Fixed Point vs. First-Order Logic on Finite Ordered Structures with Unary Relations

We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.

Efficient Support for Common Relations in Lightweight Formal Reasoning Systems

In work that involves mathematical rigor, there are numerous benefits to adopting a representation of models and arguments that can be supplied to a formal reasoning or verification system: reusability, automatic evaluation of examples, and verification of consistency and correctness. However, accessibility has not been a priority in the design of formal verification tools that can provide these benefits. In earlier work [Lap09a], we attempt to address this broad problem by proposing several specific design criteria organized around the notion of a natural context: the sphere of awareness a working human user maintains of the relevant constructs, arguments, experiences, and background materials necessary to accomplish the task at hand. This work expands one aspect of the earlier work by considering more extensively an essential capability for any formal reasoning system whose design is oriented around simulating the natural context: native support for a collection of mathematical relations that deal with common constructs in arithmetic and set theory. We provide a formal definition for a context of relations that can be used to both validate and assist formal reasoning activities. We provide a proof that any algorithm that implements this formal structure faithfully will necessary converge. Finally, we consider the efficiency of an implementation of this formal structure that leverages modular implementations of well-known data structures: balanced search trees and transitive closures of hypergraphs.

Anglo-Irish relations in the framework of the EEC and Northern Ireland, 1969-1975

This thesis will analyse Anglo-Irish relations between 1969 and 1975, when two topics dominated the relationship: Northern Ireland and the entry of Britain and Ireland into the European Economic Community (hereafter EEC). In 1969 entry to the EEC was still only a possibility and awaited political developments, while the Northern Ireland problem had yet to escalate. 1975 on the other hand confirmed that Ireland would remain in the EEC even if Britain left while Direct Rule for Northern Ireland was confirmed as the British policy for the foreseeable future. These dates are significant because they encompass firstly pre and post entry to the EEC and how this transformed Anglo-Irish relations. Secondly they contain the commencement and then deterioration of the Northern Ireland problem and the attempts to resolve it that finally led to direct rule by Westminster. The study will examine the fluctuating nature of the relationship between Britain and Ireland. Special regard will be devoted to the demands of internal British politics and how such demands affected the relationship. Overall, the study will demonstrate how the bilateral relationship evolved under the pressure of events in Northern Ireland and adapted to the multilateral context of the EEC. It will compare the dynamics of the states’ interactions in two extremely different areas. The thesis will demonstrate how entry to the EEC transformed the unequal Anglo-Irish economic relationship and created one of partners within the EEC. It will also analyse how the developing Northern Ireland problem caused changes to British policy. In particular, it will examine how the British Government came to recognise the beneficial role that the Republic of Ireland might play in resolving the Troubles in Northern Ireland.

Towards enhanced divine-human-earth relations: a Christian-Buddhist contribution

The central claim of the dissertation is that lesser known and somewhat neglected, yet influential thinkers, within classical religious traditions have something worthwhile to contribute to the kind of ethos we should adopt in the face of the world’s various environmental crises. Moreover an exploration of such perspectives is best done in dialogue, particularly between Eastern and Western thought. I examine this claim primarily through a dialogue between the Christian philosopher John Scottus Eriugena and the Japanese Buddhist philosopher Kūkai (Kōbō Daishi). This dialogue, framed by the triad of divine-human-earth relations, primarily emphasises the oneness of all reality, and it finds expression in Eriugena’s concept of natura or phusis and Kūkai’s central teaching that the phenomenal world is the cosmic Buddha Dainichi. By highlighting this focus, I contribute to the existing academic field of ecology and religion on the subject of holism. However, I go beyond the materialist focus that generally marks such ecological holism within that field, offering instead a more metaphysical approach. This is indicated through my use of the concept of ‘immanental transcendence’ to describe Eriugena’s and Kūkai’s dynamic, numinous and mysterious notion of reality, as well as my exploration of Eriugena’s concept of theophany and Kūkai’s notion of kaji. I further explore how both philosophers highlight the human role in the process of reaching enlightenment—understood as attaining union with the whole. In that regard, I note significant differences in their positions: in particular, I note that Kūkai’s emphasis on bodily practices contrasts with Eriugena’s more conceptual approach. Finally to bolster my claim, I examine some ecologically oriented understandings of contemporary phenomenological approaches found particularly in the work of Jean-Luc Marion and to a lesser extent Merleau-Ponty, arguing that these reflect notions of reality and of the human role similar to those of the medieval philosophers.

