VictorJuiz/thesis huggingface dataset:
Signatures of Gaussian processes and SLE curves 
Keywords: Chen series
Gaussian processes
SLE curves
Rough path theory
Quasi-sure analysis

This thesis contains three main results.
The first result states that, outside a slim set associated with a Gaussian process with long time memory, paths can be canonically enhanced to geometric rough paths. This allows us to apply the powerful Universal Limit Theorem in rough path theory to study the quasi-sure properties of the solutions of stochastic differential equations driven by Gaussian processes. The key idea is to use a norm, invented by B. Hambly and T.Lyons, which dominates the p-variation distance and the fact that the roughness of a Gaussian sample path is evenly distributed over time.
The second result is the almost-sure uniqueness of the signatures of SLE kappa curves for kappa less than or equal to 4. We prove this by first expressing the Fourier transform of the winding angle of the SLE curve in terms of its signature. This formula also gives us a relation between the expected signature and the n-point functions studied in the SLE and Statistical Physics literature. It is important that the Chordal SLE measure in D is supported on simple curves from -1 to 1 for kappa between 0 and 4, and hence the image of the curve determines the curve up to reparametrisation.
The third result is a formula for the expected signature of Gaussian processes generated by strictly regular kernels. The idea is to approximate the expected signature of this class of processes by the expected signature of their piecewise linear approximations. This reduces the problem to computing the moments of Gaussian random variables, which can be done using Wick’s formula.
The economic development of the Rhine river basin in the Roman period (30 BC - AD 406)
Keywords: Roman economy
Rhine River
Roman archaeology
Roman Germany
Roman history
Roman frontiers

The economic development of frontier regions has been neglected in the study of the Roman economy. Traditional core/periphery models suggest that frontiers were marginal zones dependent on a wealthy Mediterranean core, and this view has dominated scholarship for more than thirty years. In light of recent work on the Roman economy, it is clear that many old models need to be reappraised; this thesis examines the economic development of frontiers through the case study of the Rhine River Basin. This region formed one of Rome’s northern frontiers for more than 400 years and has a rich tradition of detailed archaeological and historical research. Using data from the Rhine frontier, this thesis re-examines the nature of frontier economies, arguing that they were dynamic, versatile, and complex rather than subaltern and undeveloped. A new model, based in the analytic framework of economic geography, is suggested as a replacement in order to appreciate the realities and potential of frontier economies.
The roles played by the transcriptional regulators PPARalpha, HIF-1alpha and SIRT1 in the control of cardiac metabolism
Keywords: Cardiac metabolism

The failing heart is characterised by altered energy substrate metabolism, which is a potential target for the development of new heart failure treatments. Transcriptional regulatory proteins orchestrate long-term control of cardiac metabolism by altering gene expression patterns. Thus, these proteins may be viable targets for such metabolic therapies. The work in this thesis aimed to increase understanding of the roles and interactions of three important transcriptional regulators, PPARα, HIF-1α and SIRT1 in the heart, using a combination of animal and cell culture models. Wild type (controls) and PPARα knockout mice were fasted for 24 hours, with PPARα shown to be non-essential for mediating metabolic flexibility through pyruvate dehydrogenase (PDH) down-regulation. Aged male and female PPARα knockout mice had increased cardiac PDH flux in the fed and fasted states relative to controls, indicating a role for PPARα in aging-associated metabolic changes. Subsequently, the HL-1 cardiomyocyte cell line was characterised as an in vitro model of cardiac metabolism, with studies of hypoxia and hypoxia mimetic treatment demonstrating mitochondrial metabolic changes of a HIF-1α-dependent or independent nature. Male Wistar rats were treated with nicotinamide, to investigate its ability to modulate cardiac SIRT1 activity through increasing tissue NAD levels. Nicotinamide treatment altered cardiac metabolism by decreasing PDH activity and modulating mitochondrial metabolic pathways, as well as increasing cardiac SIRT1 activity after 8 weeks of treatment. To assess the interactions between SIRT1, PPARα and HIF-1α, rats were subjected to fasting, high fat feeding or hypoxia treatments. Cardiac SIRT1 activity was respectively increased and decreased by fasting and high fat feeding treatments in rats, and hypoxic exposure decreased SIRT1 activity, demonstrating cross talk between the activities of PPARα, HIF-1α and SIRT1 in the heart. The results presented here increase knowledge of cardiac transcriptional regulation, which is important for our understanding of how manipulating cardiac metabolism may enable the development of therapies to improve energy metabolism in cardiac disease states.
Graphical Gaussian models with symmetries
Keywords: statistics
symmetry
Gaussian distribution
graphical models

