On Finding Sensitivity of Quantum and Classical Gates

We consider a fault model of Boolean gates, both classical and quantum, where some of the inputs may not be connected to the actual gate hardware. This model is somewhat similar to the stuck-at model which is a very popular model in testing Boolean circuits. We consider the problem of detecting such faults; the detection algorithm can query the faulty gate and its complexity is the number of such queries. This problem is related to determining the sensitivity of Boolean functions. We show how quantum parallelism can be used to detect such faults. Specifically, we show that a quantum algorithm can detect such faults more efficiently than a classical algorithm for a Parity gate and an AND gate. We give explicit constructions of quantum detector algorithms and show lower bounds for classical algorithms. We show that the model for detecting such faults is similar to algebraic decision trees and extend some known results from quantum query complexity to prove some of our results.

Roots and wings: orthodoxy, tradition, and creativity in Irish folk Catholicism

The present work is an exploration of the beliefs and practices of three lay Catholic devotional communities in and around the city of Cork, Ireland. The research is guided by the theory that folk, or popular, religion is a dynamic process in which individuals and groups utilise the resources of orthodoxy, popular tradition, and personal creativity, to better interpret, articulate, and create religious experiences. Ethnographic fieldwork was the principal method of data collection. Four areas of folk religion are given special attention: the use of religious narrative to represent and reproduce religious experience, the use of material artefacts to create channels for sacred presence and activity, the use of ritual and pilgrimage to establish sacred time and space, and the use of prayer to accomplish all of these goals. These sections are followed by a more holistic analysis of the material, a critical examination of the work, and suggestions for further research.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

The Celtic dragon slayer - a literary analysis of Tochmarc Emire in connection with Tristan et Iseut

As Celtic scholars have long noted, the medieval Irish tale Tochmarc Emire “The Courtship of Emer” is heavily indebted to other medieval Irish texts. In this tale of courtship and otherworldly quests, the Irish hero Cú Chulainn must prove himself worthy of the hand of the noblewoman Emer. Among his overseas adventures, Cú Chulainn rescues a princess from three attackers of the Fomoire. This episode may represent the only medieval Irish example of AT300 “The Dragon Slayer”, a story pattern known from classical models such as the stories of Perseus and Andromeda; and Hercules and Hesione. Moreover, in the company of Cú Chulainn we find a character otherwise unknown to Irish tradition by the name of Drust mac Seirb. This has led scholars to argue that Tochmarc Emire may preserve a Celtic precursor of the Continental Tristan legend, seeing in Drust the Pictish origin of the character Tristan, himself a famous dragon slayer. In this interdisciplinary dissertation, a number of questions are addressed. If the redactor of Tochmarc Emire drew on material from outside Irish tradition, what does this tell us about medieval Irish concepts of literature and genre? Further, what evidence do we have for tracing the origin of the Continental Tristan legend back to Pictland, and what explanation might we offer for a putative Pictish prince featuring in an Irish Dragon Slayer story? Finally, what place does the Dragon Slayer episode occupy within Tochmarc Emire and can we find other narratives, Celtic or classical or other, fitting the pattern of AT300, which may strengthen the link between Tochmarc Emire and Tristan?

Na marbhnaí do Shéamas Óg Mac Coitir (1689-1720)

