Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Symbiotic Cities: Buenos Aires, Montevideo, and Mass Culture, 1910-1960

This dissertation examines how Buenos Aires emerged as a creative capital of mass culture and cultural industries in South America during a period when Argentine theater and cinema expanded rapidly, winning over a regional marketplace swelled by transatlantic immigration, urbanization and industrialization. I argue that mass culture across the River Plate developed from a singular dynamic of exchange and competition between Buenos Aires and neighboring Montevideo. The study focuses on the Argentine, Uruguayan, and international performers, playwrights, producers, cultural impresarios, critics, and consumers who collectively built regional cultural industries. The cultural industries in this region blossomed in the interwar period as the advent of new technologies like sound film created profitable opportunities for mass cultural production and new careers for countless theater professionals. Buenos Aires also became a global cultural capital in the wider Hispanic Atlantic world, as its commercial culture served a region composed largely of immigrants and their descendants. From the 1920s through the 1940s, Montevideo maintained a subordinate but symbiotic relationship with Buenos Aires. The two cities shared interlinked cultural marketplaces that attracted performers and directors from the Atlantic world to work in theatre and film productions, especially in times of political upheaval such as the Spanish Civil War and the Perón era in Argentina. As a result of this transnational process, Argentine mass culture became widely consumed throughout South America, competing successfully with Hollywood, European, and other Latin American cinemas and helping transform Buenos Aires into a cosmopolitan metropolis. By examining the relationship between regional and national frames of cultural production, my dissertation contributes to the fields of Latin American studies and urban history while seeking to de-center the United States and Europe from the central framing of transnational history.

Forensic Injustice: Human Rights, Archival Science and Racialized Feminicide in Guatemala

The call to access and preserve the state records that document crimes committed by the state during Guatemala’s civil war has become an archival imperative entangled with neoliberal human rights discourses of “truth, justice, and memory.” 200,000 people were killed and disappeared in Guatemala’s civil war including acts of genocide in which 85% of massacres involved sexual violence committed against Mayan women. This dissertation argues that in an attempt to tell the official story of the civil war, American Human Rights organizations and academic institutions have constructed a normative identity whose humanity is attached to a scientific and evidentiary value as well as an archival status representing the materiality and institutionality of the record. Consequently, Human Rights discourses grounded in Western knowledges, in particular archival science and law, which prioritize the appearance of truth erase the material and epistemological experience of indigenous women during wartimes. As a result, the subjectivity that has surfaced on the record as most legible has mostly pertained to non-indigenous, middle class, urban, leftist men who were victims of enforced disappearance not genocide. This dissertation investigates this conflicting narrative that remembers a non-indigenous revolutionary masculine hero and grants him justice in human rights courtrooms simply because of a document attesting to his death. A main research question addressed in this project is why the promise of "truth and justice" under the name of human rights becomes a contentious site for gendered indigenous bodies? I conduct a discursive and rhetorical analysis of documentary film, declassified Guatemalan police and military records such as Operation Sofia, a military log known for “documenting the genocide” during rural counterinsurgencies executed by the military. I interrogate the ways in which racialized feminicides or the hyper-sexualized racial violence that has historically dehumanized indigenous women falls outside of discourses of vision constructed by Western positivist knowledges to reinscribe the ideal human right subject. I argue for alternative epistemological frames that recognize genocide as sexualized and gendered structures that have simultaneously produced racialized feminicides in order to disrupt the colonial structures of capitalism, patriarchy and heterosexuality. Ironically, these structures of power remain untouched by the dominant human rights discourse and its academic, NGO, and state collaborators that seek "truth and justice" in post-conflict Guatemala.