VictorJuiz/thesis huggingface dataset:
Bayesian methods for multivariate phenotype analysis in genome-wide association studies
Keywords: bayesian
GWAS
modelling
phenotype
method
genotype
statistics
multivariate

Most genome-wide association studies search for genetic variants associated to a single trait of interest, despite the main interest usually being the understanding of a complex genotype-phenotype network. Furthermore, many studies collect data on multiple phenotypes, each measuring a different aspect of the biological system under consideration, therefore it can often make sense to jointly analyze the phenotypes. However this is rarely the case and there is a lack of well developed methods for multiple phenotype analysis. Here we propose novel approaches for genome-wide association analysis, which scan the genome one SNP at a time for association with multivariate traits.
The first half of this thesis focuses on an analytic model averaging approach which bi-partitions traits into associated and unassociated, fits all such models and measures evidence of association using a Bayes factor. The discrete nature of the model allows very fine control of prior beliefs about which sets of traits are more likely to be jointly associated. Using simulated data we show that this method can have much greater power than simpler approaches that do not explicitly model residual correlation between traits. On real data of six hematological parameters in 3 population cohorts (KORA, UKNBS and TwinsUK) from the HaemGen consortium, this model allows us to uncover an association at the RCL locus that was not identified in the original analysis but has been validated in a much larger study.
In the second half of the thesis we propose and explore the properties of models that use priors encouraging sparse solutions, in the sense that genetic effects of phenotypes are shrunk towards zero when there is little evidence of association. To do this we explore and use spike and slab (SAS) priors. All methods combine both hypothesis testing, via calculation of a Bayes factor, and model selection, which occurs implicitly via the sparsity priors. We have successfully implemented a Variational Bayesian approach to fit this model, which provides a tractable approximation to the posterior distribution, and allows us to approximate the very high-dimensional integral required for the Bayes factor calculation. This approach has a number of desirable properties. It can handle missing phenotype data, which is a real feature of most studies. It allows for both correlation due to relatedness between subjects or population structure and residual phenotype correlation. It can be viewed as a sparse Bayesian multivariate generalization of the mixed model approaches that have become popular recently in the GWAS literature. In addition, the method is computationally fast and can be applied to millions of SNPs for a large number of phenotypes. Furthermore we apply our method to 15 glycans from 3 isolated population cohorts (ORCADES, KORCULA and VIS), where we uncover association at a known locus, not identified in the original study but discovered later in a larger one. We conclude by discussing future directions.
Mathematical models of cranial neural crest cell migration
Keywords: mathematical biology
developmental biology
modelling and simulation of cellular migration
chemotaxis
volume exclusion

From the developing embryo to the evacuation of football stadiums, the migration and movement of populations of individuals is a vital part of human life. Such movement often occurs in crowded conditions, where the space occupied by each individual impacts on the freedom of others. This thesis aims to analyse and understand the effects of occupied volume (volume exclusion) on the movement of the individual and the population.
We consider, as a motivating system, the rearrangement of individuals required to turn a clump of cells into a functioning embryo. Specifically, we consider the migration of cranial neural crest cells in the developing chick embryo. Working closely with experimental collaborators we construct a hybrid model of the system, consisting of a continuum chemoattractant and individual-based cell description and find that multiple cell phenotypes are required for successful migration. In the crowded environment of the migratory system, volume exclusion is highly important and significantly enhances the speed of cell migration in our model, whilst reducing the numbers of individuals that can enter the domain. The developed model is used to make experimental predictions, that are tested in vivo, using cycles of modelling and experimental work to give greater insight into the biological system.
Our formulated model is computational, and is thus difficult to analyse whilst considering different parameter regimes. The second part of the thesis is driven by the wish to systematically analyse our model. As such, it concentrates on developing new techniques to derive continuum equations from diffusive and chemotactic individual-based and hybrid models in one and two spatial dimensions with the incorporation of volume exclusion. We demonstrate the accuracy of our techniques under different parameter regimes and using different mechanisms of movement. In particular, we show that our derived continuum equations almost always compare better to data averaged over multiple simulations than the equivalent equations without volume exclusion. Thus we establish that volume exclusion has a substantial effect on the evolution of a migrating population.
Some problems on the dynamics of nematic liquid crystals
Keywords: Partial Differential Equations - Liquid Crystals - Condensed Matter Physics

In this thesis, we consider two problems in the Q-tensor theory of nematic liquid crystals. The first concerns eigenvalue constraints on the Q-tensor order parameter. In particular, by employing a singular potential constructed by Ball and Majumdar, we consider the existence, regularity and "strict physicality" of weak solutions to the Beris-Edwards equations of nemato-hydrodynamics. In the second part of the thesis, we consider a gradient flow of the well-studied Landau-de Gennes energy. We prove some rigorous results on the average long-time statistical behaviour of its solutions, which are in agreement with experimental observations in the condensed matter physics literature.
Triune Elohim
Keywords: Hunnius
Drusius
De Tribus Elohim
Antitrinitarianism
Pareus
Confessionalization
Elohim
Reformation Hebrew
Zanchi
Heidelberg
Junius
Tremellius