Go príomha, is tráchtas é seo a dhéanann staidéar ar ghné de litríocht iar-chlasaiceach na Gaeilge. Baineann sé go háirithe leis an sraith chaointe nó marbhnaí i bhfoirm véarsaíochta a cumadh do Shéamas Óg Mac Coitir (1689-1720), duine uasal Caitliceach ó Charraig Tuathail, Co. Chorcaí, nuair a ciontaíodh é in éigniú Elizabeth Squibb, bean de Chumann na gCarad; nuair a cuireadh pionós an bháis air; agus nuair a crochadh é i gCathair Chorcaí an 7 Bealtaine, 1720. Ó thaobh na staire de, scrúdaítear Clann Choitir mar shampla de theaghlach nár cheil a ndílseacht do chúis pholaitiúil na Stíobhartach agus a sheas an fód go cróga faoi mar a bhí a ngreim polaitiúil á dhaingniú ag an gCinsealacht Phrotastúnach ó dheireadh an 17ú haois amach. Tagraítear do sheicteachas na sochaí comhaimseartha agus don teannas idir an pobal Caitliceach agus an pobal Protastúnach ag an am. Déantar scagadh ar an véarsaíocht mar fhoinse luachmhar do dhearcadh míshásta an mhóraimh Chaitlicigh ar struchtúr polaitiúil chontae Chorcaí (agus na hÉireann) i dtosach an 18ú haois. Is feiniméan liteartha an dlús véarsaíochta seo a bhaineann go háirithe le traidisiún liteartha Chorcaí. Tá na dánta curtha in eagar agus aistriúchán go Béarla curtha ar fáil: is é seo croí an tráchtais. Tá an t-eagrán bunaithe ar scrúdú cuimsitheach ar thraidisiún na lsí; pléitear modheolaíocht na heagarthóireachta. Déantar iarracht ar na dánta a shuíomh sa traidisiún casta liteartha sa tráchtaireacht tosaigh; sa chuid eile den bhfearas scoláiriúil, scrúdaítear ceisteanna a bhaineann le cúrsaí teanga, foclóra, meadarachta agus stíle. Tá innéacsanna agus liosta foinsí le fáil i ndeireadh an tráchtais.

Religious memory as a conveyor of authoritative tradition: The necessary and essential component in a definition of religion

In a landmark book published in 2000, the sociologist Danièle Hervieu-Léger defined religion as a chain of memory, by which she meant that within religious communities remembered traditions are transmitted with an overpowering authority from generation to generation. After analysing Hervieu-Léger’s sociological approach as overcoming the dichotomy between substantive and functional definitions, this article compares a ritual honouring the ancestors in which a medium becomes possessed by the senior elder’s ancestor spirit among the Shona of Zimbabwe with a cleansing ritual performed by a Celtic shaman in New Hampshire, USA. In both instances, despite different social and historical contexts, appeals are made to an authoritative tradition to legitimize the rituals performed. This lends support to the claim that the authoritative transmission of a remembered tradition, by exercising an overwhelming power over communities, even if the memory of such a tradition is merely postulated, identifies the necessary and essential component for any activity to be labelled “religious”.

TRADITION AND INNOVATION: ANALYSIS AND PERFORMANCE OF SELECTED COMPOSITIONS FOR VIOLONCELLO BY HEITOR VILLA-LOBOS

Brazilian composer Heitor Villa-Lobos (1887-1959) began his musical career as a cellist. When he was only twelve years old, it became imperativeupon the sudden and untimely death of his fatherthat the young Villa-Lobos earn money as a cellist to provide financial support for his mother and sisters. Villa-Lobos's intimate relationship with the cello eventually inspired him to compose great music for this instrument. This dissertation explores both the diversity of compositional technique and the evolution of style found in the music for cello written by Villa-Lobos. The project consists of two recorded recital performances and a written document exploring and analyzing those pieces. In the study of the music of Villa-Lobos, it is of great interest to consider the music's traditional European elements in combination (or even juxtaposition) with its imaginative and sometimes wildly innovative Brazilian character. His early works were greatly influenced by European Romantic composers such as Robert Schumann, Frédéric Chopin, and the virtuoso cellist/composer David Popper (whom Villa-Lobos idolized). Later, Villa-Lobos flourished in a newfound compositional independence and moved away from Euro-romanticism and toward the folk music of his Brazilian homeland. It is intriguing to experience this transition through an exploration of his cello compositions. The works examined and performed in this dissertation project are chosen from among the extensive number of Villa-Lobos's cello compositions and are his most important works for cello with piano, cello with another instrument, and cello with orchestra. The chosen works demonstrate the evolving range and combination of characteristic elements found in Villa-Lobos's compositional repertoire.

