UC Santa Barbara

The field of machine learning is witnessing a rapid expansion in the literature that explores techniques and applications of sparse and low-rank matrix decompositions. Typically formulated as an optimization problem involving nuclear norm minimization, this paradigm offers computational efficiency and robust statistical recovery guarantees, contrasting with the NP-hard nature of rank-based objectives. This thesis dedicates attention to the development of new methodology (Chapter 2) and also its application to finance (Chapter 3), as described below. Chapter 1 furnishes the necessary background and conducts a comprehensive survey of the related literature.

Chapter 2 concerns dimensionality reduction methods such as principal component analysis (PCA) and factor analysis, which are central to many problems in data science. There are, however, serious and well-understood challenges to finding robust low dimensional approximations for data with significant heteroscedastic noise. This Chapter introduces a relaxed version of Minimum Trace Factor Analysis (MTFA), a convex optimization method with roots dating back to the work of Ledermann in 1940. This relaxation is particularly effective at not overfitting to heteroskedastic perturbations and addresses the commonly cited Heywood cases in factor analysis and the recently identified ``curse of ill-conditioning" for existing spectral methods. We provide theoretical guarantees on the accuracy of the resulting low rank subspace and the convergence rate of the proposed algorithm to compute that matrix. We develop a number of interesting connections to existing methods, including Hetero PCA, Lasso, and Soft-Impute, to fill an important gap in the already large literature on low rank matrix estimation. Numerical experiments benchmark our results against several recent proposals for dealing with heteroskedastic noise.

In Chapter 3, we shift focus to factor analysis applied to security returns. Traditionally, commercially successful factor analysis relies on fundamental models, despite a rich academic literature exploring statistical models. Traditional statistical approaches like PCA and maximum likelihood exhibit success but suffer from drawbacks, such as a lack of robustness and insensitivity to narrow factors. To address these limitations, we propose convex optimization methods inspired by the techniques from Chapter 2. These methods aim to decompose a security return covariance matrix into its low-rank and sparse components. The low-rank component captures broad factors affecting most securities, while the sparse component accounts for narrow factors and security-specific effects. We illustrate the efficacy of this approach by measuring the variance forecasting accuracy of a low-rank plus sparse covariance matrix estimator through simulations and an empirical analysis of global equity data, showcasing improvements over PCA-based methods.

This dissertation investigates the prominence of incest tropes in Australian and U.S. Rural Gothic literature and film of the late nineteenth through early twenty-first century. Through a comparative study of texts from and about Tasmania and Appalachia, regions of low-economic status historically imagined to be on the fringe of their respective nations, I trace how stereotypes about inbreeding among the white rural poor reflect an anxiety over state biopower that originated during the founding of these settler colonies. I argue that the fear of “failed” yeoman farmers, whose non-normative sexuality, gender, racial identity, and refusal of labor are understood to degrade the settlement from within, led to the creation of an “inbred” hillbilly figure that can be found throughout the media of settler colonial states. I coin the term “inbred grotesque” to refer to the aesthetic pattern associated with this stock character, whose prominent physical differences, deformities, and disabilities are designed to reflect their internal opposition to settler values. I examine how the inbred grotesque transformed incest into a form of cultural shorthand for alternative and queer kinship patterns that challenge the foundational unit of settler states—the patriarchal nuclear family. Throughout the dissertation, I outline how the hillbilly and inbred grotesque shaped and were shaped by eugenic theory, industrialization, and nationalist movements.