Afro-Cuban Bata Drum Aesthetics: Developing Individual and Group Technique, Sound and Identity

The Lucumi religion (also Santeria and Regla de Ocha) developed in 19th-century colonial Cuba, by syncretizing elements of Catholicism with the Yoruba worship of orisha. When fully initiated, santeros (priests) actively participate in religious ceremonies by periodically being possessed or "mounted" by a patron saint or orisha, usually within the context of a drumming ritual, known as a toque de santo, bembe, or tambor. Within these rituals, there is a clearly defined goal of trance possession, though its manifestation is not the sole measure of success or failure. Rather than focusing on the fleeting, exciting moments that immediately precede the arrival of an orisha in the form of a possession trance, this thesis investigates the entire four- to six-hour musical performance that is central to the ceremony. It examines the brief pauses, the moments of reduced intensity, the slow but deliberate build-ups of energy and excitement, and even the periods when novices are invited to perform the sacred bata drums, and places these moments on an equal footing with the more dynamic periods where possession is imminent or in progress. This document approaches Lucumi ritual from the viewpoint of bata drummers, ritual specialists who, during the course of a toque de santo, exercise wide latitude in determining the shape of the event. Known as omo Ana (children of the orisha Ana who is manifest in drums and rhythms), bata drummers comprise a fraternity that is accessible only through ritual initiation. Though they are sensitive to the desires of the many participants during a toque de santo, and indeed make their living by satisfying the expectations of their hosts, many of the drummers' activities are inwardly focused on the cultivation and preservation of this fraternity. Occasionally interfering with spirit possession, and other expectations of the participants, these aberrant activities include teaching and learning, developing group identity or signature sound, and achieving a state of intimacy among the musicians known as "communitas."

The Evolution of the Russian Romance Through the Nineteenth and Twentieth centuries

This performance dissertation traced the evolution of the Russian romance from 1800 to the present. The Russian romance is a relatively unknown and greatly neglected genre of classical art songs. It is commonly believed that the Russian romance began with Dargomizhsky and Glinka proceeding directly to Tchaikovsky and Rachmaninoff. Forgotten are the composers before Dargornizhsky and Glinka, the bridge composers, and the post-Tchaikovsky and post-Rachmaninoff composers. This may be, in part, because of the difficulties in obtaining Russian vocal scores. While most of the musical world is acquainted with the magnificent Russian instrumental music, the "true soul" of the Russian people lies in its romances. I presented examples of the two different schools of composition, reflecting their philosophical differences in thinking that came about in the 1860s: (1) Russian National school, (2) Western European school. Each school's influence on generations of Russian composers and their pupils have been represented in the recital programs. Also represented was the effect of the October Revolution on music and the voice of the Russian people, Anna Akhmatova. The amount of music that could be included in this dissertation greatly exceeds the amount of available performance time and represents a selected portion of the repertoire. The first recital included repertoire from the beginning of the romance in the early nineteenth century to the beginning of the twentieth century and the second recital focused on the music of the twentieth century, pre and post, the October Revolution. Finally, given the status of Anna Akhmatova and her contributions, the third recital was devoted entirely to her poetry. The "Russian soul" is one of deep, heartfelt emotions and sorrow. Happiness and joy are also present, but always with a touch of melancholy. The audience did not simply go through a musical journey, but took a journey through the "Russian soul". With the strong response of the audience to these recitals, my belief that this repertoire deserves a prominent place in recital programming was confirmed.

