Doctor of Philosophy

dissertationWe first study the inverse problem of recovering a complex Schro ?dinger potential from a discrete set of measurements of the solution to the Schro ?dinger equation using different source terms. We solve this problem by generalizing the inverse Born series method to nonlinear mappings between Banach spaces. In this general setting, we show convergence and stability of inverse Born series follow from a single problem- specific bound. We show this bound for the inverse Schro ?dinger problem, and study numerically an application of this inverse problem to transient hydraulic tomography. Additionally, we develop a family of iterative methods based on truncated inverse Born series that are akin to iterative methods based on truncated Taylor series. Next, we study the inverse problem of imaging scatterers in a homogeneous medium when only intensities of wavefields can be measured. Classic imaging meth- ods, such as Kirchhoff migration, rely on phase information contained in full waveform data and thus cannot be used directly with intensity-only data. In situations where scattered wavefields are small compared to the incident wavefields, we can form and solve a linear least squares problem to recover a projection (on a known subspace) of full waveform data from intensity data. We show that for sufficiently high frequencies, this projection gives a Kirchhoff image asymptotically equivalent to the Kirchhoff image obtained from full waveform data. We also generalize this imaging method to using stochastic incident fields with autocorrelation measurements. Finally, we study a mathematical model of grain growth in polycrystalline mate- rials. We review a simplified 1D grain growth model and an entropy-based theory for the evolution of an important statistic harvested from this model, the GBCD. The theory suggests the GBCD evolves according to a Fokker-Planck equation, which we validate numerically. We derive methods to estimate times from the GBCD, thus fitting it to Fokker-Planck time scales. This allows for direct comparisons of the GBCD with the Fokker-Planck solution, where we find qualitative agreement. We alsofind an energy dissipation identity which Fokker-Planck solutions must satisfy. We verify the GBCD satisfies this identity both qualitatively and quantitatively, further validating the Fokker-Planck model of GBCD evolution

Truth and Consequences

International audienc

Development of an integrated pest management strategy for control of pollen beetles in winter oilseed rape (HGCA Project Report No 504)

We have developed an integrated pest management strategy (IPM) for pollen beetles in winter oilseed rape (OSR) based on risk assessment, monitoring and alternative crop management that can be used as a framework by growers and crop consultants to manage pollen beetles with reduced insecticide inputs - and the confidence to do so. This will prolong insecticide life by reducing selection for resistance, reduce environmental impacts and contribute towards the sustainability and profitability of OSR in the UK. One of the major limitations to the use of action thresholds is that proper monitoring of the populations is time consuming and has to be conducted over a prolonged period. To encourage and facilitate their use, we tested and developed tools to improve risk assessment and monitoring. We conducted a pollen beetle monitoring study over 4 years in 178 OSR crops across the UK. Pollen beetles were sampled using sticky traps and plant sampling along transects in the crop. The data were used to help test a decision support system (DSS) for pollen beetles and to develop a monitoring trap. proPlant Expert is a DSS available in mainland Europe that uses a model of pollen beetle immigration and local meteorological data to forecast the start and end of pollen beetle immigration into the crop and main risk periods and advises when to monitor. We tested the model under UK conditions using data from our study and compared monitoring advice with the current advice system on the CropMonitor website (advises monitoring when the crop is at green-yellow bud stage and temperature >15°C). Both performed reassuringly well in prompting monitoring that would detect breaches of spray thresholds. However there were considerable reductions provided by proPlant in the need for consultation of the system (30%) and advised monitoring days (34-53%) in comparison with current advice. Use of the proPlant DSS could therefore focus monitoring effort to when it is most needed. It could also help to reduce unnecessary sprays in cases where beetle numbers are approaching threshold but consultation of the system returns a poor immigration risk forecast or an immigration complete result. The proPlant tool is now freely available to growers and crop consultants in the UK via the Bayer CropScience website. A monitoring trap for pollen beetles would help to more easily and accurately identify when spray thresholds have been breached than monitoring plants in the crop. We developed a baited monitoring trap for pollen beetles which will be commercially available from Oecos. The trap comprises a yellow sticky card mounted at 45°, baited with phenylacetaldehyde, a floral volatile produced naturally by several plant species. Unfortunately using data from our study we were unable to calibrate the trap catch to a given action threshold expressed as the number of beetles per plant using a simple linear relationship. However, the monitoring trap still has value for risk assessment, especially if used together with DSS. We tested the potential of turnip rape (TR) trap crops, planted as borders to the main OSR crop to reduce pollen beetle numbers in a field scale experiment conducted over three years on two sites. We found evidence that the strategy worked well in some years, but not others. This tactic is probably practically and economically worthwhile only for organic growers

