VictorJuiz/thesis huggingface dataset:
Numerical methods for approximating solutions to rough differential equations
Keywords: rough differential equation
rough paths
numerical solution
cubature
Stochastic differential equations
Wiener space
weak approximation

The main motivation behind writing this thesis was to construct numerical methods to approximate solutions to differential equations driven by rough paths, where the solution is considered in the rough path-sense. Rough paths of inhomogeneous degree of smoothness as driving noise are considered. We also aimed to find applications of these numerical methods to stochastic differential equations.
After sketching the core ideas of the Rough Paths Theory in Chapter 1, the versions of the core theorems corresponding to the inhomogeneous degree of smoothness case are stated and proved in Chapter 2 along with some auxiliary claims on the continuity of the solution in a certain sense, including an RDE-version of Gronwall's lemma.
In Chapter 3, numerical schemes for approximating solutions to differential equations driven by rough paths of inhomogeneous degree of smoothness are constructed. We start with setting up some principles of approximations. Then a general class of local approximations is introduced. This class is used to construct global approximations by pasting together the local ones. A general sufficient condition on the local approximations implying global convergence is given and proved. The next step is to construct particular local approximations in finite dimensions based on solutions to ordinary differential equations derived locally and satisfying the sufficient condition for global convergence. These local approximations require strong conditions on the one-form defining the rough differential equation. Finally, we show that when the local ODE-based schemes are applied in combination with rough polynomial approximations, the conditions on the one-form can be weakened.
In Chapter 4, the results of Gyurko & Lyons (2010) on path-wise approximation of solutions to stochastic differential equations are recalled and extended to the truncated signature level of the solution. Furthermore, some practical considerations related to the implementation of high order schemes are described. The effectiveness of the derived schemes is demonstrated on numerical examples.
In Chapter 5, the background theory of the Kusuoka-Lyons-Victoir (KLV) family of weak approximations is recalled and linked to the results of Chapter 4. We highlight how the different versions of the KLV family are related. Finally, a numerical evaluation of the autonomous ODE-based versions of the family is carried out, focusing on SDEs in dimensions up to 4, using cubature formulas of different degrees and several high order numerical ODE solvers. We demonstrate the effectiveness and the occasional non-effectiveness of the numerical approximations in cases when the KLV family is used in its original version and also when used in combination with partial sampling methods (Monte-Carlo, TBBA) and Romberg extrapolation.
Mechanisms of Type 2 diabetes susceptibility
Keywords: Genome-wide association
Complex Disease Genetics
Type 2 Diabetes

Type 2 diabetes (T2D) has a genetic component which is only partially understood. The majority of genetic variance in disease susceptibility is unaccounted for, whilst the precise transcripts and molecular mechanisms through which most risk variants exert their effect is unclear. A complete understanding of T2D susceptibility mechanisms could have benefits in risk prediction, and in drug discovery through the identification of novel therapeutic targets. Work presented in this thesis aims to define relevant transcripts and disease mechanisms at known susceptibility loci, and to identify disease association with classes of genetic variation other than common single nucleotide polymorphisms (SNPs).
KCNQ1 contains intronic variants associated with T2D susceptibility and β-cell dysfunction, but only maternally-inherited alleles confer increased disease risk. It maps within an imprinted domain with an established role in congenital and islet-specific growth phenotypes. Using human adult islet and foetal pancreas samples, I refined the transcripts and developmental stage at which T2D susceptibility must be conferred by demonstrating developmentally plastic monoallelic and biallelic expression. I identified a potential risk mechanism through the effect of T2D risk alleles upon DNA methylation.
The disease-associated regions identified through genome-wide association (GWA) studies often contain multiple transcripts. I performed mRNA expression profiling of genes within loci associated with raised proinsulin/insulin ratios in human islets and metabolically relevant tissues. Some genes (notably CT62) were not expressed and therefore excluded from consideration for a risk effect, whilst others (for example C2CD4A) were highlighted as good regional candidates due to specific expression in relevant tissues.
GWA studies for T2D risk have focused predominantly upon common single nucleotide polymorphisms. As part of a consortium conducing GWA analysis for copy number variation (CNV) and T2D risk, I optimised and compared alternative methods of CNV genotyping, before using this information to validate two signals of disease association. I genotyped three rare single nucleotide variants emerging from an association study with T2D risk based on imputed data, providing an indication of imputation accuracy and more powerful disease association analysis.
These data underscore the challenge of translating association signals to causal mechanisms, and of identifying alternative forms of genomic variation which contribute to T2D risk. My work highlights candidates for functional analysis around proinsulin-associated loci, and makes significant progress towards uncovering risk mechanisms at the KCNQ1 locus.
Deictic categories in Toda Sedeq (Austronesian, Taiwan)
Keywords: deixis
time
Sedeq
person
place
Atayalic
Austronesian
linguistics
grammar
Taiwan

