VictorJuiz/thesis huggingface dataset:
On low-rank plus sparse matrix sensing
Keywords: PCA
Robust PCA
low-rank approximation
low-rank plus sparse
numerical analysis

Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data, and is the foundation of robust principal component analysis (Candès et al., 2011). This thesis is concerned with low-rank plus sparse matrix sensing - the problem of recovering a matrix that is formed as the sum of a low-rank and a sparse matrix, and the two components, from a number of measurements far smaller than the dimensionality of the matrix.
It is well-known, that inverse problems over low-rank matrices, such as robust principal component analysis and matrix completion, require a low coherence between the low-rank matrix and the canonical basis. However, in this thesis, we demonstrate that the well-posedness issue is even more fundamental; in some cases, both robust principal component analysis and matrix completion can fail to have any solutions due to the fact that the set of low-rank plus sparse matrices is not closed. As a consequence, the lower restricted isometry constants (RICs) cannot be upper bounded for some low-rank plus sparse matrices unless further restrictions are imposed on the constituents. We close the set of low-rank plus sparse matrices by posing an additional bound on the Frobenius norm of the low-rank component, and ensure the optimisation is well-posed and that the RICs can be bounded. We show that constraining the incoherence of the low-rank component also closes the set provided μ < √mn/ (r √s) and satisfies a certain additivity property necessary for the analysis of recovery algorithms.
Compressed sensing, matrix completion, and their variants have established that data satisfying low complexity models can be efficiently measured and recovered from a number of measurements proportional to the model complexity rather than the ambient dimension (Foucart and Rauhut, 2013). This thesis develops similar guarantees showing that m × n matrices that can be expressed as the sum of a rank-r matrix and a s-sparse matrix can be recovered by computationally tractable methods from 𝒪(r(m+n-r)+s)log(mn/s) linear measurements. More specifically, we establish that the RICs for the aforementioned matrices remain bounded independent of problem size provided p/mn, s/p, and r(m+n-r)/p remain fixed. Additionally, we show that semidefinite programming and two hard threshold gradient descent algorithms, NIHT and NAHT, converge to the measured matrix provided the measurement operator's RICs are sufficiently small. The convex relaxation and NAHT also provably solve Robust PCA with the optimal order of the number of corruptions s = 𝒪(mn/(μ2 r2)). Numerical experiments illustrating these results are shown for synthetic problems, dynamic-foreground/static-background separation, and multispectral imaging.
Counting partial objects
Keywords: Philosophy of language
Semantics
Counting
Formal semantics

In this thesis, I develop a theory of counting. Chapter 1 introduces the topic and explains why it is important to give a theory of counting whole and partial objects. Chapter 2 shows that giving a theory of counting is surprisingly difficult because counting has five special features: counting is kind sensitive, source sensitive, context dependent, graded in felicity, and underspecified. Based on the observation that counting is tightly connected with the notion of mentally merging objects, I develop a theory of counting in Chapter 3 that accounts for all these features. Roughly speaking, we can count objects with respect to a predicate P iff we can merge them such that they form objects that are sufficiently similar to whole Ps and at most one partial P. Chapter 4 argues that this theory of counting performs better than its competitors. Chapter 5 refines the proposed theory in three ways, while Chapter 6 replies to six objections against the theory. Chapter 7 concludes these discussions by exploring potential future research questions.
Molecular carbon allotropes: cyclo[n]carbons
Keywords: polyyne
cyclo[n]carbons
carbon allotropes
aromatic

