Isospectral algorithms, Toeplitz matrices and orthogonal polynomials

An isospectral algorithm is one which manipulates a matrix without changing its spectrum. In this thesis we study three interrelated examples of isospectral algorithms, all pertaining to Toeplitz matrices in some fashion, and one directly involving orthogonal polynomials. The first set of algorithms we study come from discretising a continuous isospectral flow designed to converge to a symmetric Toeplitz matrix with prescribed eigenvalues. We analyse constrained, isospectral gradient flow approaches and an isospectral flow studied by Chu in 1993. The second set of algorithms compute the spectral measure of a Jacobi operator, which is the weight function for the associated orthogonal polynomials and can include a singular part. The connection coefficients matrix, which converts between different bases of orthogonal polynomials, is shown to be a useful new tool in the spectral theory of Jacobi operators. When the Jacobi operator is a finite rank perturbation of Toeplitz, here called pert-Toeplitz, the connection coefficients matrix produces an explicit, computable formula for the spectral measure. Generalisation to trace class perturbations is also considered. The third algorithm is the infinite dimensional QL algorithm. In contrast to the finite dimensional case in which the QL and QR algorithms are equivalent, we find that the QL factorisations do not always exist, but that it is possible, at least in the case of pert-Toeplitz Jacobi operators, to implement shifts to generate rapid convergence of the top left entry to an eigenvalue. A fascinating novelty here is that the infinite dimensional matrices are computed in their entirety and stored in tailor made data structures. Lastly, the connection coefficients matrix and the orthogonal transformations computed in the QL iterations can be combined to transform these pert-Toeplitz Jacobi operators isospectrally to a canonical form. This allows us to implement a functional calculus for pert-Toeplitz Jacobi operators.UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1

Volume preservation by Runge–Kutta methods

This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.apnum.2016.06.010It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge–Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and Tse and independently by Chartier and Murua that no B-Series method can be volume preserving for all volume preserving vector fields. In this paper, we show that despite this result, symplectic Runge–Kutta methods can be volume preserving for a much larger class of vector fields than Hamiltonian systems, and discuss how some Runge–Kutta methods can preserve a modified measure exactly.This research was supported by the Marie Curie International Research Staff Exchange Scheme, grant number DP140100640, within the 7th European Community Framework Programme; by the Australian Research Council grant number 269281; and by the UK Engineering and Physical Sciences Research Council grant EP/H023348/1 for the Cambridge Centre for Analysis

Molecular alignment relaxation in polymer optical fibers for sensing applications

A systematic study of annealing behavior of drawn PMMA fibers was performed. Annealing dynamics were investigated under different environmental conditions by fiber longitudinal shrinkage monitoring. The shrinkage process was found to follow a stretched exponential decay function revealing the heterogeneous nature of the underlying molecular dynamics. The complex dependence of the fiber shrinkage on initial degree of molecular alignment in the fiber, annealing time and temperature was investigated and interpreted. Moreover, humidity was shown to have a profound effect on the annealing process, which was not recognized previously. Annealing was also shown to have considerable effect on the fiber mechanical properties associated with the relaxation of molecular alignment in the fiber. The consequences of fiber annealing for the climatic stability of certain polymer optical fiber-based sensors are discussed, emphasizing the importance of fiber controlled pre-annealing with respect to the foreseeable operating conditions

A population of gamma-ray emitting globular clusters seen with the Fermi Large Area Telescope

