VictorJuiz/thesis huggingface dataset:
Data-driven discovery of Green's functions
Keywords: PDE learning
Green's functions
deep learning

Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. Theoretical results and deep learning algorithms are introduced to learn Green's functions associated with linear partial differential equations and rigorously justify PDE learning techniques.
A theoretically rigorous algorithm is derived to obtain a learning rate, which characterizes the amount of training data needed to approximately learn Green's functions associated with elliptic PDEs. The construction connects the fields of PDE learning and numerical linear algebra by extending the randomized singular value decomposition to non-standard Gaussian vectors and Hilbert--Schmidt operators, and exploiting the low-rank hierarchical structure of Green's functions using hierarchical matrices.
Rational neural networks (NNs) are introduced and consist of neural networks with trainable rational activation functions. The highly compositional structure of these networks, combined with rational approximation theory, implies that rational functions have higher approximation power than standard activation functions. In addition, rational NNs may have poles and take arbitrarily large values, which is ideal for approximating functions with singularities such as Green's functions.
Finally, theoretical results on Green's functions and rational NNs are combined to design a human-understandable deep learning method for discovering Green's functions from data. This approach complements state-of-the-art PDE learning techniques, as a wide range of physics can be captured from the learned Green's functions such as dominant modes, symmetries, and singularity locations.
Exploring the molecular underpinnings of neuropathic pain in primary afferent subtypes
Keywords: sensory neuroscience
neuropathic pain
bioinformatics
RNA-seq
scATAC-seq

Dorsal root ganglia (DRG) neurons have been well described for their role in driving both acute and chronic pain. With cell bodies clustered in the spinal column, these neurons project from the periphery into the dorsal horn. Subtypes convert a range of stimuli into electrical signals, and have been traditionally defined by size, histological markers, projection pathways, and electrophysiological phenotypes. With the advance of sequencing technologies, DRG transcriptomes have been examined through whole ganglia, single cell, and more recently, deep subpopulation sequencing in naïve lines. Here, we study the deep transcriptional profiles of multiple murine DRG populations in acute and chronic pain states while considering sex interactions.
We have exploited currently available transgenics to label and purify subtypes after injury for high throughput sequencing. Using bulk tissue samples, we are able to circumvent the issues of low transcript coverage and drop-outs seen with single cell datasets, increasing our power to detect changes in gene expression.
In one experiment, we have studied the molecular changes in five populations, classified by their functional and molecular signatures in naive states. These include general nociceptors, peptidergic nociceptors, non-peptidergic nociceptors, C-LTMRs, and Ad + AB-RA-LTMRs. We see both stereotyped and unique subtype signatures in injured states after nerve injury at both an acute and chronic timepoint. While all populations contribution to a general injury signature, subtype enrichment changes can also be seen, possibly driven by the loss of transected NP neurons by 4 weeks. Within populations, there is not a strong intersection of sex and injury, but sex differences in na\"ive states - particularly in Ad + AB-RA-LTMRs - still contribute to differences in injured neurons.
Using an SNI model of neuropathic pain, ipsilateral DRG contain both injured and intact neurons. The contributions of these populations to pain have yet to be delineated. Mirroring the techniques above, we next used an Atf3creERT2 line to label and sort fluorescent neurons prior to RNA-seq. We have complemented this with a pilot snATAC-seq study, showing that neurons cluster by subtype in naive and injured states.
We have curated this data into an accessible, online platform. Together, this contributes a resource to the pain community to probe subpopulation and sex-specific differences after nerve injury at multiple timepoints.
Systematics of the Stictocardia clade (Ipomoea L., Convolvulaceae)
Keywords: EOO
Stictocardia
Monograph
Ipomoea
AOO

