Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

Variations of the FEAST Eigenvalue Algorithm

FEAST is a recently developed eigenvalue algorithm which computes selected interior eigenvalues of real symmetric matrices. It uses contour integral resolvent based projections. A weakness is that the existing algorithm relies on accurate reasoned estimates of the number of eigenvalues within the contour. Examining the singular values of the projections on moderately-sized, randomly-generated test problems motivates orthogonalization-based improvements to the algorithm. The singular value distributions provide experimentally robust estimates of the number of eigenvalues within the contour. The algorithm is modified to handle both Hermitian and general complex matrices. The original algorithm (based on circular contours and Gauss-Legendre quadrature) is extended to contours and quadrature schemes that are recursively subdividable. A general complex recursive algorithm is implemented on rectangular and diamond contours. The accuracy of different quadrature schemes for various contours is investigated.

Detection of cryptic pathogenic copy number variations and constitutional loss of heterozygosity using high resolution SNP microarray analysis in 117 patients referred for cytogenetic analysis and impact on clinical practice

BACKGROUND: Microarray genome analysis is realising its promise for improving detection of genetic abnormalities in individuals with mental retardation and congenital abnormality. Copy number variations (CNVs) are now readily detectable using a variety of platforms and a major challenge is the distinction of pathogenic from ubiquitous, benign polymorphic CNVs. The aim of this study was to investigate replacement of time consuming, locus specific testing for specific microdeletion and microduplication syndromes with microarray analysis, which theoretically should detect all known syndromes with CNV aetiologies as well as new ones. METHODS: Genome wide copy number analysis was performed on 117 patients using Affymetrix 250K microarrays. RESULTS: 434 CNVs (195 losses and 239 gains) were found, including 18 pathogenic CNVs and 9 identified as "potentially pathogenic". Almost all pathogenic CNVs were larger than 500 kb, significantly larger than the median size of all CNVs detected. Segmental regions of loss of heterozygosity larger than 5 Mb were found in 5 patients. CONCLUSIONS: Genome microarray analysis has improved diagnostic success in this group of patients. Several examples of recently discovered "new syndromes" were found suggesting they are more common than previously suspected and collectively are likely to be a major cause of mental retardation. The findings have several implications for clinical practice. The study revealed the potential to make genetic diagnoses that were not evident in the clinical presentation, with implications for pretest counselling and the consent process. The importance of contributing novel CNVs to high quality databases for genotype-phenotype analysis and review of guidelines for selection of individuals for microarray analysis is emphasised.

Antigenic and genetic variations in European and North American equine influenza virus strains (H3N8) isolated from 2006 to 2007

Equine influenza virus (EIV) surveillance is important in the management of equine influenza. It provides data on circulating and newly emerging strains for vaccine strain selection. To this end, antigenic characterisation by haemaggluttination inhibition (HI) assay and phylogenetic analysis was carried out on 28 EIV strains isolated in North America and Europe during 2006 and 2007. In the UK, 20 viruses were isolated from 28 nasopharyngeal swabs that tested positive by enzyme-linked immunosorbent assay. All except two of the UK viruses were characterised as members of the Florida sublineage with similarity to A/eq/Newmarket/5/03 (clade 2). One isolate, A/eq/Cheshire/1/06, was characterised as an American lineage strain similar to viruses isolated up to 10 years earlier. A second isolate, A/eq/Lincolnshire/1/07 was characterised as a member of the Florida sublineage (clade 1) with similarity to A/eq/Wisconsin/03. Furthermore, A/eq/Lincolnshire/1/06 was a member of the Florida sublineage (clade 2) by haemagglutinin (HA) gene sequence, but appeared to be a member of the Eurasian lineage by the non-structural gene (NS) sequence suggesting that reassortment had occurred. A/eq/Switzerland/P112/07 was characterised as a member of the Eurasian lineage, the first time since 2005 that isolation of a virus from this lineage has been reported. Seven viruses from North America were classified as members of the Florida sublineage (clade 1), similar to A/eq/Wisconsin/03. In conclusion, a variety of antigenically distinct EIVs continue to circulate worldwide. Florida sublineage clade 1 viruses appear to predominate in North America, clade 2 viruses in Europe.