Globular clusters with their large populations of millisecond pulsars (MSPs) are believed to be potential emitters of high-energy gamma-ray emission. Our goal is to constrain the millisecond pulsar populations in globular clusters from analysis of gamma-ray observations. We use 546 days of continuous sky-survey observations obtained with the Large Area Telescope aboard the Fermi Gamma-ray Space Telescope to study the gamma-ray emission towards 13 globular clusters. Steady point-like high-energy gamma-ray emission has been significantly detected towards 8 globular clusters. Five of them (47 Tucanae, Omega Cen, NGC 6388, Terzan 5, and M 28) show hard spectral power indices $(0.7 < \Gamma <1.4)$ and clear evidence for an exponential cut-off in the range 1.0-2.6 GeV, which is the characteristic signature of magnetospheric emission from MSPs. Three of them (M 62, NGC 6440 and NGC 6652) also show hard spectral indices $(1.0 < \Gamma < 1.7)$, however the presence of an exponential cut-off can not be unambiguously established. Three of them (Omega Cen, NGC 6388, NGC 6652) have no known radio or X-ray MSPs yet still exhibit MSP spectral properties. From the observed gamma-ray luminosities, we estimate the total number of MSPs that is expected to be present in these globular clusters. We show that our estimates of the MSP population correlate with the stellar encounter rate and we estimate 2600-4700 MSPs in Galactic globular clusters, commensurate with previous estimates. The observation of high-energy gamma-ray emission from a globular cluster thus provides a reliable independent method to assess their millisecond pulsar populations that can be used to make constraints on the original neutron star X-ray binary population, essential for understanding the importance of binary systems in slowing the inevitable core collapse of globular clusters.Comment: Accepted for publication in A&A. Corresponding authors: J. Kn\"odlseder, N. Webb, B. Pancraz

Random Matrix Theories in Quantum Physics: Common Concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.Comment: 178 pages, Revtex, 45 figures, submitted to Physics Report

Effect on Adherence to Nicotine Replacement Therapy of Informing Smokers Their Dose Is Determined by Their Genotype: A Randomised Controlled Trial

BACKGROUND: The behavioural impact of pharmacogenomics is untested. We tested two hypotheses concerning the behavioural impact of informing smokers their oral dose of NRT is tailored to analysis of DNA. METHODS AND FINDINGS: We conducted an RCT with smokers in smoking cessation clinics (N = 633). In combination with NRT patch, participants were informed that their doses of oral NRT were based either on their mu-opioid receptor (OPRM1) genotype, or their nicotine dependence questionnaire score (phenotype). The proportion of prescribed NRT consumed in the first 28 days following quitting was not significantly different between groups: (68.5% of prescribed NRT consumed in genotype vs 63.6%, phenotype group, difference = 5.0%, 95% CI -0.9,10.8, p = 0.098). Motivation to make another quit attempt among those (n = 331) not abstinent at six months was not significantly different between groups (p = 0.23). Abstinence at 28 days was not different between groups (p = 0.67); at six months was greater in genotype than phenotype group (13.7% vs 7.9%, difference = 5.8%, 95% CI 1.0,10.7, p = 0.018). CONCLUSIONS: Informing smokers their oral dose of NRT was tailored to genotype not phenotype had a small, statistically non-significant effect on 28-day adherence to NRT. Among those still smoking at six months, there was no evidence that saying NRT was tailored to genotype adversely affected motivation to make another quit attempt. Higher abstinence rate at six months in the genotype arm requires investigation. TRIAL REGISTRATION: Controlled-Trials.com ISRCTN14352545.</p

Recruitment and retention of women in a large randomized control trial to reduce repeat preterm births: the Philadelphia Collaborative Preterm Prevention Project