In the first and second chapters, I focus on the literary and historical origins of incest stereotypes in Appalachia and Tasmania, taking as my primary case studies John Fox Jr.’s Virginian “local color” novel The Trail of the Lonesome Pine (1908) and Marcus Clarke’s Van Diemonian convict narrative For the Term of His Natural Life (1874). In my third chapter, I perform a comparative reading of Cormac McCarthy’s novel Outer Dark (1968) and Louis Nowra’s play The Golden Age (1985), examining how these American and Australian writers harnessed the inbred grotesque to express their opposition to postmodernist challenges to reproductive futurism. In my fourth chapter, I move to the birth of the “killbilly” horror genre, the dominant form of the inbred grotesque from the 1970s to the present day, and consider how cult films featuring inbred cannibal families such as The Texas Chain Saw Massacre (1974), The Hills Have Eyes (1977), and House of 1000 Corpses (2003) have both sustained and challenged hillbilly tropes. Finally, in my epilogue, I discuss the fate of the hillbilly today, considering how this figure has played a key role in the rhetoric of the contemporary Australian and American far- and alt-right movements and how the Left might itself learn to embrace the inbred grotesque.

Plastics, a pivotal product of the last century, have dramatically transformed industries ranging from healthcare and food safety to textiles, electronics, and construction, making consumer goods more accessible worldwide. Plastic production has soared from its early days, and is projected to continue growing significantly. This increase is primarily due to polyolefins like polyethylene (PE) and polypropylene (PP), which make up about half of all plastic production. However, this manufacturing boom has led to a massive surge in plastic waste, with poor waste management practices causing significant environmental issues. A small portion of this waste is recycled, mainly through mechanical methods that degrade quality.

Chemical recycling to monomers is effective for condensation polymers but less so for polyolefins due to their strong carbon-carbon bonds, often resulting in low-value products. Upcycling is a possible alternative for managing polyolefin waste. The aim is to selectively cleave specific C-C bonds in polyolefins, converting them into building blocks that can be used as feedstocks for chemical manufacturing.

Catalytic conversion of waste polyolefins to value-added alkylaromatics could contribute to carbon recycling. Tandem catalytic conversion by platinum supported on g-alumina converts various polyethylene (PE) grades into valuable long chain alkylaromatics and alkylnaphthalenes (average ~C30, dispersity Ð = 1.1) with high yields, in the absence of added solvent or molecular hydrogen. Coupling exothermic hydrogenolysis with endothermic aromatization renders the overall transformation thermodynamically accessible despite the moderate reaction temperature of 280 °C.

Compared to tandem hydrogenolysis/aromatization of PE catalyzed by Pt/g-Al2O3 at 280°C, both a five-fold enhancement in the rate of C-C bond scission and a doubling of the molar yield of alkylaromatics were realized using a more acidic Pt/F-Al2O3 catalyst instead. Bifunctional (metal/acid) catalysts also generate alkylaromatic products with lower average carbon numbers (ca. C20), similar to conventional anionic surfactants. Since physical mixtures of weakly acidic Pt/g-Al2O3 or non-acidic Pt/SiO2 with strongly Brønsted acidic Cl-Al2O3 or F-Al2O3 are also effective, the tandem reaction does not require nano-scale intimacy between metal and acid active sites. Kinetic studies using triacontane (norm-C30H62) as a model for PE show that the Pt-catalyzed dehydrogenation/hydrogenation reactions are quasi-equilibrated, while the acid-catalyzed C-C bond scission and skeletal transformations (isomerization and cyclization) determine the overall rates of depolymerization and aromatic formation.

Different from hydrocracking, aromatic formation must be conducted without high pressure H2. Depolymerization can be performed without adding any external H2, depending instead on redistribution of PE-derived H2 to value-added alkylbenzenes. However, moderate external H2 pressures (1-8 bar) significantly enhance the depolymerization rate and alkylbenzene yield (maximum yield at 4 bar H2). The rate of C-C bond scission is pseudo-zeroth-order. It increases with external P(H2) at lower pressures (< 10 bar), then decreases at higher pressures. Modifying the traditional hydrocracking mechanism to include competitive adsorption of aromatics explains the P(H2) dependence of the rate. Dynamic control of the reactor atmospheres can further increase the alkylbenzene yield, especially in the desired molecular weight range for anionic surfactants.