The purpose of this account of how deixis is encoded in Toda Sedeq, an Austronesian language indigenous to Taiwan, is two-fold; to contribute to 1) the description of a completely neglected dialect of a poorly understood language which faces language replacement and is in urgent need of description and 2) the theoretical understanding of deixis.
From a theoretical standpoint, deixis has five categories, with a hierarchy as to which are most often represented in various language phenomena, viz.,: 1) ‘space’, 2) ‘person’, 3) ‘time’, 4) ‘social relations’ and 5) ‘discourse’ (in descending order). This hierarchy helps explain numbers of phenomena representing each category in the grammar of a given language, and also how likely a given category is to serve as the ‘template’ for combinations with other categories (e.g., ‘space’ is a template for ‘spatio-personal deixis’).
For the target language, the categories are represented by numbers of phenomena that support the following hierarchy: 1) the most, with 2)-3) following, and practically nothing for 4)-5). Additionally, for two-way category combinations, 1) space was found to combine with all other categories, but 2) person with only two and the other three categories with none at all - also in keeping with the hierarchy. Finally, in the only triple category combination (spatio-personal-temporal deixis), categories 1) - 3) were all found to play important roles.
The Sedeq deictic morphemes work in groups rather than independently (seven morphemes are combined into eight groups, each of which forms a grammatical subsystem, with multiple membership for all morphemes).
The five-category deixis, category combinations, and morpheme grouping models have resulted in what I believe accounts for the deictic phenomena of the language more completely than any previous attempt. It also has implications for theoretical linguistics and raises questions to be addressed in the future description of other languages.
The activities of various antimalarial drugs on Plasmodium falciparum isolates in Kilifi Kenya and studies on mechanisms of resistance
Keywords: genomics
molecular markers
public health
drug resistance
malaria
pharmacology

Drug resistance is a significant challenge in the fight against malaria. Importantly, reduced efficacy has been reported against artemether (ATM)/Lumefantrine (LM) (LM-ATM), amodiaquine (AQ)/artesunate (AS) (AQ-AS), two important combination treatment regimens in Africa, and against piperaquine (PQ), a drug which has been evaluated as a potential alternative in Africa, in combination with dihydroarteminisin (DHA). Chloroquine (CQ) resistance in P.falciparum is associated with two main transporters PfCRT and PfMDR1. I investigated the mechanisms of resistance to PQ, LM and AQ, with the overall goal of identifying molecular markers that can be used to track resistance. I used CQ as a reference.
The key antimalarial drugs were highly active against clinical isolates from Kilifi, Kenya with median inhibitory concentrations (IC50s) of <5nM for DHA and <55 nM for CQ, AQ, PQ, LM and DEAQ (desethylamodiaquine, the active metabolite of AQ). pfcrt-76 and pfmdr1-86 mutations were associated with AQ, DEAQ and LM but not DHA or PQ activity. Interestingly, > 20% of analysed isolates had decreased susceptibility to LM (IC50 >100nM); these isolates were the most susceptible to CQ and carried wild type genotypes at pfcrt-76 and pfmdr1-86. I observed that CQ resistance had been declining in Kilifi since 1993 (prior to CQ withdrawal) to 2006 (7 years after its withdrawal), similar to observations in Malawi. My results support the hypothesis that susceptibility to antimalarial drugs returns when drug pressure is removed, and suggest that the use of LM-ATM may hasten the return of CQ susceptibility.
Continued monitoring of drug susceptibility is crucial. pfcrt-76 and pfmdr1-86 may be useful molecular markers of LM-ATM efficacy in Kilifi and other African sites. Using a microarray approach, I identified additional genes (including various transporters) that may contribute to LM resistance. I recommend further studies to clarify the exact roles of the identified genes.
Cardiosphere-derived stem cell culture, characterisation and labelling for in vivo testing in the infarcted heart
Keywords: extracellular matrix
myocardial infarction
cardiospheres
Cardiac stem cells