This thesis is concerned with graphical Gaussian models with equality constraints on the concentration or partial correlation matrix introduced by Højsgaard and Lauritzen (2008) as RCON and RCOR models. The models can be represented by vertex and edge coloured graphs G = (V,ε), where parameters associated with equally coloured vertices or edges are restricted to being identical.
In the first part of this thesis we study the problem of estimability of a non-zero model mean μ if the covariance structure Σ is restricted to satisfy the constraints of an RCON or RCOR model but is otherwise unknown. Exploiting results in Kruskal (1968), we obtain a characterisation of suitable linear spaces Ω such that if Σ is restricted as above, the maximum likelihood estimator μ(with circumflex) and the least squares estimator μ* of μ coincide for μ ∈ Ω, thus allowing μ and Σ to be estimated independently. For the special case of Ω being specified by equality relations among the entries of μ according to a partition M of the model variables V, our characterisation translates into a necessary and sufficient regularity condition on M and (V,ε).
In the second part we address model selection of RCON and RCOR models. Due to the large number of models, we study the structure of four model classes lying strictly within the sets of RCON and RCOR models, each of which is defined by desirable statistical properties corresponding to colouring regularity conditions. Two of these appear in Højsgaard and Lauritzen (2008), while the other two arise from the regularity condition ensuring equality of estimators μ(with circumflex) = μ* we find in the first part. We show each of the colouring classes to form complete lattices, which qualifies the corresponding model spaces for an Edwards-Havránek model selection procedure (Edwards and Havránek, 1987). We develop a coresponding algorithm for one of the model classes and give an algorithm for a systematic search in accordance with the Edwards-Havránek principles for a second class. Both are applied to data sets previously analysed in the literature, with very encouraging performances.
Quantum materials explored by neutron scattering
Keywords: magnetism
superconductivity
neutrons - scattering

This thesis describes neutron scattering experiments on strongly correlated systems exhibiting a range of emergent phenomena: antiferromagnetism, charge order, superconductivity and multiferroicity. I have examined the La_{2}CoO_{4} compound which is a Mott insulator and orders antiferromagnetically near room temperature. The La_{2}CoO_{4} sample was studied using spherical neutron polarimetry and I present magnetic structure models to describe the two antiferromagnetic phases of the compound. Furthermore, the magnetic fluctuations have been investigated using neutron time-of-flight technique. This has allowed us to extract the dominant exchange interactions in the system. More interestingly, the work on La_{2}CoO_{4} presented in this thesis provides a basis for the experimental evidence of an hourglass dispersion in La_{5/3}Sr_{1/3}CoO_{4}, previously only observed in the copper oxide based superconductors. This dispersion has been understood in terms of a stripe ordered magnetic phase and was found to be well described by a linear spin-wave model.
Neutron scattering experiments were also carried out on the new iron-based high-temperature superconductors, FeSe_{x}Te_{1−x}. A range of compositions were studied, including both antiferromagnetically ordered and superconducting. Below the superconducting phase transition temperature, a spin resonance mode was found centred on the antiferromagnetic wavevector. This is an important feature shared by many unconventional superconductors. The spin resonance intensity was found to reflect the order parameter of the superconducting state. Polarised inelastic neutron scattering experiments have revealed a small anisotropy between the in-plane and out-of-plane magnetic fluctuations at the resonance. This anisotropy cannot be readily explained by the usual anisotropic terms in the Hamiltonian. This could be evidence of new physics in the FeSe_{x}Te_{1−x} superconductors.
Finally, I have studied CuO – a high-temperature multiferroic. Analysis of polarised neutron diffraction experiments shows that the magnetic domain population can be varied using an externally applied electric field. This unambiguously demonstrates coupling between the magnetic and ferroelectric degrees of freedom. Using representation analysis I derive the incommensurate magnetic structure in the multiferroic phase. The origin of the magnetoelectric coupling is consistent with models based on the inverse Dzyaloshinskii-Moriya interaction.
TCR signalling in response to affinity stimulation
Keywords: T cell receptor
Themis
pMHC tetramers
T cells
affinity signalling
TCR

