Remarks on the boundary set of spectral equipartitions

Given a bounded open set $\Omega$ in $\mathbb{R}^n$ (or a compact Riemannian manifold with boundary), and a partition of $\Omega$ by $k$ open sets $\omega_j$, we consider the quantity $\max_j \lambda(\omega_j)$, where $\lambda(\omega_j)$ is the ground state energy of the Dirichlet realization of the Laplacian in $\omega_j$. We denote by $\mathfrak{L}_k(\Omega)$ the infimum of $\max_j \lambda(\omega_j)$ over all $k$-partitions. A minimal $k$-partition is a partition which realizes the infimum. The purpose of this paper is to revisit properties of nodal sets and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We focus on the length of the boundary set of the partition in the 2-dimensional situation.Comment: Final version to appear in the Philosophical Transactions of the Royal Society

Incentives for breastfeeding and for smoking cessation in pregnancy: An exploration of types and meanings

Financial or tangible incentives are a strategy for improving health behaviours. The mechanisms of action of incentives are complex and debated. Using a multidisciplinary integrated mixed methods study, with service-user collaboration throughout, we developed a typology of incentives and their meanings for initiating and sustaining smoking cessation in pregnancy and breastfeeding. The ultimate aim was to inform incentive intervention design by providing insights into incentive acceptability and mechanisms of action. Systematic evidence syntheses of incentive intervention studies for smoking cessation in pregnancy or breastfeeding identified incentive characteristics, which were developed into initial categories. Little published qualitative data on user perspectives and acceptability was available. Qualitative interviews and focus groups conducted in three UK regions with a diverse socio-demographic sample of 88 women and significant others from the target population, 53 service providers, 24 experts/decision makers, and conference attendees identified new potential incentives and providers, with and without experience of incentives. Identified incentives (published and emergent) were classified into eight categories: cash and shopping vouchers, maternal wellbeing, baby and pregnancy-related, behaviour-related, health-related, general utility, awards and certificates, and experiences. A typology was refined iteratively through concurrent data collection and thematic analysis to explore participants' understandings of ‘incentives’ and to compare and contrast meanings across types. Our typology can be understood in three dimensions: the degree of restriction, the extent to which each is hedonic and/or utilitarian, and whether each has solely monetary value versus monetary with added social value. The layers of autonomy, meanings and the social value of incentive types influence their acceptability and interact with structural, social, and personal factors. Dimensions of incentive meaning that go beyond the simple incentive description should inform incentive programme design and are likely to influence outcomes

Recent Langley helicopter acoustics contributions

The helicopter acoustics program at NASA Langley has included technology for elements of noise control ranging from sources of noise to receivers of noise. The scope of Langley contributions for about the last decade is discussed. Specifically, the resolution of two certification noise quantification issues by subjective acoustics research, the development status of the helicopter system noise prediction program ROTONET are reviewed and the highlights from research on blade rotational, broadband, and blade vortex interaction noise sources are presented. Finally, research contributions on helicopter cabin (or interior) noise control are presented. A bibliography of publications from the Langley helicopter acoustics program for the past 10 years is included

The Apollo Virtual Microscope Collection: Lunar Mineralogy and Petrology of Apollo 11, 12, 14, 15 and 16 Rocks

We report on the new Virtual Microscopes on Apollo 16 lunar samples in our Apollo Virtual Microscope collection

Mapping language to the world: the role of iconicity in the sign language input

Most research on the mechanisms underlying referential mapping has assumed that learning occurs in ostensive contexts, where label and referent co-occur, and that form and meaning are linked by arbitrary convention alone. In the present study, we focus on iconicity in language, that is, resemblance relationships between form and meaning, and on non-ostensive contexts, where label and referent do not co-occur. We approach the question of language learning from the perspective of the language input. Specifically, we look at child-directed language (CDL) in British Sign Language (BSL), a language rich in iconicity due to the affordances of the visual modality. We ask whether child-directed signing exploits iconicity in the language by highlighting the similarity mapping between form and referent. We find that CDL modifications occur more often with iconic signs than with non-iconic signs. Crucially, for iconic signs, modifications are more frequent in non-ostensive contexts than in ostensive contexts. Furthermore, we find that pointing dominates in ostensive contexts, and suggest that caregivers adjust the semiotic resources recruited in CDL to context. These findings offer first evidence for a role of iconicity in the language input and suggest that iconicity may be involved in referential mapping and language learning, particularly in non-ostensive contexts

Genetics, odor perception and food liking: The intriguing role of cinnamon

Humans use a repertoire of > 400 olfactory receptors (ORs) to perceive odorants. The sense of smell is a complex trait whereby genetics and environmental factors interplay. To date, still little is known regarding the genetics of smell, even though the high genetic variability of ORs genes has already been demonstrated. Recently a significant association between cinnamon odorant recognition and the rs317787 polymorphism, located in a cluster of OR genes, has been described. Based on this data, here, we replicated the effect of the same variant (rs317787) on cinnamon odorant identification as well as looked at any possible association with liking for wine whose bouquet frequently smells of cinnamon. Our analysis in a cohort of individuals from two Italian genetic isolates confirmed that rs317787-T allele is associated with an improved cinnamon detection (p-value 5.18 7 10 1206, n = 971) but also with a greater liking for red wine (p-value 0.017, n = 2374). Present results further confirm the association of rs31778 SNP and cinnamon odorants detection and provide additional details about the role of the ORs genes in food liking. Overall, our work contributes to better deciphering the genetic basis of smell and food liking aimed at a more in-depth elucidation of the role of the ORs genes