In 1563, the publication of the Heidelberg Catechism marked the conversion of the Rhineland Palatinate to a stronghold for Reformed religion. Immediately thereafter, however, the Palatinate church experienced a deeply unsettling surge in the popularity of antitrinitarianism. To their Lutheran and Catholic opponents, this development revealed a toxic connection between Reformed theology and the tenets of antitrinitarianism. As early as 1565, for instance, the Catholic Cardinal Stanislaus Hosius argued anonymously that the Reformed principle of sola scriptura was indistinguishable from the biblicism which had led heretics to reject the doctrine of the Trinity on the grounds that it was nowhere explicitly justified in the biblical text.
Seven years later, the displaced Italian theologian and Heidelberg professor, Girolamo Zanchi, countered this argument in his De Tribus Elohim (1572). This huge landmark of this early theological crisis in Heidelberg sought to oppose the biblicism of the early antitrinitarians by arguing that the doctrine of the Trinity was explicitly taught within the Hebrew divine names Jehovah and Elohim. The following year De Tribus Elohim received an Imperial Privilege from the Catholic court in Vienna, a distinction virtually unheard of for a Reformed theological text. Zanchi’s argument was then widely promulgated in the marginal notations of the tremendously influential Biblia Sacra of Franciscus Junius and Immanuel Tremellius, and became a staple of refutations of antitrinitarianism thereafter.
Yet Zanchi’s confidence that trinitarian theology was contained within the Hebrew of the Old Testament was not shared by many of his own Reformed colleagues. John Calvin’s exegetical works had explicitly rejected this argument; and theologians like David Pareus (Zanchi’s younger colleague in Heidelberg) and the Dutch Hebraist Johannes Drusius preferred a more historical-grammatical reading of the Old Testament and dismissed Zanchi’s reading of the name Elohim despite the danger that this might sacrifice a valuable defence against antitrinitarianism. Complicating the picture further, the Lutheran polemicist Aegidius Hunnius directed Zanchi’s arguments against Calvin in his Calvinus Iudaizans (1593).
This variety of responses to Zanchi’s argument demonstrates the diversity of assumptions about the nature of the biblical text within the Reformed church, contradicting the notion that the Reformed world in the age of “confessionalization” was becoming increasingly homogenous or that the works of John Calvin had become the authoritative touchstone of Reformed orthodoxy in this period.
Specifying the dimensions of care that matter to people with long-term conditions (LTCs) and improving our understanding of patient-centred care (PCC)
Keywords: Medical sciences

Background
The term patient-centred care (PCC) is commonly used in the academic literature and UK health policy. However, this concept is ill defined and little is known about its applicability to the management of people with long-term conditions (LTCs). Several methodologies were used to explore the meaning of PCC, identify key experiences that matter to people with LTCs and consider the implications of these findings for the measurement of patient reported experiences of health care.
Method
Four stages of research were conducted for this thesis. First, a conceptual synthesis of existing PCC and patient experience frameworks to produce an overarching framework of PCC. Second, secondary qualitative analysis of patient interviews to identify key experiences of PCC that matter to people with LTCs. Third, development of a PCC questionnaire for people with LTCs, based on findings from the conceptual synthesis and secondary analysis. Fourth, further exploration of the questionnaire through cognitive debriefing interviews with people with LTCs and health professionals.
Results
The overarching framework of PCC consisted of 8 domains; access, availability and choice, information, communication and education, relationship with health professionals, involvement in care, respect and dignity, responsiveness to individual needs and preferences, consistency, continuity and co-ordination, and effectiveness of treatment and care. Findings from secondary analysis suggested that many of the domains from the framework were also important in care for people with LTCs, but that some aspects of care held an additional meaning. The themes identified in the secondary analysis were used to generate items for a generic PCC experience questionnaire for people with LTCs. The final questionnaire, ‘Your Experiences of Care in Long-Term Conditions’ consisted of 47 questions across three sections. Feedback from the debriefing interviews suggested that the questionnaire had asked important questions about care for people with LTCs and that it was relevant to people with a range of different LTCs.
Conclusion
Development of an overarching framework of PCC demonstrated some conceptual problems in understanding and evaluating the notion of PCC. Findings from this thesis suggest that an overarching questionnaire of experiences of PCC is feasible and acceptable to people with a range of different LTCs. Future research needs examine standard features of the newly developed PCC experience questionnaire for people with LTCs and consider the potential use and contribution of data in enhancing care for people with LTCs.
Connectivity and related properties for graph classes 
Keywords: Combinatorics
Graph Theory
Analytic Combinatorics