This thesis details the first structural characterisation of a cyclo[n]carbon. Carbon allotropes built from rings of two-coordinate atoms, known as cyclo[n]carbons, have fascinated chemists for many years, but until now they could not be isolated or structurally characterised, due to their high reactivity. This thesis describes two different routes to cyclo[18]carbon by atomic manipulation of a cyclocarbon oxide C24O6 and a bromocyclocarbon C18Br6 precursor on bilayer NaCl on Cu(111) at 5 K. It then discusses initial attempts towards the on-surface synthesis of antiaromatic cyclo[n]carbons.
Chapter 1 reviews the history of synthetic carbon allotropes, in particular the cyclo[n]carbons, including all theoretical and experimental investigations into these molecular carbon allotropes. An introduction to the field of scanning probe microscopy is then detailed.
Chapter 2 discusses the on-surface generation of cyclo[18]carbon by elimination of carbon monoxide from a cyclocarbon oxide molecule, C24O6. Characterisation of cyclo[18]carbon by high-resolution atomic force microscopy reveals a polyynic structure with defined positions of alternating triple and single bonds. The high reactivity of cyclocarbon and the cyclocarbon oxides allows covalent coupling by atom manipulation, which has significant promise for the synthesis of other carbon allotropes and carbon-rich materials from the coalescence of cyclocarbon molecules.
Chapter 3 details the synthesis of cyclo[18]carbon by dehalogenation of a bromocyclocarbon precursor, C18Br6, in 64% yield. This method generates cyclo[18]carbon in a higher yield than from the cyclocarbon oxide, C24O6. The experimental images of C18 are compared with simulated images for four theoretical model geometries, including possible bond-angle alternation: D18h cumulene, D9h polyyne, D9h cumulene and C9h polyyne. Cumulenic structures with (D9h) and without (D18h) bond-angle alternation can be excluded. Polyynic structures with (C9h) and without (D9h) bond-angle alternation both show a good agreement with the experiment and are challenging to differentiate.
Chapter 4 explores the synthesis and properties of a series of cyclocarbon oxides as precursors to antiaromatic cyclo[n]carbons. The synthesis of cyclocarbon oxide precursors to cyclo[24]carbon (C32O8) and cyclo[20]carbon (C28O8) is discussed however the on-surface sublimation of both molecules proves unsuccessful. Initial investigations into the synthesis of a cyclo[16]carbon precursor, C22O6, are also detailed. Finally, a number of possible future avenues for this project are described.
Dissecting the contribution of dipeptide repeats to the toxicity in C9orf72 iPSC-derived neurons from ALS/FTD patients
Keywords: Neuroscience
Doxycycline inducible system
Lentivirus
Neurodegeneration
Calcium physiology
Cellular stress
Motor neurone disease
Cloning
Induced pluripotent stem cells
Amyotrophic lateral sclerosis
C9ORF72

A large (GGGGCC) repeat expansion in C9ORF72 gene is the commonest genetic cause of amyotrophic lateral sclerosis (ALS). It causes both loss- and gain-of-function, but the relative contribution of the different mechanisms to the development of ALS remains uncertain. One of the pathomechanisms is the production of dipeptide repeat proteins (PR, PA, GR, GP and GA) via repeat-associated non-ATG translation (DPRs). Animal and cellular models have suggested that the arginine-rich DPRs are toxic, but staining in fixed brains of C9orf72 patients show that the same DPRs are not very abundant compared to GA, GP and PA. Moreover, the DPR-related phenotypes exhibited in in vitro models are not always verified in C9orf72 patients. For these reasons I developed a doxycycline-inducible lentiviral system to regulate DPR expression in induced pluripotent stem cell (iPSC)-derived motor neuron (MN) cultures. The effects of GA and PR expression in CRISPR/Cas9 corrected C9orf72 iPSC-derived MNs were compared to the phenotypes of C9orf72 mutant lines. Both DPRs were partially accountable for altered ER and mitochondrial calcium homeostasis, and stress granule formation. Moreover, PR expression may reduce maximal mitochondrial respiration, while GA induced lysosomal activation. The activation of chaperone-mediated autophagy cleared CRISPR/Cas9 corrected iPSC-derived MNs from GA and PR, but it did not rescue C9orf72 mutant lines. Moreover, I studied the effects of a peptide designed to reduce RNA foci, and I showed that it may improve mitochondrial respiration in C9orf72 mutant iPSC-derived MNs.
Income and asthma-related outcomes in children: a longitudinal study in the United Kingdom
Keywords: child health
income-gradient
wheezing
longitudinal
health-related income inequality
asthma