Botanical monographs are comprehensive taxonomic accounts of a specific group of plants. This thesis reviews relevant taxonomic literature and investigates a subsumed genus – Stictocardia - nested within Ipomoea (Convolvulaceae), one of the species-rich genera of Angiosperms. A large number of specimens representing twelve out of 13 species of Stictocardia, both herbarium sheets and digital images from 35 herbaria, are the source of quantitative morphological data (115 samples) and leaf material for DNA sequencing (36 samples). Morphological characters and DNA sequence data are two lines of evidence that interact through reciprocal illumination within the scope of integrative taxonomy. Principal Component Analysis and Mann-Whitney test were conducted on several indistinct taxa to ensure rigorous hypothesis testing on species delimitation. Phylogenetic study consistently identifies seven species of Stictocardia in a clade named Stictocardia (non-italic) based on independent data sets - nrITS and plastome - and various inference methods (MP, A-ML and BI). This clade of seven species is characterised by a set of homoplastic morphological characters. These seven species are monographed for the first-time including clade circumscription, identification key, distribution maps and a comprehensive taxonomic account (nomenclature, description, illustration, habitat, notes and specimens seen). Conservation assessments based upon Area of Occupancy (AOO) and Extent of Occurrence (EOO) analyses, were conducted to this clade. In addition, four species of Stictocardia are recovered outside of the clade Stictocardia and more closely related to other species of Ipomoea. Two species require further investigation to resolve their placements whether inside or outside the clade Stictocardia.
Reginald Pole and the legations of 1537 and 1539 : diplomatic and polemical responses to the break with Rome
Keywords: Reginald Pole
16th century
polemical
break with Rome
diplomatic
legations
sixteenth century
Rome

The thesis deals with the diplomatic career of Reginald Pole at the beginning of his time as a Roman cardinal. Pole's elevation to the cardinalate in 1536 and his quest to persuade Charles V and Francis I to help re-establishing Roman obedience in England are portrayed. Pole's two legations of 1537 and 1539 both failed, it is argued, because of the ongoing hostilities between the houses of Habsburg and Valois: neither the emperor nor the French king could afford to alienate the powerful English ruler, nor were they interested in taking up a costly and risky enterprise on behalf of religion. The differences between the two legations and the different reasons for their failing are discussed. The reaction of the English policy makers both to the legations themselves and to Pole's activities is also considered. The almost complete annihilation of Pole's family in England is linked with Pole's efforts against the English king, and it is shown that the Poles in England lost their lives not because of their alleged treasonable activities in combination with the so-called "Exeter Conspiracy" but because they were used as hostages by Henry VIII against Reginald Pole: it is argued that the "Exeter Conspiracy" is a misnomer, and that the two families involved suffered for reasons of raison d'état and personal revenge. Pole's major writings against the English king in the 1530s, De ecclesiasticae unitatis defensione and the Apologia ad Carlum Quintum, are then examined with regard to Pole's political maxims and his use of anti-Machiavellism in his fight against the English schism. Overall, it is argued in the thesis that Pole was an able politician whose failure is to be explained by the untimeliness of his attempts to unite Charles V and Francis I in a fight for religion and by his own exclusively religious motivation in political affairs.
Learning and inference over relational data
Keywords: Knowledge graph embedding models
Knowledge base completion
Knowledge graph completion
Graph neural networks
Message passing neural networks
Graph representation learning
Graph machine learning
Relational data

Relational data is ubiquitous in modern-day computing, and drives several key applications across multiple domains, such as information retrieval, question answering, recommendation systems, and drug discovery. As a result, a main research question in artificial intelligence (AI) is to build models that exploit relational data in an efficient and reliable way, while injecting the relevant inductive biases and being robust to input noise. In recent years, neural models such as graph neural networks (GNNs) and shallow node embedding models have enabled significant breakthroughs in learning representations over relational structures. However, the abilities and limitations of these systems are not completely understood, and several challenges remain to endow these models with reliability guarantees, enrich their relational inductive bias, and apply them in more challenging problem settings. In this thesis, we study learning and inference over relational data. More specifically, we analyse the properties and limitations of existing models both theoretically and empirically, and propose new approaches with improved relational inductive bias and representation power.
Modelling and monitoring the behaviour of predators and prey in the context of anthropogenic risk
Keywords: African lion
behavioural ecology

