VictorJuiz/thesis huggingface dataset:
Vectorial problems: sharp Lipschitz bounds and borderline regularity
Keywords: nonautonomous functionals
Regularity
nonuniform ellipticity

This thesis is devoted to the proof of fine regularity properties of solutions to a broad class of variational problems including models from geometry, material science, continuum mechanics and particle physics. Our starting point is the analysis of the behavior of manifold-constrained minima to certain non-homogeneous functionals: under sharp assumptions, we prove that they are regular everywhere, except on a negligible, "singular" set of points. The presence of the singular set is in general unavoidable. Looking at minima as solutions to the associated Euler-Lagrange system does not help: it presents an additional component generated by the curvature of the manifold having critical growth in the gradient variable. For instance, sphere-valued harmonic maps satisfy in a suitably weak sense
−∆u = |Du|2u.
This turns out to be an insurmountable obstruction to regularity. It is then natural to consider general systems of type
− div a(x, Du) = f (0.0.1)
and study how the features of f and of the partial map x 7→ a(x, z) influence the regularity of solutions. In this respect, we are able to cover non-linear tensors with exponential type growth conditions as well as with unbalanced polynomial growth: we prove everywhere Lipschitz regularity for vector-valued solutions to (0.0.1) under optimal assumptions on forcing term and space-depending coefficients, [76]. When the system in (0.0.1) has the Double Phase structure:
− div (|Du|p−2Du + a(x)|Du|q−2Du)= − div (|F|p−2F + a(x)|F| q−2F)
0 ≤ a(·) ∈ C0,α, 1 ≤ q/p ≤ 1 + α/n,
we complete the Calderón-Zygmund theory started in [62] by dealing with the delicate borderline case
q/p = 1 + α/n,
which has been left open so far. Finally, we propose a new approach to the analysis of variational integrals with (p, q)-growth based on convex duality.
Adaptive optics retinal imaging in patients with retinal disease
Keywords: High-resolution retinal imaging
AOSLO
Adaptive optics
Retinal imaging
Image analysis

High-resolution in vivo retinal imaging with an adaptive optics scanning laser ophthalmoscope (AOSLO) allows visualisation of degenerative changes at the cellular level. The improvement in resolution with this type of imaging when compared to conventional retinal imaging technologies has made the use of cell-specific imaging biomarkers possible. With the development of new therapies for retinal disease, cell-specific biomarkers of disease are becoming increasingly important for monitoring treatment outcomes. This thesis aims to investigate the AOSLO as a clinical tool and to develop fully automated image processing and analysis pipelines for AOSLO images from patients with retinal disease.
Participants with Stargardt disease were investigated using multimodal conventional clinical imaging and high-resolution in vivo retinal imaging. Hyper-reflective spots, that were termed discrete hyper-reflective foci, were identified in AOSLO images in areas of retinal degeneration. We hypothesize that they may be cellular in nature and could represent cellular debris related to ongoing retinal degeneration. To optimise AOSLO image quality in patients with retinal disease, recommendations for future participant selection criteria and AOSLO image acquisition protocols are described.
Reference frames are used to measure and correct intraframe eye motion in order to produce averaged AOSLO images with a high signal to noise ratio. A fully automated algorithm for reference frame selection was developed and validated using synthetic data simulating normal retinae. Although the results did not show a significant difference between selected reference frames, averaged images generated using the developed algorithm were significantly better when compared to the default method used for reference frame selection with the Oxford AOSLO. We hypothesise that the improvement in averaged images may be due to clustering of spatially overlapping frames that occurs in the developed algorithm, which may lead to an improvement in the subsequent step of eye motion correction.
A deep learning approach for automated cone identification in AOSLO images of the photoreceptor mosaic was developed and validated. There was good agreement between the developed convolutional neural network (CNN), trained with synthetic and real data, and the current gold standard of manual marking. The developed CNN also marginally outperformed the results of current state-of-the-art automated cone detection algorithms. Although high-resolution in vivo retinal imaging provides substantial advantages over conventional clinical imaging, a number of technical, image processing and image analysis related challenges need to be overcome to promote its widespread clinical application.
Unconventional superconductivity and Majorana modes
Keywords: Topological superconductivity
Majorana modes
Strontium ruthenate
Unconventional superconductivity
Hubbard model