<p>Abstract</p> <p>Background</p> <p>Recruitment and retention of patients for randomized control trial (RCT) studies can provide formidable challenges, particularly with minority and underserved populations. Data are reported for the Philadelphia Collaborative Preterm Prevention Project (PCPPP), a large RCT targeting risk factors for repeat preterm births among women who previously delivered premature (< 35 weeks gestation) infants.</p> <p>Methods</p> <p>Design of the PCPPP incorporated strategies to maximize recruitment and retention. These included an advanced database system tracking follow-up status and assessment completion rates; cultural sensitivity training for staff; communication to the community and eligible women of the benefits of participation; financial incentives; assistance with transportation and supervised childcare services; and reminder calls for convenient, flexibly scheduled appointments. Analyses reported here: 1) compare recruitment projections to actual enrollment 2) explore recruitment bias; 3) validate the randomization process 4) document the extent to which contact was maintained and complete assessments achieved 5) determine if follow-up was conditioned upon socio-economic status, race/ethnicity, or other factors.</p> <p>Results</p> <p>Of eligible women approached, 1,126 (77.7%) agreed to participate fully. Of the 324 not agreeing, 118 (36.4%) completed a short survey. Consenting women were disproportionately from minority and low SES backgrounds: 71.5% consenting were African American, versus 38.8% not consenting. Consenting women were also more likely to report homelessness during their lifetime (14.6% vs. 0.87%) and to be unmarried at the time of delivery (81.6% versus 47.9%). First one-month postpartum assessment was completed for 83.5% (n = 472) of the intervention group (n = 565) and 76% (426) of the control group. Higher assessment completion rates were observed for the intervention group throughout the follow-up. Second, third, fourth and fifth postpartum assessments were 67.6% vs. 57.5%, 60.0% vs. 48.9%, 54.2% vs. 46.3% and 47.3% vs. 40.8%, for the intervention and control group women, respectively. There were no differences in follow-up rates according to race/ethnicity, SES or other factors. Greater retention of the intervention group may reflect the highly-valued nature of the medical and behavior services constituting the intervention arms of the Project.</p> <p>Conclusion</p> <p>Findings challenge beliefs that low income and minority women are averse to enrolling and continuing in clinical trials or community studies.</p

Global collision-risk hotspots of marine traffic and the world’s largest fish, the whale shark

© The Author(s), 2022. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Womersley, F. C., Humphries, N. E., Queiroz, N., Vedor, M., da Costa, I., Furtado, M., Tyminski, J. P., Abrantes, K., Araujo, G., Bach, S. S., Barnett, A., Berumen, M. L., Bessudo Lion, S., Braun, C. D., Clingham, E., Cochran, J. E. M., de la Parra, R., Diamant, S., Dove, A. D. M., Dudgeon, C. L., Erdmann, M. V., Espinoza, E., Fitzpatrick, R., González Cano, J., Green, J. R., Guzman, H. M., Hardenstine, R., Hasan, A., Hazin, F. H. V., Hearn, A. R., Hueter, R. E., Jaidah, M. Y., Labaja, J., Ladinol, F., Macena, B. C. L., Morris Jr., J. J., Norman, B. M., Peñaherrera-Palmav, C., Pierce, S. J., Quintero, L. M., Ramırez-Macías, D., Reynolds, S. D., Richardson, A. J., Robinson, D. P., Rohner, C. A., Rowat, D. R. L., Sheaves, M., Shivji, M. S., Sianipar, A. B., Skomal, G. B., Soler, G., Syakurachman, I., Thorrold, S. R., Webb, D. H., Wetherbee, B. M., White, T. D., Clavelle, T., Kroodsma, D. A., Thums, M., Ferreira, L. C., Meekan, M. G., Arrowsmith, L. M., Lester, E. K., Meyers, M. M., Peel, L. R., Sequeira, A. M. M., Eguıluz, V. M., Duarte, C. M., & Sims, D. W. Global collision-risk hotspots of marine traffic and the world’s largest fish, the whale shark. Proceedings of the National Academy of Sciences of the United States of America, 119(20), (2022): e2117440119, https://doi.org/10.1073/pnas.2117440119.Marine traffic is increasing globally yet collisions with endangered megafauna such as whales, sea turtles, and planktivorous sharks go largely undetected or unreported. Collisions leading to mortality can have population-level consequences for endangered species. Hence, identifying simultaneous space use of megafauna and shipping throughout ranges may reveal as-yet-unknown spatial targets requiring conservation. However, global studies tracking megafauna and shipping occurrences are lacking. Here we combine satellite-tracked movements of the whale shark, Rhincodon typus, and vessel activity to show that 92% of sharks’ horizontal space use and nearly 50% of vertical space use overlap with persistent large vessel (>300 gross tons) traffic. Collision-risk estimates correlated with reported whale shark mortality from ship strikes, indicating higher mortality in areas with greatest overlap. Hotspots of potential collision risk were evident in all major oceans, predominantly from overlap with cargo and tanker vessels, and were concentrated in gulf regions, where dense traffic co-occurred with seasonal shark movements. Nearly a third of whale shark hotspots overlapped with the highest collision-risk areas, with the last known locations of tracked sharks coinciding with busier shipping routes more often than expected. Depth-recording tags provided evidence for sinking, likely dead, whale sharks, suggesting substantial “cryptic” lethal ship strikes are possible, which could explain why whale shark population declines continue despite international protection and low fishing-induced mortality. Mitigation measures to reduce ship-strike risk should be considered to conserve this species and other ocean giants that are likely experiencing similar impacts from growing global vessel traffic.Funding for data analysis was provided by the UK Natural Environment Research Council (NERC) through a University of Southampton INSPIRE DTP PhD Studentship to F.C.W. Additional funding for data analysis was provided by NERC Discovery Science (NE/R00997/X/1) and the European Research Council (ERC-AdG-2019 883583 OCEAN DEOXYFISH) to D.W.S., Fundação para a Ciência e a Tecnologia (FCT) under PTDC/BIA/28855/2017 and COMPETE POCI-01–0145-FEDER-028855, and MARINFO–NORTE-01–0145-FEDER-000031 (funded by Norte Portugal Regional Operational Program [NORTE2020] under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund–ERDF) to N.Q. FCT also supported N.Q. (CEECIND/02857/2018) and M.V. (PTDC/BIA-COM/28855/2017). D.W.S. was supported by a Marine Biological Association Senior Research Fellowship. All tagging procedures were approved by institutional ethical review bodies and complied with all relevant ethical regulations in the jurisdictions in which they were performed. Details for individual research teams are given in SI Appendix, section 8. Full acknowledgments for tagging and field research are given in SI Appendix, section 7. This research is part of the Global Shark Movement Project (https://www.globalsharkmovement.org)

