VictorJuiz/thesis huggingface dataset:
The Complexity of Composition: New Approaches to Depth and Space
Keywords: catalytic computing
communication complexity
composition
depth
space complexity
tree evaluation problem

The __composition__ of two given functions f and g is a fixed way of combining them into a single new function f ◦ g. A __composition theorem__ for a complexity measure s(·) states that s(f ◦ g) ≈ s(f) + s(g); in other words, computing the combined function f ◦ g is no easier (with respect to s) than computing f and g individually. If true, then we would gain a natural approach towards proving lower bounds on s(F) for an explicit F by repeatedly composing smaller hard functions in such a way that their complexities are additive by the composition theorem. We study the composition problem for two measures: __formula depth__ and __space complexity.__ The KRW conjecture [KRW95] states that the formula depth required to compute f ◦g is approximately depth(f)+depth(g), where f ◦g is the function given by replacing every input variable of f with a disjoint copy of g. This conjecture is known to imply NC1 ⊊ P. We work towards proving this conjecture by way of proving new __lifting theorems__ from query complexity to communication complexity. Our new proof of the classic result of Raz and McKenzie [RM99] allows us to intimately connect lifting to combinatorics, and in doing so we provide a novel improvement to a key parameter called the gadget size. This result also allows us to prove conditional hardness for __automating__ the __Cutting Planes__ proof system. Cook et al. [CMW+12] introduced the __tree evaluation problem__ as a way of showing L ⊊ P; their central conjecture partially relies on showing that the space to compute a function f while remembering the output of another function g is approximately the space to compute f plus the size of g’s output. This conjecture, which we call the __z-f conjecture__, was challenged by Buhrman et al. [BCK+14], who defined a new type of space computation called __catalytic computing__ and used it to show that composition does not hold for space-bounded computation in some settings. We give further evidence against composition by using the catalytic computing framework to give the first upper bounds on tree evaluation since the problem’s definition in [CMW+12], refuting their central conjecture. Using these techniques we also prove new results on __amortized__ computation by improving constructions for __catalytic branching programs__.
Making Humans: Waldorf Educators and Colonial Entanglements of Childhood
Keywords: Childhood
Colonialism
Coloniality
Waldorf

This dissertation examines how Waldorf educators navigate the colonial logics entangled in common-sense understandings of childhood. Dominant Western understandings of childhood—including, for example, children as innocent, irrational, or developmentally-in-progress—are constructed by placing the child in relation to Man, a story of the human as a biological actor who progresses towards rationality through exploration. This story of the human was produced alongside and through Western colonialism. The overrepresentation of Man as a universal and singular story of the human lends an air of intuitable or common-sense truth to the constructions about childhood that it supports, making the coloniality of childhood difficult to perceive. In this study, I connect childhood studies with studies of colonialism in order to think through how these colonial logics that structure childhood are negotiated within the particular context of Waldorf education. Waldorf education is an alternative schooling model based on the works of Rudolf Steiner, a philosopher prominent in early twentieth-century Germany. Educators at Waldorf schools pride themselves on protecting childhood through a holistic pedagogy that emphasizes the arts, play, and natural materials. For the purposes of this dissertation, I spoke with Waldorf teachers and Waldorf teacher educators about childhood, and prominent stories about childhood that emerged were that children belong in nature and in a family home, that children are innocent spiritual beings, and that children grow progressively over time. These common-sense stories are rooted in colonial logics, and I found that they served to protect and reify Man through rationalizing the exclusion of racialized and disabled children. Educators’ reliance on these understandings of childhood as felt truths made it difficult for them to challenge them, even when they were seriously troubled by the appearance of exclusionary logics embedded within these beliefs. This study touches, then, on the ways in which work against the racist and ableist contours of dominant constructions of childhood must necessarily address the colonial epistemologies which can make prejudicial logic feel like unquestionable truth.
Development and Investigation of Accurate High-order Generalized Summation-by-parts Discretizations for Computational Fluid Dynamics
Keywords: computational fluid dynamics
dual consistency
functional superconvergence
high-order methods
simultaneous approximation terms
summation-by-parts

