Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Some factors affecting variation in milk yield in crossbred dairy cows on smallholder farms in north-east Tanzania

A 2-year longitudinal survey was carried out to investigate factors affecting milk yield in crossbred cows on smallholder farms in and around an urban centre. Sixty farms were visited at approximately 2-week intervals and details of milk yield, body condition score (BCS) and heart girth measurements were collected. Fifteen farms were within the town (U), 23 farms were approximately 5 km from town (SU), and 22 farms approximately 10 km from town (PU). Sources of variation in milk yield were investigated using a general linear model by a stepwise forward selection and backward elimination approach to judge important independent variables. Factors considered for the first step of formulation of the model included location (PU, SU and U), calving season, BCS at calving, at 3 months postpartum and at 6 months postpartum, calving year, herd size category, source of labour (hired and family labour), calf rearing method (bucket and partial suckling) and parity number of the cow. Daily milk yield (including milk sucked by calves) was determined by calving year (p < 0.0001), calf rearing method (p = 0.044) and BCS at calving (p < 0.0001). Only BCS at calving contributed to variation in volume of milk sucked by the calf, lactation length and lactation milk yield. BCS at 3 months after calving was improved on farms where labour was hired (p = 0.041) and BCS change from calving to 6 months was more than twice as likely to be negative on U than SU and PU farms. It was concluded that milk production was predominantly associated with BCS at calving, lactation milk yield increasing quadratically from score 1 to 3. BCS at calving may provide a simple, single indicator of the nutritional status of a cow population.

Some factors affecting reproductive success in crossbred dairy cows on smallholder farms in coastal north-east Tanzania

A 2-year longitudinal survey was carried out to investigate factors affecting reproduction in crossbred cows on smallholder farms in and around an urban centre. Sixty farms were visited at approximately 2-week intervals and details of reproductive traits and body condition score (BCS) were collected. Fifteen farms were within the town (U), 23 farms were approximately 5 km from town (SU), and 22 farms approximately 10 km from town (PU). Sources of variation in reproductive traits were investigated using a general linear model (GLM) by a stepwise forward selection and backward elimination approach to judge important independent variables. Factors considered for the first step of formulation of the model included location (PU, SU and U), type of insemination, calving season, BCS at calving, at 3 months postpartum and at 6 months postpartum, calving year, herd size category, source of labour (hired and family labour), calf rearing method (bucket and partial suckling) and parity number of the cow. The effects of the independent variables identified were then investigated using a non-parametric survival technique. The number of days to first oestrus was increased on the U site (p = 0.045) and when family labour was used (p = 0.02). The non-parametric test confirmed the effect of site (p = 0.059), but effect of labour was not significant. The number of days from calving to conception was reduced by hiring labour (p = 0.003) and using natural service (p = 0.028). The non-parametric test confirmed the effects of type of insemination (p = 0.0001) while also identifying extended calving intervals on U and SU sites (p = 0.014). Labour source was again non-significant. Calving interval was prolonged on U and SU sites (p = 0.021), by the use of AI (p = 0.031) and by the use of family labour (p = 0.001). The non-parametric test confirmed the effect of site (p = 0.008) and insemination type (p > 0.0001) but not of labour source. It was concluded that under favourable conditions (PU site, hired labour and natural service) calving intervals of around 440 days could be achieved.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

The hemodynamic impulse response to a single neural event

This article investigates the relation between stimulus-evoked neural activity and cerebral hemodynamics. Specifically, the hypothesis is tested that hemodynamic responses can be modeled as a linear convolution of experimentally obtained measures of neural activity with a suitable hemodynamic impulse response function. To obtain a range of neural and hemodynamic responses, rat whisker pad was stimulated using brief (less than or equal to2 seconds) electrical stimuli consisting of single pulses (0.3 millisecond, 1.2 mA) combined both at different frequencies and in a paired-pulse design. Hemodynamic responses were measured using concurrent optical imaging spectroscopy and laser Doppler flowmetry, whereas neural responses were assessed through current source density analysis of multielectrode recordings from a single barrel. General linear modeling was used to deconvolve the hemodynamic impulse response to a single "neural event" from the hemodynamic and neural responses to stimulation. The model provided an excellent fit to the empirical data. The implications of these results for modeling schemes and for physiologic systems coupling neural and hemodynamic activity are discussed.