Depolymerization and upcycling are promising approaches to managing plastic waste. However, quantitative measurements of reaction rates and analyses of complex hydrocarbon product mixtures arising from the depolymerization of polyolefins constitute significant challenges in this emerging field. The methods for recovery and analysis of all products arising from batch depolymerization of polyethylene are detailed. The quantitative analyses of reaction rates and selectivity for alkanes and aromatic products are described. This protocol can be extended to depolymerization of other plastics such as polypropylene, and to characterization of other product mixtures (including long-chain olefins).

Polymers containing a backbone of repeated Si–O bonds, referred to as siloxanes or silicones, are a ubiquitous class of materials due to their collection of unique properties. The exceptionally wide Si–O bond angle and high deformability of the backbone bonds results in a low glass transition temperature of –120 °C and a crystallization temperature below room temperature. Additionally, the high bond dissociation energy gives rise to decomposition temperatures above 300 °C and results in a chemically inert polymer. The combination of these features result in a massive temperature window while maintaining inert. With a market size of over $4 billion, polydimethylsiloxane (PDMS) is the most common siloxane and has been the subject of decades of research. These research and development efforts have led to the material being used in numerous environments ranging from cosmetics to aerospace. The utility of PDMS arises from the sophisticated methods used to tune the polymer chemistry, which result in a range of properties appropriate for numerous different applications. Robust chemical reactions, like hydrosilylation, have led to an extremely broad scope of functional groups that can be synthetically bonded to the siloxane backbone. This same strategy has been used to attach polymers, polymerization initiators, or polymerizable moieties to the siloxane chain, leading to a broad scope of possible siloxane-based copolymer architectures. One architecture that is lacking in synthetic versatility, however, is graft copolymers with a siloxane backbone and polymeric grafts based on vinyl monomers. Chapter 2 of this dissertation outlines a methodology to synthesize graft copolymers with siloxane backbones using a combination of thiol–ene click chemistry and atom-transfer radical polymerization. Optimization of polymerization conditions enabled the synthesis of graft copolymers with a range of grafting densities and molecular weights > 5 MDa. Degradation of the siloxane backbone enabled characterization of the polymerized grafts, showcasing dispersities around 1.2 and molecular weights close to the targeted values. In order to form a freestanding polymeric material, the siloxane must be crosslinked. The network architecture is an important parameter that can be manipulated to control the properties of the material. Additionally, novel functionality can be incorporated through the usage of a dynamic crosslinker. An example of such a material is Silly Putty, which is PDMS crosslinked through borosiloxane bonds. The method of synthesizing this material, however, has remained largely unchanged since the 1940s and remains a time and energy intensive process with limited tunabilty. In Chapter, 3 we demonstrate a novel methodology to synthesize polyborosiloxane networks using hydrosilylation in minutes. While the current state-of-the-art is limited to end-functionalized PDMS chains, our developed method gives access to backbone-functionalized PDMS starting materials, which drastically increases the degree of tunability over the final network properties. In Chapter 4, we expand upon this method by synthesizing boronate esters containing varying functional groups to investigate the impact of the crosslinker chemical environment on the stress relaxation dynamics. We demonstrate an unprecedented level of control over the rate of stress relaxation for polyborosiloxane materials while maintaining a facile and robust crosslinking method. The newly developed methodologies for graft copolymers and functional polymeric networks will enable future investigations into the properties of these materials and their incorporation into complex composite systems to expand upon the current availability of silicone materials.