There is evidence that children from socially disadvantaged families tend to have poorer health outcomes than their richer counterparts. However, evidence on the association between family income and specific outcomes, such as asthma and wheezing, is limited. This thesis therefore applies different methodological approaches to investigate the relationship between family income and asthma-related outcomes in children, in the United Kingdom.
Chapter 1 presents the motivation and background to the thesis, and Chapter 2 describes the data and gives an overview of the methods used. Three asthma-related outcomes were used, as derived from the Millennium Cohort Study. These were: ever asthma, wheezing in the last 12 months and asthma medication use. Chapter 3 examines cross-sectionally, the association between family income and asthma-related outcomes. The results showed that income is a statistically significant driver of asthma-related outcomes, after taking into account potential confounding factors. Furthermore, for outcomes ever asthma and asthma medication use, there was some evidence that the child health-income gradient strengthened with age, novel findings in the United Kingdom.
Chapter 4 considers heterogeneity in asthma-related outcomes in children, and constructed four phenotypes based on the duration and onset of wheezing. Multinomial regression models were fitted to analyse the association between income and wheezing phenotype. Results showed statistically significant associations between income and the late-onset and persistent wheezing phenotypes, which are both likely to persist into adult life.
In Chapter 5, empirical methods are used to exploit the longitudinal nature of the data. Two approaches were used: firstly, panel data methods, where fixed and random effects models were fitted to the data. Income effects were statistically weak across all asthma-related outcomes. Secondly, a single regression model was fitted on the combined data across all age groups for each outcome, including an interaction term between income and survey age. Results showed that higher income decreased the probability of asthma-related outcomes.
Chapter 6 examines income-related inequity of asthma-related outcomes. The first part of the analysis used Erreygers’ Indices to estimate income-related inequality. Negative indices indicated income-related inequality for all ages and outcomes. Income-related inequality was then decomposed into contributing factors, and showed that income itself is the main driver.
Overall, the findings show that children from low-income families are at higher risk of adverse asthma-related outcomes, and that the burden of asthma-related disease is more concentrated in low-income children. In light of this, policies should therefore focus on reducing the degree of income-related inequality in asthma outcomes in children, by tackling the key drivers of inequality.
A polymath from Amdo: the many hats of Sumpa Khenpo Yeshe Paljor (1704–1788)
Keywords: Tibetan social history
life writing
Tibetan and Himalayan studies
Qing

The eighteenth century is a key period for Amdo, a region which sits at the crossroads between Tibetan, Mongolian, and Chinese cultural and political spheres of influence. Due to the shifting geo-political landscape of this period, studies have frequently focused on the many historic events, overlooking more localised and personal accounts. This thesis will add to the growing trend of studying personal histories by focusing on the experiences and perspectives of one individual; Sumpa Khenpo Yeshe Paljor (Sum pa mkhan po Ye shes dpal 'byor; 1704–1788). An influential and respected incarnate lama, research on this figure in the West has shown him to be an important diplomat in these tripartite relations and he is often labelled as an interlocutor between the Tibetan, Mongolian, and Chinese cultural spheres.
The main text investigated in this thesis is the autobiography of Sumpa Khenpo titled 'A Description of the Activities of the Khenpo Known as Erdeni Paṇḍita, [which is like] Nectar for the Ear' (mKhan po erte ni Paṇḍi tar grags pa'i spyod tshul brjod pa sgra 'dzin bcud len). As a starting point for my investigation, I translated and analysed the work in its historical, religious and political context. During the research, it became clear that Sumpa Khenpo’s role as diplomat was only one of the many roles he assumed. The most interesting facet of his writings, and a key contribution of this thesis, is how he blends all these many roles – or, as the title of this thesis suggests, wears his many hats – and can switch between them as required across the networks he develops.
This thesis will highlight three important roles that feature prominently in Sumpa Khenpo’s autobiography. The first aspect studied in this thesis is his influence as a pilgrim; while the main aims of his travels were religious, these journeys also opened and developed networks to further religious, institutional and economic goals as it was expected of the head of monastic institutions. The second aspect is his use of rhetoric to further his roles as a peacekeeper, teacher, and abbot, and to encourage virtue and build his own reputation. The final aspect is more practical in nature, focusing on the use of medicine in his role as healer, teacher, and writer of medical literature, which is still in use today.
Sumpa Khenpo’s autobiography bears witness to the fact that he was a true polymath; a frontier cosmopolitan scholar whose many skills, knowledge, and prominence allowed him to comfortably navigate across cultural boundaries and build a reputation to spread the dharma across the region and across time, through his autobiography.
The challenges of developing diagnostic assessments in countries rooted in rote learning – a case study around assessment in India
Keywords: MEA
MEA 2020