The numerical solution of the equations governing turbulent fluid flows, whether the Reynolds-averaged Navier-Stokes equations or other approaches involving the Navier-Stokes equations, as in direct and large-eddy simulations, is computationally expensive. High-order methods have the potential to reduce this computational cost by providing higher accuracy per degree of freedom relative to low-order schemes. Spatial discretization schemes based on the generalized summation-by-parts property have been developed in recent years as a general approach for designing high-order numerical methods. This thesis presents work that delineates how to obtain accurate solutions and, particularly, superconvergent functionals when solving linear and nonlinear partial differential equations governing computational fluid dynamics problems of increasing practical relevance. The specific focus is on numerical schemes constructed on block-structured grids, where the spatial derivatives in the governing equations are approximated with high-order tensor-product generalized summation-by-parts operators. To begin, various components of high-order flow solvers based on generalized summation-by-parts operators are developed including novel artificial dissipation operators and two approaches for high-order grid generation and refinement for traditional and element-type operators. Next, it is shown that functional superconvergence is retained for generalized summation-by-parts discretizations of the linear convection equation in curvilinear coordinates. Furthermore, four dual-consistent discretizations of the two-dimensional linear convection equation based on the mortar-element and global summation-by-parts-operator approaches are derived and characterized in terms of truncation error, solution accuracy, and functional accuracy. Finally, using information gained from the analysis of the linear convection equation, a generalized summation-by-parts discretization for obtaining superconvergent functionals when solving sufficiently smooth problems governed by the Euler equations is proposed. Furthermore, the key features of a given discretization having an impact on solution and functional accuracy are delineated and analyzed. These features are identified to include the representation of the geometry, the approximation of the metrics, and the approximation of the wall normal in the flow tangency boundary condition.
Flying Flat Out: Fast Multirotor Flight Using Vision-based Navigation in Real-world Environments
Keywords: Aerial Vehicles
Differential Flatness
Nonlinear Control
Vision-Based Flight

Multirotor unmanned aerial vehicles (UAVs) are mechanically simple and highly maneuverable robots that are suitable to a wide range of applications such as infrastructure inspection, transportation, search-and-rescue missions, and mapping operations. Reliable autonomous multirotor flight needs to expand beyond lab demonstrations to real-world environments. To enable this, in the first part of this thesis, we present computationally efficient control algorithms, by exploiting a property of the dynamics known as differential flatness. We exploit this property to enable efficient prediction and safe learning from online data. As a result, we develop safe high-performance control by accounting for nonlinear and unknown dynamics in a computationally tractable way. In the second part of this thesis, we explore some of the challenges to high-speed autonomous vision-based flight. Real-world environments may be GPS-denied and vision-based navigation, relying predominantly on an onboard camera, is a lightweight and cost-effective alternative. Most standard controllers are perception-agnostic and tend to assume (i) the action computed by the controller has no effect on the ability of vision-based navigation to determine location and (ii) perfect state estimation is obtained. These assumptions often limit the reliability and performance of perception-agnostic controllers for autonomous vision-based flight. In contrast, we present perception-aware control algorithms that account for partial visual knowledge of the environment and plan despite imperfect state estimation. These approaches are validated through outdoor experiments on a DJI M600 multirotor where we demonstrate autonomous vision-based flight at speeds up to 10 m/s.
Fiber-matrix Adhesion in Thermoplastic Composites
Keywords: Fiber reinforced composites
Fiber-matrix adhesion
Interface
Single fiber pullout
Thermoplastic