Class III Spine Grafts

This chapter is focused on the USFDA regulation and the related efficacy evidence of bone graft materials, especially Class III drug-device combination products for use in the spine. Nonstructural allograft and cellular allograft products that do not rely on the metabolic activity of living cells are HCT/P products, which require no premarket review for safety and efficacy. Synthetic bone grafts and demineralized bone matrices (DBMs) fall under Class II and require a 510(k) for market clearance, generally on the basis of an animal study. Drug-device combination bone grafts are Class III and require an investigational device exemption (IDE) clinical trial followed by a premarket approval (PMA) application with the FDA to review safety and effectiveness. Currently, there are only two PMA-supported Class III drug-device bone graft substitutes with Level I data that demonstrate equivalence to autograft for safety and effectiveness in spine: Infuse® (rhBMP-2) and i-FACTOR (P-15 peptide). Both of these products have been shown to be effective autograft replacement options, vs. the other technologies, which are autograft extenders. The OP-1 Implant (rhBMP-7) was marketed for a period of time, but it has been removed from the market. This chapter will discuss these products along with their supporting clinical data

Free-space quantum key distribution

A working free-space quantum key distribution (QKD) system has been developed and tested over a 205-m indoor optical path at Los Alamos National Laboratory under fluorescent lighting conditions. Results show that free-space QKD can provide secure real-time key distribution between parties who have a need to communicate secretly.Comment: 5 pages, 2 figures, 2 tables. To be published in Physical review A on or about 1 April 199

High Pressure Gas Permeation and Liquid Diffusion Studies of Coflon and Tefzel Thermoplastics

The life of fluid-carrying flexible or umbilical pipes during service at elevated temperatures and pressures depends inter alia on their resistance to attack by the fluids present and the rate at which these fluids are absorbed by the pipe lining materials. The consequences of fluid ingress into the thermoplastic lining could mean a) a reduction in its mechanical strength, to increase chances of crack formation and growth and thus a loss of integrity, b) the occurrence of permeation right through the lining material, with pressure build- up in the outer pipe wall construction (of flexible pipes) or chemical attack (from a hostile permeant) on outer layers of reinforcements. Therefore it is important within this project to have relevant permeation data for Coflon and Tefzel thermoplastics: the former is plasticised, the latter is not. A previous report (CAPP/M.2) described experimental equipment and techniques used by MERL when measuring high pressure (up to 5000 psi) gas permeation and liquid diffusion through thermoplastic samples cut from extruded bar or pipe, and provided the basic theory involved. Norsk Hydro are also performing gas permeation tests on pipe sections, at up to 100 bars (1450 psi) pressure or so, and reporting separately. Some comparisons between data from Norsk Hydro and MERL have been made herein. The tests should be considered as complementary, as the Norsk Hydro test has the obvious benefit of using complete pipe sections, whilst MERL can test at much higher pressures, up to 1000 bar if necessary. The sophisticated analytical measuring equipment of Norsk Hydro can distinguish the individual components of mixed gases and hence the various permeation-linked coefficients whereas MERL, in using pressure increase at constant volume to determine permeation rate, is limited to obtaining single gas data, or apparent (or representative) coefficients for a mixed gas as a whole. Except for the initial fluid diffusion data for Tefzel described in CAPP/M.2, the present report covers all aspects of fluid permeation and diffusion for Coflon and Tefzel, including all the pen-neation data accumulated in the project to date. Test gases have mainly been methane (CH4) and carbon dioxide (CO2). More high pressure (HP) gas permeation tests have been performed since the last issue of this report, most being concerned with changes in permeation characteristics brought about by ageing in various relevant fluids. This revision supersedes previous issues

Correlation of Chemical and Physical Test Data for the Environmental Ageing of Tefzel (ETFE)

In a similar approach to that used for the previously issued correlation report for Coflon (CAPP/M.10), this report aims to identify any correlations between mechanical property changes and chemical/morphological changes for Tefzel, using information supplied in other MERL and TRI project reports (plus latest data which will be included in final reports for Phase 1). Differences identified with Coflon behaviour will be of scientific interest as well as appropriate to project applications, as Tefzel and Coflon are chemical isomers. Owing to the considerable chemical resistance of Tefzel, much of its testing so far has been based on mechanical properties. Where changes have occurred, chemical analysis can now be targeted more effectively. Relevant test data collated here include: tensile modulus and related properties, permeation coefficients, % crystallinity, and other observations where significant. Fluids based on methanol and amine (Fluid G), a mixture of methane, carbon dioxide and hydrogen sulphide gases plus an aqueous amine solution (Fluid F), and an aromatic oil mix of heptane, cyclohexane, toluene and I-propanol (Fluid 1) have affected Tefzel to varying degrees, and are discussed in some detail herein