Participatory research approaches in the development of improved management practices in indigenous chickens production systems with smallholder farmers in Kenya

This thesis is concerned with development of improved management practices in indigenous chicken production systems in a research process that includes participatory approaches with smallholder farmers and other stakeholders in Kenya. The research process involved a wide range of activities that included on-station experiments, field surveys, stakeholder consultations in workshops, seminars and visits, and on-farm farmer participatory research to evaluate the effect of some improved management interventions on production performance of indigenous chickens. The participatory research was greatly informed from collective experiences and lessons of the previous activities. The on-station studies focused on hatching, growth and nutritional characteristics of the indigenous chickens. Four research publications from these studies are included in this thesis. Quantitative statistical analyses were applied and they involved use of growth models estimated with non-linear regressions for the growth characteristics, chi-square determinations to investigate differences among different reciprocal crosses of indigenous chickens and general linear models and covariance determination for the nutrition study. The on-station studies brought greater understanding of performance and production characteristics of indigenous chickens and the influence of management practices on these characteristics. The field surveys and stakeholder consultations helped in understanding the overarching issues affecting the productivity of the indigenous chickens systems and their place in the livelihoods of smallholder farmers. These activities created strong networking opportunities with stakeholders from a wide spectrum. The on-farm farmer participatory research involved selection of 200 farmers in five regions followed by training and introduction of interventions on improved management practices which included housing, vaccination, deworming and feed supplementation. Implementation and monitoring was mainly done by individual farmers continuously for close to one and half years. Six quarterly visits to the farms were made by the research team to monitor and provide support for on-going project activities. The data collected has been analysed for 5 consecutive 3-monthly periods. Descriptive and inferential statistics were applied to analyse the data collected involving treatment applications, production characteristics and flock demography characteristics. Out of the 200 farmers initially selected, 173 had records on treatment applications and flock demography characteristics while 127 farmers had records on production characteristics. The demographic analysis with a dissimilarity index of flock size produced 7 distinct farm groups from among the 173 farms. Two of these farm groups were represented in similar numbers in each of the five regions. The research process also involved a number of dissemination and communication strategies that have brought the process and project outcomes into the domain of accessibility by wider readership locally and globally. These include workshops, seminars, field visits and consultations, local and international conferences, electronic conferencing, publications and personal communication via emailing and conventional posting. A number of research and development proposals were also developed based on the knowledge and experiences gained from the research process. The thesis captures the research process activities and outcomes in 8 chapters which include in ascending order – introduction, theoretical concepts underpinning FPR, research methodology and process, on-station research output, FPR descriptive statistical analysis, FPR inferential statistical analysis on production characteristics, FPR demographic analysis and conclusions. Various research approaches both quantitative and qualitative have been applied in the research process indicating the possibilities and importance of combining both systems for greater understanding of issues being studied. In our case, participatory studies of the improved management of indigenous chickens indicates their potential importance as livelihood assets for poor people.

Organic soils promote the efficacy of entomopathogenic nematodes, with different foraging strategies, in the control of a major forest pest: a meta-analysis of field trial data

The large pine weevil, Hylobius abietis, is a serious pest of reforestation in northern Europe. However, weevils developing in stumps of felled trees can be killed by entomopathogenic nematodes applied to soil around the stumps and this method of control has been used at an operational level in the UK and Ireland. We investigated the factors affecting the efficacy of entomopathogenic nematodes in the control of the large pine weevil spanning 10 years of field experiments, by means of a meta-analysis of published studies and previously unpublished data. We investigated two species with different foraging strategies, the ‘ambusher’ Steinernema carpocapsae, the species most often used at an operational level, and the ‘cruiser’ Heterorhabditis downesi. Efficacy was measured both by percentage reduction in numbers of adults emerging relative to untreated controls and by percentage parasitism of developing weevils in the stump. Both measures were significantly higher with H. downesi compared to S. carpocapsae. General linear models were constructed for each nematode species separately, using substrate type (peat versus mineral soil) and tree species (pine versus spruce) as fixed factors, weevil abundance (from the mean of untreated stumps) as a covariate and percentage reduction or percentage parasitism as the response variable. For both nematode species, the most significant and parsimonious models showed that substrate type was consistently, but not always, the most significant variable, whether replicates were at a site or stump level, and that peaty soils significantly promote the efficacy of both species. Efficacy, in terms of percentage parasitism, was not density dependent.

