Bounding the norm of a log-concave vector via thin-shell estimates

Chaining techniques show that if X is an isotropic log-concave random vector in R^n and Gamma is a standard Gaussian vector then E |X| < C n^{1/4} E |Gamma| for any norm |*|, where C is a universal constant. Using a completely different argument we establish a similar inequality relying on the thin-shell constant sigma_n = sup ((var|X|^){1/2} ; X isotropic and log-concave on R^n). In particular, we show that if the thin-shell conjecture sigma_n = O(1) holds, then n^{1/4} can be replaced by log (n) in the inequality. As a consequence, we obtain certain bounds for the mean-width, the dual mean-width and the isotropic constant of an isotropic convex body. In particular, we give an alternative proof of the fact that a positive answer to the thin-shell conjecture implies a positive answer to the slicing problem, up to a logarithmic factor.Comment: preliminary version, 13 page

Selection and validation of a classification system for a child-centred caries-specific utility measure

Background: Caries Impacts and Experiences Questionnaire for Children (CARIES-QC) is a child-centred caries-specific quality of life measure. This study aimed to select, and validate with children, a classification system for a paediatric condition-specific preference-based measure, based on CARIES-QC. Methods: First, a provisional classification system for a preference-based measure based on CARIES-QC was developed using Rasch analysis, psychometric testing, involvement of children and parents, and the developer of CARIES-QC. Second, qualitative, semi-structured ‘think aloud’ validation interviews were undertaken with a purposive sample of children with dental caries. The interviewer aimed to identify whether items were considered important and easily understood, whether any were overlapping and if any excluded items should be reintroduced. Interview recordings were transcribed verbatim and thematic analysis conducted. Results: Rasch analysis identified poor item spread for the items ‘cross’ and ‘school’. Items relating to eating were correlated and the better performing items were considered for selection. Children expressed some confusion regarding the items ‘school’ and ‘food stuck’. Parent representatives thought that impacts surrounding toothbrushing (‘brushing’) were encompassed by the item ‘hurt’. Five items were selected from CARIES-QC for inclusion in the provisional classification system; ‘hurt’, ‘annoy’, ‘carefully’, ‘kept awake’ and ‘cried’. Validation interviews were conducted with 20 children aged 5-16 years old. Participants thought the questionnaire was straightforward and covered a range of impacts. Children thought an item about certain foods being ‘hard to eat’ was more relevant than one about having to eat more carefully because of their teeth and so the ‘carefully’ item was replaced with ‘hard to eat’. Conclusion: Following child-centred modification, the preliminary five-item classification system is considered valid and suitable for use in a valuation survey. The innovative child-centred methods used to both identify and validate the classification system can be applied in the development of other preference-based measures

Economic evaluations in paediatric dentistry clinical trials

Economic evaluations play an important role in identifying the cost‐effectiveness of alternative healthcare programmes, informing decisions surrounding funding and the allocation of resources. This paper outlines the basic principles of economic evaluation and how it can be conducted alongside a clinical trial. Furthermore, it considers the ways in which evidence from these studies can be used, and the challenges researchers are faced with when conducting economic evaluations in the field of children’s oral health

The relationship between caries-specific quality of life and generic wellbeing in a Dutch pediatric population

Dental caries has significant negative impacts on the lives of children and young people. Whilst the impacts on children’s oral health-related quality of life (OHRQoL) have been increasingly investigated, the effect on children’s overall wellbeing remains largely unknown. Data were obtained from a survey conducted across four cities in the Netherlands. Children and their parents completed a series of questionnaires, which included Dutch versions of a caries-specific pediatric measure of OHRQoL (CARIES-QC-NL) and a generic pediatric health utility measure (CHU9D-NL). The participating children underwent dental examinations to determine their caries status. A total of 486 11-year-old children participated in the study, of which 184 had caries experience (38%). The mean number of decayed, missing and filled teeth (DMFT) was 0.71. The CARIES-QC-NL was found to have statistically significant correlations with the DMFT and CHU9D-NL. There were no statistically significant correlations between the CHU9D and the clinical variables. The CARIES-QC-NL had acceptable internal consistency and construct validity in this population despite the low prevalence of active caries. A relationship was demonstrated between OHRQoL and generic wellbeing in this population. Despite this, the CHU9D did not show any correlation with the clinical data, which may limit its application in studies of the impact of dental caries

Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation

It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using supersymmetric, or Darboux, transformations. The general solution of the transformed equation is expressed in terms of the solution of the original one. Both iterations of these transformations and irreducible transformations of second order in derivatives are considered to obtain the chain of mutually related Ermakov-Milne-Pinney equations. The behaviour of the Lewis invariant and the quantum number function for bound states is investigated. This construction is illustrated by the simple example of an infinite square well.Comment: 8 page

Selection and validation of a classification system for a child-centred preference-based measure of oral health-related quality of life specific to dental caries