Identification of a BRCA2-Specific modifier locus at 6p24 related to breast cancer risk

Common genetic variants contribute to the observed variation in breast cancer risk for BRCA2 mutation carriers; those known to date have all been found through population-based genome-wide association studies (GWAS). To comprehensively identify breast cancer risk modifying loci for BRCA2 mutation carriers, we conducted a deep replication of an ongoing GWAS discovery study. Using the ranked P-values of the breast cancer associations with the imputed genotype of 1.4 M SNPs, 19,029 SNPs were selected and designed for inclusion on a custom Illumina array that included a total of 211,155 SNPs as part of a multi-consortial project. DNA samples from 3,881 breast cancer affected and 4,330 unaffected BRCA2 mutation carriers from 47 studies belonging to the Consortium of Investigators of Modifiers of BRCA1/2 were genotyped and available for analysis. We replicated previously reported breast cancer susceptibility alleles in these BRCA2 mutation carriers and for several regions (including FGFR2, MAP3K1, CDKN2A/B, and PTHLH) identified SNPs that have stronger evidence of association than those previously published. We also identified a novel susceptibility allele at 6p24 that was inversely associated with risk in BRCA2 mutation carriers (rs9348512; per allele HR = 0.85, 95% CI 0.80-0.90, P = 3.9×10−8). This SNP was not associated with breast cancer risk either in the general population or in BRCA1 mutation carriers. The locus lies within a region containing TFAP2A, which encodes a transcriptional activation protein that interacts with several tumor suppressor genes. This report identifies the first breast cancer risk locus specific to a BRCA2 mutation background. This comprehensive update of novel and previously reported breast cancer susceptibility loci contributes to the establishment of a panel of SNPs that modify breast cancer risk in BRCA2 mutation carriers. This panel may have clinical utility for women with BRCA2 mutations weighing options for medical prevention of breast cancer

An original phylogenetic approach identified mitochondrial haplogroup T1a1 as inversely associated with breast cancer risk in BRCA2 mutation carriers

Introduction: Individuals carrying pathogenic mutations in the BRCA1 and BRCA2 genes have a high lifetime risk of breast cancer. BRCA1 and BRCA2 are involved in DNA double-strand break repair, DNA alterations that can be caused by exposure to reactive oxygen species, a main source of which are mitochondria. Mitochondrial genome variations affect electron transport chain efficiency and reactive oxygen species production. Individuals with different mitochondrial haplogroups differ in their metabolism and sensitivity to oxidative stress. Variability in mitochondrial genetic background can alter reactive oxygen species production, leading to cancer risk. In the present study, we tested the hypothesis that mitochondrial haplogroups modify breast cancer risk in BRCA1/2 mutation carriers. Methods: We genotyped 22,214 (11,421 affected, 10,793 unaffected) mutation carriers belonging to the Consortium of Investigators of Modifiers of BRCA1/2 for 129 mitochondrial polymorphisms using the iCOGS array. Haplogroup inference and association detection were performed using a phylogenetic approach. ALTree was applied to explore the reference mitochondrial evolutionary tree and detect subclades enriched in affected or unaffected individuals. Results: We discovered that subclade T1a1 was depleted in affected BRCA2 mutation carriers compared with the rest of clade T (hazard ratio (HR) = 0.55; 95% confidence interval (CI), 0.34 to 0.88; P = 0.01). Compared with the most frequent haplogroup in the general population (that is, H and T clades), the T1a1 haplogroup has a HR of 0.62 (95% CI, 0.40 to 0.95; P = 0.03). We also identified three potential susceptibility loci, including G13708A/rs28359178, which has demonstrated an inverse association with familial breast cancer risk. Conclusions: This study illustrates how original approaches such as the phylogeny-based method we used can empower classical molecular epidemiological studies aimed at identifying association or risk modification effects.Peer reviewe