In this thesis superconductivity with unconventional pairing symmetries arising from repulsive interactions is investigated. Anyonic quasiparticles within the subclass of chiral p-wave superconductors are also examined.
In Chapter 2 we study weak-coupling superconductivity in a repulsive Hubbard model on the tetragonal lattice. With the weak-coupling approximation we establish the superconducting phase diagram as the out-of-plane hopping strength and electron filling is varied. For four Fermi surface topologies we identify a total of five types of p- and d-wave ground state orders, several of which have accidental line nodes and break time-reversal symmetry.
The weak-coupling scheme is adapted to strontium ruthenate (Sr2RuO4) in Chapter 3. We compute and compare odd- and even-parity superconducting order parameters using a realistic three-dimensional band structure. Two superconducting phases are identified: a helical p-wave spin triplet and a d-wave spin singlet phase. Both orders are roughly found to be compatible with specific heat data and recent nuclear magnetic resonance measurements [A. Pustogow et al., Nature 574, 72 (2019)]. We suggest that a d-wave order is likely involved in the superconducting phase, although certain experiments appear to remain incompatible with this conclusion.
In Chapter 4 we describe anyonic (Majorana) quasiparticles in chiral p-wave superconductors at temperatures non-negligible compared to the superconducting gap. We consider the impact of thermally occupying in-gap vortex states on the hybridisation of two Majorana modes. The hybridisation, reflecting the state of the qubit defined by the two Majorana modes, is found to decay algebraically with temperature just above the first-excited state energy scale. In novel iron-based superconductors our results suggest that there is an appreciable temperature range in which qubit read-out can be achieved via the inter-vortex force derived from the hybridisation.
Confinement and mobility in artificial lipid bilayer interfaces
Keywords: clathrin
GUV-SLB interfaces
DNA-lipid interactions
DNA origami
Artificial bilayer interfaces

All biological components are enclosed by membranes. Interfaces formed between membranes enable the transport of matter, information and energy between these components, but also serve as functional platforms for other processes. In these interfaces, membrane components such as lipids and proteins are recruited, sequestered and segregated to accomplish a range of operations. Often, sections of membranes are excised or inserted via transient interface formation. Due to the complexity of these processes, artificial models which represent reduced systems are used to understand the underlying physical, chemical and biological mechanisms. This thesis initiates an investigation into two key behaviours of membrane interfaces. Namely, the effects of substrates and intermembrane spacing on membrane mobility are studied using DNA linkers to alter the interactions between two model membranes; and the organisation of membrane components is studied using an artificial construct designed to mimic the structural properies of the membrane-deforming protein clathrin.
Beyond translation technique:  linguistic approaches to the Septuagint’s translation of the Aramaic verbal system in Old Greek Daniel, Theodotion Daniel, and 2 Esdras
Keywords: Greek Verb
Translation Technique
Relevance Theory
Linguistic Typology
Aspect
Verbal Syntax
Forensic Linguistic
Aramaic Verb
Tense
and Modality
Language Contact

This thesis applies four distinct linguistic methods to the philological data mined from translation technique of the Aramaic verbal system in Old Greek Daniel, Theodotion Daniel, and 2 Esdras. After briefly setting the present work within the context of previous studies (ch. 1), an exhaustive catalogue of the Aramaic verbal forms and their Greek translations occur, followed by the Greek forms and the Aramaic forms they translate (ch. 2). Chapter 3 applies linguistic typology and typological studies of tense, aspect, and modality (TAM) to the enigmatic Aramaic prefix conjugation (PC). Chapter 4 uses the concepts of language contact to explore Aramaic dialect differences (both lexical and grammatical) between the Aramaic of the Bible and the spoken Aramaic of the translators. Chapter 5 applies the concepts of idiolect as developed in forensic linguistics to Greek verbal syntax in the pluses of Old Greek Daniel, which in turn informs our understanding of the textual problem that is Old Greek Daniel 4-6. Chapter 6 problematizes minority translation equivalents in terms of Relevance Theory, showing how translators’ use aspectual choice functions as a procedural constraint to guide their readers toward intended inferences. The closing chapter (ch. 7) reviews the conclusions of the work and suggests new avenues for research.
Swift's art of allusion
Keywords: literary criticism
allusion
Swift
eighteenth-century
satire

