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.

Integrating Aeon and Interlibrary Loan

Presentation from the MARAC conference in Roanoke, VA on October 7–10, 2015. S16 - A Tectonic Shift: Using Aeon to Improve Operations in Archives and Special Collections

Integrating Environmental Justice and Social-Ecological Resilience for Successful Adaptation to Climate Change: Lessons from African American Communities on the Eastern Shore of the Chesapeake Bay

This research concerns the conceptual and empirical relationship between environmental justice and social-ecological resilience as it relates to climate change vulnerability and adaptation. Two primary questions guided this work. First, what is the level of resilience and adaptive capacity for social-ecological systems that are characterized by environmental injustice in the face of climate change? And second, what is the role of an environmental justice approach in developing adaptation policies that will promote social-ecological resilience? These questions were investigated in three African American communities that are particularly vulnerable to flooding from sea-level rise on the Eastern Shore of the Chesapeake Bay. Using qualitative and quantitative methods, I found that in all three communities, religious faith and the church, rootedness in the landscape, and race relations were highly salient to community experience. The degree to which these common aspects of the communities have imparted adaptive capacity has changed over time. Importantly, a given social-ecological factor does not have the same effect on vulnerability in all communities; however, in all communities political isolation decreases adaptive capacity and increases vulnerability. This political isolation is at least partly due to procedural injustice, which occurs for a number of interrelated reasons. This research further revealed that while all stakeholders (policymakers, environmentalists, and African American community members) generally agree that justice needs to be increased on the Eastern Shore, stakeholder groups disagree about what a justice approach to adaptation would look like. When brought together at a workshop, however, these stakeholders were able to identify numerous challenges and opportunities for increasing justice. Resilience was assessed by the presence of four resilience factors: living with uncertainty, nurturing diversity, combining different types of knowledge, and creating opportunities for self-organization. Overall, these communities seem to have low resilience; however, there is potential for resilience to increase. Finally, I argue that the use of resilience theory for environmental justice communities is limited by the great breadth and depth of knowledge required to evaluate the state of the social-ecological system, the complexities of simultaneously promoting resilience at both the regional and local scale, and the lack of attention to issues of justice.