Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma_n Z_i$ and the $Y$'s and $Z$'s are independent. Assume that the $Y$'s are unobservable and that they have the density $f$ and also that the $Z$'s have a known density $k.$ Furthermore, let $\sigma_n$ depend on $n$ and let $\sigma_n\to 0$ as $n\to\infty.$ We consider the deconvolution problem, i.e. the problem of estimation of the density $f$ based on the sample $X_1,...,X_n.$ A popular estimator of $f$ in this setting is the deconvolution kernel density estimator. We derive its asymptotic normality under two different assumptions on the relation between the sequence $\sigma_n$ and the sequence of bandwidths $h_n.$ We also consider several simulation examples which illustrate different types of asymptotics corresponding to the derived theoretical results and which show that there exist situations where models with $\sigma_n\to 0$ have to be preferred to the models with fixed $\sigma.$Comment: 22 pages, 8 figure

Can corals form aerosol particles through volatile sulphur compound emissions?

Acropora dominated coral reefs are a substantial source of atmospheric dimethylsulphide (DMSa), one of the most abundant reduced sulphur gases present in the marine boundary layer. DMS is believed to act as a climate regulator of solar radiation and sea surface temperatures through the formation of non-sea-salt sulphate aerosols and cloud condensation nuclei (CCN), although this regulation has not yet been demonstrated. A bubbling chamber experiment was conducted on coral reef seawater containing a branch of Acropora pulchra, to investigate whether the coral-generated DMSa could be oxidised to non-seasalt sulphate aerosols under treatment with UV light and O3. Results indicated that A. pulchra produced significant amounts of dimethylsulphoniopropionate (DMSP) and dissolved DMS although emissions of DMSa in the chamber headspace were reduced by the presence of the coral, probably as a result of antioxidant activity in the coral tissue. Significant amounts of carbon disulphide (CS2) and ethanethiol (ESH), other sulphur gases that could be involved in CCN formation, were also indicated in the bubbling chamber, most likely from coral production. A decrease in DMSa and CS2 in the presence of UV light and O3 followed by an occurrence of freshly nucleated nanoparticles (<10nm) suggested that these two sulphur compounds were oxidised and potentially participated in aerosol particle formation and thus could be involved in CCN formation and possibly climate regulation. The study provided insights into the production of sulphur compounds by Acropora dominated coral reefs with potential impact on local climate

Regional Differences in Presence of Shiga toxin-producing Escherichia coli Virulence-Associated Genes in the Environment in the North West and East Anglian regions of England

Shiga toxin-producing Escherichia coli is carried in the intestine of ruminant animals, and outbreaks have occurred after contact with ruminant animals or their environment. The presence of STEC virulence genes in the environment was investigated along recreational walking paths in the North West and East Anglia regions of England. In all, 720 boot sock samples from walkers’ shoes were collected between April 2013 and July 2014. Multiplex PCR was used to detect E. coli based on the amplification of the uidA gene and investigate STEC-associated virulence genes eaeA, stx1 and stx2. The eaeA virulence gene was detected in 45·5% of the samples, where stx1 and/or stx2 was detected in 12·4% of samples. There was a difference between the two regions sampled, with the North West exhibiting a higher proportion of positive boot socks for stx compared to East Anglia. In univariate analysis, ground conditions, river flow and temperature were associated with positive boot socks. The detection of stx genes in the soil samples suggests that STEC is present in the English countryside and individuals may be at risk for infection after outdoor activities even if there is no direct contact with animals. Significance and Impact of the Study: Several outbreaks within the UK have highlighted the danger of contracting Shiga toxin-producing Escherichia coli from contact with areas recently vacated by livestock. This is more likely to occur for STEC infections compared to other zoonotic bacteria given the low infectious dose required. While studies have determined the prevalence of STEC within farms and petting zoos, determining the risk to individuals enjoying recreational outdoor activities that occur near where livestock may be present is less researched. This study describes the prevalence with which stx genes, indicative of STEC bacteria, were found in the environment in the English countryside

IDEA intervention to prevent depressive symptoms and promote well-being in early-stage dementia: protocol for a randomised controlled feasibility study