This thesis explores the challenges of developing diagnostic assessments to measure skills and competencies in an education system where assessments are rooted in a rote-learning culture. The research in this thesis applied the work of Marsh and Hau’s 2007 research that issued a challenge to researchers that their methodology should be adopted in the analysis of substantive data. This challenge was applied to a ‘real’ (substantive) data set from a newly created diagnostic assessment in India, a country rooted in rote learning. The methodology describes a multi-stage process for exploratory factor analysis alongside practical cautions around limited use of rules-of-thumb, and considerations of missing data and interpretation of causality. The Marsh and Hau (2007) assertion is that the “polarization of substantive and methodological approaches to research and research training” must be reduced. The assessment at the centre of the research in this thesis was conceived, designed, developed and marketed by bringing together assessment implementors – experts, assessment developers, teachers, school leaders and examination board reviewers. This thesis concludes that the Marsh and Hau (2007) methodology is useful in a substantive research setting but argues that there is further polarisation to consider – that between researchers (methodological or substantive) and implementors of educational assessments.
Online intergroup conflict: How the dynamics of online communication drive extremism and violence between groups
Keywords: Social Media
Social Psychology
Internet
Extremism
Polarisation
Intergroup Conflict

In the early days of the Internet, the social web was suggested to hold the power to reduce conflict, prejudice, and discrimination, by promoting connection between those with diverse backgrounds and experiences. However, this optimistic view has not materialised. Instead, evidence shows that Western societies are increasingly polarised and divided, and social media has been particularly implicated with the promotion of violent extremism and the spread of hate speech. The exact role social media plays in driving these processes remains poorly understood. This thesis investigates the mechanisms through which social media may foster and exacerbate intergroup conflict both online and offline, and explores different intergroup and intragroup dynamics which may drive this trend. This work firstly investigates the prevalence and impact of online communication between opposing groups on offline intergroup relations, demonstrating how intergroup communication does frequently occur online, but can be confrontational, hostile, and fails to improve intergroup relations, instead predicting future offline violence. Following this, we then develop a novel approach to detect online hate speech by leveraging datasets from multiple social media platforms in order to train natural language machine learning classifiers. We use these classifiers to explore the influence of extreme outgroup denigration in ingroup discussions on fringe social media platforms popular with the far-right. We demonstrate how exposure to online hate plays a role in shaping individual radicalisation trajectories, increasing the likelihood of offline hate crimes, and driving mutual radicalisation with opposing groups. Finally, we explore the effect of hostile manipulation from state actors on the dynamics of online conversations, presenting novel techniques to reveal how manipulation of these discussions increases the polarisation of online conversations from genuine users. Together these findings shed light on the mechanisms by which the Internet promotes intergroup conflict, extremism, and violence, providing new insight into initial steps that could be used to counter these effects.
Russia's escalating opposition to popular revolutions in the Post-Soviet region and Middle East: A quest for domestic legitimacy
Keywords: Syria
Russia
Vladimir Putin
Popular Protests
Constructivism
Ukraine
Color Revolutions

