A covariance formula for the number of excursion set components of Gaussian fields and applications

We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on $\mathbb{R}^d$ contained in compact domains. We also present two applications of this formula: (1) for fields whose correlations are integrable we prove that the variance of the component count in large domains is of volume order and give an expression for the leading constant, and (2) for fields with slower decay of correlation we give an upper bound on the variance which is of optimal order if correlations are regularly varying, and improves on best-known bounds if correlations are oscillating (e.g.\ monochromatic random waves)

Smoothness and monotonicity of the excursion set density of planar Gaussian fields

Nazarov and Sodin have shown that the number of connected components of the nodal set of a planar Gaussian field in a ball of radius R, normalised by area, converges to a constant as R -> infinity. This has been generalised to excursion/level sets at arbitrary levels, implying the existence of functionals c(ES)(l) and c(LS)(l) that encode the density of excursion/level set components at the level l. We prove that these functionals are continuously differentiable for a wide class of fields. This follows from a more general result, which derives differentiability of the functionals from the decay of the probability of 'four-arm events' for the field conditioned to have a saddle point at the origin. For some fields, including the important special cases of the Random Plane Wave and the Bargmann-Fock field, we also derive stochastic monotonicity of the conditioned field, which allows us to deduce regions on which c(ES)(l) and c(LS)(l) are monotone.Peer reviewe

Sinorhizobium Meliloti, A Bacterium Lacking The Autoinducer-2 (AI-2) Synthase, Responds To AI-2 Supplied By Other Bacteria

Many bacterial species respond to the quorum-sensing signal autoinducer-2 (AI-2) by regulating different niche-specific genes. Here, we show that Sinorhizobium meliloti, a plant symbiont lacking the gene for the AI-2 synthase, while not capable of producing AI-2 can nonetheless respond to AI-2 produced by other species. We demonstrate that S. meliloti has a periplasmic binding protein that binds AI-2. The crystal structure of this protein (here named SmlsrB) with its ligand reveals that it binds (2R,4S)-2-methyl-2,3,3,4-tetrahydroxytetrahydrofuran (R-THMF), the identical AI-2 isomer recognized by LsrB of Salmonella typhimurium. The gene encoding SmlsrB is in an operon with orthologues of the lsr genes required for AI-2 internalization in enteric bacteria. Accordingly, S. meliloti internalizes exogenous AI-2, and mutants in this operon are defective in AI-2 internalization. S. meliloti does not gain a metabolic benefit from internalizing AI-2, suggesting that AI-2 functions as a signal in S. meliloti. Furthermore, S. meliloti can completely eliminate the AI-2 secreted by Erwinia carotovora, a plant pathogen shown to use AI-2 to regulate virulence. Our findings suggest that S. meliloti is capable of \u27eavesdropping\u27 on the AI-2 signalling of other species and interfering with AI-2-regulated behaviours such as virulence

Mathematical Modelling of Metabolic Regulation in Aging

The underlying cellular mechanisms that characterize aging are complex and multifaceted. However, it is emerging that aging could be regulated by two distinct metabolic hubs. These hubs are the pathway defined by the mammalian target of rapamycin (mTOR) and that defined by the NAD+-dependent deacetylase enzyme, SIRT1. Recent experimental evidence suggests that there is crosstalk between these two important pathways; however, the mechanisms underpinning their interaction(s) remains poorly understood. In this review, we propose using computational modelling in tandem with experimentation to delineate the mechanism(s). We briefly discuss the main modelling frameworks that could be used to disentangle this relationship and present a reduced reaction pathway that could be modelled. We conclude by outlining the limitations of computational modelling and by discussing opportunities for future progress in this area

Education along border regions in Ireland: challenges and opportunities

A one-year research project with communities along the border in Ireland, the only land border between the UK and the European Union, examined primary schooling. Created just over a century ago, the border’s permeability has varied over time. Some children cross the border to attend primary school, in both directions, but no formal research appears to have been conducted in relation to this movement, its scale or its impact on the. The 229 primary schools within 3 miles of the border serve diverse communities, some of which appear to straddle the border. Some schools attract some of their intake from across the border, and some schools rely on that movement of learners to keep them sustainable, but there has been no published research into how schools in these communities operate, the challenges they face and the opportunities that they can exploit due to their location. In this study, the degree to which the opportunities to use schools across the border is examined and the impact that this has on parents and children and on the schools themselves is explored. Visits to a range of schools on each side of the border and events open to the communities along the border provided considerable information, and a Geographical Information System was used to analyse potential movements of children across the border. The research is original and, while sample sizes are relatively small, this is an important first step to better understand the education provision in these communities. While particularly significant for the people who live in these complex communities, it also contributes to a greater understanding of border education provision which will be important as consideration about the future of the border in Ireland intensifies. Border communities elsewhere may also find consideration of educational provision for liminal communities of interest