There has been a recent drive in many industries to replace legacy metallic components with lightweight fiber reinforced polymer composites. Thermoplastic matrix composites are becoming increasingly more prominent due to their inherent benefits such as the ability to be re-melted and re-shaped or recycled, fatigue and impact resistance, and corrosion resistance. Macromechanical properties of fiber reinforced polymers depend on a variety of factors from the mechanical properties of the fibers and matrix, the geometrical properties of the reinforcing fibers, voids and cracks in the composite, and the strength of the fiber-matrix adhesion. The fiber-matrix adhesion governs the effectiveness of the transfer of stress from the typically weak polymer matrix to the reinforcing fibers. Poor fiber-matrix interfacial shear strengths (IFSS) can lead to premature debonding of the fiber from the matrix which allows for the propagation of micro-cracks throughout the material, ultimately leading to failure. Various micromechanical tests, such as single-fiber pullout, have been developed to directly measure the adhesive strength between fibers and polymers. In this research, a novel single-fiber pullout test methodology has been utilized to measure the fiber-matrix adhesion for a variety of industrially relevant fiber reinforced thermoplastic composites. Carbon fiber proved to have greater adhesion to thermoplastic polyester elastomers than poly(p-phenylene-2,6-benzobisoxazole) (PBO) fibers due to their increased roughness and chemical functionality. Carbon content at higher binding energies of glass fiber sizings correlated to increased IFSS with polyketone matrices. Modification of high-density polyethylene (HDPE) with maleic anhydride is effective to improve adhesion to both carbon and glass fibers, and the effect of carbon fiber sizing to the IFSS was weaker than matrix modification. Surface texturing of carbon fiber with graphene nanoplatelets led to increased adhesion to HDPE matrices through mechanical interlocking effects due to increased fiber surface roughness. Fiber-matrix adhesion was found to decrease with increasing temperature due to the reduction of the compressive stresses at the fiber-matrix interface formed from polymer shrinkage during cooling. In general, the chemical properties of the matrix were the most critical factor to adhesion. The results of this research can be used to further the development of fiber reinforced thermoplastics.
Applying Ultrafast Electron Diffraction and Spectroscopy to Visualize Structural Changes in Inorganic and Organic Systems
Keywords: isomerization
pump-probe spectroscopy
quantum dots
structure-function
ultrafast electron diffraction
ultrafast structural dynamics

Observing the atom in real time with an adequate spatial and temporal resolution capable of resolving something so small (~10^-10 m) and so fast (~10^-15 s) presents an inherent challenge in ultrafast measurement. Modern X-ray and electron diffraction techniques provide insight in to the transient structural dynamics in a system following external perturbation, such as light. Ultrafast electron diffraction (UED) methods originating in the early 2000s gave scientists a means to monitor chemistry in action by directly probing the atomic motions through a modification of established pump-probe optical experiments. In UED, the pump is a laser pulse, whereas the probe is an electron bunch, capable of probing the atomic positions within a sample. UED can be used to monitor the structural dynamics in a variety of gaseous, liquid, and solid state systems that experience a phenomena that may directly affect their nuclear coordinates. Before performing any UED experiments, the electronic dynamics must be characterized by optical pump-probe transient absorption (TA) experiments. A modified azobenzene sample, 1,2-bis(8-bromo-6-methoxy-2,3-dihydrobenzo[b][1,4]dioxin-5-yl)diazene, was studied using TA spectroscopy to reveal three time constants describing the trans to cis photoisomerization process, indicating isomerization via a predominantly torsional mode. This experiment shows that isomerization in azobenzene systems can happen even in a sterically-hindered environment such as a crystal lattice. UED was used to characterize the effects of spin crossover (SCO) in single crystal [Fe(II)(bpy)3]^2+, wherein transient changes in Bragg peak intensities were modelled by four global parameters to describe changes in the Fe-N bond distance and the rotation of the ligands surrounding the metal center. Then, UED was used to study the surface trapping of excitons in a size and capping series of lead sulfide (PbS) quantum dots (QDs). Analysis of the intensities and positions of diffraction rings revealed a surface-mediated trapping process following photoexcitation due to QD and ligand interactions at the interface. These works describe the process of performing UED and the structural dynamics that can be elucidated to then better understand atomic changes. The latter study highlights the ability of UED to resolve surface-level phenomena, which was previously unexplored with UED.
Hybrid Removal of End-of-life Geostationary Satellites using Solar Radiation Pressure and Impulsive Thrusts
Keywords: Feedback pseudospectral method
GEO debris removal
Hybrid optimal control
Hybrid pseudospectral method
Impulsive thrusts
Solar radiation pressure