Analyses of germline variants associated with ovarian cancer survival identify functional candidates at the 1q22 and 19p12 outcome loci.

We previously identified associations with ovarian cancer outcome at five genetic loci. To identify putatively causal genetic variants and target genes, we prioritized two ovarian outcome loci (1q22 and 19p12) for further study. Bioinformatic and functional genetic analyses indicated that MEF2D and ZNF100 are targets of candidate outcome variants at 1q22 and 19p12, respectively. At 19p12, the chromatin interaction of a putative regulatory element with the ZNF100 promoter region correlated with candidate outcome variants. At 1q22, putative regulatory elements enhanced MEF2D promoter activity and haplotypes containing candidate outcome variants modulated these effects. In a public dataset, MEF2D and ZNF100 expression were both associated with ovarian cancer progression-free or overall survival time. In an extended set of 6,162 epithelial ovarian cancer patients, we found that functional candidates at the 1q22 and 19p12 loci, as well as other regional variants, were nominally associated with patient outcome; however, no associations reached our threshold for statistical significance (p<1×10-5). Larger patient numbers will be needed to convincingly identify any true associations at these loci.The OCAC Oncoarray genotyping project was funded through grants from the U.S. National Institutes of Health 2 (NIH) (CA1X01HG007491-01, U19-CA148112, R01-CA149429 and R01-CA058598); Canadian Institutes of Health 3 Research (MOP-86727) and the Ovarian Cancer Research Fund (OCRF). Funding for the iCOGS infrastructure came from: the European Community’s Seventh Framework Programme under grant agreement n° 223175 (HEALTH-F2-2009-223175) (COGS), Cancer Research UK (C1287/A10118, C1287/A 10710, C12292/A11174, C1281/A12014, C5047/A8384, C5047/A15007, C5047/A10692, C8197/A16565), the National Institutes of Health (CA128978) and Post-Cancer GWAS initiative (1U19 CA148537, 1U19 CA148065 and 1U19 CA148112 - the GAME-ON initiative), the Department of Defence (W81XWH-10-1-0341), the Canadian Institutes of Health Research (CIHR) for the CIHR Team in Familial Risks of Breast Cancer, Komen Foundation for the Cure, the Breast Cancer Research Foundation, and the Ovarian Cancer Research Fund. AUS studies (Australian Ovarian Cancer Study and the Australian Cancer Study) were funded by the U.S. Army Medical Research and Materiel Command (DAMD17-01-1-0729), National Health & Medical Research Council of Australia (199600 and 400281), Cancer Councils of New South Wales, Victoria, Queensland, South Australia and Tasmania, Cancer Foundation of Western Australia (Multi-State Application Numbers 191, 211 and 182). The Bavarian study (BAV) was supported by ELAN Funds of the University of Erlangen-Nuremberg. The Belgian study (BEL) was funded by Nationaal Kankerplan. The BVU study was funded by Vanderbilt CTSA grant from the National Institutes of Health (NIH)/National Center for Advancing Translational Sciences (NCATS) (ULTR000445). The CNIO Ovarian Cancer Study (CNI) study was supported by Instituto de Salud Carlos III (PI 12/01319); Ministerio de Economía y Competitividad (SAF2012). The Hawaii Ovarian Cancer Study (HAW) was supported the U.S. National Institutes of Health (R01-CA58598, N01-CN-55424 and N01-PC-67001). The Hannover-Jena Ovarian Cancer Study (HJO) study was funded by intramural funding through the Rudolf-Bartling Foundation. The Hormones and Ovarian Cancer Prediction study (HOP) was