This thesis attempts to explain the sources of Russia’s opposition to popular uprisings in the post-Soviet region and Middle East since the colour revolutions in Georgia (2003) and Ukraine (2004). Although Russia has experienced few major episodes of unrest in recent years, Moscow’s opposition to popular uprisings has escalated from rhetorical criticisms of the colour revolutions to its military interventions in Ukraine and Syria. This thesis argues that existing neoclassical realist, English School and constructivist arguments incompletely explain this phenomenon, and instead advances a novel theoretical approach called “instrumental constructivism.” This theory contends that Russia’s counter-revolutionary policy is an integral component of its foreign policy identity that crystallised in an incremental fashion. Soviet and transition-era framings of popular unrest conditioned the Russian public to associate mass protests with rampant disorder, and Western interference and expansionism.
As Vladimir Putin’s presidency progressed, the Russian public also linked successful challenges to the Western-dominated liberal order to domestic perceptions of great power status. In order to align Russian foreign policy more closely with public opinion, Russian officials constructed a counter-revolutionary foreign policy identity, which exploited popular insecurities about mass protests and appealed to domestic status aspirations. To provide empirical evidence for instrumental constructivism’s key contentions, this thesis explores Russia’s responses to the colour revolutions and Arab Spring and uses Ukraine after the Euro-Maidan revolution and the Syrian civil war as its two primary case studies. The thesis concludes by assessing instrumental constructivism’s potential transferability to the foreign policy conduct of other authoritarian states, and to related dimensions of Russia’s global offensive against liberal democracy.
Structural disorder in two-dimensional network-forming materials
Keywords: Bilayer Materials
Persistent Homology
Complex Networks
Disordered Materials
Monte Carlo Methods
2D Materials
Voronoi Diagrams

Investigations into two-dimensional network-forming materials have renewed importance due to the experimental synthesis of ultra-thin films of carbon, silica and aluminosilicate glasses. Microscopy on the disordered phases of these materials reveals a percolating ring structure, identifying them as candidates for a range of technologically useful materials, with applications including catalysis and gas separation. The ability to characterise, understand and control the structure of the pore landscape in such materials is therefore central to their further development.
The overall aim of this thesis is to improve the simulation and characterisation of two-dimensional disordered materials. The key is to accurately quantify and reproduce the ring structure, described by the ring size distribution and ring-ring correlations. This will be achieved by relating previous empirical laws (namely Lemaître’s law and the Aboav-Weaire law), to well-defined metrics in network science, and developing a variety of Monte Carlo methods to generate networks with controllable ring structures and topologies.
The first of these methods will be a sequential growth algorithm to construct triangle rafts (a proxy for silica bilayers), which will be shown to produce configurations commensurate with those from experiment. Following from this, a modified bond switching algorithm will be used to investigate more generic systems, spanning a variety of atomic coordination environments, potential models and topologies. Fundamental relationships between these measures and the ring structure will be demonstrated by systematically varying the system parameters. In addition, hard particle Monte Carlo techniques will be used to generate Voronoi diagrams, making contact with experimental studies on quasi-two-dimensional colloidal systems.
Treating these diverse physical systems as complex networks allows a gener- alised network theory to be developed. Traditional ring measures will be related to well-defined metrics from network theory, namely the node degree distribution and the assortativity. This will enable seemingly disparate physical systems to be compared and ties them into the wider field of network science.
Further applications of this work to real systems will be illustrated with analyses on a range of experimental (or experimentally motivated) data. The appropriateness of weighted and unweighted Voronoi constructions will be eval- uated for colloidal monolayers. The ring structure of procrystalline lattices will be demonstrated to be related to the underlying parent lattice and atomic coordination environments. Finally, a tool from topological data analysis, termed persistent homology, will be investigated and shown to be a potential complement to more traditional measures of structural disorder.