Almost sure exponential stability of numerical solutions for stochastic delay differential equations

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least $k$ column vectors, where $k$ is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension $k$. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where $k$ is much smaller than the matrix dimension. We also give an extension of the method to the case where $k$ is larger than the matrix dimension. The quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours. Using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

The UK risk assessment scheme for all non-native species

1. A pest risk assessment scheme, adapted from the EPPO (European and Mediterranean Plant Protection Organisation) scheme, was developed to assess the risks posed to UK species, habitats and ecosystems by non-native taxa. 2. The scheme provides a structured framework for evaluating the potential for non-native organisms, whether intentional or unintentional introductions, to enter, establish, spread and cause significant impacts in all or part of the UK. Specialist modules permit the relative importance of entry pathways, the vulnerability of receptors and the consequences of policies to be assessed and appropriate risk management options to be selected. Spreadsheets for summarising the level of risk and uncertainty, invasive attributes and economic impact were created. In addition, new methods for quantifying economic impact and summarising risk and uncertainty were explored. 3. Although designed for the UK, the scheme can readily be applied elsewhere

Psychometric assessment of the short-form Child Perceptions Questionnaire: an international collaborative study.

OBJECTIVE: To examine the factor structure and other psychometric characteristics of the most commonly used child oral-health-related quality-of-life (OHRQoL) measure (the 16-item short-form CPQ11-14 ) in a large number of children (N = 5804) from different settings and who had a range of caries experience and associated impacts. METHODS: Secondary data analyses used subnational epidemiological samples of 11- to 14-year-olds in Australia (N = 372), New Zealand (three samples: 352, 202, 429), Brunei (423), Cambodia (244), Hong Kong (542), Malaysia (439), Thailand (220, 325), England (88, 374), Germany (1055), Mexico (335) and Brazil (404). Confirmatory factor analysis (CFA) was used to examine the factor structure of the CPQ11-14 across the combined sample and within four regions (Australia/NZ, Asia, UK/Europe and Latin America). Item impact and internal reliability analysis were also conducted. RESULTS: Caries experience varied, with mean DMFT scores ranging from 0.5 in the Malaysian sample to 3.4 in one New Zealand sample. Even more variation was noted in the proportion reporting only fair or poor oral health; this was highest in the Cambodian and Mexican samples and lowest in the German sample and one New Zealand sample. One in 10 reported that their oral health had a marked impact on their life overall. The CFA across all samples revealed two factors with eigenvalues greater than 1. The first involved all items in the oral symptoms and functional limitations subscales; the second involved all emotional well-being and social well-being items. The first was designated the 'symptoms/function' subscale, and the second was designated the 'well-being' subscale. Cronbach's alpha scores were 0.72 and 0.84, respectively. The symptoms/function subscale contained more of the items with greater impact, with the item 'Food stuck in between your teeth' having greatest impact; in the well-being subscale, the 'Felt shy or embarrassed' item had the greatest impact. Repeating the analyses by world region gave similar findings. CONCLUSION: The CPQ11-14 performed well cross-sectionally in the largest analysis of the scale in the literature to date, with robust and mostly consistent psychometric characteristics, albeit with two underlying factors (rather than the originally hypothesized four-factor structure). It appears to be a sound, robust measure which should be useful for research, practice and policy

Structural Determinants and Children's Oral Health: A Cross-National Study

Much research on children's oral health has focused on proximal determinants at the expense of distal (upstream) factors. Yet, such upstream factors-the so-called structural determinants of health-play a crucial role. Children's lives, and in turn their health, are shaped by politics, economic forces, and social and public policies. The aim of this study was to examine the relationship between children's clinical (number of decayed, missing, and filled teeth) and self-reported oral health (oral health-related quality of life) and 4 key structural determinants (governance, macroeconomic policy, public policy, and social policy) as outlined in the World Health Organization's Commission for Social Determinants of Health framework. Secondary data analyses were carried out using subnational epidemiological samples of 8- to 15-y-olds in 11 countries ( N = 6,648): Australia (372), New Zealand (three samples; 352, 202, 429), Brunei (423), Cambodia (423), Hong Kong (542), Malaysia (439), Thailand (261, 506), United Kingdom (88, 374), Germany (1498), Mexico (335), and Brazil (404). The results indicated that the type of political regime, amount of governance (e.g., rule of law, accountability), gross domestic product per capita, employment ratio, income inequality, type of welfare regime, human development index, government expenditure on health, and out-of-pocket (private) health expenditure by citizens were all associated with children's oral health. The structural determinants accounted for between 5% and 21% of the variance in children's oral health quality-of-life scores. These findings bring attention to the upstream or structural determinants as an understudied area but one that could reap huge rewards for public health dentistry research and the oral health inequalities policy agenda

Protein sequence and structure: Is one more fundamental than the other?