Cardiac stem cells (CSCs), isolated from heart tissue explants and expanded via the formation of cardiospheres (Csp), are a promising candidate for cell therapy to prevent heart failure following myocardial infarction. To allow early administration to patients, isolation and expansion of CSCs must be performed in the shortest time possible. Hence, this project aimed to optimize culture conditions and characterize the cardiac explant-derived cells (EDCs), Csp and Csp-derived cells (CDCs) produced. Rat neonatal EDCs contained 4-7% c-kit+ cells, measured using flow cytometry. Optimal Csp growth conditions were determined, such that plating 3 x 10^4 EDCs per well of a 24-well plate coated with 16.7 µg/ml poly-D-lysine, in CGM containing 7% serum, improved Csp production and generated 1.5 x 10^7 CDCs in 16 days, a sufficient number for cell therapy. The CDCs expressed the stemness markers; c-kit, Oct3/4, SOX2, and Klf-4, and the cardiac differentiation markers; GATA4 and Nkx2.5. The therapeutic effect of CDCs may be limited by the low, 3 ± 0.1%, c-kit+ cell numbers. To increase c-kit+ cells in CDCs, an alternate culture method for Csp and different extracellular matrices (ECM) for cell expansion were tested. The hanging drop culture method produced Csp with higher levels of c-kit+ cells (9 ± 2%) than poly-D-lysine-coated and low-bind culture dishes. Of five ECM tested, collagen IV was found to enhance EDC migration and CDC proliferation, and produced 11 ± 0.4% c-kit+ cells, with Csp cultured in hanging drops. Intramyocardial injection of CDCs improved left ventricular ejection fractions of infarcted rat hearts by 9% and prevented the peri-infarct wall from thinning, measured in vivo using MRI over 16 weeks. To improve cell tracking using MRI, two MR positive contrast agents, gadolinium-DTPA and gadonanotubes were tested. Gd-DTPA had low sensitivity after labelling (1.4 x 10^5 cells/mm2); whereas gadonanotubes did not provide positive contrast at 11.7 T. Thus, neither contrast agent could be used for cell tracking using high magnetic field. In conclusion, CDCs were an effective source of stem cells that could be used for heart repair, although cells could not be tracked using positive MR contrast.
Addressing the issue of equity in health care provision during the transition period in Bulgaria
Keywords: income inequality
health inequalities
poverty
socio-economic inequalities
minority health

The collapse of the communist regimes in Central and Eastern Europe in 1989-1990 heralded the beginning of an economic transition from central planning to market economies. The subsequent period was marked by malfunctioning of these countries’ social sectors, including their health care systems, raising serious issues of equity. This thesis examines the impact of the transition period and the introduction of social insurance on equity in health care provision in Bulgaria. Equity in health care is investigated with respect to function - i.e. financing (according to ability to pay) and delivery (according to need) - and outcomes - i.e. health status, income inequality and poverty. Differences in health, health care financing and delivery are explored by income, education, ethnic, employment, marital status, age and sex groups. Furthermore, the thesis outlines the impact of health care provision, in particular social insurance, on poverty and health inequalities. The thesis employs empirical analysis based on household data. Its methodology includes concentration and decomposition analysis, and provides new ways of modelling health care financing and delivery, as well as the link between health and health care delivery. The thesis concludes that social insurance does not provide a uniform means of improving equity and that the root cause of the problem lies in the large proportion of out-of-pocket payments and the rather limited size of the health insurance sector. Inequity in health care provision leads to poverty and untreated illness. The data suggests that there are differences between socio-economic groups as regards their likelihood to seek treatment for their ill health, which result in differences in their health status. The social factors that have impacted the most on health are low education and low income.
An epidemiological study of pneumonia in migrant infants and children on the Thai-Myanmar border
Keywords: Infants
Paediatric
Pneumonia
Epidemiology
Children
Aetiology