Fluctuations of the number of excursion sets of planar Gaussian fields

For a smooth, stationary, planar Gaussian field, we consider the number of connected components of its excursion set (or level set) contained in a large square of area $R^2$. The mean number of components is known to be of order $R^2$ for generic fields and all levels. We show that for certain fields with positive spectral density near the origin (including the Bargmann-Fock field), and for certain levels $\ell$, these random variables have fluctuations of order at least $R$, and hence variance of order at least $R^2$. In particular, this holds for excursion sets when $\ell$ is in some neighbourhood of zero, and it holds for excursion/level sets when $\ell$ is sufficiently large. We prove stronger fluctuation lower bounds of order $R^\alpha$, $\alpha \in [1,2]$, in the case that the spectral density has a singularity at the origin. Finally, we show that the number of excursion/level sets for the Random Plane Wave at certain levels has fluctuations of order at least $R^{3/2}$, and hence variance of order at least~$R^3$. We expect that these bounds are of the correct order, at least for generic levels.Comment: 38 pages, 2 figure

Calibration of pelagic stereo-BRUVs and scientific longline surveys for sampling sharks

Our understanding of the ecology of sharks and other highly mobile marine species often relies on fishery-dependent data or extractive fishery-independent techniques that can result in catchability and size-selectivity biases. Pelagic Baited Remote Underwater stereo-Video Systems (pelagic stereo-BRUVs) provide a standardized, non-destructive and fishery-independent approach to estimate biodiversity measures of fish assemblages in the water column. However, the performance of this novel method has not yet been assessed relative to other standard sampling techniques. We compared the catch composition, relative abundance and length distribution of fish assemblages sampled using pelagic stereo-BRUVs and conventional scientific longline surveys. In particular, we focused on sharks of the family Carcharhinidae (requiem sharks) to assess the sampling effectiveness of this novel technique along a latitudinal gradient off the coast of Western Australia. We calibrated the sampling effort required for each technique to obtain equivalent samples of the target species and discuss the advantages, limitations and potential use of these methods to study highly mobile species.The proportion of sharks sampled by pelagic stereo-BRUVs and scientific longline surveys was comparable across the latitudinal gradient. Carcharhinus plumbeus was the most abundant species sampled by both the techniques. Longline surveys selected larger individuals of the family Carcharhinidae in comparison with the length distribution data obtained from pelagic stereo-BRUVs. However, the relative abundance estimates (catch per unit of effort) from the pelagic stereo-BRUVs were comparable to those from 5 to 30 longline hooks. Pelagic stereo-BRUVs can be calibrated to standard techniques in order to study the species composition, behaviour, relative abundance and size distribution of highly mobile fish assemblages at broad spatial and temporal scales. This technique offers a non-destructive fishery-independent approach that can be implemented in areas that may be closed to fishing and is suitable for studies on rare or threatened species

Visual signals and children's communication: negative effects on task outcome

Previous research has found that young children fail to adapt to audio-only interaction (e.g. Doherty-Sneddon & Kent, 1996), and perform difficult communication tasks better face-to-face. In this new study, children aged 6- and 10 year-olds were compared in face-to-face and audio-only interaction. A problem-solving communication task involving description of abstract stimuli was employed. When describing the abstract stimuli both groups of children showed evidence of face-to-face interference rather than facilitation. It is concluded that, contrary to previous research, for some communication tasks access to visual signals (such as facial expression and eye gaze) may hinder rather than help children’s communication

Reducing drug related deaths : a pre-implementation assessment of knowledge,barriers and enablers for naloxone distribution through general practice

Peer reviewedPublisher PD

Are nanoparticles spherical or quasi-spherical?

The geometry of quasi-spherical nanoparticles is investigated. The combination of SEM imaging and electrochemical nano-impact experiments is demonstrated to allow sizing and characterization of the geometry of single silver nanoparticles