VictorJuiz/thesis huggingface dataset:
A Riemannian perspective on matrix recovery and constrained optimization

Nonlinear matrix recovery is an emerging paradigm in which specific classes of high-rank matrices can be recovered from an underdetermined linear system of measurements. In particular, we consider matrices whose columns, seen as data points, belong to an algebraic variety, namely, a set defined by finitely many polynomial equations. The nonlinear structure is exploited using an appropriately chosen feature map, which induces a low-rank structure in the feature space, thus allowing recovery of the original (high-rank) matrix. The same framework is applicable to matrices whose columns are divided in clusters, so that we can address clustering tasks with missing entries.
We formulate the rank minimization of the feature matrix as the minimization of a smooth cost function on a Riemannian manifold, which then allows us to employ the theoretically rigorous Riemannian optimization framework, that calls on differential geometry tools to construct feasible iterative algorithms on specific Riemannian manifolds. In particular, we show the potential benefits of using second-order algorithmic variants --- instead of first-order ones --- as they are able to achieve recovery of the original data with high accuracy. We additionally develop an alternating minimization method to solve the recovery problem, for which we give convergence and complexity guarantees.
Considering algebraic varieties also leads us to propose a new approach for the denoising of point clouds that approximately fit such structures, as well as for their registration, namely, the task of estimating a transformation which overlaps two point clouds representing the same shape in different coordinate systems.
Finally, we consider general optimization problems with smooth equality constraints. Due to the challenge of achieving feasibility for generic nonlinear equality constraints, we must depart from the Riemannian framework and we propose an infeasible algorithm which minimizes a smooth penalty function, known as Fletcher's augmented Lagrangian. We provide optimal worst-case bounds on the number of iterations that are required to find an approximate first- and second-order critical point.

Keywords: constrained optimization
nonlinear matrix recovery
Riemannian optimization
registration
nonconvex optimization
denoising
Advisor: Cartis, C
Eftekhari, A
Super-resolution microscopy with spatial modes of light

The resolution of imaging devices is ultimately limited by the diffraction of light. This limit can be circumvented by exploiting near-field phenomena, non-linearities of the sample or specific illumination schemes, which led to the recent explosion of optical super-resolution techniques. However, it would be desirable to reach the nanoscale in the most general way possible, with far-field linear imaging of uniformly illuminated samples.
In the last few years, the answer to that came with the field of quantum-inspired super-resolution (QISR), where quantum metrological techniques were used to find novel measurement schemes that, beyond the conventional direct imaging of light, would achieve higher precisions. Interestingly, these ideas would always in some way or another involve transverse spatial modes of light. This thesis presents our work on the subject, with novel theoretical and experimental results.
Firstly, we develop the traditional theory of QISR, with has mostly focused on either the estimation of separation of two point sources or on geometric moments of samples. Then, we introduce our own results on optical imaging of general distributions of point sources, in a step to take QISR from toy examples to real imaging scenarios.
Secondly, we apply all the concepts studied on a experimental, proof-of-principle implementation of a QISR scheme dubbed Hermite-Gaussian Microscopy (HGM), which uses heterodyne detection with several Hermite-Gaussian modes as local oscillator in order to reconstruct the object sample and achieve super-resolution. We report the techniques necessary for the manipulation of spatial modes of light, as well as our results, where we demonstrated 2D imaging with twofold resolution enhancement beyond the diffraction limit.

Keywords: quantum metrology
microscopy
super resolution
quantum optics
imaging
Advisor: Lvovsky, A
Approximate message passing for compressed sensing magnetic resonance imaging

Magnetic Resonance Imaging (MRI) is a non-invasive, non-ionising imaging modality with unrivalled soft tissue contrast. A key consideration for MRI is data acquisition time, which is limited by inherent technological and physiological constraints. Compressed sensing is a relatively recent framework that can reduce the MRI acquisition time by undersampling randomly and exploiting presumed redundancies in the data.
The Approximate Message Passing (AMP) algorithm is an iterative compressed sensing method that efficiently reconstructs signals that have been sampled with i.i.d. sub-Gaussian sensing matrices. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in MRI, AMP performs poorly in practice.
In response, this thesis proposes the Variable Density Approximate Message Passing (VDAMP) algorithm for undersampled MRI data. We present three versions of VDAMP: single-coil VDAMP, where receiver coil sensitivities are ignored, Parallel-VDAMP (P-VDAMP), which includes coil sensitivities, and Denoising-P-VDAMP (D-P-VDAMP), which incorporates the statistical modelling capabilities of neural networks. Central to VDAMP is a property that we term "coloured state evolution", where the difference between the intermediate image estimate at a given iteration and the ground truth is distributed according to a zero-mean Gaussian with known covariance. We demonstrate that coloured state evolution can be leveraged to yield an algorithm that converges rapidly, and to a competitive reconstruction quality, without the need to hand-tune model parameters.