This thesis proposes novel analytical and numerical control approaches to achieve the removal of end-of-life geostationary equatorial orbit (GEO) satellites to the GEO graveyard region using solar radiation pressure (SRP), and the hybrid removal using SRP and impulsive thrusts. The dynamic model of a GEO spacecraft equipped with a solar sail is first built upon the magnitude comparisons of different accelerations exerted on the spacecraft, and the drifts of the orbital elements due to each perturbative term during the removal time. Then the continuous and hybrid dynamic systems are constructed based on Gauss’s variation of parameter (VOP) equations. A realistic solar sail model is proposed and applied in the debris removal mission. Eclipse by the Earth is considered in this thesis. In the analytical control approach, the non-linear time-varying dynamic system is first linearized along a nominal state trajectory, then a linear optimal hybrid disturbance-accommodation tracking controller is developed and utilized to find the optimal solar sail control angles and impulsive thrust vectors. The required minimum area-to-mass ratio of the spacecraft for ideal/realistic solar sails using the proposed control approach is presented. When the nominal state trajectory deviates too far from the desired state trajectory, the linear time-varying (LTV) dynamic system obtained from linearization cannot accurately approximate the non-linear time-varying dynamic system, and this causes terminal state error. This problem is solved by the following numerical control approach. In the numerical control approach, the local Legendre-Gauss-Lobatto (LGL) pseudospectral (PS) method is first extended to a hybrid PS method by breaking the state continuity constraints between the segments and governing the dynamics of the LGL points on segment boundaries using discrete dynamic equations. Then a hybrid feedback PS method is proposed, in which a hybrid linear feedback controller is developed to stabilize the open-loop hybrid PS method when it converges to a local minimum. The real-time control is the composition of the feedforward control generated by the open-loop hybrid PS method and the feedback control given by the hybrid linear feedback controller. The terminal state error is greatly reduced using the hybrid feedback PS method. At last, a two-impulse-per-orbit debris removal strategy is proposed to reduce the computational cost of the hybrid feedback PS method. The long-term (one year, two years and ten years) hybrid end-of-life GEO satellites removal is presented, and the relationship between the area-to-mass ratio of the spacecraft and the required $\Delta V$ of the impulsive thrusts using this strategy is built.
Clustered Protocadherins: A Molecular Barcode for Neuronal Wiring and Survival
Keywords: dendrite development
dendrites
protocadherins
self-avoidance
starburst amacrine cell