The dictatorship of General Augusto Pinochet (1973-1990) has left a prominent and polarizing mark on the national memory of Chile. Thirty-three years after the return to democracy, the nation has diverging ideas on how to remember this period. In 2023, as I am writing this thesis, an entire generation has grown up in democratic Chile and personal memories of the military government and the violent coup d’état have begun to fade. In this context, the system of national education becomes a key resource for younger generations to develop and understanding of the history that shapes their present-day lives. After Pinochet was removed from power via plebiscite in 1990 and the first civilian-President inherited the administration, the nation underwent a series of changes. Many of these changes focused on the denouncing of human rights violations which took place during the dictatorship and forging a way forward. There was a notable rise in activism and public interest in this period. Chileans were demanding both truth and justice for the abuses committed by the state during the dictatorship. In this atmosphere of activism and openness, a distinct memory movement is born in Chile, echoing similar conversations taking place across Latin America and in other “transitional” states. The memory movement in Chile specifically fights against the objective of oblivion surrounding the Pinochet years. Many of those fighting for the memory are those who will never be able to forget the traumatic cost of dictatorship; they are the family members and loved ones of those who were tortured, disappeared, or exiled during the dictatorship. These familiares-activistas were also incredibly influential in defeating Pinochet in the 1989 plebiscite. After decades of governments from the left (center) political coalition, La Concertación, the Chilean right gained political ground for the first time since the dictatorship with the presidential election of Sebastián Piñera in 2010 and again in 2018. Under the Piñera administration, I argue, the politics of memory shifted. From the memory narratives established by activists and the governments of Concertación leaders, Piñera’s ministers worked to promote a vague narrative of the dictatorship years. Such a narrative distances specific actors and removes some culpability of the military and right-wing politicians. Thirty some years after the return to democracy and after years of the state promoting ideals of compromiso y conviviencia, present-day memory politics in Chile highlight the continuing and deepening polarization of the country.

This thesis will argue that the Chilean state uses the public education system to continually readjust the portrayal of the memory of the Pinochet dictatorship to match or combat political trends. During the alternating presidencies of Michelle Bachelet (2006-2010, 2014-2018) and Sebastián Piñera (2010-2014, 2018-2022), each administration used K-12 education to promote and promulgate a specific vision of the dictatorship that corresponded with their parties’ political and memorial goals.  

This dissertation presents a path toward silicon photonic short reach dense wave-length division multiplexing interconnects capable of scaling to 1 Tbps with link energy consumption approaching 200 fJ/bit and areal densities exceeding 5 Tbps/mm2 within ambient operating temperatures ranging from 20 to 80 °C. The system’s architecture in the electronic and photonic domains, along with its evolution, are outlined with an em- phasis on the photonic aspects. Such a transceiver photonic integrated circuit contains hundreds of photonic elements that have stringent performance requirements with regards to footprint, energy consumption, and fabrication reproducibility, among other things. As such, the measured performance of many of these photonic elements is detailed; fur- ther, methods are shown for modelling the performance of some of these components for practical design, namely elements formed using Mach-Zehnder interferometers and microring resonators.

Forming a system of that is appropriately electrically and optically interconnected toperform requires extensive packaging, which is outlined in this work with a focus on the silicon photonics chip. Co-packaging validation experiments are shown, building towards a demonstration of a discrete silicon photonic transceiver and a packaged mode-locked laser comb source at 27 Gbps per wavelength.

Finally, to further the goal of quantifying fabrication uncertainties and their impacton silicon photonic systems, this work also introduces an experimental methodology to estimate the lithographic overlay error between a waveguiding layer and another layer capable of perturbing the guided mode; steps capable of introducing perturbations include ion implantation, etching of the waveguide layer, and deposition of material layers within close proximity to the waveguide. Such a tool should allow for more precise uncertainty quantification in photonic elements such as modulators, photodiodes, and passive mode- evolution based devices, which should in turn lead to more optimized component designs.

Ambitious presumptivism says that all our testimony based beliefs are on-balance immediately and defeasibly warranted. The rational deception objection says that ambitious presumptivism is not true because it is sometimes rational for a speaker to assert lies rather than truths. One logically possible reply is to argue that it is never rational for a speaker to assert lies rather than truths. In this essay, I develop such a non-conciliatory response to the rational deception objection.