There has been much recent interest in random graphs sampled uniformly from the set of (labelled) graphs on n vertices in a suitably structured class A. An important and well-studied example of such a suitable structure is bridge-addability, introduced in 2005 by McDiarmid et al. in the course of studying random planar graphs. A class A is bridge-addable when the following holds: if we take any graph G in A and any pair u,v of vertices that are in different components in G, then the graph G′ obtained by adding the edge uv to G is also in A. It was shown that for a random graph sampled from a bridge-addable class, the probability that it is connected is always bounded away from 0, and the number of components is bounded above by a Poisson law. What happens if ’bridge-addable’ is replaced by something weaker? In this thesis, this question is explored in several different directions.
After an introductory chapter and a chapter on generating function methods presenting standard techniques as well as some new technical results needed later, we look at minor-closed, labelled classes of graphs. The excluded minors are always assumed to be connected, which is equivalent to the class A being decomposable - a graph is in A if and only if every component of the graph is in A. When A is minor-closed, decomposable and bridge-addable various properties are known (McDiarmid 2010), generalizing results for planar graphs. A minor-closed class is decomposable and bridge-addable if and only if all excluded minors are 2-connected. Chapter 3 presents a series of examples where the excluded minors are not 2-connected, analysed using generating functions as well as techniques from graph theory. This is a step towards a classification of connectivity behaviour for minor-closed classes of graphs. In contrast to the bridge-addable case, different types of behaviours are observed. Chapter 4 deals with a new, more general vari- ant of bridge-addability related to edge-expander graphs. We will see that as long as we are allowed to introduce ’sufficiently many’ edges between components, the number of components of a random graph can still be bounded above by a Pois- son law. In this context, random forests in Kn,n are studied in detail. Chapter 5 takes a different approach, and studies the class of labelled forests where some vertices belong to a specified stable set. A weighting parameter y for the vertices belonging to the stable set is introduced, and a graph is sampled with probability proportional to y*s where s is the size of its stable set. The behaviour of this class is studied for y tending to ∞. Chapters 6 concerns random graphs sampled from general decomposable classes. We investigate the minimum size of a component, in both the labelled and the unlabelled case.
Analysis of the quasicontinuum method
Keywords: error analysis
atomistic models
coarse-graining
quasicontinuum method

The aim of this work is to provide a mathematical and numerical analysis of the static quasicontinuum (QC) method. The QC method is, in essence, a finite element method for atomistic material models. By restricting the set of admissible deformations to linear splines with respect to a finite element mesh, the computational complexity of atomistic material models is reduced considerably.
We begin with a general review of atomistic material models and the QC method and, most importantly, a thorough discussion of the correct concept of static equilibrium. For example, it is shown that, in contrast to global energy minimization, a ‘dynamic’ selection procedure based on gradient flows models the physically correct behaviour.
Next, an atomistic model with long-range Lennard–Jones type interactions is analyzed in one dimension. A rigorous demonstration is given for the existence and stability of elastic as well as fractured steady states, and it is shown that they can be approximated by a QC method if the mesh is sufficiently well adapted to the exact solution; this can be measured by the interpolation error.
While the a priori error analysis is an important theoretical step for understanding the approximation properties of the QC method, it is in general unclear how to compute the QC deformation whose existence is guaranteed by the a priori analysis. An a posteriori analysis is therefore performed as well. It is shown that, if a computed QC deformation is stable and has a sufficiently small residual, then there exists a nearby exact solution and the error is estimated. This a posteriori existence idea is also analyzed in an abstract setting.
Finally, extensions of the ideas to higher dimensions are investigated in detail.
Identification of molecular-genetic determinants of quality traits of tomato fruit
Keywords: Solanum lycopersicum
aspartate
malate
glutamate
introgression lines
tomato
citrate

Tomato is an important food crop and a model for fleshy fruit development. The process of fruit ripening involves changes in chemical composition and in particular the accumulation of sugars, organic, amino acids and carotenes. The research described in this thesis aimed to identify key regulatory aspects associated with the accumulation of the major acids in tomato fruit by analysis of introgression lines resulting from a cross between a cultivated variety, Solanum lycopersicum, and a wild progenitor species, Solanum pennellii. Line 2-5 showed increases in citrate, malate, aspartate and glutamate in fruit grown under greenhouse conditions.
The genetic differences between line 2-5, its overlapping lines, sub-introgression lines and the recurrent parent were used to link the metabolite phenotypes to smaller chromosomal regions. This analysis suggested multiple epistatic loci control fruit metabolite accumulation. Investigation of the biochemical differences between line 2-5 and the recurrent parent revealed that organic and amino acid accumulation did not dependent upon increased TCA cycle capacity. Regulation at the metabolic level was identified for citrate accumulation with changes in cytosolic aconitase in line 2-5. As these metabolites accumulate in the vacuole, tonoplast transport was investigated. Correlation of ATPase-dependent malate influx with altered malate content suggested malate tonoplast transport plays a role in malate accumulation and highlights the importance of vacuolar storage and transport in the regulation of organic and amino acid accumulation.
Numerical modelling of damage to masonry buildings due to tunnelling
Keywords: tunnelling
settlement