Evidence for past variations in methane availability in a Siberian thermokarst lake based on δ13C of chitinous invertebrate remains

Understanding past methane dynamics in arctic wetlands and lakes is crucial for estimating future methane release. Methane fluxes from lake ecosystems have increasingly been studied, yet only few reconstructions of past methane emissions from lakes are available. In this study, we develop an approach to assess changes in methane availability in lakes based on δ13C of chitinous invertebrate remains and apply this to a sediment record from a Siberian thermokarst lake. Diffusive methane fluxes from the surface of ten newly sampled Siberian lakes and seven previously studied Swedish lakes were compared to taxon-specific δ13C values of invertebrate remains from lake surface sediments to investigate whether these invertebrates assimilated 13C-depleted carbon typical for methane. Remains of chironomid larvae of the tribe Orthocladiinae that, in the study lakes, mainly assimilate plant-derived carbon had higher δ13C than other invertebrate groups. δ13C of other invertebrates such as several chironomid groups (Chironomus, Chironomini, Tanytarsini, and Tanypodinae), cladocerans (Daphnia), and ostracods were generally lower. δ13C of Chironomini and Daphnia, and to a lesser extent Tanytarsini was variable in the lakes and lower at sites with higher diffusive methane fluxes. δ13C of Chironomini, Tanytarsini, and Daphnia were correlated significantly with diffusive methane flux in the combined Siberian and Swedish dataset (r = −0.72, p = 0.001, r = −0.53, p = 0.03, and r = −0.81, p < 0.001, respectively), suggesting that δ13C in these invertebrates was affected by methane availability. In a second step, we measured δ13C of invertebrate remains from a sediment record of Lake S1, a shallow thermokarst lake in northeast Siberia. In this record, covering the past ca 1000 years, δ13C of taxa most sensitive to methane availability (Chironomini, Tanytarsini, and Daphnia) was lowest in sediments deposited from ca AD 1250 to ca AD 1500, and after AD 1970, coinciding with warmer climate as indicated by an independent local temperature record. As a consequence the offset in δ13C between methane-sensitive taxa and bulk organic matter was higher in these sections than in other parts of the core. In contrast, δ13C of other invertebrate taxa did not show this trend. Our results suggest higher methane availability in the study lake during warmer periods and that thermokarst lakes can respond dynamically in their methane output to changing environmental conditions.

Social and regional variations in health status and health behaviours among Swiss young adults

OBJECTIVE To provide nationwide data on health status and health behaviours among young adults in Switzerland, and to illustrate social and regional variations. METHODS Data came from the Swiss Federal Surveys of Adolescents, conducted in 2010/11. The sample consisted of 32,424 young men and 1,467 young women. We used logistic regression models to examine patterns of social inequality for three measures of health status and three measures of health behaviour. RESULTS Among men, lower self-rated health, overweight and lower physical fitness levels were associated with lower educational and fewer financial resources. Patterns were similar among young women. Unfavourable self-rated health (odds ratio [OR]: men 0.83, women 0.75) and overweight (OR: men 0.84, women 0.85; p >0.05) were less common in the French- than in the German-language region. Low physical fitness was more common in the French- than in the German-language region. In both sexes, daily smoking was associated with fewer educational resources, and physical inactivity was associated with lower educational and fewer financial resources. Males from the Italian-language region were three times more likely to be physically inactive than their German-speaking counterparts (OR 2.95). Risk drinking was more widespread among males in the French- than in the German-speaking language region (OR 1.47). CONCLUSIONS Striking social and moderate regional differences exist in health status and health behaviours among young Swiss males and females. The current findings offer new empirical evidence on social determinants of health in Switzerland and suggest education, material resources and regional conditions to be addressed in public health practice and in more focused future research.

THE SOLAR WIND AS A POSSIBLE SOURCE OF FAST TEMPORAL VARIATIONS OF THE HELIOSPHERIC RIBBON

We present a possible source of pickup ions (PUIs) the ribbon observed by the Interstellar Boundary EXplorer (IBEX). We suggest that a gyrating solar wind and PUIs in the ramp and in the near downstream region of the termination shock (TS) could provide a significant source of energetic neutral atoms (ENAs) in the ribbon. A fraction of the solar wind and PUIs are reflected and energized during the first contact with the TS. Some of the solar wind may be reflected propagating toward the Sun but most of the solar wind ions form a gyrating beam-like distribution that persists until it is fully thermalized further downstream. Depending on the strength of the shock, these gyrating distributions can exist for many gyration periods until they are scattered/thermalized due to wave-particle interactions at the TS and downstream in the heliosheath. During this time, ENAs can be produced by charge exchange of interstellar neutral atoms with the gyrating ions. In order to determine the flux of energetic ions, we estimate the solar wind flux at the TS using pressure estimates inferred from in situ measurements. Assuming an average path length in the radial direction of the order of a few AU before the distribution of gyrating ions is thermalized, one can explain a significant fraction of the intensity of ENAs in the ribbon observed by IBEX. With a localized source and such a short integration path, this model would also allow fast time variations of the ENA flux.