Generalized DPW method and an application to isometric immersions of space forms

Let $G$ be a complex Lie group and $\Lambda G$ denote the group of maps from the unit circle ${\mathbb S}^1$ into $G$, of a suitable class. A differentiable map $F$ from a manifold $M$ into $\Lambda G$, is said to be of \emph{connection order $(_a^b)$} if the Fourier expansion in the loop parameter $\lambda$ of the ${\mathbb S}^1$-family of Maurer-Cartan forms for $F$, namely F_\lambda^{-1} \dd F_\lambda, is of the form $\sum_{i=a}^b \alpha_i \lambda^i$. Most integrable systems in geometry are associated to such a map. Roughly speaking, the DPW method used a Birkhoff type splitting to reduce a harmonic map into a symmetric space, which can be represented by a certain order $(_{-1}^1)$ map, into a pair of simpler maps of order $(_{-1}^{-1})$ and $(_1^1)$ respectively. Conversely, one could construct such a harmonic map from any pair of $(_{-1}^{-1})$ and $(_1^1)$ maps. This allowed a Weierstrass type description of harmonic maps into symmetric spaces. We extend this method to show that, for a large class of loop groups, a connection order $(_a^b)$ map, for $a<0<b$, splits uniquely into a pair of $(_a^{-1})$ and $(_1^b)$ maps. As an application, we show that constant non-zero curvature submanifolds with flat normal bundle of a sphere or hyperbolic space split into pairs of flat submanifolds, reducing the problem (at least locally) to the flat case. To extend the DPW method sufficiently to handle this problem requires a more general Iwasawa type splitting of the loop group, which we prove always holds at least locally.Comment: Some typographical correction

Scattering from Singular Potentials in Quantum Mechanics

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r variable. The present paper extends those early results to an arbitrary number of spatial dimensions. The Hill-type equation which leads, in principle, to the evaluation of the polydromy parameter, is obtained from the Hill equation for a two-dimensional problem by means of a simple change of variables. The asymptotic forms of the wave function as r tends to zero and as r tends to infinity are also derived. The Darboux technique of intertwining operators is then applied to obtain an algorithm that makes it possible to solve the Schrodinger equation with a singular potential containing many negative powers of r, if the exact solution with even just one term is already known.Comment: 19 pages, plain Tex. In this revised version, the analysis of Eq. (5.29) has been amended, and an appendix has been added for completenes

Policy and practice certainty for effective uptake of diffuse pollution practices in a light touch regulated country

Although the link between agriculture and diffuse water pollution has been understood for decades, there is still a need to implement effective measures to address this issue. In countries with light-touch regulation, such as New Zealand and Australia, most efforts to promote environmental management practices have relied on voluntary initiatives such as participatory research and extension programmes; the success of which is largely dependent on farmers’ willingness and ability to adopt these practices. Increased understanding of the factors influencing farmer decision-making in this area would aid the promotion of effective advisory services. This study provides insights from 52 qualitative interviews with farmers and from observations of nine farmer meetings and field days. We qualitatively identify factors that influence farmer decision-making regarding the voluntary uptake of water quality practices and develop a typology for categorising farmers according to the factors that influence their decision-making. We find that in light-touch regulated countries certainty around policy and also around the effectiveness of practices is essential, particularly for farmers who delay action until compelled to act due to succession or regulation. The contribution of this paper is threefold: (i) it identifies factors influencing decision-making around the uptake of water quality practices in a light-touch regulated country; (ii) it develops a typology of different farmer types; and (iii) it provides recommendations on policy approaches for countries with light-touch regulation, which has potential relevance for any countries facing changes regarding their agricultural policy, such as post-Brexit policy in the UK

Economic values for ecosystem services:A global synthesis and way forward

This paper presents a global synthesis of economic values for ecosystem services provided by 15 terrestrial and marine biomes. Information from over 1,300 studies, yielding over 9,400 value estimates in monetary units, has been collected and organised in the Ecosystem Services Valuation Database (ESVD). This is a substantial expansion of data since the de Groot et al. (2012) description of the ESVD and provides an important juncture to explore developments in the use of valuation methods and the contexts in which valuations are conducted. In this paper we provide summary values for 23 ecosystem services from 15 biomes to represent the magnitude, variation and gaps in economic values. To enable the comparison and synthesis of values, estimates in the ESVD are standardised to a common set of units (Int$/ha/year at 2020 price levels). This data provides a basis for value transfers to inform decision-making in current policy contexts but requires due consideration and adjustment for context specific determinants of value. Although the coverage of the ESVD is global, the geographic distribution of data is not even. There is a particularly high representation of European ecosystems and relatively little information for Russia, Central Asia and North Africa. Therefore, the data are not globally representative of biophysical and socio-economic contexts. The distribution of data across ecosystem services is also far from even, with some services very well represented (e.g. recreation, wild fish and wild animals, ecosystem and species appreciation, air filtration and global climate regulation) and others with almost no value estimates (e.g. disease control, water baseflow maintenance, rainfall pattern regulation). In the past decade, there has been a notable increase in demand for information on the economic value of ecosystem services from both public and private institutions to improve the conservation and management of natural capital. The literature is developing to meet this demand but there is a need for targeted and refined valuation research to ensure sufficient certainty, comparability, and representativeness of the data, and to enable transferability and fill knowledge gaps. This paper concludes by identifying avenues for future development to further increase the amount, quality, representativeness and application of data on economic values for ecosystem services.</p