supported by US National Cancer Institute: K07-CA80668; R01CA095023; P50-CA159981; R01-CA126841; US Army Medical Research and Materiel Command: DAMD17-02-1-0669; NIH/National Center for Research Resources/General Clinical Research Center grant MO1- RR000056. The Women’s Cancer Program (LAX) was supported by the American Cancer Society Early Detection Professorship (120950-SIOP-06-258-06-COUN) and the National Center for Advancing Translational Sciences (NCATS), Grant UL1TR000124. The Mayo Clinic Case-Only Ovarian Cancer Study (MAC) and the Mayo Clinic Ovarian Cancer Case-Control Study (MAY) were funded by the National Institutes of Health (R01-CA122443, P30-CA15083, P50-CA136393); Mayo Foundation; Minnesota Ovarian Cancer Alliance; Fred C. and Katherine B. Andersen Foundation; Fraternal Order of Eagles. The MALOVA study (MAL) was funded by research grant R01- CA61107 from the National Cancer Institute, Bethesda, Md; research grant 94 222 52 from the Danish Cancer Society, Copenhagen, Denmark; and the Mermaid I project. The North Carolina Ovarian Cancer Study (NCO) National Institutes of Health (R01-CA76016) and the Department of Defense (DAMD17-02-1-0666). The New England-based Case-Control Study of Ovarian Cancer (NEC) was supported by NIH grants R01 CA 054419-10 and P50 CA105009, and Department of Defense CDMRP grant W81XWH-10-1-0280. The University of Bergen, Haukeland University Hospital, Norway study (NOR) was funded by Helse Vest, The Norwegian Cancer Society, The Research Council of Norway. The Oregon study (ORE) was funded by the Sherie Hildreth Ovarian Cancer Research Fund and the OHSU Foundation. The Ovarian Cancer Prognosis and Lifestyle Study (OPL) was funded by National Health and Medical Research Council (NHMRC) of Australia (APP1025142) and Brisbane Women’s Club. The Danish Pelvic Mass Study (PVD) was funded by Herlev Hospitals Forskningsråd, Direktør Jacob Madsens og Hustru Olga Madsens fond, Arvid Nilssons fond, Gangsted fonden, Herlev Hospitals Forskningsråd and Danish Cancer Society. The Royal Brisbane Hospital (RBH) study was funded by the National Health and Medical Research Council of Australia. The Scottish Randomised Trial in Ovarian Cancer study (SRO) was funded by Cancer Research UK (C536/A13086, C536/A6689) and Imperial Experimental Cancer Research Centre (C1312/A15589). The Princess Margaret Cancer Centre study (UHN) was funded by Princess Margaret Cancer Centre Foundation-Bridge for the Cure. The Gynaecological Oncology Biobank at Westmead (WMH) is a member of the Australasian Biospecimen Network-Oncology group, funded by the Australian National Health and Medical Research Council Enabling Grants ID 310670 & ID 628903 and the Cancer Institute NSW Grants ID 12/RIG/1-17 and 15/RIG/1-16. OVCARE Gynecologic Tissue Bank and Outcomes Unit (VAN) study was funded by BC Cancer Foundation, VGH & UBC Hospital Foundation. Stuart MacGregor acknowledges funding from an Australian Research Council Future Fellowship and an Australian National Health and Medical Research Council project grant (APP1051698). Anna deFazio was funded by the University of Sydney Cancer Research Fund and the Cancer Institute NSW through the Sydney West-Translational Cancer Research Centre. Dr. Beth Y. Karlan is supported by American Cancer Society Early Detection Professorship (SIOP-06-258-01-COUN) and the National Center for Advancing Translational Sciences (NCATS), Grant UL1TR000124. Irene Orlow was supported by NCI CCSG award (P30-CA008748). GCT, PW and TO’M were funded by NHMRC Fellowships

