Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Long-chain n−3 PUFA: plant v. marine sources

Increasing recognition of the importance of the long-chain n-3 PUFA, EPA and DHA, to cardiovascular health, and in the case of DHA to normal neurological development in the fetus and the newborn, has focused greater attention on the dietary supply of these fatty acids. The reason for low intakes of EPA and DHA in most developed countries (0 center dot 1-0 center dot 5hairspg/d) is the low consumption of oily fish, the richest dietary source of these fatty acids. An important question is whether dietary intake of the precursor n-3 fatty acid, alpha-linolenic acid (alpha LNA), can provide sufficient amounts of tissue EPA and DHA by conversion through the n-3 PUFA elongation-desaturation pathway. alpha LNA is present in marked amounts in plant sources, including green leafy vegetables and commonly-consumed oils such as rape-seed and soyabean oils, so that increased intake of this fatty acid would be easier to achieve than via increased fish consumption. However, alpha LNA-feeding studies and stable-isotope studies using alpha LNA, which have addressed the question of bioconversion of alpha LNA to EPA and DHA, have concluded that in adult men conversion to EPA is limited (approximately 8%) and conversion to DHA is extremely low (< 0 center dot 1%). In women fractional conversion to DHA appears to be greater (9%), which may partly be a result of a lower rate of utilisation of alpha LNA for beta-oxidation in women. However, up-regulation of the conversion of EPA to DHA has also been suggested, as a result of the actions of oestrogen on Delta 6-desaturase, and may be of particular importance in maintaining adequate provision of DHA in pregnancy. The effect of oestrogen on DHA concentration in pregnant and lactating women awaits confirmation.

Treatment of written verb and written sentence production in an individual with aphasia: A clinical study

Background: Although the efficacy of treatments for spoken verb and sentence production deficits in aphasia has been documented widely, less is known about interventions for written verb and written sentence production deficits. Aims: This study documents a treatment aiming to improve production of (a) written subject-verb sentences (involving intransitive verbs) and (b) written subject-verb-object sentences (involving transitive verbs). Methods & Procedures: The participant, a 63-year-old female aphasic speaker, had a marked language comprehension deficit, apraxia of speech, relatively good spelling abilities, and no hemiplegia. The treatment involved intransitive verbs producing subject-verb active sentences and transitive verbs producing subject-verb-object active non-reversible sentences. The treatment was undertaken in the context of current UK clinical practice. Outcomes & Results: Statistical improvements were noted for the trained sets of verbs and sentences. Other improvements were also noted in LW's ability to retrieve some non-treated verbs and construct written sentences. Treatment did not generalise to sentence comprehension and letter spelling to dictation. Conclusions: Our participant's ability to write verbs and sentences improved as a result of the treatment.

Estimators in capture–recapture studies with two sources

This paper investigates the applications of capture–recapture methods to human populations. Capture–recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln–Petersen estimator and its modified version, the Chapman estimator, Chao’s lower bound estimator, the Zelterman’s estimator, McKendrick’s moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao’s estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao’s and Chapman’s estimator. Results indicate that Chao’s estimator is less biased than Chapman’s estimator unless both sources are independent. Chao’s estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

An application of the DEA double bootstrap to examine sources of efficiency in Bangladesh rice farming

In this article we examine sources of technical efficiency for rice farming in Bangladesh. The motivation for the analysis is the need to close the rice yield gap to enable food security. We employ the DEA double bootstrap of Simar and Wilson (2007) to estimate and explain technical efficiency. This technique overcomes severe limitations inherent in using the two-stage DEA approach commonly employed in the efficiency literature. From a policy perspective our results show that potential efficiency gains to reduce the yield gap are greater than previously found. Statistically positive influences on technical efficiency are education, extension and credit, with age being a negative influence.

In vitro evaluation of fibrolytic enzymes as additives for maize (Zea mays L.) silage - III. Comparison of enzymes derived from psychrophilic, mesophilic or thermophilic sources

A completely randomised study was completed to examine the influence of fibrolytic enzymes derived from psychrophilic, (F), mesophilic, (L) or thermophilic (Ta) sources, applied at ensiling, on the chemical characteristics and in vitro rumen fermentation of maize silage, assessed using the Reading Pressure Technique (RPT). Treatments, all in triplicate, consisted of untreated maize forage or treated with preparations F, L, Ta or a mixture (1: 1, v/v) of F and L (FL), at two levels each, and ensiled for 210 days in plastic mini-silos. Addition of enzymes L decreased (P < 0.05) silage pH relative to the control, whereas enzyme Ta tended (P < 0.10) to reduce it. Preparations F, L and Ta tended to reduce (P < 0.10) the fibre contents of the silages, with effects being attributable to a decrease in the cellulose fraction. Starch contents were reduced (P < 0.05) in the treatments including enzyme F. End-point (96 h) gas production (GP) values did not differ among treatments, suggesting that enzymes did not change the total amount of fermentable substrate. However, consistent with the decrease in starch contents, adding enzyme F reduced (P < 0.05) GP at most incubation times. Addition of enzymes increased (P < 0.05) the initial (6 h) organic matter degradation (OMD) levels in all but one treatment (F), with increases of 14, 19, and 26% for preparations L, Ta, and FL, respectively, averaged across levels. Furthermore, the addition of enzymes increased (P < 0.05) the soluble OM losses, however, these increases did not fully account for the initial increase in OMD. The latter suggests that enzymes increased solubility and also altered silage structure, making it more amenable to degradation by ruminal microorganisms. As a result of the increase in OMD, without a concomitant increase in GP, the fermentation efficiency was greatly increased (P < 0.05) in enzyme treatments. Addition of enzymes to maize at ensiling, particularly those from the mesophilic and thermophilic sources used here, have the potential to increase the initial rate of silage OMD. (C) 2003 Elsevier B.V. All rights reserved.