THE GREAT RUSSIAN PIANO TRADITION: SELECTED REPERTOIRE BY TCHAIKOVSKY, RACHMANINOFF AND PROKOFIEV

This dissertation explores representative piano music by three great Russian composers: Tchaikovsky, Rachmaninoff and Prokofiev. The areas of research include: 1) the short character piece; 2) the Russian piano transcription tradition; 3) the concerto and sonata cycle; 4) extra-musical imagery; 5) the influence of popular and dance music of the period. Perhaps the most important result of this research is learning how the art of incorporating a singing quality at the piano stands at the center of Russian pianistic heritage. The first recital features compositions by Sergei Prokofiev. The Seventh Sonata exhibits rebellious, uncompromisingly dissonant treatment of its musical content. Ten Pieces from “Cinderella” shows an ascetic approach to piano texture - a common characteristic in Prokofiev’s late works. The Third Concerto is Prokofiev’s masterpiece in the genre. One of the 20th century’s most performed concerti, it overflows with pianistic challenges. For my second dissertation recital, I have chosen Peter Ilich Tchaikovsky’s The Seasons. These short character pieces were inspired by literary sources. The text portrays Russian rural life, nature, moments of intimate reflection, and imaginary experiences and impressions. Tchaikovsky’s gift as a melodist and remarkable musical individualist is represented in his two Nocturnes as well as in the Nutcracker Suite, masterfully transcribed by Mikhail Pletnev. The final program features Sergei Rachmaninoff’s Ten Preludes, Op. 23, regarded as a culmination of the turn-of-the-century grand Russian pianistic style. The Fantasy Pieces helped establish Rachmaninoff’s reputation as a pianist-composer, a profoundly lyrical poet of the piano. The three Rachmaninoff transcriptions, the Minuet, the Hopak and the Polka de W.R. preserve the spirit of the Golden Era’s musical salon. These pieces were written to delight and dazzle audiences with their bold character, musical taste, virtuosic tricks and technical finesse. The three recitals comprising this dissertation were presented in Gildenhorn Recital at the University of Maryland School of Music on November 13, 2010, April 11, 2011 and February 27, 2012. The recitals were recorded on compact discs and are archived within the Digital Repository at the University of Maryland (DRUM).

RUSSIAN THREADS: THE PRESENCE OF RUSSIAN INFLUENCES IN TWENTIETH­ CENTURY ENGLISH CELLO MUSIC

A cursory glance at cello works by English composers during the twentieth- century yields an unexpected relationship to Russian musicians, history, culture, and religion. One must wonder how this connection or "Russian thread" came to be. When considering the working relationship of Benjamin Britten and Mstislav Rostropovich, the likelihood of such a connection is tangible, since their deeply personal friendship influenced Britten's music for cello. However, what is perhaps more interesting is the emergence of connections to Russia in the works of other English composers of the twentieth-century, featuring works from 1913-1996. This project was conceived after close study and analysis of Benjamin Britten's Third Suite for Solo Cello, Op. 87 (1971). Britten's inclusion of Russian folk tunes and an Orthodox Church hymn signaled the penetrating presence of Russian elements in his works. Britten's First Suite for Solo Cello, Op. 72, Third Suite for Cello, Op. 87, and Sonata for Piano and Cello in C, Op. 65 are presented in this project. Further exploration of works for cello by English composers unveiled similar connections to Russia. The Sonata for Cello and Piano of Frank Bridge is likened to Russian romanticism and the Cello Sonata of Sergei Rachmaninoff. William Walton's Cello Concerto was written for the Russian-American cellist Gregor Piatigorsky. Wake Up ...and die is John Tavener's deeply spiritual work, which is rooted in his Russian Orthodoxy. John Ireland, influenced by models of French and Russian Impressionism, contributed works colored with Russian folk influences, of which his Piano Trio No. 2 is an example. Finally, Arnold Bax traveled to Russia as a young man and his Folk Tale and Legend Sonata are imbued with the spirit of Russian folk music and architecture. This dissertation project is comprised of three recitals featuring English works for cello connected by a "Russian Thread." All events took place on the campus of University of Maryland, College Park: Recital #1 on December 4, 2011 in the Gildenhorn Recital Hall of the Clarice Smith Performing Arts Center, Recital #2 on February 11,2012, and Recital #3 on April 15, 2012, both in the Ulrich Recital Hall.