In chapter 1, I explain ambitious presumptivism and the rational deception objection. I identify Kant's prohibition against lying as a historical predecessor to the non-conciliatory response to the rational deception objection. I then identify Burge as the heir apparent to a neo-Kantian non-conciliatory response to the rational deception objection. In chapter 2, I explain my interpretation of how Burge is heir apparent to a neo-Kantian non-conciliatory response. I call Burge's response the ``functional unity'' argument.

In chapter 3, I defend my attribution to Burge of the functional unity argument. In chapters 4 and 5, I defend the functional unity argument itself from the most influential objections raised against it. in chapter 6, I defend the functional unity argument from the classic murderer-at-the-door objection that dogged Kant's prohibition against lying.

This research examines several demonologists, ranging from well-known writers including Henri Boguet and Père Jean Baptiste Labat, to several lesser-known men, including the French judges and lawyers, Jean Chenu and Gilbert Gaulmin, and two Scottish writers, professor George Sinclair, and judge and Lord Advocate George Mackenzie. All of these men had personal, political, and religious stakes in the success or failure in the circulation of their publications. These writers also had similar upbringings: they were educated elites with law or philosophy degrees from prestigious universities who worked their way up within their respective legal systems or in universities where they were able to educate and influence the people around them. This level of local prominence allowed them a platform from which to deliver personal views on witchcraft and demonology, which in turn reinforced their own political power and religious piety.These middling men were active members of their communities who saw it as their moral and legal duty to protect and educate the public from witches and other supernatural activity. They published collections of notable stories of the supernatural, judicial procedures, advice on how to approach witches, and examples of their own legal successes trying cases of witchcraft. Local judges, lawyers, and demonologists dealt with cases of witchcraft and the supernatural under the guidance of their respective legal systems, but my research has shown that religious beliefs, personal experience, knowledge of other demonological practices, and legal training all played equally important roles in how a judge or lawyer conducted his trials. I argue that a textual community of demonologists, judges, lawyers, and urban professionals developed throughout the 16th and 17th centuries in Europe, which resulted in a specific level of expertise required in order to conduct witchcraft trials and publish demonological works. This level of expertise also helped boost personal reputation within these writers’ respective communities. By examining cases in France, Franche-Comté, Scotland, and French Martinique, this research presents a trans-European and trans-Atlantic view of demonology and judicial culture in the 16th and 17th centuries. My research provides a new way to look at witchcraft and demonology by utilizing a comparative methodology, and by examining the development of French judicial practices and witchcraft beliefs in comparison to Scotland and French Martinique, this work specifically traces the evolution of patterns of influence of Protestantism and Catholicism on demonology in these regions.

Fish move through the ocean unaware of the socially-constructed spatial boundaries imposed on them by legal and administrative systems. The vast majority of marine species move beyond a single national jurisdiction and these species play a pivotal role in global food security. However, movement across boundaries increases competitive incentives among nations, leading to overfishing. One way to slow this ‘race to fish’ is by forming agreements, where countries come together to manage how marine resources are shared. Because agreements are self-enforcing, agreement success depends on the strategic manipulation of incentives. Here I measure how effective an existing agreement has been at preventing overfishing, how a different agreement that has failed to curb illegal fishing can use competition from aquaculture to reduce poaching, and how fish movement can incentivize a marine reserve agreement. First, I use an econometric approach to measure how effective a tuna agreement management measure has been at reducing fishing mortality for highly mobile, boundary-spanning tuna and billfishes. Next, I use a bioeconomic model to find new solutions for an international wildlife trade agreement, specifically examining how competitive responses to aquaculture can disrupt a lucrative illegal trade in Mexico. Finally, I create a dynamic and spatial game to examine how fish movement can incentivize the development of a bilateral transboundary marine reserve agreement, which can help countries meet their commitment to protect 30% of the ocean by 2030. These results demonstrate how successful agreements can resolve externalities generated from the movement of fish and fish products across boundaries, and how effective agreements can be measured and designed.

