Spaces of finite element differential forms

We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds., Springer 2013. v2: a few minor typos corrected. v3: a few more typo correction

Net Gain: Seeking better outcomes for local people when mitigating biodiversity loss from development

Economic development projects are increasingly applying the mitigation hierarchy to achieve No Net Loss, or even a Net Gain, of biodiversity. Because people value biodiversity and ecosystem services, this can affect the wellbeing of local people, however these types of social impacts from development receive limited consideration. We present ethical, practical and regulatory reasons why development projects applying the mitigation hierarchy should consider related social impacts. We highlight risks to local wellbeing where projects restrict access to biodiversity and ecosystem services in biodiversity offsets. We then present a framework laying out challenges and associated opportunities for delivering better biodiversity and local wellbeing outcomes. Greater coordination between social and biodiversity experts, and early and effective integration of local people in the process, will ensure that efforts to reduce the negative impacts of development on biodiversity can contribute to, rather than detract from, local people’s wellbeing

Development and psychometric validation of the gum health experience questionnaire

Aim To develop and validate a new health-related quality of life measure to capture a wide range of gum-related impacts. Materials and Methods The measure was developed using a multi-stage approach and a theoretical model. Development involved semi-structured interviews, pilot testing, cross-sectional analysis among a general population (n = 152) to assess psychometric properties and test–retest reliability among a subsample (n = 27). Results Psychometric analysis supports the validity and reliability of the measure's impact scale. The measure has excellent internal reliability (nearly all item-total correlations above .4; Cronbach's alpha between .84 and .91 for subscales), with test–retest reliability also performing well (Intra-class correlation coefficient [ICC] of .91–.97 for subscales). Good content validity (indicated by large standard deviations for item and total scores) and construct validity (correlations of .54–.73 with global gum health rating for subscales, all p < .05) were also observed. Qualitative and quantitative data indicate that people with gum health-related symptoms experience different degrees of discomfort and impacts caused by their condition. Conclusions The gum health experience questionnaire holds substantial promise as a measure of gum-related quality of life in people across the gum health–disease continuum. Further face validity, refining and reducing the number of items and longitudinal studies to test evaluative properties are required before the measure can be used with confidence

The everyday impact of dentine sensitivity: personal and functional aspects

Research into oral health status and the impact of oral conditions on everyday life has been developed over the last 30 years. To date it is not clear the degr ee to which these measures can be applied to the pr oblems and impacts associated with dentine sensitivity. Th ere has been very little research on the everyday i mpact of dentine sensitivity. The aim of this study was t o explore the everyday experiences of dentine sensi tivity; in particular we were interested in the personal and f unctional aspects of living with the condition. Par ticipants were purposively recruited from a general populatio n to secure a range of experiences and views about the everyday impact of dentine sensitivity. Participant s were adults (≥18) currently experiencing dentine sensitiv - ity and were initially recruited using the research team’s contacts and snowball sampling. Data were a nalysed through a framework induced from the data and infor med by the literature on chronic illness, coping, i llness beliefs along with the general literature on the bi opsychosocial impact of oral health. Data analysis focussed on detailing the range of impacts associated with t he condition. Twenty three interviews were conducte d with 15 females and 8 males. The principal impacts on ev eryday life were described as pain, impacts on func tional status and everyday activities such as eating, drin king, talking, tooth brushing and social interactio n in gen - eral. Impacts appeared to be related to a range of individual and environmental inluences. The data in dicate the depth and complexity of the pain experiences as sociated with dentine sensitivity. The length of a partici - pant’s illness career appeared to be related to the ir degree of control over the condition. These indi ngs are compatible with the psychological literature on pai n and conirm that there are signiicant impacts asso ciated with dentine sensitivity in everyday life. Further research into the everyday nature of dentine sensit ive pain would be beneicial

Discrete peakons

We demonstrate for the first time the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form $\exp(-|n|)$, i.e., a discrete peakon. These discrete analogs of the well-known, continuum peakons of the Camassa-Holm equation [Phys. Rev. Lett. {\bf 71}, 1661 (1993)] are found in a model different from their continuum siblings. Namely, we observe discrete peakons in Klein-Gordon-type and nonlinear Schr\"odinger-type chains with long-range interactions. The interesting linear stability differences between these two chains are examined numerically and illustrated analytically. Additionally, inter-site centered peakons are also obtained in explicit form and their stability is studied. We also prove the global well-posedness for the discrete Klein-Gordon equation, show the instability of the peakon solution, and the possibility of a formation of a breathing peakon.Comment: Physica D, in pres

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

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

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys. Rev.