The thesis is a study of Jonathan Swift’s library and reading, and a literary-critical examination of his art of allusion. Much scholarship on eighteenth-century literature seeks to affirm its formal clarity and decorum, perceiving — particularly in Augustan poetry — a strain for order and scholarly care. The claim of this thesis is that Swift provided an alternative to, and a critique of, these standards in literature, alluding to other texts with the kinds of obliquity, parody, and playful misanthropy which were germane both to his own writing and to satire as a genre.
The introduction examines Swift’s obligations at Marsh’s Library, Dublin, showing how he seems to have capitalised on opportunities to steal books and re-use fragments from them. This opens up a discussion of what constitutes a literary allusion, and how satirists such as Swift are invested at once in unsettling an allusion’s plausibility and expanding its possibilities. Chapter 1 immediately responds to these claims, showing how Swift subjected his scholarly editions of ancient writers to processes of breaking and remaking. It reveals his fondness for scholarly errors and distortions of mythology, and his attraction to areas of pseudo-learning which he could inhabit and parody. Chapter 2 pursues a closely-related argument in relation to Swift’s reading of modern literature, looking at the ways in which Swift ignored or affected ignorance of literature written in his own time: alluding, often, to their opening lines, or to cant phrases.
Chapter 3 shows how Swift’s allusions rejected any concept of literary dependance or gratitude; and depended, instead, on his own mock-tyrannical behaviour. The chapter takes special interest in Swift’s reading of classic accounts of tyranny, suggesting that many of his most eccentric allusions were thinly-veiled parodies of his own unfriendly characteristics. Chapter 4, a study of Swift’s allusions to the King James Bible, builds on this work, and examines the range of allusive practices to which he subjected passages of scripture, situating him in a context of clerical learning in eighteenth-century Dublin, and as a Dean in the Church of Ireland.
The thesis closes with an account of the ‘hint’ in eighteenth-century literature (an important word for an allusion in the period), showing how Swift related to a much wider context of allusive practice. The conclusion examines some of the ways in which Swift himself was alluded to, both in England and Ireland, and suggests that one of his legacies to satire was a species of obscurity that derived its local energies from genuinely acquired forces of erudition.
Experimental investigation of accelerator beam dynamics with a linear Paul trap
Keywords: Nonlinear Integrable Optics
Paul Trap
Accelerator Physics
Transverse Dynamics

This thesis describes a range of experiments performed using a linear Paul trap to investigate the transverse beam dynamics of intense hadron accelerators. Due to the complexity of the dynamics in intense hadron accelerators, it is advantageous to use a scaled experiment to gain insight into these machines. A Paul trap is used to study accelerator dynamics, as the Hamiltonians of the two systems are equivalent.
The IBEX Paul trap at the Rutherford Appleton Laboratory, Oxfordshire, has been commissioned. The first trapping of argon ions is observed, and the system is characterised, developing an understanding of the ion creation process, ion lifetime, longitudinal temperature, transverse emittance, and the process of ion extraction from the trap. A Faraday cup and MCP are used as diagnostics for the trap and are calibrated carefully to detect accurately the number of ions confined.
Both the IBEX and S-POD (Hiroshima University, Japan) linear Paul traps are used to study space-charge-driven resonances quantitatively for the first time. The particle-in-cell code Warp is used to gain a deeper understanding of the experiment and to assist with the interpretation of results. Values are extracted describing the location of the greatest ion loss in tune space for a given intensity for equal transverse tunes. These values are compared to values predicted both analytically and through simulation.
In the second half of this thesis, a design for a novel particle accelerator is considered, using the theory of Nonlinear Integrable Optics (NIO). In NIO, a highly nonlinear magnet is inserted into a linear lattice (known as a T-insert), resulting in regular and bounded particle motion. Detailed studies are undertaken to ascertain whether a simpler version of this theory, Quasi-Integrable nonlinear Optics (QIO), can be tested in a Paul trap.
A T-insert lattice is designed to meet the constraints of QIO, as well as the constraints imposed by the IBEX hardware. A number of these lattices are tested on the IBEX trap, confirming that enough ions are confined to study QIO in the presence of space-charge forces and that it is possible to create a T-insert with sufficient precision. To verify that the T-insert lattice created within the Paul trap meets the conditions for QIO, a method to measure the beta function in a Paul trap has been designed and tested.
Finally, a series of simulations are presented, showing that with a simple upgrade to the IBEX trap it is possible to create an octupole potential of high-enough quality to test QIO, while also retaining the ability to create a high-quality quadrupole to make the T-insert lattice. The impact of misalignment and scraping within the trap on the dynamic aperture and tune spread is studied using Warp. The resistance of the lattice to resonant excitation is investigated.
The experimental and simulation studies described show that QIO can be tested in a Paul trap, and pave the way for a range of studies of this exciting concept.
Magnetism in topological materials
Keywords: Magnetism
Weyl
Topology