Sonata Development at the Turn of the Century: From Liszt to Stravinsky

The sonata began to lose its position of predominance among compositions in the middle of the 19th century. Having been the platform for harmonic and thematic development of music since the late baroque period the sonata entered a process of reevaluation and experimentation with form. As a result fewer sonatas were being composed with some composers dropping the genre completely. This dissertation looks at the different approaches taken by the German, French and Russian schools of composition and compares the solo and chamber music applications of the sonata form. In the German tradition Franz Liszt's Sonata in b minor sets the standard for the revolutionary approach to form while the Berg Sonata is a very conservative application of form to an innovative use of extended chromaticism. Both composers chose to write one movement through composed pieces with Liszt working with a very expansive use of form and Berg being extremely compact and efficient. Among the Russian composers, Prokofieff's third sonata is also a one movement sonata, but he falls between Liszt and Berg in terms of the length of the piece and the use of innovative musical language. Scriabin uses a two movement approach, but keeps the element of a through composed piece with the same important material spanning both movements. Stravinsky is the most conservative of these with a three movement sonata that uses a mix of chromaticism and baroque and classical style influences. The French almost stopped composing true sonatas except for chamber music where Franck and Fauré write late romantic sonatas, while Debussy is very innovative within a three movement sonata. Estampes, by Debussy, are taken in almost as an afterthought to illustrate the direction Debussy takes in his piano solo music. While Estampes is by definition a set of character pieces they function like a sonata with three movements.

Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Three Voices in the Wilderness: Foote, Bloch, and Korngold in the Early Twentieth-Century America

Barbara Hanning points out in her book Concise History of Western Music, that "Twentieth-century American music was in large measure an extension of European music" (Hanning 1998, 515). My dissertation/perforrnance project features cello works written by three contemporary composers who lived in America but were connected to the European heritage in different ways; each contributed significantly to the development of American classical concert life, music education, and even popular culture. Programs of my performances are intended to illustrate their unique compositional styles. The first recital consists of five cello compositions of Massachusetts-born Arthur Foote (1853 - 1937): Drei Stucke fur Pianoforte und Violoncello, Op. 1; Scherzo, Op.22; Romanza, Op.33; Aubade, Op.77; and Sonata for Violoncello and Piano, Op.78. Foote was influenced by the German-trained John Knowles Paine at Harvard University; he composed music famous for its extensive chromaticism in both harmony and melodic line, and for clearly-defined formal structure. The second recital explores the music of Swiss-American composer Ernest Bloch (1880-1959): a short Meditation Hebraique, a Suite No. I for Violoncello Solo and the famous rhapsody Schelomo. Born in Geneva, Switzerland, and settling in the United States in 1916, Bloch is a composer deeply influenced by the European late-Romantic tradition and is also well-known for employing "Hebraic" elements into his works. The final performance comprises two other of Bloch's cello works and one cello concerto by the Austrian-American composer, Erich Wolfgang Korngold (1897- 1957). Bloch's Voice in the Wilderness is a symphonic poem for orchestra and cello (accompanied by piano in this performance), consisting of six movements performed without pause. His Suite No.3 for Cello Solo is shorter and has a simpler style than the first Suite. Korngold was recognized as a child prodigy in his native Austria. After a Nazi-induced exile, he immigrated to America and became a film music composer in Hollywood. The Cello Concerto was used in the movie "Deception" (1 946), for which Korngold provided the film score. The impassioned harmonic language and lavish melodic lines inherited from the high-romanticism make this work one of comparative discordant beauty among other compositions of his time.

The `Ulama' and the State: Negotiating Tradition, Authority and Sovereignty in Contemporary Pakistan

This dissertation is an account of how contemporary Pakistani ulama grapple with their political realities and the Islamic state of Pakistan. The central conceptual question that scaffolds my dissertation is: How do Pakistani ulama negotiate tradition, authority and sovereignty with the Islamic Republic of Pakistan? In engaging with this issue, this dissertation employs a methodology that weds ethnography with rigorous textual analysis. The ulama that feature in this study belong to a variety of sectarian persuasions. The Sunni ulama are Deobandi and Barelvi; the Shia ulama in this study are Ithna Ashari.