An HLA-I signature favouring KIR-educated Natural Killer cells mediates immune control of HIV in children and contrasts with the HLA-B-restricted CD8+T-cell-mediated immune control in adults

Natural Killer (NK) cells contribute to HIV control in adults, but HLA-B-mediated T-cell activity has a more substantial impact on disease outcome. However, the HLA-B molecules influencing immune control in adults have less impact on paediatric infection. To investigate the contribution NK cells make to immune control, we studied >300 children living with HIV followed over two decades in South Africa. In children, HLA-B alleles associated with adult protection or disease-susceptibility did not have significant effects, whereas Bw4 (p = 0.003) and low HLA-A expression (p = 0.002) alleles were strongly associated with immunological and viral control. In a comparator adult cohort, Bw4 and HLA-A expression contributions to HIV disease outcome were dwarfed by those of protective and disease-susceptible HLA-B molecules. We next investigated the immunophenotype and effector functions of NK cells in a subset of these children using flow cytometry. Slow progression and better plasma viraemic control were also associated with high frequencies of less terminally differentiated NKG2A+NKp46+CD56dim NK cells strongly responsive to cytokine stimulation and linked with the immunogenetic signature identified. Future studies are indicated to determine whether this signature associated with immune control in early life directly facilitates functional cure in children

Mitigation of Moral Hazard and Adverse Selection in Venture Capital Financing: The Influence of the Country’s Institutional Setting

A venture capitalist (VC) needs to trade off benefits and costs when attempting to mitigate agency problems in their investor-investee relationship. We argue that signals of ventures complement the VC’s capacity to screen and conduct a due diligence during the pre-investment phase, but its attractiveness may diminish in institutional settings supporting greater transparency. Similarly, whereas a VC may opt for contractual covenants to curb potential opportunism by ventures in the post-investment phase, this may only be effective in settings supportive of shareholder rights enforcement. Using an international sample of VC contracts, our study finds broad support for these conjectures. It delineates theoretical and practical implications for how investors can best deploy their capital in different institutional settings whilst nurturing their relationships with entrepreneurs

Data quality and practical challenges of thyroid volume assessment by ultrasound under field conditions - observer errors may affect prevalence estimates of goitre

<p>Abstract</p> <p>Background</p> <p>The ultrasonographic estimation of thyroid size has been advocated as being more precise than palpation to diagnose goitre. However, ultrasound also requires technical proficiency. This study was conducted among Saharawi refugees, where goitre is highly prevalent. The objectives were to assess the overall data quality of ultrasound measurements of thyroid volume (Tvol), including the intra- and inter-observer agreement, under field conditions, and to describe some of the practical challenges encountered.</p> <p>Methods</p> <p>In 2007 a cross-sectional study of 419 children (6-14 years old) and 405 women (15-45 years old) was performed on a population of Saharawi refugees with prevalent goitre, who reside in the Algerian desert. Tvol was measured by two trained fieldworkers using portable ultrasound equipment (examiner 1 measured 406 individuals, and examiner 2, 418 individuals). Intra- and inter-observer agreement was estimated in 12 children selected from the study population but not part of the main study. In the main study, an observer error was found in one examiner whose ultrasound images were corrected by linear regression after printing and remeasuring a sample of 272 images.</p> <p>Results</p> <p>The intra-observer agreement in Tvol was higher in examiner 1, with an intraclass correlation coefficient (ICC) of 0.97 (95% CI: 0.91, 0.99) compared to 0.86 (95% CI: 0.60, 0.96) in examiner 2. The ICC for inter-observer agreement in Tvol was 0.38 (95% CI: -0.20, 0.77). Linear regression coefficients indicated a significant scaling bias in the original measurements of the AP and ML diameter and a systematic underestimation of Tvol (a product of AP, ML, CC and a constant). The agreement between re-measured and original Tvol measured by ICC (95% CI) was 0.76 (0.71, 0.81). The agreement between re-measured and corrected Tvol measured by ICC (95% CI) was 0.97 (0.96, 0.97).</p> <p>Conclusions</p> <p>An important challenge when using ultrasound to assess thyroid volume under field conditions is to recruit and train qualified personnel to perform the measurements. Methodological studies are important to assess data quality and can facilitate statistical corrections and improved estimates.</p

Partial costs of global climate change adaptation for the supply of raw industrial and municipal water: a methodology and application

Despite growing recognition of the importance of climate change adaptation, few global estimates of the costs involved are available for the water supply sector. We present a methodology for estimating partial global and regional adaptation costs for raw industrial and domestic water supply, for a limited number of adaptation strategies, and apply the method using results of two climate models. In this paper, adaptation costs are defined as those for providing enough raw water to meet future industrial and municipal water demand, based on country-level demand projections to 2050. We first estimate costs for a baseline scenario excluding climate change, and then additional climate change adaptation costs. Increased demand is assumed to be met through a combination of increased reservoir yield and alternative backstop measures. Under such controversial measures, we project global adaptation costs of $12 bn p.a., with 83-90$73 bn p.a.), which supports the notion of mainstreaming climate change adaptation into broader policy aims. The method provides a tool for estimating broad costs at the global and regional scale; such information is of key importance in international negotiations. © 2010 IOP Publishing Ltd