Keywords: approximate message passing
magnetic resonance imaging
image reconstruction
compressed sensing
Advisor: Tanner , J
Hess, A
Mailhe, B
Orbits and outflows of emission-line stars

The optical spectra of some stars exhibit spectral lines in emission, which is characteristic of them having powerful radiatively driven winds. These stars are known as emission-line stars. In this thesis, I study the orbits and outflows of the most luminous and massive emission-line stars: Luminous Blue Variables and Wolf-Rayet stars.
Orbital parameters are typically determined by fitting Keplerian models to radial velocity measurements. For stars with powerful winds, the broad emission lines are formed far out in the stellar wind, encoding dynamical information from an extensive volume of outflowing gas, in a complex and stratified circumstellar environment, which may lead to systematics in the observables. I tackle these problems twofold. (1) I formulate a novel semi-analytical model which encapsulates both the star's orbital motion and the propagation of the wind. (2) I devise a statistical framework for validating the performance of algorithms, and utilise a marginalised Gaussian process to account for residual systematics. I benchmark our models with synthetic data and apply them to several prototypical emission-line binaries, namely Eta Carinae, GG Carinae, WR 140, and WR 133. I find our models identify a consistent set of orbital parameters, independent of the emission line used, and given validation on benchmark datasets, the estimated parameter distributions and dynamical masses are more accurate than those previously calculated.
The Global Jet Watch affords unprecedented coverage of Eta Carinae throughout apastron, revealing the distinct dynamics of the emitting versus the absorbing components of the He I profiles. Cognisant of the known Helium ionisation maps, I model these absorption velocities as tracers of the geometry of the post-shock gas in the colliding winds. I find the modelling is concordant with the panchromatic observations and simulations of Eta Carinae and demonstrate how the model can be used to probe the latitudinal dependence of stellar mass loss. Finally, I describe the Global Jet Watch's photometric datastream, and detail the innovation of new algorithms and the resulting light curves.

Advisor: Blundell, K
Taste and see: real presence as revelation in Heideggerian perspective

This project addresses the Christian of doctrine of revelation by asking how Christians are able to translate an ontological expression of divine self-communication (i.e., the Incarnation of Jesus Christ) into intellectual faith statements in a way that retains something essential of that ontological revelation. The argument of this project is that such incarnational revelation must be understood through encounter, so that the Eucharist—as the site of Christ’s attested real presence—becomes the natural site in which to explore such encounter as the ground of Christian speech. What follows is a theological experiment in which the Eucharist is evaluated in terms of its capacity to reveal the person of Jesus Christ in a post-metaphysical milieu and to shape the understanding of Christians who encounter Christ therein.
In order to establish this constructive argument, this project consults the work of Martin Heidegger. Heidegger’s notion of Being-in-the-world opens up a new definition of understanding, where what is primary is praxis in the form of worldly involvement, so that understanding in the form of habits, mood, and know-how becomes foundational for any knowledge of the beings with which we interact. Language is then linked up with this pre-reflective understanding, first as discourse and then later as poetry, both of which disclose a fundamental world-orientation to language.
As the sacrament where Christ is attested as really present, the material event of the Eucharist becomes a world in the Heideggerian sense, in which Christian participants come to understanding through dynamic involvement. Rather than rooting Christian hermeneutics in mental processes disengaged from embodiment, then, Heidegger helps us relocate the root of Christian understanding in the material reality that is, in the Incarnation and continued in Christ’s real sacramental presence, the very stuff of divine revelation.

Keywords: phenomenology
real presence
Eucharist
revelation
Heidegger
Advisor: Rasmussen, J
Generative modelling for supervised, unsupervised and private learning

In this thesis we develop several state-of-the-art generative modelling-based approaches for a variety of supervised, unsupervised and private learning problems. In the (almost) supervised domain, we tackle the problems of treatment effect estimation, imputation and feature selection. For treatment effect estimation we begin by developing a GAN-based approach that generates the
missing'' counterfactuals, which enables learning a fully supervised model. In SCIGAN, we then go on to adapt this method to the continuous-intervention setting, introducing novel generator and discriminator architectures to handle the continuous nature of the treatments. For imputation, we introduce GAIN, a GAN-based imputation approach that maximally leverages both the adversarial and generative nature of GANs to learn to impute missing data according to the ground truth distribution while simultaneously allowing for multiple imputation to improve reliability and robustness of the imputed data. Finally, for feature selection, we introduce KnockoffGAN, a GAN-based knockoff generation procedure which again leverages the adversarial nature of GANs to learn the appropriate
knockoff'' distribution. In using a GAN, we are able to learn to generate knockoff non-parametrically and thus reliable performance on non-Gaussian data.
In the domain of private learning we address the problem of private synthetic data generation. This challenge has three key components: (1) generating faithful synthetic data; (2) ensuring privacy; and (3) measuring the quality of the generated data. In PATEGAN, we tackle all 3 of these problems by proposing a GAN-based approach to generating differentially private synthetic data. In addition, we introduce a new synthetic data metric, the Synthetic Ranking Agreement, which measures how well machine learning research on the synthetic data represents the same research on the real data. In the final paper presented, we present a new differential privacy building block - a differentially private classification/prediction algorithm, that builds upon the subsample-and-aggregate paradigm. The new method affords better privacy and utility than subsample-and-aggregate and can be used in place of PATE in the PATEGAN framework.