Background Caries Impacts and Experiences Questionnaire for Children (CARIES-QC) is a child-centred caries-specific quality of life measure. This study aimed to select, and validate with children, a classification system for a paediatric condition-specific preference-based measure, based on CARIES-QC. Methods First, a provisional classification system for a preference-based measure based on CARIES-QC was identified using Rasch analysis, psychometric testing, involvement of children and parents, and the developer of CARIES-QC. Second, qualitative, semi-structured ‘think aloud’ validation interviews were undertaken with a purposive sample of children with dental caries. The interviewer aimed to identify whether items were considered important and easily understood, whether any were overlapping and if any excluded items should be reintroduced. Interview recordings were transcribed verbatim and thematic analysis conducted. Results Rasch analysis identified poor item spread for the items ‘cross’ and ‘school’. Items relating to eating were correlated and the better performing items were considered for selection. Children expressed some confusion regarding the items ‘school’ and ‘food stuck’. Parent representatives thought that impacts surrounding toothbrushing (‘brushing’) were encompassed by the item ‘hurt’. Five items were selected from CARIES-QC for inclusion in the provisional classification system; ‘hurt’, ‘annoy’, ‘carefully’, ‘kept awake’ and ‘cried’. Validation interviews were conducted with 20 children aged 5–16 years old. Participants thought the questionnaire was straightforward and covered a range of impacts. Children thought an item about certain foods being ‘hard to eat’ was more relevant than one about having to eat more carefully because of their teeth and so the ‘carefully’ item was replaced with ‘hard to eat’. Conclusion Following child-centred modification, the preliminary five-item classification system is considered valid and suitable for use in a valuation survey. The innovative child-centred methods used to both identify and validate the classification system can be applied in the development of other preference-based measures

Adolescent valuation of CARIES-QC-U : a child-centred preference-based measure of dental caries

Objectives This study develops an adolescent value set for a child-centred dental caries-specific measure of oral health-related quality of life (OHRQoL) based upon CARIES-QC (Caries Impacts and Experiences Questionnaire for Children). This study develops a new approach to valuing child health by eliciting adolescent preferences and anchoring these onto the 1–0 full health-dead QALY (quality adjusted life year) scale using ordinal adult preferences. Methods Two online surveys were created to elicit preferences for the CARIES-QC classification system. The first comprised best–worst scaling (BWS) tasks for completion by adolescents aged 11–16 years. The second comprised discrete choice experiment tasks with a duration attribute (DCETTO) for completion by adults aged over 18 years. Preferences were modelled using the conditional logit model. Mapping regressions anchored the adolescent BWS data onto the QALY scale using adult DCETTO values, since the BWS survey data alone cannot generate anchored values. Results 723 adolescents completed the BWS survey and 626 adults completed the DCETTO survey. The samples were representative of UK adolescent and adult populations. Fully consistent and robust models were produced for both BWS and DCETTO data. BWS preferences were mapped onto DCETTO values, resulting utility estimates for each health state defined by the classification system. Conclusion This is the first measure with predetermined scoring based on preferences to be developed specifically for use in child oral health research, and uses a novel technique to generate a value set using adolescent preferences. The estimates can be used to generate QALYs in economic evaluations of interventions to improve children’s oral health

Theoretical study of incoherent phi photoproduction on a deuteron target

We study the photoproduction of phi mesons in deuteron, paying attention to the modification of the cross section from bound protons to the free ones with the aim of comparing with recent results at LEPS. For this purpose we take into account Fermi motion in single scattering and rescattering of the phi to account for phi absorption on a second nucleon as well as the rescattering of the proton. We find that the contribution of the double scattering is much smaller than the typical cross section of gamma p to phi p in free space, which implies a very small screening of the phi production in deuteron. The contribution from the proton rescattering, on the other hand, is found to be not negligible compared to the cross section of gamma p to phi p in free space, and leads to a moderate reduction of the phi photoproduction cross section on a deuteron at forward angles if LEPS set up is taken into account. The Fermi motion allows contribution of the single scattering in regions forbidden by phase space in the free case. In particular, we find that for momentum transferred squared close to the maximum value, the Fermi motion changes drastically the shape of d sigma / dt, to the point that the ratio of this cross section to the free one becomes very sensitive to the precise value of t chosen, or the size of the bin used in an experimental analysis. Hence, this particular region of t does not seem the most indicated to find effects of a possible phi absorption in the deuteron. This reaction is studied theoretically as a function of t and the effect of the experimental angular cuts at LEPS is also discussed, providing guidelines for future experimental analyses of the reaction.Comment: 17 pages, 16 figure

Gene expression analysis of rocket salad under pre-harvest and postharvest stresses : a transcriptomic resource for Diplotaxis tenuifolia

Diplotaxis tenuifolia L. is of important economic value in the fresh-cut industry for its nutraceutical and sensorial properties. However, information on the molecular mechanisms conferring tolerance of harvested leaves to pre- and postharvest stresses during processing and shelf-life have never been investigated. Here, we provide the first transcriptomic resource of rocket by de novo RNA sequencing assembly, functional annotation and stress-induced expression analysis of 33874 transcripts. Transcriptomic changes in leaves subjected to commercially-relevant pre-harvest (salinity, heat and nitrogen starvation) and postharvest stresses (cold, dehydration, dark, wounding) known to affect quality and shelf-life were analysed 24h after stress treatment, a timing relevant to subsequent processing of salad leaves. Transcription factors and genes involved in plant growth regulator signaling, autophagy, senescence and glucosinolate metabolism were the most affected by the stresses. Hundreds of genes with unknown function but uniquely expressed under stress were identified, providing candidates to investigate stress responses in rocket. Dehydration and wounding had the greatest effect on the transcriptome and different stresses elicited changes in the expression of genes related to overlapping groups of hormones. These data will allow development of approaches targeted at improving stress tolerance, quality and shelf-life of rocket with direct applications in the fresh-cut industries