Accurate assessment of the damage to buildings due to tunnelling in soft ground becomes an important issue when a tunnel is constructed under historic masonry buildings in urban areas. The current two-stage approach in which settlement estimated from a Gaussian curve are applied to a building does not consider soil-structure interaction and fails to give a correct prediction of the damage. This thesis describes a complete three-dimensional finite element model for assessment of the settlement damage to masonry buildings induced by tunnelling in London Clay, and an investigation of the interaction between a masonry building and the ground. A macroscopic elastic no tension model, which assumes the material has zero tensile strength but infinite compressive strength, is developed to simulate the behaviour of masonry. Numerical techniques are proposed to improve the stability of the calculation. The comparison of the no tension and elastic models, by applying Gaussian curve settlement troughs to both a plain wall and a facade, shows that the no tension model predicts different behaviour of the masonry building during tunnelling, including different cracking patterns and damage grades. Two-dimensional finite element analyses combining the building, modelled by the no tension material, and the ground, modelled by a nested yield surface model, give insight into the interaction between the masonry structure and the ground. They suggest the importance of the stresses in the soil prior to the excavation in affecting the ground movements during tunnelling. Thus the weight of the building controls the overall magnitude of the ground movements beneath the building, while the stiffness of the building affects the shape of the trough. A key aspect of the behaviour of the masonry building is the formation of stress arches. Finally the three-dimensional finite element analyses are described. Both symmetric and unsymmetric cases are analysed. The results show that the three-dimensional analysis gives more realistic modelling of the problem and is likely to be necessary for practical situations, especially when a building is not symmetrically located with respect to the tunnel - a case which cannot be analysed in two-dimensions. A special tying scheme is proposed for the connection of the nodes belonging to elements of different types, which are defined in their own local co-ordinate systems. Different types of tie elements are formulated and implemented for connection between two-dimensional and three-dimensional elements in various combinations.
Images and identities in the funerary art of Western Anatolia, 600 - 450 BC: Phrygia, Hellespontine Phrygia, Lydia
Keywords: Greco-Persian
Granicus
Arslan Tas
Graeco-Persian
stelae
Bursa
Aslan Tash
archaic Asia Minor
Troad
Kelainai
Perso-Anatolian art
stelai
wall paintings
Biga Plain
Sultaniye
Sardis
Afyon
burial
Phrygian Highlands
ekphora
chamber tombs
Odemis
Daskyleion
banquets
Yilan Tas
convoys
Tatarli
Polyxena Sarcophagus

The dissertation analyses the reliefs and paintings on thirty-one different tombs in Western Anatolia erected between 600 and 450 BC, in order to illuminate the ways in which non-Greek elites were identified on their memorials. The tombs from three areas are treated: Phrygia, Hellespontine Phrygia and Lydia, where the primary language groups were Phrygian, Mysian and Lydian. There is little literary evidence for these regions, and what there is tends to focus on political developments. Descriptions of people and society are few, and tend to represent them from an outside perspective, grouping them according to cultural characteristics which differentiate them from Greeks. It is clear, however, that the regions were important, prosperous places, controlled by illustrious grandees and land marked with a relatively high proportion of monumental tombs. Of these monumental tombs, there is a relatively high number decorated with striking and articulate images. There is much to be gained from examining the images on these tombs, as ‘indigenous’ sources for how elite Western Anatolians described themselves. Previous approaches to the tombs and their images have tended to look at them individually or in smaller groups, and to concentrate on the transmission and reception of Persian and Greek culture in the Achaemenid provinces. This dissertation contributes a broader comparative study of the decorated tombs, focussing on the kinds of statuses the images represent and the cultural forms these took. By comparing the various methods of self-representation, it clarifies patterns of identities in Western Anatolia and their relationship to historical circumstances. The dissertation is divided into five chapters. An introduction outlines the scope and sample, the historical background, previous studies of the monuments, the definition of ‘identity’ and the methods of analysis adopted here. Three case study chapters present the regions and the decorated monuments within them. A concluding chapter synthesises three aspects: social identities (roles and spheres of life represented); geographic and chronological patterns; and cultural affiliations and orientations. The dissertation concludes that a tension between Persian identities and local traditions is evident in some of the tomb images, which relates to the political upheavals in Western Anatolia and the Aegean at the time of the Persian Wars.