Predator-prey dynamics help shape the populations and behavioural interactions of wildlife at all trophic levels. Risk effects are animals’ behavioural responses to the risk of predation and their associated costs. Humans impose risk effects on both predators and prey, and it’s important to understand those effects when developing conservation strategies. Here I examine the behaviours of Uganda kob (Kobus kob thomasi) and African lions (Panthera leo), both living in carnivore-ungulate systems within human-dominated landscapes. By recording kobs’ flight distances relative to road networks and snare poaching activity, I find that kobs’ antipredator responses do not seem to be affected by proximity to roads or local snaring intensity. However, sexual differences in flight distance may suggest intraspecific competition influences kobs’ risk tolerance. I also develop a model of lions’ energy expenditure over space and time as a result of habitat covariates. The construction of behavioural decision-making models could allow researchers to identify how lions and other carnivores perceive anthropogenic risk, given enough data to distinguish risk effects from other variables influencing their decisions. The aim of this thesis is to better understand the extent to which humans influence the behaviours of predators and prey and how human activities influence other animals’ perceptions of risk in dynamic ways.
The holographic swampland and other topics in string phenomenology
Keywords: string cosmology
holography
string phenomenology
swampland

The main topic of this thesis is to explore the consistency and structure of realistic, 4d vacua of String Theory through the AdS/CFT correspondence. As a first step, we investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, the type IIA DGKT flux vacua and both perturbative and racetrack stabilisation. We also point out an intriguing connection to the Swampland Distance Conjecture, both in its original and refined versions. A second, unexpected consequence of this analysis is that the CFT data for some of these vacua takes a universal form, independent of the compactification details. For the type IIA examples, we then give a concise argument that supersymmetric AdS DGKT flux vacua on general Calabi-Yaus always have integer conformal dimensions for all low-lying scalar primaries in the dual CFT. These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold. We give a tentative discussion of the origin of these integers and effects that would modify these results.
In the last part of the thesis, we take a more phenomenological approach and study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). We show that in LVS, provided the existence of a large hierarchy between the inflationary and the weak scales, initial seed radiation will localize the system onto a tracker solution where the problem is solved. The consistency require- ment of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales – an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins (both universal and model- dependent) of the initial seed radiation, with a particular emphasis on the possibility of having an LVS fundamental string network.
Reconstructing the timing and location of North-West Saharan rainfall with spatially distributed secondary carbonates
Keywords: Uranium-Thorium
Climate
Rainfall
Stalagmite
Sahara
Paleoclimate
Chronology
Speleothem
Geochemistry
Stable Isotopes

There is significant evidence that the presently hyper-arid Sahara belt stretching across North Africa has experienced periods of increased rainfall and surface moisture coverage at numerous times during the middle to late Pleistocene. During these times, there was increased vegetation coverage, greater mega-fauna distributions and more extensive human occupation. However, our understanding of precisely where and when rainfall increased is currently limited due to a paucity of high-resolution paleoclimate data. Furthermore, present records are over-extrapolated in their interpretations of moisture source and the spatial distribution of rainfall. In this thesis, periods of past in- creased rainfall are assessed in the central and northern Sahara using the formation age, stable isotope compositions and trace element concentrations of radiometrically dated secondary carbonate deposits. Stalagmites from the High- and Anti-Atlas Mountains provide evidence that sub-tropical rainfall occurs in response to increasing North-South inter-hemispheric temperature anomalies during the mid-Holocene African Humid Pe- riod, rather than as the direct result of a northwards extension of the West African Monsoon. Subsequently, older periods of Saharan-, High- and Anti-Atlas speleothem formation throughout the middle to late Pleistocene identifies periods of increased northern Sahara rainfall during a number of major northern hemisphere interglacial and interstadials. In the central Sahara, chronology from flowstone-like secondary cal- cite samples provides the first evidence of carbonate deposition from this region formed from direct, local rainfall rather than as a result of increased surface moisture avail- ability. Calcite formation during Marine Isotope Stage 11 suggests a consistent tropical source of rainfall in the central and northern Sahara. This thesis presents the north- west Sahara as a unique and climatically significant Saharan region, from which the activation of perennial southward flowing river systems was critical for human migration and development. Furthermore, this work better characterises the minimum geographic extent of increased north-west Saharan rainfall and identifies the need to move away from overly-generalised “Green Sahara” interpretations of Saharan climate.
The higher lattice gauge theory model for topological phases of matter
Keywords: Anyon physics
Higher lattice gauge theory
Topological phases of matter