Keywords: imputation
knockoffs
generative modelling
GANs
differential privacy
treatment effect estimation
Advisor: van der Schaar, M
Mudigonda, P
Learning physical intuition for robotic manipulation

When we compare object manipulation capabilities in humans and contemporary robots, we observe an intriguing dichotomy: On one hand, robots have access to advanced compute capacity and precise models of physics, yet their object manipulation skills are comparatively narrow and brittle. On the other hand, the human understanding of physics is allegedly acquired from experience and exhibits many predictive shortcomings, yet their manipulation skills far exceed any contemporary robot’s. Motivated by this observation, this thesis studies the question how much robotic manipulation can benefit from embracing data-driven, approximate models of physics and poses the hypothesis that a tight integration of intuition and control can unlock sophisticated manipulation behaviour.
In particular, three aspects of physical intuition are investigated: (i) high-level intuitions for visual task assessment and their application in object stacking and tool use, (ii) low-level intuitions for rigid-body motions and their application in rearrangement planning and visuomotor control, (iii) the integration of dynamics approximation into control policy learning and its application in structured exploration of an environment.
In the first part, we demonstrate the effectiveness of a visual stability classifier in planning and constructing stable stacks of objects with varying geometries. We also employ a similar task classification technique in a goal-reaching task and show that the associated variational latent space induces an affordance manifold which can be traversed to synthesise suitable tools for a given task. In the second part, we demonstrate that the introduction of dynamics modelling into an object-centric latent space facilitates object disentanglement from raw visual training data and allows to generate physically plausible scenes and videos from scratch. Visual dynamics approximation is also used in our novel, goal-conditioned, visuomotor control architecture where it enables zero-shot transfer to unseen object rearrangement tasks. Finally, we integrate dynamics forecasting and control policy learning in the third part of this thesis and optimise both components using a curiosity objective. This setup leads to the unsupervised emergence of complex, human interpretable manipulation and locomotion behaviour and highlights the crucial importance of physical intuition in the learning process of sophisticated, embodied behaviour.

Keywords: artificial curiosity
visuomotor control
structured latent space
physical intuition
Advisor: Posner, I
Vedaldi, A
Ecology and conservation of critically endangered Leopard (Panthera pardus) in Southeast Asia

Although widely considered the epitome of adaptability, the Leopard (Panthera pardus) has experienced severe declines in distribution and numbers worldwide, yet its conservation status in several regions remains unknown. This is especially true for Southeast Asia where two understudied subspecies of Leopard occur: the Indochinese (P. pardus delacouri) and Javan (P. pardus melas) Leopard. The present study was conducted to gather information on the current status and ecology of these Leopard subspecies in Southeast Asia. Chapter 2 showed that the Indochinese Leopard now likely occurs in about 2-6% of its historical range, which led to its recent uplisting as Critically Endangered by the IUCN. Using data from the largest camera-trap study ever conducted for Leopard in the region, Chapter 3 revealed that densities within key populations in Cambodia, Thailand, Malaysia, and Indonesia were among the lowest ever reported for the species, suggesting the overall prognosis of the Leopard is becoming increasingly bleak in the region. Illegal human activities, which likely were influenced by religious beliefs, socio-economic status, and geographical location, affected the densities, habitat use and activity patterns of Leopard. Using Leopard as case study, Chapter 4 investigated the performance of spatially explicit capture-recapture (SCR) models in low-density populations surveyed with camera traps, and provided recommendations to facilitate the applicability of SCR methods under similar conditions for Leopard and other low-density species. By using DNA confirmed scats, Chapter 5 corroborated the dietary adaptability of Leopard, including the unexpected predation on Banteng (Bos javanicus; 600-800 kg), and showed that predation by this apex carnivore only had a relatively small impact on ungulate populations in eastern Cambodia. Using a novel approach, Chapter 6 investigated the long-term population dynamics of the Indochinese Leopard in a priority site in eastern Cambodia, and found that this unique population is under imminent risk of extirpation, likely due to increases in human-caused mortalities. Chapter 7 looked at the implications of the findings of this thesis and highlighted priorities for Leopard conservation in Southeast Asia. This thesis offers new insights and novel approaches to study Leopard using reliable and repeatable techniques, thus aiding future studies. Overall, this thesis improves the knowledge of the species in the region and provides baseline data for several globally important populations, thereby facilitating monitoring and guiding conservation efforts for Leopard in the extremely biodiversity rich but highly threatened ecosystems of Southeast Asia.