OBJECTIVE: Depressive symptoms are common among people with dementia, impacting quality of life and cognitive and functional decline. Currently, little is known about the acceptability and feasibility of psychological interventions for people with mild dementia, with recent reviews identifying the need for further evidence. Developing and evaluating psychological interventions to prevent and treat these symptoms is, therefore, an important clinical and research priority. This protocol describes a study testing the acceptability and feasibility of a manual-based behavioural activation (BA) intervention for preventing and treating depressive symptoms in people with mild dementia. The aim of this study is to explore the feasibility of conducting a pragmatic multicentre randomised controlled trial of clinical effectiveness of an eight-session intervention. The Intervention to prevent Depressive symptoms and promote well-being in EArly-stage dementia (IDEA) programme supports people with dementia and their family carers in identifying and scheduling enjoyable and meaningful activities. METHODS AND ANALYSIS: Sixty people who have received a diagnosis of dementia of any type in the last 6 months will be recruited via memory clinics. Further criteria are a Mini-Mental State Examination score of ≥20, and a family carer who can assist with the intervention. Consenting participants will be randomised in a ratio of 2:1 to BA or to treatment as usual. Analyses will estimate parameters such as rates of recruitment, retention and number of sessions completed. Questionnaires measuring depressive symptoms and quality of life for both the person with dementia and their carer will be completed at baseline, 3 and 6 months. Qualitative interviews will explore acceptability of the intervention, study procedures and experiences of the sessions. ETHICS AND DISSEMINATION: This study received a favourable ethical opinion from the London Camberwell St Giles Research Ethics Committee (16/LO/0540). We will disseminate findings at key conferences, the Alzheimer’s Society and University College London websites and local stakeholder events. TRIAL REGISTRATION NUMBER: ISRCTN75503960; Pre-results

Vacuum Stability of the wrong sign (−ϕ6)(-\phi^{6}) Scalar Field Theory

We apply the effective potential method to study the vacuum stability of the bounded from above $(-\phi^{6})$ (unstable) quantum field potential. The stability ($\partial E/\partial b=0)$ and the mass renormalization ($\partial^{2} E/\partial b^{2}=M^{2})$ conditions force the effective potential of this theory to be bounded from below (stable). Since bounded from below potentials are always associated with localized wave functions, the algorithm we use replaces the boundary condition applied to the wave functions in the complex contour method by two stability conditions on the effective potential obtained. To test the validity of our calculations, we show that our variational predictions can reproduce exactly the results in the literature for the $\mathcal{PT}$-symmetric $\phi^{4}$ theory. We then extend the applications of the algorithm to the unstudied stability problem of the bounded from above $(-\phi^{6})$ scalar field theory where classical analysis prohibits the existence of a stable spectrum. Concerning this, we calculated the effective potential up to first order in the couplings in $d$ space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but $\mathcal{PT}$-symmetric effective theory characterized by a pure imaginary vacuum condensate is stable (bounded from below) which is against the classical predictions of the instability of the theory. We assert that the work presented here represents the first calculations that advocates the stability of the $(-\phi^{6})$ scalar potential.Comment: 21pages, 12 figures. In this version, we updated the text and added some figure

Network analysis of competitive state anxiety

Copyright © 2021 Mullen and Jones. Competitive state anxiety is an integral feature of sports performance but despite its pervasiveness, there is still much debate concerning the measurement of the construct. Adopting a network approach that conceptualizes symptoms of a construct as paired associations, we proposed re-examining competitive state anxiety as a system of interacting components in a dataset of 485 competitive athletes from the UK. Following a process of data reduction, we estimated a network structure for 15 items from the modified Three Factor Anxiety Inventory using the graphical LASSO algorithm. We then examined network connectivity using node predictability. Exploratory graph analysis was used to detect communities in the network and bridge expected influence calculated to estimate the influence of items from one community to items in other communities. The resultant network produced a range of node predictability values. Community detection analysis derived three communities that corresponded with previous research and several nodes were identified that bridged these communities. We conclude that network analysis is a useful tool to explore the competitive state anxiety response and we discuss how the results of our analysis might inform the assessment of the construct and how this assessment might inform interventions

Sources of uncertainty in future projections of the carbon cycle

This is the final version of the article. Available from the publisher via the DOI in this record.The inclusion of carbon cycle processes within CMIP5 Earth System Models provides the opportunity to explore the relative importance of differences in scenario and climate model representation to future land and ocean carbon fluxes. A two-way ANOVA approach was used to quantify the variability owing to differences between scenarios and between climate models at different lead times. For global ocean carbon fluxes, the variance attributed to differences between Representative Concentration Pathway scenarios exceeds the variance attributed to differences between climate models by around 2025, completely dominating by 2100. This contrasts with global land carbon fluxes, where the variance attributed to differences between climate models continues to dominate beyond 2100. This suggests that modelled processes that determine ocean fluxes are currently better constrained than those of land fluxes, thus we can be more confident in linking different future socio-economic pathways to consequences of ocean carbon uptake than for land carbon uptake. The apparent agreement in atmosphere-ocean carbon fluxes, globally, masks strong climate model differences at a regional level. The North Atlantic and Southern Ocean are key regions, where differences in modelled processes represent an important source of variability in projected regional fluxesMOHC authors were supported by the Joint DECC / Defra Met Office Hadley Centre Cli- mate Programme (GA01101). SY was supported by the Hong Kong Polytechnic University grant “Bayesian Modelling for Quantifying Uncertainty in Climate Predictions” (1-ZV9Z). We acknowl- edge use of R software package (R Core Team 2013). We acknowledge the World Climate Re- search Programme’s Working Group on Coupled Modelling, which is responsible for CMIP and we thank the climate modelling groups for providing their GCM output (listed in Table 1). Support of this dataset was provided by the Office of Science, U.S. Department of Energy