Topological phases of matter are characterised by long-range entanglement between their constituent degrees of freedom, which allows them to host excitations with non-trivial exchange statistics. While topological phases in 2+1d are relatively well studied, less is known about their 3+1d counterparts. In this thesis, we examine features of these higher-dimensional phases in a tractable example model, based on a generalisation of lattice gauge theory called higher lattice gauge theory. As well as hosting point-like excitations, the model supports loop-like excitations with non-trivial loop-loop and point-loop braiding statistics. We explicitly construct operators to produce and move these excitations, and use these to find the loop-loop and point-loop braiding relations. These creation operators also reveal that some of the excitations are confined, costing energy to separate, while others are condensed and can be produced locally. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also explain a method for measuring topological charge and use explicit measurement operators to re-derive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the higher lattice gauge theory model on the 3-torus. From these measurement operators, we can see that the ground state degeneracy on the 3-torus is related to the number of types of linked loop-like excitations.
Structural patterns in William Faulkner's major novels
Keywords: Literary style
20th century
William Faulkner
novels
twentieth century
American literature
Faulkner
Structural patterns

William Faulkner wrote nineteen novels. Continually experimenting with the structure of the narrative, he produced a few superbly successful technical achievements, an intermediate body of works that are fascinating for what they attempt and the ways they attempt it, and more than several outright failures. With an experimenter, even a failure is usually of some interest.
"(I)t was simply because to me that seemed the most effective way to tell that story,"! Faulkner would answer to questions about his use of a particular unorthodox structure. But in spite of that disavowal, and in spite of the fact that it is undoubtedly true, that the novels were certainly first and foremost independent units, with structures selected as purely as possible to present most effectively the given story and theme; still, there are connections to be made among the various novels. At least eight of the major works, in fact, are built on the pattern of two types of structure, which might be given the labels contrapuntal and centripetal.
"To what extent does Faulkner work in terms of polarities, oppositions, paradoxes, inversions of roles?" Robert Penn Warren asked, reviewing Malcolm Cowley's compilation of The Portable Faulkner, in August, 1946. "How much does he employ a line of concealed (or open) dialectic progression as a principle for his fiction? The study of these questions may lead to the discovery of principles of organization in his work not yet defined by criticism."! Such a study has yet to be systematically done.
Continued in thesis ...
The life and times of the Empress Wu Tse-t'ien of the T'ang dynasty
Keywords: Biography

The Life and Times of the Empress Wu Tse-t'ien of the T'ang Dynasty is an attempt to describe and place in perspective the régime of perhaps the most controversial ruler in the history of medieval China. It is an attempt also, to define an imperial vision, to show the shifting priorities and stages of policy by which the Empress Wu set out to achieve certain aims; and it offers comment on the successes and failures of her career. Within this context, the Empress herself emerges as a woman whose consistency of character and virtuosity of mind is reflected only palely in previous studies.
Emphasis is placed in several areas. The first of these is the question of her position and her power. How did she win recognition as the legitimate sovereign of a state and a culture which had never before been ruled by a woman? And why, after this unique achievement, did she fail to preserve her position until her death? What influence did her unorthodox governmental role have upon the T'ang dynasty? And did her half-century of power leave any enduring marks upon China?
Out of these considerations grows a second emphasis-- the tension between Confucian state-theory and the anomaly of a female ruler. In this clash, the tradition proved to be of greater flexibility than is generally recognized, but at the same time, proved to be so durable and so resilient that in the Chou, the Empress found herself increasingly frustrated and finally defeated by it. This study suggests that while husband or son occupied the throne, she was able to borrow their legitimacy and make great strides in the achievement of her two principal goals: the creation of a viable centralization, and of an imperial institution which would be free, secure, and supreme in its relationship with a new bureaucracy. In the Chou, however, the contemporary power structure came increasingly to resist innovation and with increasing success. As a result, the dynasty is best regarded as it was at the restoration, as a "caretaker" régime, a period of consolidation and continuity of policies initiated in the preceding quarter century. The Empress Wu seized the throne to preserve rather than to innovate.
Continued in thesis ...