We argue that protein native state structures reside in a novel "phase" of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a sequence-independent free energy landscape with relatively few low energy minima with funnel-like character. The choice of a sequence that fits well into one of these predetermined structures facilitates rapid and cooperative folding. Our model calculations show that this novel phase facilitates the formation of an efficient route for sequence design starting from random peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy

SMIM1 absence is associated with reduced energy expenditure and excess weight

Background: Obesity rates have nearly tripled in the past 50 years, and by 2030 more than 1 billion individuals worldwide are projected to be obese. This creates a significant economic strain due to the associated non-communicable diseases. The root cause is an energy expenditure imbalance, owing to an interplay of lifestyle, environmental, and genetic factors. Obesity has a polygenic genetic architecture; however, single genetic variants with large effect size are etiological in a minority of cases. These variants allowed the discovery of novel genes and biology relevant to weight regulation and ultimately led to the development of novel specific treatments. Methods: We used a case-control approach to determine metabolic differences between individuals homozygous for a loss-of-function genetic variant in the small integral membrane protein 1 (SMIM1) and the general population, leveraging data from five cohorts. Metabolic characterization of SMIM1−/− individuals was performed using plasma biochemistry, calorimetric chamber, and DXA scan. Findings: We found that individuals homozygous for a loss-of-function genetic variant in SMIM1 gene, underlying the blood group Vel, display excess body weight, dyslipidemia, altered leptin to adiponectin ratio, increased liver enzymes, and lower thyroid hormone levels. This was accompanied by a reduction in resting energy expenditure. Conclusion: This research identified a novel genetic predisposition to being overweight or obese. It highlights the need to investigate the genetic causes of obesity to select the most appropriate treatment given the large cost disparity between them. Funding: This work was funded by the National Institute of Health Research, British Heart Foundation, and NHS Blood and Transplant.</p

Influence of storm surge on tidal range energy

The regular and predictable nature of the tide makes the generation of electricity with a tidal lagoon or barrage an attractive form of renewable energy, yet storm surges affect the total water-level. Here, we present the first assessment of the potential impact of storm surges on tidal-range power. Water-level data (2000–2012) at nine UK tide gauges, where tidal-range energy is suitable for development (e.g. Bristol Channel), was used to predict power. Storm surge affected annual resource estimates −5% to +3%, due to inter-annual variability, which is lower than other sources of uncertainty (e.g. lagoon design); therefore, annual resource estimation from astronomical tides alone appears sufficient. However, instantaneous power output was often significantly affected (Normalised Root Mean Squared Error: 3%–8%, Scatter Index: 15%–41%) and so a storm surge prediction system may be required for any future electricity generation scenario that includes large amounts of tidal-range generation. The storm surge influence to tidal-range power varied with the electricity generation strategy considered (flooding tide only, ebb-only or dual; both flood and ebb), but with some spatial and temporal variability. The flood-only strategy was most affected by storm surge, mostly likely because tide-surge interaction increases the chance of higher water-levels on the flooding tide

'Education, education, education' : legal, moral and clinical

This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students

Charged pion form factor between Q^2=0.60 and 2.45 GeV^2. II. Determination of, and results for, the pion form factor

The charged pion form factor, Fpi(Q^2), is an important quantity which can be used to advance our knowledge of hadronic structure. However, the extraction of Fpi from data requires a model of the 1H(e,e'pi+)n reaction, and thus is inherently model dependent. Therefore, a detailed description of the extraction of the charged pion form factor from electroproduction data obtained recently at Jefferson Lab is presented, with particular focus given to the dominant uncertainties in this procedure. Results for Fpi are presented for Q^2=0.60-2.45 GeV^2. Above Q^2=1.5 GeV^2, the Fpi values are systematically below the monopole parameterization that describes the low Q^2 data used to determine the pion charge radius. The pion form factor can be calculated in a wide variety of theoretical approaches, and the experimental results are compared to a number of calculations. This comparison is helpful in understanding the role of soft versus hard contributions to hadronic structure in the intermediate Q^2 regime.Comment: 18 pages, 11 figure