T cells are an essential part of the adaptive immune system and protect the body from intracellular infections. The specificity with which αßTCR-bearing T cells recognize cognate antigen presented on MHC molecules is paramount to maintaining the balance between mounting effector functions against pathogens and establishing peripheral tolerance to self. The mechanism by which T cells translate qualitative differences in TCR:pMHC binding to sensitive proximal signalling events which ultimately result in specific Tcell effector responses to infected cells but not to self is mostly unknown.
To address how T cell signalling responds to qualitative differences in TCR triggering by pMHC, I established a system of stimulating T cells bearing the 1G4 TCR specifically in vitro with a panel of four NY-ESO-1156-165 peptide variant MHC tetramers. Single amino acid substitutions to the NY-ESO-1156-165 peptide conferred a maximum 35-fold difference in the monomeric affinity for the 1G4 TCR. The system allows the highly controlled investigation of very rapid TCR proximal signalling events simultaneously and quantitatively using flow cytometry. Stimulations with pMHC tetramers showed rapid sensitive sequential signalling responses which were able to confer ligand discrimination. Very early signalling events such as CD3ζ phosphorylation showed analogue responses to the different affinity pMHC tetramers. Later signalling events including phospho-ERK showed a distinct on/off switch-like response. The amplitude of the very early analogue signalling responses determined the extent of later digital ERK signals. This indicates that a certain analogue signalling threshold must be passed to result in T cell activation.
The thymocyte protein Themis has been shown proximal TCR signalling to modulate thymocyte selection thresholds. Its deletion results in profound defects in positive thymocyte selection. Themis locates to the LAT signalosome of the TCR signalling cascade via Grb2, yet its molecular function is unknown. Employing the system I established, I demonstrate that Themis-k/d cells show increased levels of CD3z-chain phosphorylation, phospho-ERK signalling and signal-induced apoptosis which was independent of the ERK signal. This shows that Themis is a global attenuator of proximal TCR signalling. We are currently investigating possible associations of Themis to proteins phosphastases such as SHP-1 which could attenuate TCR proximal protein tyrosine signalling events.
A causal approach to transitivity
Keywords: transitivity
object omission
event individuation
Web data
causality

The present thesis presents a causal approach to transitivity and proposes a model of transitivity based on the view that a single event is a single ‘causal impact’, which consists of a single causation and a single effect. It defines semantic intransitivity as events where the effect is borne by and expressed through the actor and semantic transitivity as events where the effect is borne by and expressed through the patient. It finds evidence for this definition in the phenomenon of ‘selective specification’ of action or result by verbs with actor and patient. Furthermore, it proposes that the verb eat has dual event structures, intransitive and transitive, and uses a Web data test to test and confirm this hypothesis.
‘Abominable crime': examining the constitutionality of the Jamaican sodomy law through the lens of the general savings law clause
Keywords: sexuality
human rights
Commonwealth Caribbean
Comparative law
Constitutional law

In jurisdictions where the criminalization of sodomy has been invalidated by judicial order, this has generally been achieved through a determination that an identified right is infringed and that there is justification for that infringement. However, in Jamaica, a modified approach is required owing to the existence of the General Savings Law Clause (GSLC), which shields laws existing before the entry into force of the Constitution of Jamaica from invalidity with the fundamental rights provisions in the Constitution. The sodomy law is one such existing law. Accordingly, it is advisable to begin the analytical process with the general savings law clause. Therefore, my thesis presents two arguments for obviating the clause. The first is an argument that the sodomy law is inconsistent with the constitutional principle of rule of law (as opposed to a provision). Accordingly, the GSLC does not apply here because the clause only saves laws inconsistent with constitutional provisions but does not speak to constitutional principles. The thesis then presents a case for a substantive conception of the rule of law and discusses whether the rule of law includes a conception of equality which requires invalidation of prohibitions of consensual anal intercourse between consenting adults. The second argument is that a reinterpretation of the GSLC could enable a successful challenge to the criminalization of sodomy by permitting the court to modify the law that criminalizes it. This argument relies on the use of a clause in the Constitution (Order in Council) that mandates the modification of existing laws in particular circumstances. I propose that, by this method of modification, the court could decriminalize anal intercourse between consenting adults.
Tradition and poetic experimentation in Gaspard de la Nuit: Aloysius Bertrand and cultural exchange in French romanticism
Keywords: Aloysius Bertrand
Romanticism
French Provinces
Gaspard de la Nuit
Prose Poetry
Fantastic