REQUITE: A prospective multicentre cohort study of patients undergoing radiotherapy for breast, lung or prostate cancer

Purpose: REQUITE aimed to establish a resource for multi-national validation of models and biomarkers that predict risk of late toxicity following radiotherapy. The purpose of this article is to provide summary descriptive data. Methods: An international, prospective cohort study recruited cancer patients in 26 hospitals in eight countries between April 2014 and March 2017. Target recruitment was 5300 patients. Eligible patients had breast, prostate or lung cancer and planned potentially curable radiotherapy. Radiotherapy was prescribed according to local regimens, but centres used standardised data collection forms. Pre-treatment blood samples were collected. Patients were followed for a minimum of 12 (lung) or 24 (breast/prostate) months and summary descriptive statistics were generated. Results: The study recruited 2069 breast (99% of target), 1808 prostate (86%) and 561 lung (51%) cancer patients. The centralised, accessible database includes: physician-(47,025 forms) and patient-(54,901) reported outcomes; 11,563 breast photos; 17,107 DICOMs and 12,684 DVHs. Imputed genotype data are available for 4223 patients with European ancestry (1948 breast, 1728 prostate, 547 lung). Radiation-induced lymphocyte apoptosis (RILA) assay data are available for 1319 patients. DNA (n = 4409) and PAXgene tubes (n = 3039) are stored in the centralised biobank. Example prevalences of 2-year (1-year for lung) grade >= 2 CTCAE toxicities are 13% atrophy (breast), 3% rectal bleeding (prostate) and 27% dyspnoea (lung). Conclusion: The comprehensive centralised database and linked biobank is a valuable resource for the radiotherapy community for validating predictive models and biomarkers. Patient summary: Up to half of cancer patients undergo radiation therapy and irradiation of surrounding healthy tissue is unavoidable. Damage to healthy tissue can affect short-and long-term quality-of-life. Not all patients are equally sensitive to radiation "damage" but it is not possible at the moment to identify those who are. REQUITE was established with the aim of trying to understand more about how we could predict radiation sensitivity. The purpose of this paper is to provide an overview and summary of the data and material available. In the REQUITE study 4400 breast, prostate and lung cancer patients filled out questionnaires and donated blood. A large amount of data was collected in the same way. With all these data and samples a database and biobank were created that showed it is possible to collect this kind of information in a standardised way across countries. In the future, our database and linked biobank will be a resource for research and validation of clinical predictors and models of radiation sensitivity. REQUITE will also enable a better understanding of how many people suffer with radiotherapy toxicity