Notions of topology are of considerable interest currently in physics, especially in the way topology influences the electronic properties of crystalline solids. This thesis concerns the experimental investigation of four different magnetic materials, which have been predicted to display a strong interplay between magnetism and the topology of the electronic band structure.
I demonstrate that EuCd2Sb2, below TN= 7.4 K, displays an A-type anti-ferromagnetic order on the Eu sub-lattice with a magnetic propagation vector of k=(0,0,1/2). I also establish that the C3 rotational symmetry along the crystal c axis (essential for the stabilisation of band crossings called Dirac nodes) is broken by the in-plane orientation of the Eu moments.
Following the initial discoveries of crystalline solids which can host topologically-protected band crossings called Weyl nodes, there is now a need for better material realisations, ideally comprising a single pair of nodes located at or very close to the Fermi level and in an energy window free from other overlapping bands. I propose that EuCd2As2, in a magnetic field of B >1.6 T along the c axis, to be such a system. This material is of general interest as it represents the simplest possible Weyl semimetal, and is therefore a model system for fundamental investigations of Weyl physics.
I refute the proposition that semimetallic YbMnBi2 hosts Weyl nodes induced by the time-reversal symmetry breaking mechanism. Furthermore, the full magnetic excitation spectrum of YbMnBi2, which has been mapped for the first time, demonstrates that the magnetic order of the Mn sub-lattice is weakly coupled to the charge carriers in the Bi square net.
Finally, the complex magnetic order of the Mn sub-lattice in Mn3Ge has been elucidated for the first time. This will shed light on the origin of the large anomalous Hall effect in Mn3Ge, which is unusual for an antiferromagnet.
Optimizing an AAV-CRISPR system for retinal gene therapy
Keywords: Gene therapy
Retinal degeneration
CRISPR/Cas9
Retina

Introduction: CRISPR/Cas9 is a bacterial defence system which evolved to cleave and deactivate bacteriophage DNA. The elements involved in the CRISPR/Cas9 system may be modified for gene therapy. CRISPR/Cas9 consists of two components, a single guide RNA (sgRNA) and a Cas9 protein. The sgRNA allows for sequence-specific binding. “Active” Cas9 creates a double-stranded break in the target region while the “deactivated” form can inhibit transcription. CRISPR/Cas9 can be packaged within adeno-associated viral vectors, which opens the possibility of using CRISPR/Cas9 to target mutations in the retina. We examine several optimizations to the AAV-CRISPR/Cas9 system in vitro in HEK293-eGFP cells.
Materials and Methods: We compare the effects of sgRNA orientation in both active SaCas9 constructs and deactivated SaCas9 constructs with the KRAB repressor (dSaCas9-KRAB). We also examine the cleavage ability of GeoCas9.
Results: There was no difference in Cas9 and sgRNA levels between the in cis and in trans SaCas9 constructs. We also found no difference in Cas9 levels, sgRNA levels, and target knock-down between the cis and trans orientations of the dSaCas9-KRAB constructs. For GeoCas9, we found that DNA cleavage levels were undetectable, despite confirmed expression of both sgRNA and GeoCas9 protein.
Conclusion: When delivering CRISPR/Cas9 in an AAV-based expression cassette, the efficacy appears unrelated to the orientation of the sgRNA (in cis or in trans) relative to the Cas9 gene. Furthermore, GeoCas9 may not be as efficacious as SaCas9, since it was unable to cleave DNA detectably in similar experiments.
Exotic phases of interacting Majorana fermions and parafermions
Keywords: Conformal Field Theory
Majorana fermions
Duality
Parafermions