In mainstream literary histories, Aloysius Bertrand (1807-1841) is still remembered as the canonical inventor of the prose poem in France. The established classification of Gaspard de la Nuit (1842) within the realm of the prose poem inevitably involves a retrospective appreciation of Bertrand’s work in light of the better-known authors that succeeded him in the history of this genre, such as Baudelaire and Mallarmé. The result is that Bertrand is often viewed as the inventor and/or the precursor of this genre; an important but, ultimately, minor contributor to its development. This hindsight brings with it a risk of critical anachronism against which Bertrand's contribution is often downplayed, especially because his thematic choices are seen to be outmoded, when compared to works by poets writing decades later. This thesis is a re-examination of Bertrand's Gaspard de la Nuit, incorporating an analysis of the cultural context that contributed to its production. The central argument is that in order to fairly assess Bertrand’s work, it is crucial to consider the poet’s contribution to, as well as his position in, the wider cultural exchange typical of his time. Using this contextual and historical approach, this thesis examines and challenges some of the main traditional considerations of Bertrand, such as his being a petit romantique, his provincialism, his unoriginality, and his role as the precursor and/or inventor of the prose poem. The overall aim is to assess fairly Bertrand’s unique synthesis of contemporary cultural and literary material with his own original work. By emphasising the crucial role of cultural exchange at the time of Gaspard de la Nuit’s production, we are thus able to begin to understand Bertrand in his own terms, rather than those of his successors, ourselves included, challenging commonly-held views and opening up new avenues for research.
Regenerative and biomimetic strategies in spinal surgery
Keywords: spinal surgery
orthopaedics
tissue engineering

Degenerative conditions of the spine are a major public health problem, leading to severe back pain, reduced quality of life and chronic disablement in a proportion of sufferers. For some of these patients, spinal fusion surgery is a treatment that can alleviate back pain and restore normal function. However, limitations in the availability of graft material mean that alternative grafts are needed and tissue-engineering approaches have been employed.
Using a novel self-organising collagen scaffold combined with nano-hydroxyapatite and chondroitin sulphate and by employing the latest materials techniques, I have studied the osteogenic capability of a biomimetic graft for use in spinal fusion surgery. The mineralised collagen scaffold has compressive strength comparable to human cancellous bone and can support the proliferation of viable human mesenchymal stem cells.
This porous scaffold can be combined with human mesenchymal stem cells to further promote bone growth, as evidenced by an upregulation in the levels of bone-forming genes and mineralisation of the scaffold. This scaffold can act as a carrier system for BMP-2, with wider application for other growth factors or drugs, providing sustained release when fabricated as a layer-by-layer scaffold.
An alternative bone substitute for use in spinal surgery has been designed and characterised, with exciting potential for use in vivo.
China and the international human rights regime: 1982-2011
Keywords: United Nations
human rights
China

This thesis examines the People's Republic of China's posture toward the international human rights regime between 1982 and 2011. It focuses on three case studies, including China's participation in the drafting and adoption of the Convention against Torture and the Optional Protocol to the Convention against Torture, its role during the negotiations to replace the UN Commission on Human Rights with the UN Human Rights Council, and its posture in the International Labour Organization's Conference Committee on the Application of Standards. To explain China's conduct in these contexts, I offer a framework of five possible roles a state can adopt toward a regime—maker, promoter, taker, constrainer, and breaker. I argue that China's posture was determined by three key explanatory variables that include the PRC government's preferences and ideas about international human rights, its concerns with cultivating a positive international image, and the degree of its familiarity with the international human rights regime. In addition, China's willingness and ability to work with other countries acted as a scope condition that influenced the manner in which it played its particular role. Although I find that the PRC played a range of roles, including maker, taker, and constrainer, overall it tended toward a low-profile posture even when it was playing the more demanding role of maker or constrainer. This thesis draws on documentary records, including United Nations reports, International Labour Organization reports, UN Human Rights Council documents, Chinese government statements, and reports from non-governmental organizations, including the International Service for Human Rights and Amnesty International's New York office. It also uses material from over 90 interviews conducted with diplomats from a range of countries, including China and key countries with similar views such as Pakistan and Egypt; representatives of non-governmental organizations that participate in the international human rights regime; and Chinese officials and scholars, including several affiliated with the Chinese government.