mild cognitive impairment and dementia. It is possible that patterns of cognitive performance within the wide range of normal functioning have predictive utility for mild cognitive impairment or dementia. These cross-sectional analyses sought to determine whether cognitive patterns, or “clusters,” could be identified among individuals with essential tremor diagnosed as cognitively normal. We also determined whether such clusters, if identified, were associated with demographic or clinical characteristics of patients.
Elderly subjects with essential tremor (age >55 years) underwent comprehensive neuropsychological testing. Domain means (memory, executive function, attention, visuospatial abilities, and language) from 148 individuals diagnosed as cognitively normal were partitioned using k-means cluster analysis. Individuals in each cluster were compared according to cognitive functioning (domain means and test scores), demographic factors, and clinical variables.
There were three clusters. Cluster 1 (n = 64) was characterized by comparatively low memory scores (p < .001), Cluster 2 (n = 39) had relatively low attention and visuospatial scores (p < .001), and Cluster 3 (n = 45) exhibited consistently high performance across all domains. Cluster 1 had lower Montreal Cognitive Assessment scores and reported more prescription medication use and lower balance confidence.
Three patterns of cognitive functioning within the normal range were evident and tracked with certain clinical features. Future work will examine the extent to which such patterns predict conversion to mild cognitive impairment and/or dementia.
In this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.
Non-tuberculous mycobacterium encephalitis is rare. Since 2013, a global outbreak of Mycobacterium chimaera infection has been attributed to point-source contamination of heater cooler units used in cardiac surgery. Disseminated M. chimaera infection has presented many unique challenges, including non-specific clinical presentations with delays in diagnosis, and a high mortality rate among predominantly immunocompetent adults. Here, we describe three patients with fatal disseminated Mycobacterium chimaera infection showing initially non-specific, progressively worsening neurocognitive decline, including confusion, delirium, depression and apathy. Autopsy revealed widespread granulomatous encephalitis of the cerebrum, brain stem and spinal cord, along with granulomatous chorioretinitis. Cerebral involvement and differentiation between mycobacterial granulomas and microangiopathic changes can be assessed best on MRI with contrast enhancement. The prognosis of M. chimaera encephalitis appears to be very poor, but might be improved by increased awareness of this new syndrome and timely antimicrobial treatment.
This presentation will enable the learner to:
1.Describe the clinical, radiological and neuropathological findings of Mycobacterium chimaera encephalitis
2.Be aware of this rare form of encephalitis, and explain its diagnosis, prognosis and management
Bog bodies are among the best-known archaeological finds worldwide. Much of the work on these often extremely well-preserved human remains has focused on forensics, whereas the environmental setting of the finds has been largely overlooked. This applies to both the ‘physical’ and ‘cultural’ landscape and constitutes a significant problem since the vast spatial and temporal scales over which the practice appeared demonstrate that contextual assessments are of the utmost importance for our explanatory frameworks. In this article we develop best practice guidelines for the contextual analysis of bog bodies, after assessing the current state of research and presenting the results of three recent case studies including the well-known finds of Lindow Man in the United Kingdom, Bjældskovdal (Tollund Man and Elling Woman) in Denmark, and Yde Girl in the Netherlands. Three spatial and chronological scales are distinguished and linked to specific research questions and methods. This provides a basis for further discussion and a starting point for developing approaches to bog body finds and future discoveries, while facilitating and optimizing the re-analysis of previous studies, making it possible to compare deposition sites across time and space.
The rocky shores of New Zealand (NZ) and Australia provide many interesting comparisons in their intertidal species and structuring processes. Both countries are in the biogeographic realm of temperate Australasia and share many common species and closely related taxa. Here we review similarities and contrasts in communities and structuring processes, especially involving grazing invertebrates and macroalgae. We consider the similarity of the structure of intertidal shores of NZ and south-eastern Australia, a suite of important trophic interactions within and between regions, the utility of local-scale experiments in understanding large-scale processes and how we might better plan for and manage our coasts. The major comparisons are between warm-temperate areas of northern NZ and New South Wales, and the cooler areas of southern NZ and south-eastern Australia. In the quest for ‘ecosystem’-level understanding, which perforce involves large-scale events, there is an increasing tendency to minimise or ignore the hard-won insights gained from well-structured experiments across multiple sites. Because all large-scale effects must be manifested at local sites, it is incumbent on us to determine what scales up or down, and the caveats that make comparisons across biogeographic regions challenging. Here, we discuss these issues using austral shores as models.
To evaluate the association between three behavioural economics ‘nudges’ and store sales of promoted healthier foods.
Multiple interrupted time series.
Two predominantly rural counties in central North Carolina, USA.
Aggregated store transaction data from two grocery stores (one intervention, one control) and two convenience stores (one intervention, one control) were analysed using ANOVA to examine the association between three ‘nudges’ and store sales of promoted items. The nudges included: a ‘cognitive fatigue’ experiment, in which floor arrows guided customers to the produce sections; a ‘scarcity’ experiment, in which one sign in one area of the produce section portrayed a ‘limited amount’ message; and a ‘product placement’ experiment, where granola bars were moved into the candy bar aisle.