Keywords: IUCN status
Species distribution
Sampling design
Spatial capture-recapture (SCR)
Indochinese Leopard
Diet
Southeast Asia
Habitat use
Javan Leopard
Bayesian analysis
Density estimation
Threatened species monitoring
Population dynamics
Camera trapping
Occupancy model
Prey selection
Leopard ecology
Low-density populations
Advisor: Macdonald, D
Kamler, J
Sollmann, R
Molecular pathways leading to sleep and wakefulness in Drosophila

Sleep is a universal and highly conserved phenomenon across species; yet its operational mechanisms remain one of the greatest biological mysteries. In Drosophila, sleep homeostasis is largely mediated by the activity of neurons projecting to the dorsal fan-shaped body (dFB). Dopamine promotes wakefulness by inhibiting the activity of dFB neurons, switching them to a silent state. This wake-promoting effect is hypothesised to require the exocytosis of the potassium “leak” channel, Sandman, to the plasma membrane, where it exerts its effects by blunting the firing of the neurons. In the chronically sleep-deprived flies bearing a mutation for the crossveinless-c (cv-c) gene, the dFB neurons were previously found in electrical quiescence as well. It is therefore possible that in these mutants, Sandman resides at the plasma membrane of the neurons, reducing their excitability and causing insomnia in the flies. However, the signals responsible for Sandman’s recycling to and from the plasma membrane remain elusive.
To visualise the exo-endocytic pathway of Sandman, I attempted to localise the channel with different fluorescent probes and identify proteins acting in the same pathway using genetic interaction experiments. Depletion of Sandman from the dFB neurons rescues the sleep loss of cv-c mutants, supporting the notion that insomnia in these flies results from the channel’s presence at the plasma membrane. As cv-c encodes for a Rho GTPase-activating protein (Rho-GAP) and small GTPases are often regulated by neurotrophin-related pathways, sleep induction involving the Cv-c-Sandman pathway may further couple to the upstream action of neurotrophic molecules.
dFB-restricted interference with Toll-6, a receptor with neurotrophic function, reduces sleep. Toll-6/cv-c mutants mirror the sleepless phenotype of cv-c mutants, suggesting that Toll-6 may signal through Cv-c, conveying sleep pressure to the neurons. A mutation for Drosophila neurotrophin 1 (DNT1), a ligand of Toll-6, also diminishes sleep. RNAi-mediated knockdown of DNT1 in the R5 neurons, a defined input to the dFB, decreases sleep and abolishes sleep drive encoded by the circuit.
It is proposed here that activity-dependent release of DNT1 from the R5 neurons signals sleep pressure that is transduced by the Toll-6 receptor in the dFB neurons. Activation of the receptor likely feeds into a small GTPase cascade that involves Cv-c and Sandman.

Keywords: sleep
dFB neurons
Drosophila
Advisor: Miesenböck, G
Development of tri-layered biomimetic atelocollagen scaffolds with interfaces for osteochondral tissue engineering

The development of biomimetic scaffolds for cartilage, calcified cartilage and bone regeneration for precise osteochondral repair remains a challenge. In this study, we used liquid-phase co-synthesis to construct a novel tri-layered scaffold with the top layer containing type II atelocollagen and chondroitin sulphate for cartilage regeneration, the intermediate layer with type II atelocollagen and hydroxyapatite for calcified cartilage formation and the bottom layer with type I atelocollagen and hydroxyapatite for bone growth. The tri-layered scaffold designed in this study is mechanically superior to other tri-layered scaffolds with hard interfaces and has a lower risk of delamination owing to higher cohesion resulting from the interfaces between the layers of the scaffold. In vitro analyses revealed that although monolayered scaffolds stimulated bone marrow stem cells to differentiate and form cartilage, calcified cartilage and bone separately (detected using quantitative PCR analysis and staining with safranin-O and alizarin red S), the tri-layered scaffolds supported the regeneration of cartilage, calcified cartilage and bone simultaneously after 2 and 4 months of implantation (detected using gross and micro-CT imaging, histological staining and Avizo, a three-dimensional reconstruction tool used to detect micro-level defects usually in metals). Therefore, our study presents a promising approach to devising strategies for the precise repair of osteochondral defects.

Advisor: Czernuszka, J