In this thesis exotic phases of models preserving the symmetries of the one-dimensional quantum Ising and three-state Potts chains are considered, the natural habitats of Majorana fermions and parafermions, respectively. Along with numerical techniques, conformal field theory (CFT) is used to study the resulting physics.
Chapter 1 gives an introduction to the field and explains the basics of the numerical techniques to be used throughout the thesis. CFT is briefly introduced in Chapter 2 before the key results necessary for the thesis are given.
In Chapter 3, self-dual interactions are added to the critical Ising model, giving a range of different phases. A tricritical Ising point separates the Ising phase from an order-disorder coexistence phase on the chirally symmetric line, while a supersymmetric line provides the transition to an incommensurate phase in the general model. The model is solved exactly on a free-fermionic line giving insight into the points where only numerical analysis can be performed. This is supplemented by Appendix A, where the qualitative difference between similar perturbations is considered.
Chapters 4 and 5 consider models with the symmetries of the three-state Potts model. Various phases are found including an order-disorder coexistence phase, a second critical Potts phase, a "not-A" phase, and a representation symmetry protected topological phase. The effect of lattice momentum on the stability of phases and the connection with conformal field theory operators is studied. Lattice realizations of several CFTs are found, such as the tricritical Potts CFT and a CFT expressible in two different forms, either in terms of a boson and fermion, or Potts and tricritical Ising CFTs.
Palaeogenomics of animal domestication: computational modelling of ancestry, demography and selection
Keywords: domestication
bioinformatics
aDNA
palaeogenomics

The study of animal domestication is in the midst of a genomic revolution, as technological advances dramatically increase the availability of DNA sequence data from ancient and modern domestic populations. For the first time, palaeogenomic datasets are being produced of sufficient size and scope to directly observe anthropological and evolutionary processes through time; from the emergence of domestic animals in the Neolithic, to the formation of modern breeds in the Victorian era.
This thesis applies computational modelling of ancient and modern DNA to infer ancestry, demography, and selection in domestic cattle (Bos taurus), horses (Equus ferus caballus), and dogs (Canis familiaris).
Chapter 1 reviews the substantial contribution palaeogenomics has made to the study of animal domestication, and details the latest theoretical and empirical advances, alongside individual profiles of sixteen major domestic species.
Chapter 2 reconstructs the allele frequency trajectories of genetic variants linked to quantitative traits in genome-wide associations studies (GWAS) of cattle and horses. Using a Bayesian modelling approach, and a dataset of more than 350 ancient genomes spread across the last 10,000 years, the age of the allele under selection for thousands of GWAS variants is inferred, along with the selection coefficients for hundreds of polygenic traits.
Chapter 3 analyses the first ancient genome-wide DNA from pre-contact North American dogs. Admixture analyses show that the earliest American dogs were not independently domesticated, and originated from a population of arctic dogs in Eastern Siberia. These dogs likely accompanied humans during the peopling of the continent, and rapidly diversified after their arrival, until their sudden replacement following the arrival of European colonists. Remarkably, their most closely related living relatives are now an 8,000-year-old contagious cancer clone known as Canine Transmissible Venereal Tumour (CTVT).
Chapter 4 presents an ancestry analysis of a rare breed of humpless, dwarf shorthorn cattle from the remote island of Socotra, in the Arabian Sea. Admixture analyses show that contrary to published hypotheses, these cattle are predominantly Eurasian taurine (Bos taurus) in ancestry, with only minimal African taurine heritage, and preliminary results indicate possible admixture with a basal clade of zebu cattle (Bos indicus).