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.

Crises and Crisis Generations: International Conflict and Military Participation in Politics

Why do states facing high levels of international threat sometimes have militaries that are heavily involved in politics and at other times relatively apolitical, professional militaries? I argue that the answer to this puzzle lies in a state's history of 'acute' international crises rather than its 'chronic' threat environment. Major international crises lead to professionalization and de-politicization of militaries in both the short- and long-term. International crises underscore the need for the military to defend the state and highlight military deficiencies in this regard. Accordingly, major international crises lead to military professionalization and withdrawal from politics in order to increase military effectiveness. This effect persists years, and decades, later due to generational shifts in the officer corps. As the "Crisis Generation" of officers become generals, they bring with them a preference for professionalization and de-politicization. They guide the military towards abstention from politics. I test this theory using a new global dataset on military officers in national governing bodies from 1964-2008 and find strong support for the theory. Major international crises lead to two waves of military withdrawal from government, years apart. Further statistical analysis finds that this effect is most strongly felt in the non-security areas of governing, while in some cases, international crises may lead to militaries increasing their involvement in security policy-making. Further, international crises that end poorly for a state — i.e., defeats or stalemates — are found to drive more rapid waves of military withdrawal from government. The statistical analysis is supported by a case illustration of civil-military relations in the People's Republic of China, which demonstrates that the crisis of the Korean War (1950-53) led to two waves of military professionalization and de-politicization, decades apart. The first occurred immediately after the war. The second wave, occurring in the 1980s, involved wholesale military withdrawal from governing bodies, which was made possible by the ascent of the "Crisis Generation" of officers in the military, who had served as junior officers in the Korean War, decades prior.

Cortisol Awakening Response in Preschoolers and Depression Risk: Relations with Maternal History of Depression and Child Temperament

Increasing research suggests that elevations in the cortisol awakening response (CAR), the natural increase of cortisol 30 to 40 minutes after waking, may serve as a vulnerability marker for depression. However, existing studies have focused on adolescence and adulthood; very little is known about the CAR in early childhood and the factors that are associated with it. The current study aimed to examine the validity of the CAR as a potential early-emerging vulnerability marker for depression in a sample of preschool-age children. We examined associations between the CAR and two well-established risk factors for depression: maternal psychopathology and early child temperament (high negative emotionality (NE) and/or low positive emotionality (PE)). The sample consisted of 146 preschool-age children, of whom 71 (49.3%) had a biological mother with a history of depression and 65 (45.5%) had a biological mother with a history of anxiety. To assess the CAR, salivary cortisol samples were collected from the child upon waking, 30 and 45 minutes post-waking on two weekdays. Children’s CAR was examined as the total volume of cortisol secreted (AUCg) and the total increase in cortisol (AUCi) across waking. Evening cortisol was collected 30 minutes before bedtime. Child temperament was assessed using observational laboratory measures. Maternal depression and anxiety were assessed with clinical interviews. Associations with children’s CAR, as indicated by AUCg or AUCi, appeared to be specific to maternal current psychopathology and symptoms of anhedonia. Additionally, we observed significant interactions for both maternal lifetime and current depression and anxiety, in combination with child NE and PE, on elevated evening cortisol levels and flattened diurnal cortisol rhythms, indicating altered patterns of basal cortisol activity in offspring. Our study contributes to the limited but growing knowledge on the development of the CAR in preschool age children and as a marker of early risk. Findings suggest that there is a complex interplay between familial risk, affective vulnerability, and their joint effects on neuroendocrine dysfunction in young children, and highlight the need for future research to examine which aspects of the early diurnal rhythm predict the emergence of later depressive illness.