Background: Pneumonia is the leading cause of death in children and the estimated incidence of childhood pneumonia in Myanmar is the third highest in the world. Effective interventions, including case-management and immunisations, have been established.However these focus on bacterial pneumonia and recent advances in molecular diagnostics have highlighted the substantial role played by viruses. An understanding of the local epidemiology and aetiology of childhood pneumonia is vital to ensure that current and future interventions are appropriate to the local population.
Objective: To study the severity and aetiology of childhood pneumonia, in migrant infants and children under five years old, presenting to a clinic on the Thai-Myanmar border.
Methods: A one-year prospective observational study was conducted in a rural clinic on the Thai-Myanmar border. All children attending the clinic, who were diagnosed with clinical pneumonia according to the World Health Organization definitions, were treated and investigated according to local paediatric guidelines.
Results: During the study period 175 episodes of clinical pneumonia were diagnosed. Of these 59% were male and half were infants (48%). The median age at presentation was 7.5 months (IQR 3 to 13). Clinically half (50%) had severe or very severe pneumonia. Using the WHO standardised method for interpretation, 38% of radiographs had primary endpoint pneumonia.
At least one virus was identified in 49% of patients. The most commonly identified virus was adenovirus, which was identified in 24% of cases, followed by RSV (22%), then hMPV (6%) and Influenza A (3%). The cases of pneumonia peaked at the end of the rainy season and this closely followed the RSV activity.
Conclusion: The majority of children presented with severe or very severe pneumonia, suggesting that in this population patients may present later. The substantial burden in infants suggests that future interventions should focus on this vulnerable age group. Viruses were frequently identified. Adenovirus was commonly identified, however its presence in nasopharyngeal secretions is of uncertain significance, especially in the presence of other viruses. The persistence of adenovirus and its role in acute pneumonia needs further investigation. RSV is an important and commonly found pathogen and prevention of RSV through a safe and effective vaccine could have substantial effect on the reduction of childhood pneumonia on the Thai-Myanmar border.
The importance of DNA replication termination and the MHF complex to genome stability
Keywords: DNA replication termination
DNA repair
MHF
genome stability

The final stages of replication fork termination requires the timely and orderly orchestration of catalytic and enzymatic activities. Given the complexity of this process, it is conceivable that the final stages of fork termination is susceptible to problems that could trigger recombination, which could lead to deleterious genomic rearrangements if ectopic homologous sequences are recombined. Using the site-specific RTS1 barrier in fission yeast, I demonstrated that fork termination is generally not a recombinogenic process, and that hyper-recombination-induced by fork blockage at RTS1 is largely a result of replication fork restart.
To investigate the actual mechanisms and proteins, which drive and influence recombination at a replication barrier, I studied the MHF proteins, which assist Fml1 in limiting crossovers during double-strand break (DSB) repair and promoting Rad51-mediated recombination at impeded replication forks, and are also components of the constitutive centromere-associated network (CCAN). Intriguingly, structural studies revealed that the MHF can exist as an octamer in vitro. I examined the biological significance of octameric MHF by employing three mutations that disrupt the octamer configuration in vitro. In fission yeast, these mutations cause hypersensitivity to methyl methanesulfonate (MMS), suggesting that the MHF octamer may have a role in DNA repair. One of the “octamerisation” mutants, exhibits greater hypersensitivity to MMS than the other two, and biochemical experiments indicated that this is because it confers an additional defect in MHF’s interaction with Fml1. Further genetic experiments on this mutant suggest that the ability of Fml1 to unwind D-loops depends more critically on its interaction with MHF than fork reversal. Additionally, I showed a synergistic interaction between Dcr1 and MHF, and demonstrated that in the absence of Dcr1, there is a greater need for recombination to tolerate/repair DNA damage. Lastly, I uncovered a novel function for the MHF in controlling the initiation of septation.
On the regularity of holonomically constrained minimisers in the calculus of variations
Keywords: quasiconvexity
holonomic
variational methods
harmonic maps
regularity