In assessing the relationship between Pakistani ulama and their nation-state, I assert that the ulama's dialectical engagements with the state are best understood as a dexterous navigation between affirmation, critique, contestation and cultivation. In proposing this manner of thinking about Pakistani ulama's engagements with their state, I provide a more detailed and nuanced view of the ulama-state relationship compared to earlier works. While emphasizing Pakistani ulama's vitality and their impact on their state, this dissertation also draws attention to the manners in which the state impacts the ulama. It theorizes the subject formation of the ulama and asserts the importance of understanding the ulama as formed not just by the ethico-legal tradition in which they are trained but also by the state apparatus.

USE OF VARIATION AND FUGUE IN PIANO MUSIC FOLLOWING THE CLASSICAL PERIOD

The variation and fugue originated from the 15th and 16th centuries and blossomed during the Baroque and Classical Periods. In a variation, a theme with a particular structure precedes a series of pieces that usually have the same or very similar structure. A fugue is a work written in imitative counterpoint in which the theme is stated successively in all voices of polyphonic texture. Beethoven’s use of variation and fugue in large scale works greatly influenced his contemporaries. After the Classical Period, variations continued to be popular, and numerous composers employed the technique in various musical genres. Fugues had pedagogical associations, and by the middle of 19th century became a requirement in conservatory instruction, modeled after Bach’s Well-Tempered Clavier. In the 20th century, the fugue was revived in the spirit of neoclassicism; it was incorporated in sonatas, and sets of preludes and fugues were composed. Schubert's Wanderer Fantasy presents his song Der Wanderer through thematic transformations, including a fugue and a set of variations. Liszt was highly influenced by this, as shown in his thematic transformations and the fugue as one of the transformations in his Sonata in b. In Schumann’s Symphonic Études, Rachmaninoff's Rhapsody on a Theme of Paganini and Copland’s Piano Variations, the variation serves as the basis for the entire work. Prokofiev and Schubert take a different approach in Piano Concerto No. 3 and Wanderer Fantasy, employing the variation in a single movement. Unlike Schubert and Liszt's use of the fugue as a part of the piece or movement, Franck’s Prelude Chorale et Fugue and Shchedrin’s Polyphonic Notebook use it in its independent form. Since the Classical Period, the variation and fugue have evolved from stylistic and technical influences of earlier composers. It is interesting and remarkable to observe the unique effects each had on a particular work. As true and dependable classic forms, they remain popular by offering the composer an organizational framework for musical imagination.

THE DIVERGENT PATHS OF OPERA IN THE CLASSICAL PERIOD AS SEEN THROUGH THE OPERATIC WORKS OF CHRISTOPH WILLIBALD GLUCK AND WOLFGANG AMADEUS MOZART

Although evidence of Gluck's influence on Mozart is sometimes discernible, by examining the two operas I have performed and a recital of arias by these two composers we can see clear contrasts in their approach to and expression of classical opera. The two operas discussed are Gluck's Armide and Mozart's Le Nozze di Figaro. Gluck and Mozart were both innovators but in very different ways. Gluck comes from a dramatic background (his principles have been compared to those of Wagner) and Mozart brings together dramatic excellence with the greatness of his musical genius, his gift of melody, and his ensemble writing, which is arguably unequaled in the repertory. A well-rounded performer strives to understand what the composer is really trying to say with his work, what the message to the audience is and what his particular way of conveying it is. The understanding of a composer's approach to drama and character interaction plays a huge role in character development. This applies no matter what role you are preparing whether it is baroque opera or late romantic. Discovering the ideals, style, and purpose of a composer contributes to an effective and rewarding performance experience, for those on stage, those in the pit, and those sitting in the seats.

