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.

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.

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.

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.

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.

Classical and quantum aspects of the extended antifield formalism

Agrégation de l'enseignement supérieur, Orientation sciences

Has cultural studies sounded the death-knell of classical sociology prematurely?: the view from Romani studies

The paper will argue that although Bryan S.Turner's recent defence of classical sociology was seen as apostacy by some, it points to real problems in the idealism and a-historicism of contemporary cultural studies. The paper will examine the importance of the classical sociological problematic in getting the field of Romani Studies started, and the continuing relevance of a sociological approach rooted in history and political economy. [From the Author]

Economic restructuring in New Zealand: A classical account

New Zealand's recent experiment with radical neoliberalism is well rehearsed in international policy circles. Yet, given the economic restructuring premise for the reforms, there has been little assessment of their structural impact. In this paper I take up this challenge, utilising [Shaikh, A., Tonak, E. Measuring the wealth of nations: the political economy of national accounts. Cambridge: Cambridge University Press; 1994] methodology for deriving classical value categories from official national accounts data but extending this to the industry level. This approach allows changes to the production and appropriation of surplus value in different industries during the period to be identified, underpinning a Marxian interpretation of restructuring. Beyond the methodology, the research makes four contributions. First, conventional analysis is found limited by its concentration on changes to the distribution of value rather than its creation. Second, land rents are significant. Third, the role of financial capital is found more complex than traditionally argued. Finally, the approach provides a firm grounding for the unfashionable concept of class fraction.

Classical Romantic: Identity in the Latin Poetry of Vincent Bourne

This monograph examines a selection of Vincent Bourne's Latin verse in its classical, neo-Latin and vernacular contexts, with particular attention to the theme of identity (and differing forms of identity). Its aim is to initiate the resurrection from silence of an author whose self-fashioning is achieved by investigating the identity of the self in relation to the other and by foregrounding multiple attempts to fashion other selves.

From Back Cover of published book:

Through close and perceptive analysis of Bourne's negotiation of poetic identity, Haan argues in new ways for the blend of classicism and Romanticism informing his marginalized status. As such, the book promises to revive scholarship on Bourne, and to be of use to students and scholars of Latin as well as vernacular verse.
Carla Mazzio, Professor of English, University of Chicago.


Estelle Haan is the UK's most eminent neo-Latinist. Her books with the APS on Milton (From Academia to Amicitia, Transactions 88, part 6) and Addison (Vergilius Redivivus, Transactions 95, part 2) are both important contributions to our knowledge of those authors, and their scholarship is presented in a way that accommodates the growing number of specialists who do not read Latin. Much of the content of this study is entirely new, and it is written in a way that will make it accessible to non-Latinists. The connections with English-language poets that Professor Haan adduces page after page will be a very considerable resource for students of vernacular poetry.
Gordon Campbell, Professor of Renaissance Literature, University of Leicester.


I have long thought that a modern study of Vincent Bourne was very much needed, and am greatly pleased that one has now been written. Estelle Haan offers a thoughtful and sensitive study that has remarkable depth. She capitalizes on the familiarity with other eighteenth-century English poets about whom she has previously written (Cowper, Gray, and most recently Addison) and she makes use of contempoary literary theory without becoming dependent on any single approach or disfiguring her writing with critical jargon. This work will, one hopes, provoke further research into Bourne and his poetry.
Dana F. Sutton, Professor Emeritus of Classics, The University of California, Irvine.

Simulation of quantum random walks using the interference of a classical field

We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters, and photodetectors. Our model enables us to simulate a quantum random walk using of the wave nature of classical light fields. Furthermore, the proposed setup allows the analysis of the effects of decoherence. The transition from a pure mean-photon-number distribution to a classical one is studied varying the decoherence parameters.