Neuronal branch patterns influence connectivity and function, with dendrites elaborating complex but non-overlapping distributions. One developmental process that regulates branch spacing is dendrite self-avoidance, in which dendrites originating from the same cell (self-dendrites) minimize overlap and contacts. Little is known of the cellular or molecular mechanism that underpins self-avoidance. It is hypothesized that immense extracellular diversity establishes unique molecular repertoires that confer single neuron identity, and signal for neurite avoidance. Studies suggest the clustered Protocadherins (cPcdhs) provide the molecular diversity required for these processes. The mouse cPcdh locus encodes 58 transmembrane recognition molecules in three clusters: Pcdh-alpha (Pcdha), Pcdh-beta (Pcdhb), and Pcdh-gamma (Pcdhg). cPcdhs extracellular domains vary, but isoforms within clusters share a common intracellular domain. Binding property studies showed cPcdhs engage in strict homophilic trans interactions and expression studies suggest that cPcdhs generate single neuron identity through expression of unique isoform subsets in individual neurons. In the retina, the Pcdhg cluster regulates two distinct processes: developmental apoptosis, and self-avoidance. Retinas lacking Pcdhgs display enhanced programmed cell death, and a loss of self-avoidance. However, whether Pcdhgs cooperate with other cPcdhs, or if Pcdha or Pcdhb diversity is required in cell survival or self-avoidance was unknown. Additionally, the dynamic process of dendrite self-avoidance was unknown. In my thesis I use the retina to investigate the role of cPcdh cluster diversity in cell survival and dendrite patterning. My analysis of double Pcdha; Pcdhg mutants showed cell death and self-avoidance defects are exacerbated, revealing cooperative functions between Pcdha and Pcdhg and a role for cPcdh molecular diversity. I established a novel live-imaging method to capture videos of Starburst Amacrine Cells arbour development. Through quantitative video analysis I determined that dendrite self-avoidance is a contact-dependent process. In Pcdhg knockouts, filopodia fail to retract after self-contact. Interestingly, non self-contacting filopodia dynamics are unaffected. This shows Pcdhgs are required for retraction after self-contact but dispensable for non self-contacting interactions. My work is the first study to show cooperative functions for the Pcdhas and Pcdhgs in circuit development and to directly image vertebrate dendrite self-avoidance, revealing it to be a contact-dependent and Pcdhg-mediated process.
Contemporary Interventional Management of Peripheral Artery Disease in Ontario
Keywords: Comparative effectiveness
Ontario
Peripheral artery disease
Revascularization
Temporal trends
Validation

Introduction: Despite increasing international recognition of the morbidity associated with peripheral artery disease (PAD), our understanding of PAD epidemiology and management outcomes in the province of Ontario remains based on studies of limited contemporary external validity. The overarching objective of this thesis was to characterize contemporary interventional management of PAD in Ontario. Methods: Using Ontario administrative databases, we first performed a time series analysis of the trends in hospitalization for PAD. Second, we performed a validation study to estimate the positive predictive value (PPV) of diagnostic, procedure and physician claims coding to identify lower extremity open and endovascular revascularization for PAD in Ontario administrative databases. Third, we evaluated temporal trends of lower extremity revascularizations and amputation for PAD, in the context of a rising diabetes prevalence. Finally, in a cohort study, we compared the long-term effectiveness of open and endovascular revascularization approaches with respect to amputation-free survival (AFS) and related outcomes.Results: Hospitalizations for PAD have not significantly declined (decline of 0.068/100,000 Ontarians per quarter from 2006 to 2019, p=0.10). Open and endovascular revascularization for PAD can be reliably identified in Ontario administrative databases (PPV 83% to 96%). As the prevalence of diabetes has increased, the use of revascularization for PAD has increased (from 75.1 in 2002 to 90.7/100,000 person-years in 2019; unadjusted rate ratio (RR) [95% CI]=1.11 [1.08-1.14]; diabetes-adjusted RR [95% CI]=1.00 [0.98-1.03]), and a decrease in amputations for PAD has been attenuated (from 49.5 in 2002 to 45.4/100,000 person-years in 2019; unadjusted RR [95% CI]=0.81 [0.78-0.84]; diabetes-adjusted RR [95% CI]=0.65 [0.63-0.67]). Endovascular compared to open revascularization was associated with better AFS (HR [95% CI]= 0.94 [0.91-0.98]) in the full cohort, but not among subgroups with diabetes, tissue loss or isolated infrainguinal disease. Conclusions: Hospitalizations for PAD have not significantly decreased. Ontario databases can be reliably used to identify revascularization for PAD. The rising prevalence of diabetes has influenced the temporal trends in revascularization and amputation for PAD. Open revascularization may not offer a long-term benefit over endovascular revascularization. These data answer a need for real-world evidence to guide decision-making around PAD care.