Field phenotyping of potato to assess root and shoot characteristics associated with drought tolerance

Aims Potatoes are a globally important source of food whose production requires large inputs of fertiliser and water. Recent research has highlighted the importance of the root system in acquiring resources. Here measurements, previously generated by field phenotyping, tested the effect of root size on maintenance of yield under drought (drought tolerance). Methods Twelve potato genotypes, including genotypes with extremes of root size, were grown to maturity in the field under a rain shelter and either irrigated or subjected to drought. Soil moisture, canopy growth, carbon isotope discrimination and final yields were measured. Destructively harvested field phenotype data were used as explanatory variables in a general linear model (GLM) to investigate yield under conditions of drought or irrigation. Results Drought severely affected the small rooted genotype Pentland Dell but not the large rooted genotype Cara. More plantlets, longer and more numerous stolons and stolon roots were associated with drought tolerance. Previously measured carbon isotope discrimination did not correlate with the effect of drought. Conclusions These data suggest that in-field phenotyping can be used to identify useful characteristics when known genotypes are subjected to an environmental stress. Stolon root traits were associated with drought tolerance in potato and could be used to select genotypes with resilience to drought.

Assessing species’ habitat associations from occurrence records, standardised monitoring data and expert opinion: a test with British butterflies

Accurate knowledge of species’ habitat associations is important for conservation planning and policy. Assessing habitat associations is a vital precursor to selecting appropriate indicator species for prioritising sites for conservation or assessing trends in habitat quality. However, much existing knowledge is based on qualitative expert opinion or local scale studies, and may not remain accurate across different spatial scales or geographic locations. Data from biological recording schemes have the potential to provide objective measures of habitat association, with the ability to account for spatial variation. We used data on 50 British butterfly species as a test case to investigate the correspondence of data-derived measures of habitat association with expert opinion, from two different butterfly recording schemes. One scheme collected large quantities of occurrence data (c. 3 million records) and the other, lower quantities of standardised monitoring data (c. 1400 sites). We used general linear mixed effects models to derive scores of association with broad-leaf woodland for both datasets and compared them with scores canvassed from experts. Scores derived from occurrence and abundance data both showed strongly positive correlations with expert opinion. However, only for occurrence data did these fell within the range of correlations between experts. Data-derived scores showed regional spatial variation in the strength of butterfly associations with broad-leaf woodland, with a significant latitudinal trend in 26% of species. Sub-sampling of the data suggested a mean sample size of 5000 occurrence records per species to gain an accurate estimation of habitat association, although habitat specialists are likely to be readily detected using several hundred records. Occurrence data from recording schemes can thus provide easily obtained, objective, quantitative measures of habitat association.

Assimilation of stratospheric ozone from MIPAS into a global general-circulation model: The September 2002 vortex split

Ozone and temperature profiles from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) have been assimilated, using three-dimensional variational assimilation, into a stratosphere troposphere version of the Met Office numerical weather-prediction system. Analyses are made for the month of September 2002, when there was an unprecedented split in the southern hemisphere polar vortex. The analyses are validated against independent ozone observations from sondes, limb-occultation and total column ozone satellite instruments. Through most of the stratosphere, precision varies from 5 to 15%, and biases are 15% or less of the analysed field. Problems remain in the vortex and below the 60 hPa. level, especially at the tropopause where the analyses have too much ozone and poor agreement with independent data. Analysis problems are largely a result of the model rather than the data, giving confidence in the MIPAS ozone retrievals, though there may be a small high bias in MIPAS ozone in the lower stratosphere. Model issues include an excessive Brewer-Dobson circulation, which results both from known problems with the tracer transport scheme and from the data assimilation of dynamical variables. The extreme conditions of the vortex split reveal large differences between existing linear ozone photochemistry schemes. Despite these issues, the ozone analyses are able to successfully describe the ozone hole split and compare well to other studies of this event. Recommendations are made for the further development of the ozone assimilation system.

Two-point boundary value problems for linear evolution equations

We study boundary value problems for a linear evolution equation with spatial derivatives of arbitrary order, on the domain 0 < x < L, 0 < t < T, with L and T positive nite constants. We present a general method for identifying well-posed problems, as well as for constructing an explicit representation of the solution of such problems. This representation has explicit x and t dependence, and it consists of an integral in the k-complex plane and of a discrete sum. As illustrative examples we solve some two-point boundary value problems for the equations iqt + qxx = 0 and qt + qxxx = 0.