On-line Metasearch, Pooling, and System Evaluation

This thesis presents a unified method for simultaneous solution of three problems in Information Retrieval--- metasearch (the fusion of ranked lists returned by retrieval systems to elicit improved performance), efficient system evaluation (the accurate evaluation of retrieval systems with small numbers of relevance judgements), and pooling or ``active sample selection (the selection of documents for manual judgement in order to develop sample pools of high precision or pools suitable for assessing system quality). The thesis establishes a unified theoretical framework for addressing these three problems and naturally generalizes their solution to the on-line context by incorporating feedback in the form of relevance judgements. The algorithm--- Rankhedge for on-line retrieval, metasearch and system evaluation--- is the first to address these three problems simultaneously and also to generalize their solution to the on-line context. Optimality of the Rankhedge algorithm is developed via Bayesian and maximum entropy interpretations. Results of the algorithm prove to be significantly superior to previous methods when tested over a range of TREC (Text REtrieval Conference) data. In the absence of feedback, the technique equals or exceeds the performance of benchmark metasearch algorithms such as CombMNZ and Condorcet. The technique then dramatically improves on this performance during the on-line metasearch process. In addition, the technique generates pools of documents which include more relevant documents and produce more accurate system evaluations than previous techniques. The thesis includes an information-theoretic examination of the original Hedge algorithm as well as its adaptation to the context of ranked lists. The work also addresses the concept of information-theoretic similarity within the Rankhedge context and presents a method for decorrelating the predictor set to improve worst case performance. Finally, an information-theoretically optimal method for probabilistic ``active sampling is presented with possible application to a broad range of practical and theoretical contexts

Hearing the Tonality in Microtonality

In the late 1970s and 1980s, composer-pianist Easley Blackwood wrote a series of microtonal compositions exploring the tonal and modal behavior of a dozen non–twelve-tone equal temperaments, ranging from 13 to 24 tones per octave. This dissertation investigates a central paradox of Blackwood’s microtonal music: that despite being full of intervals most Western listeners have never heard before, it still seems to “make sense” in nontrivial ways. Much of this has to do with the music’s idiosyncratic approach to tonality, which I define as a regime of culturally conditioned expectations that guides one’s attentional processing of music’s gravitational qualities over time. More specifically, Blackwood configures each tuning’s unfamiliar elements in ways that correspond to certain schematic expectations Western listeners tend to have about how tonal music “works.” This is why it is still possible to hear the forest of tonality in this music, so to speak, despite the odd-sounding trees that comprise it. Because of its paradoxical blend of expectational conformance and expectational noncompliance, Blackwood’s microtonal music makes for a useful tool to snap most Western-enculturated listeners out of their ingrained modes of musical processing and reveal certain things about tonality that are often taken for granted. Accordingly, just as Blackwood writes conventional-sounding music in unconventional tunings, this dissertation rethinks several familiar music-theoretic terms and concepts through the defamiliarizing lens of microtonality. I use Blackwood’s microtonal music as a prism to shine a light on traditional theories of tonality, scale degrees, consonance and dissonance, and harmonic function, arguing that many of these theories rely on assumptions that are tacitly tied to twelve-tone equal temperament and common-practice major/minor music. By unhooking these terms and concepts from any one specific tuning or historical period, I build up a set of analytical tools that can allow one to engage more productively with the many modalities of tonality typically heard on a daily basis today. This dissertation proceeds in six chapters. The four interior chapters each center on one of the terms and concepts mentioned above: scale degrees (Chapter 2), consonance and dissonance (Chapter 3), harmonic function (Chapter 4), and tonality (Chapter 5). In Chapter 2, I propose a system for labeling scale degrees that can provide more nuance and flexibility when reckoning with music in any diatonic mode (and in any tuning). In Chapter 3, I advance an account of consonance and dissonance as expectational phenomena (rather than purely psychoacoustic ones), and I consider the ways that non-pitched elements such as meter and notation can act as “consonating” and/or “dissonating” forces. In Chapter 4, I characterize harmonic function as arising from the interaction of generic scalar position and metrical position, and I devise a system for labeling harmonic functions that is better attuned to affective differences across the diatonic modes. In Chapter 5, I synthesize these building blocks into a conception of fuzzy heptatonic diatonic tonality that links together not only all of Blackwood’s microtonal compositions but also more familiar musics that use a twelve-tone octave, from Euroclassical to popular styles. The outer chapters are less explicitly music-analytical in focus. Chapter 1 introduces readers to Blackwood’s compositional approach and notational system, considers the question of his intended audience, and discusses the ways that enculturation mediates the cognition of microtonality (and of unfamiliar music more generally). Chapter 6 draws upon archival documents to paint a more detailed picture of who Blackwood was as a person and how his idiosyncratic worldview colors his approach to composition, scholarship, and interpersonal interaction. While my nominal focus in these six chapters is Blackwood’s microtonal music, the repertorial purview of my project is far broader. One of my guiding claims throughout is that attending more closely to the paradoxes and contradictions of Blackwood’s microtonality can help one better understand the musics they are accustomed to hearing. For this reason, I frequently compare moments in Blackwood’s microtonal music to ones in more familiar styles to highlight unexpected analogies and point up common concerns. Sharing space with Blackwood in the pages that follow are Anita Baker, Ornette Coleman, Claude Debussy, and Richard Rodgers, among others—not to mention music from Curb Your Enthusiasm, Fortnite, Sesame Street, and Star Wars. Ultimately, this project is a testament to the value of stepping outside of one’s musical comfort zone. For not only can this reveal certain things about that comfort zone that would not be apparent otherwise, but it can also help one think with greater nuance, precision, and (self-)awareness when “stepping back in” to reflect upon the music they know and love

Contributions of Continuous Max-Flow Theory to Medical Image Processing

Discrete graph cuts and continuous max-flow theory have created a paradigm shift in many areas of medical image processing. As previous methods limited themselves to analytically solvable optimization problems or guaranteed only local optimizability to increasingly complex and non-convex functionals, current methods based now rely on describing an optimization problem in a series of general yet simple functionals with a global, but non-analytic, solution algorithms. This has been increasingly spurred on by the availability of these general-purpose algorithms in an open-source context. Thus, graph-cuts and max-flow have changed every aspect of medical image processing from reconstruction to enhancement to segmentation and registration. To wax philosophical, continuous max-flow theory in particular has the potential to bring a high degree of mathematical elegance to the field, bridging the conceptual gap between the discrete and continuous domains in which we describe different imaging problems, properties and processes. In Chapter 1, we use the notion of infinitely dense and infinitely densely connected graphs to transfer between the discrete and continuous domains, which has a certain sense of mathematical pedantry to it, but the resulting variational energy equations have a sense of elegance and charm. As any application of the principle of duality, the variational equations have an enigmatic side that can only be decoded with time and patience. The goal of this thesis is to show the contributions of max-flow theory through image enhancement and segmentation, increasing incorporation of topological considerations and increasing the role played by user knowledge and interactivity. These methods will be rigorously grounded in calculus of variations, guaranteeing fuzzy optimality and providing multiple solution approaches to addressing each individual problem

Theoretical Concepts of Quantum Mechanics

Quantum theory as a scientific revolution profoundly influenced human thought about the universe and governed forces of nature. Perhaps the historical development of quantum mechanics mimics the history of human scientific struggles from their beginning. This book, which brought together an international community of invited authors, represents a rich account of foundation, scientific history of quantum mechanics, relativistic quantum mechanics and field theory, and different methods to solve the Schrodinger equation. We wish for this collected volume to become an important reference for students and researchers