This thesis concerns the regularity of holonomic minimisers of variational integrals in the context of direct methods in the calculus of variations. Specifically, we consider Sobolev mappings from a bounded domain into a connected compact Riemannian manifold without boundary, to which such mappings are said to be holonomically constrained. For a general class of strictly quasiconvex integral functionals, we give a direct proof of local C1,α-Hölder continuity, for some 0 < α < 1, of holonomic minimisers off a relatively closed 'singular set' of Lebesgue measure zero. Crucially, the proof constructs comparison maps using the universal covering of the target manifold, the lifting of Sobolev mappings to the covering space and the connectedness of the covering space. A certain tangential A-harmonic approximation lemma obtained directly using a Lipschitz approximation argument is also given. In the context of holonomic minimisers of regular variational integrals, we also provide bounds on the Hausdorff dimension of the singular set by generalising a variational difference quotient method to the holonomically constrained case with critical growth. The results are analogous to energy-minimising harmonic maps into compact manifolds, however in this case the proof does not use a monotonicity formula. We discuss several applications to variational problems in condensed matter physics, in particular those concerning the superfluidity of liquid helium-3 and nematic liquid crystals. In these problems, the class of mappings are constrained to an orbit of 'broken symmetries' or 'manifold of internal states', which correspond to a sub-group of residual symmetries.
On genetic variants underlying common disease
Keywords: population genetics
genome-wide association studies
statistical genetics

Genome-wide association studies (GWAS) exploit the correlation in ge- netic diversity along chromosomes in order to detect effects on disease risk without having to type causal loci directly. The inevitable downside of this approach is that, when the correlation between the marker and the causal variant is imperfect, the risk associated with carrying the predisposing allele is diluted and its effect is underestimated. This thesis explores four different facets of this risk dilution: (1) estimating true effect sizes from those observed in GWAS; (2) asking how the context of a GWAS, including the population studied, the genotyping chip employed, and the use of im- putation, affects risk estimates; (3) assessing how often the best-associated SNP in a GWAS coincides with the causal variant; and (4) quantifying how departures from the simplest disease risk model at a causal variant distort the observed disease risk model.
Using simulations, where we have information about the true risk at the causal locus, we show that the correlation between the marker and the causal variant is the primary driver of effect size underestimation. The extent of the underestimation depends on a number of factors, including the population in which the study is conducted, the genotyping chip employed, whether imputation is used, and the strength, frequency, and disease model of the risk allele. Suppose that a GWAS study is conducted in a European population, with an Affymetrix 6.0 genotyping chip, without imputation, and that the causal loci have a modest effect on disease risk, are common in the population, and follow an additive disease risk model. In such a study, we show that the risk estimated from the most associated SNP is very close to the truth approximately two-thirds of the time (although we predict that fine mapping of GWAS loci will infrequently identify causal variants with considerably higher risk), and that the best-associated variant is very often perfectly or nearly-perfectly correlated with, and almost always within 0.1cM of, the causal variant. However, the strong correlations among nearby loci mean that the causal and best-associated variants coincide infrequently, less than one-fifth of the time, even if the causal variant is genotyped. We explore ways in which these results change quantitatively depending on the parameters of the GWAS study. Additionally, we demonstrate that we expect to identify substantial deviations from the additive disease risk model among loci where association is detected, even though power to detect departures from the model drops off very quickly as the correlation between the marker and causal loci decreases. Finally, we discuss the implications of our results for the design and interpretation of future GWAS studies.