Efforts to improve gas turbine fuel efficiency face a significant obstacle in the degradation of thermal and environmental barrier coatings (T/EBC) made of refractory oxides. Although these coatings effectively protect against heat and water vapor, they inadequately address the challenges posed by molten silicates made of engine-ingested ash, sands, and dusts. Additionally, certain candidate coating materials are susceptible to microcracking driven by anisotropy, compromising their ability to prevent ingress of gas species that hasten component failure. This dissertation features new computational and experimental approaches to investigate and design T/EBC materials, offering fundamental insights into molten silicate attack and grain boundary microcracking.

The first aspect of this dissertation addresses the need to develop a protocol for selecting compositions of silicate deposits for the purpose of assessing performance of candidate coating materials. The crux of the study is the statistical analyses (i.e. principal component analysis and \textit{k}-means clustering) of a curated database to identify exemplary compositions. Potential chemical interactions between the exemplary silicates and several coating materials were explored using thermodynamic calculations. The computational framework is expected to inform future work on investigating potential attributes and deficiencies of new coating materials.

The second aspect of this dissertation explores the potential of HfO$_2$-based coating materials as barriers to molten silicates. (These materials are attractive candidates because of their high-temperature phase stability and resistance to water-vapor mediated volatilization.) Since pure HfO$_2$ is susceptible to extensive grain boundary microcracking, two alternatives were explored: one based on crack-free hafnia/hafnon composites, and one based on hafnate compounds, building on the understanding of corresponding zirconate compounds.

High-temperature exposures of the hafnia/hafnon composites to two exemplary silicates revealed that in all cases interactions include extensive grain boundary penetration, presumably driven by the lack of chemical equilibrium between the composite constituents and the silicate melts. The findings prompted a comparative study of the interactions of Gd-hafnate and Gd-zirconate with the exemplary silicate melts. As with the hafnia/hafnon composites, the melts readily penetrate the Gd-hafnate, but not the Gd-zirconate, owing to rapid co-formation of protective barrier layers of apatite and fluorite above the zirconate. Further insights on the underlying cause of these differences were gleaned from complementary studies in which short exposures (1-3 min) using Gd-lean versions of the compounds were used to quantify the kinetics of the interactions. The results showed that Hf$^{4+}$ diffuses in the melt more slowly than Zr$^{4+}$. Further, the findings implied that the dissolution processes are diffusion-controlled and that the slower kinetics of the processes as well as the subsequent crystallization necessary for protection of the hafnia-based systems may be the root cause of their poor resistance to silicate attack. More broadly, the work demonstrates how fundamental studies of the kinetics of dissolution, diffusion, and crystallization can inform coating material selection and assessment.

The third aspect of this dissertation responds to a longstanding need for high throughput assessments of the driving forces for grain boundary microcracking in brittle materials of high anisotropy. The framework is based on a finite element approach to computing the energy release rate (ERR) for intergranular cracking. Simulations of bicrystals and polycrystals comprising periodic arrays of hexagonal grains were performed for 35 materials covering all 7 crystal systems. The assessments reveal that, while crystal system is not a determinant of likelihood for cracking, materials with large thermal and elastic anisotropy are more sensitive to grain orientations. Moreover, ERR distributions for bicrystals and polycrystals of the same material are in reasonable agreement with one another, implying that the details of neighboring grains in the polycrystals are relatively unimportant with regard to the average crack driving forces. Therefore, future studies might avoid the computational cost of simulating large polycrystals by opting for bicrystals alone, with the recognition that the details of the tails of the ERR distributions may not be accurately depicted. From a broader perspective, the high throughput nature of the approach should find considerable utility in not only the design of monolithic and multi-phase coatings, but also patterned and textured materials that avoid microcracking.