FROM THE AETHIOPICA TO THE RENAISSANCE: RECOVERING A STAGE TRADITION OF POSITIVE REPRESENTATION OF AFRICANS IN EARLY MODERN ENGLAND

This dissertation looks at the connection between Heliodorus's fifth-century prose romance, An Aethiopian History, certain Renaissance texts, and how these texts helped influence an alternate representation of Africans in the early modern world. Through their portrayals of Africans, early modern English playwrights frequently give the impression that Africans, especially black Africans, were people without accomplishments, without culture. Previously, however, this was not the case. Africans were depicted with dignity, as a tradition existed for this kind of representation--and Renaissance Europe had long been acquainted with the achievements of Africans, dating back to antiquity. As the source of several lost plays, the Aethiopica is instrumental in dramatizing Africans favorably, especially on the early modern stage, and helped shape a stage tradition that runs alongside the stereotyping of Africans. This Heliodoran tradition can be seen in works of Greene, Heywood, Jonson, Shakespeare, and others in the motifs of crosscultural and transracial romance, male and female chastity, racial metamorphosis, lost or abandoned babies, wandering heroes, and bold heroines. In Jonson's Masque of Blackness and Masque of Beauty, I establish a connection between these two masques and Heliodorus's Aethiopica and argue for a Heliodoran stage tradition implicit in both masques through the conceit of blanching. In The English Moore, I explore how Richard Brome uses the Heliodoran and Jonsonian materials to create a negative quality of blackness that participates in the dramatic tradition of the degenerate African on the English Renaissance stage. With Othello, I contend that it is a drama that can be seen in the Heliodoran tradition by stressing certain motifs found in the play that derives from the Aethiopica. Reading Othello this way provides us with a more layered and historicized interpretation of Shakespeare's protagonists. Othello's nationality and faith make his exalted position in Venice and the Venetian army credible and logical. His nobility and heroic status become more sharply defined, giving us a fuller understanding of the emphasis he places on chastity--both for himself and for Desdemona. Instead of a traditional, compliant, and submissive Desdemona, a courageous, resourceful, witty, and pure heroine emerges--one who lives by the dictates of her conscience than by the constraints of societal norms. Recovering the tradition of positive portrayal of Africans that originated from the Aethiopica necessitated an examination of eleven plays that I contend helped to frame the dramatic tradition under investigation. Six of these plays are continental dramas, and five are English. Although three of the English plays are lost and the other two are seventeenth-century dramas, their titles and names of their protagonists, like those of the six extant continental plays, share the names of Heliodorus's hero and heroine, making an exploration of the continental plays imperative to facilitate their use as paradigms in reconstructing the three lost English plays. These continental dramas show that plays whose titles derive from the Aethiopica itself or reflect the names of its major characters follow Heliodorus's text closely, enabling an investigation of the Heliodoran tradition on the early modern English stage. Recovering the Heliodoran tradition adds to the exploration of racial politics and the understanding of the dramatic tradition that constrained and enabled Renaissance playwrights' representation of race and gender.

MUSICAL THEATER AND THE CLASSICAL VOICE: CROSSOVER SINGING IN THE TWENTIETH CENTURY

This dissertation explores the transformation of opera comique (as represented by the opera Carmen) and the impact of verismo style (as represented by the opera La Boheme) upon the development of operetta, American musical theater and the resultant change in vocal style. Late nineteenth-century operetta called for a classically trained soprano voice with a clear vibrato. High tessitura and legato were expected although the quality of the voice was usually lighter in timbre. The dissertation comprises four programs that explore the transformation of vocal and compositional style into the current vocal performance practice of American musical theater. The first two programs are operatic roles and the last two are recital presentations of nineteenth- and twentieth- century operetta and musical theater repertoire. Program one, Carmen, was presented on July 26, 2007 at the Marshall Performing Arts Center in Duluth, MN where I sang the role of Micaela. Program two, La Boheme, was presented on May 24,2008 at Randolph Road Theater in Silver Spring, MD where I sang the role of Musetta. Program three, presented on December 2, 2008 and program four, presented on May 10, 2009 were two recitals featuring operetta and musical theater repertoire. These programs were heard in the Gildenhorn Recital Hall at the Clarice Smith Performing Arts Center in College Park, MD. Programs one and two are documented in a digital video format available on digital video disc. Programs three and four are documented in a digital audio format available on compact disc. All programs are accompanied by program notes also available in digital format.