In convenience stores, there were no significant differences between sales of the promoted items during the intervention period for any of the nudges when implemented individually. However, compared with baseline sales, implementation of all three nudges simultaneously was associated with an increase in sales during the intervention period based on proportional computations (P = 0·001), whereas no significant changes in sales were observed in the control convenience store. Among the grocery stores, there were no significant differences in sales during the intervention period for any of the nudges or the combined intervention compared with baseline sales.
Implementing three nudges concurrently in a convenience store setting may increase sales of promoted items. However, before stores consider implementing these nudges to increase sales of nutritious foods, additional research is warranted.
Public health strategies have focused largely on physical health. However, there is increasing recognition that raising mental health awareness and tackling stigma is crucial to reduce disease burden. National campaigns have had some success but tackling issues locally is particularly important.
To assess the public's awareness and perception of the monthly BBC Cornwall mental health phone-in programmes that have run for 8.5 years in Cornwall, UK (population 530 000).
A consultation, review and feedback process involving a multiagency forum of mental and public health professionals, people with lived experience and local National Health Service trust's media team was used to develop a brief questionnaire. This was offered to all attendees at two local pharmacies covering populations of 27 000 over a 2-week period.
In total, 14% (95% CI 11.9–16.5) were aware of the radio show, 11% (95% CI 9.0–13.1) have listened and the majority (76%) of those who listened did so more than once. The estimated reach is 70 000 people in the local population, of whom approximately 60 000 listen regularly. The show is highly valued among respondents with modal and median scores of 4 out of 5.
Local radio is a successful, cost-effective and impactful way to reach a significant proportion of the population and likely to raise awareness, reduce stigma and be well received. The format has been adopted in other regions thus demonstrating easy transferability. It could form an essential part of a public health strategy to improve a population's mental well-being.
Declaration of interest
W.H. received support from the National Institute for Health Research (NIHR) Collaboration for Leadership in Applied Health Research and Care (CLAHRC) for the South West Peninsula UK. The views expressed in this publication are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. L.R. and D.S. were involved in delivering the programmes but had no role in their evaluation.
The jurisprudence of Robert P. George is twofold, in that he is one of the most important public law, and especially constitutional law, scholars of the late twentieth and so far in the twenty-first centuries, and, at the same time, he is America’s leading legal exponent of natural law. He is a devout Roman Catholic. But the relationship between his religious convictions and his jurisprudence will strike some readers as paradoxical. George writes: “I want to show that Christians and other believers are right to defend their positions on key moral issues as rationally superior to the alternatives proposed by secular liberals and those within the religious denominations who have abandoned traditional moral principles in favor of secularist morality.” “My criticism of secular liberal views is not that they are contrary to faith; it is that they fail the test of reason.” This chapter explains how the “paradox” is merely apparent.
Borderline personality disorder (BPD) is a severe and complex disorder characterized by instability across many life domains, including interpersonal relations, behavior, and emotions. A core feature and contributor to BPD, emotion dysegulation (ED), consists of deficits in the ability to regulate emotions in a manner that allows the individual to pursue important goals or behave effectively in various contexts. Biosocial developmental models of BPD have emphasized a transaction of environmental conditions (e.g., invalidating environments and adverse childhood experiences) with key genetically linked vulnerabilities (e.g., impulsivity and emotional vulnerability) in the development of ED and BPD. Emerging evidence has begun to highlight the complex, heterotypic pathways to the development of BPD, with key heritable vulnerability factors possibly interacting with aspects of the rearing environment to produce worsening ED and an adolescent trajectory consisting of self-damaging behaviors and eventual BPD. Adults with BPD have shown evidence of a variety of cognitive, physiological, and behavioral characteristics of ED. As the precursors to the development of ED and BPD have become clearer, prevention and treatment efforts hold great promise for reducing the long-term suffering, functional impairment, and considerable societal costs associated with BPD.
Background: Postoperative C5 palsy (C5P) is a common complication after cervical decompression, potentially related to nerve root tethering. To our knowledge, this is the first study to investigate this hypothesis by comparing C5/C6 root translation and tension before and after root untethering by cutting cervical intraforaminal ligaments (IFL). Methods: Six cadaveric dissections were performed. Nerve roots were exposed and translation and tension measured after the roots and spinal-cord were dorsally displaced 5mm before and after IFL cutting. These were also measured during shoulder depression to simulate intraoperative positioning. Clinical feasibility of IFL release was examined by comparing standard and extended foraminotomies to compare resultant root translation. Results: IFL-cutting increased translation at both C5/C6 roots (P=0.001). There was no difference between root levels (P=0.33). IFL-cutting increased translation upon shoulder depression at both C5/C6 roots (P=0.003) with a difference also being found between root levels (P=0.02). An extended cervical foraminotomy was technically feasible which enabled complete IFL release and root untethering, whereas a standard foraminotomy did not. Conclusions: IFL-cutting increases root translation, suggesting they are either protective (preventing peripheral nerve strain from being transmitted to the spinal-cord) or harmful (by tethering intraforaminal nerve roots and potentially contributing to postoperative C5P) depending on the clinical context.