THE GREAT RUSSIAN PIANO TRADITION: SELECTED REPERTOIRE BY TCHAIKOVSKY, RACHMANINOFF AND PROKOFIEV

This dissertation explores representative piano music by three great Russian composers: Tchaikovsky, Rachmaninoff and Prokofiev. The areas of research include: 1) the short character piece; 2) the Russian piano transcription tradition; 3) the concerto and sonata cycle; 4) extra-musical imagery; 5) the influence of popular and dance music of the period. Perhaps the most important result of this research is learning how the art of incorporating a singing quality at the piano stands at the center of Russian pianistic heritage. The first recital features compositions by Sergei Prokofiev. The Seventh Sonata exhibits rebellious, uncompromisingly dissonant treatment of its musical content. Ten Pieces from "Cinderella" shows an ascetic approach to piano texture - a common characteristic in Prokofiev's late works. The Third Concerto is Prokofiev's masterpiece in the genre. One of the 20th century's most performed concerti, it overflows with pianistic challenges. For my second dissertation recital, I have chosen Peter Ilich Tchaikovsky's The Seasons. These short character pieces were inspired by literary sources. The text portrays Russian rural life, nature, moments of intimate reflection, and imaginary experiences and impressions. Tchaikovsky's gift as a melodist and remarkable musical individualist is represented in his two Nocturnes as well as in the Nutcracker Suite, masterfully transcribed by Mikhail Pletnev. The final program features Sergei Rachmaninoff's Ten Preludes, Op. 23, regarded as a culmination of the turn-of-the-century grand Russian pianistic style. The Fantasy Pieces helped establish Rachmaninoff's reputation as a pianist-composer, a profoundly lyrical poet of the piano. The three Rachmaninoff transcriptions, the Minuet, the Hopak and the Polka de W.R. preserve the spirit of the Golden Era's musical salon. These pieces were written to delight and dazzle audiences with their bold character, musical taste, virtuosic tricks and technical finesse. The three recitals comprising this dissertation were presented in Gildenhorn Recital at the University of Maryland School of Music on November 13, 2010, April 11, 2011 and February 27, 2012. The recitals were recorded on compact discs and are archived within the Digital Repository at the University of Maryland (DRUM).

Developing Quantitative Methodologies for the Digital Humanities: A Case Study of 20th Century American Commentary on Russian Literature

Using scientific methods in the humanities is at the forefront of objective literary analysis. However, processing big data is particularly complex when the subject matter is qualitative rather than numerical. Large volumes of text require specialized tools to produce quantifiable data from ideas and sentiments. Our team researched the extent to which tools such as Weka and MALLET can test hypotheses about qualitative information. We examined the claim that literary commentary exists within political environments and used US periodical articles concerning Russian literature in the early twentieth century as a case study. These tools generated useful quantitative data that allowed us to run stepwise binary logistic regressions. These statistical tests allowed for time series experiments using sea change and emergency models of history, as well as classification experiments with regard to author characteristics, social issues, and sentiment expressed. Both types of experiments supported our claim with varying degrees, but more importantly served as a definitive demonstration that digitally enhanced quantitative forms of analysis can apply to qualitative data. Our findings set the foundation for further experiments in the emerging field of digital humanities.

Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.