abstract: In addition to his many other works, Russian-American composer Leo Ornstein (1893-2002) contributed a substantial body of literature for cello and piano, including Sonata No. 1 (1915-1916), Sonata No. 2 (circa 1920), Composition No. 1 (date unknown), Two Pieces (date unknown), and Six Preludes (1930-1931). His cello music is an eclectic mix of twentieth-century Neoromantic and atonal styles. This study includes a recording of the complete works for cello and piano by Leo Ornstein and a description of the music that details the formal procedures and how the cello and piano relate to one another. The discussion offers extensive musical examples in support of the descriptions. The recording was completed at the Banff Centre for the Arts in Alberta, Canada (October 2009), with R. Nicolas Alvarez, cello, in collaboration with pianist Keith Kirchoff. Andre Shrimski produced and edited the recording. / Dissertation/Thesis / Six Preludes, Prelude III / Six Preludes, Prelude IV / Six Preludes, Prelude V / Six Preludes, Prelude VI / Composition No. 1 / Sonata No. 1, Mvt.1 / Sonata No. 1, Mvt.2 / Sonata No. 1, Mvt.3 / Sonata No. 1, Mvt. 4 / Sonata No. 2 / Two Pieces, No.1 / Two Pieces, No.2 / Six Preludes, Prelude I / Six Preludes, Prelude II / D.M.A. Music 2013

This study focuses on the transformation of Leo Ornstein’s (1893-2002) musical language of his early years into the strikingly different approach found in his later years. Ornstein’s initial radical compositions from the mid-1910s were no doubt representative of the direction in which modern music was moving. Despite the intense fame and notoriety of his early works, Ornstein did not feel connected to the trends of modern music development, and by the end of the 1930s he withdrew from the public scene and turned to teaching. By the 1950s Ornstein had been almost forgotten, and in later life he became a very private person. He worked in almost total isolation composing a substantial amount of music well into his nineties, and died at the age of 109. The music of Ornstein’s “second life” is very different from the initial works of his early years, and most of it is unknown to the public and should be brought into scholarly light, especially since Ornstein has been considered by historians as a pivotal figure in twentieth-century music. This study examines selected music from different stages of Ornstein’s career: Wild Men’s Dance (1913), Suicide in an Airplane (1913), Arabesques (1918), A Long Remembered Sorrow (1964), Piano Sonata No. 7 (1988). A discussion of the selected compositions will provide an understanding of Ornstein’s compositional transformation, and will familiarize musicians and scholars with this widely unknown music.

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Tese (doutorado)—Universidade de Brasília, Instituto de Física, 2012. / Submitted by Albânia Cézar de Melo (albania@bce.unb.br) on 2013-01-25T14:27:45Z No. of bitstreams: 1 2012_ReginaCeliaBuenoFonseca.pdf: 3069024 bytes, checksum: 9d0578691efea1b3ce2d08f432b428c2 (MD5) / Approved for entry into archive by Luanna Maia(luanna@bce.unb.br) on 2013-03-01T12:42:53Z (GMT) No. of bitstreams: 1 2012_ReginaCeliaBuenoFonseca.pdf: 3069024 bytes, checksum: 9d0578691efea1b3ce2d08f432b428c2 (MD5) / Made available in DSpace on 2013-03-01T12:42:53Z (GMT). No. of bitstreams: 1 2012_ReginaCeliaBuenoFonseca.pdf: 3069024 bytes, checksum: 9d0578691efea1b3ce2d08f432b428c2 (MD5) / Generalizamos o processo de Ornstein-Uhlenbeck (OU) usando o teorema de Doob. Relaxamos as condições de aussianidade e estacionariedade, assumindo um processo linear e homogêneo no tempo. A generalização proposta mantém muita da simplicidade do processo estocástico original, enquanto apresenta um comportamento mais rico. Os resultados analíticos são obtidos utilizando a pro- babilidade de transição e o formalismo da função característica e comparados com os dados empíricos do mercado de ações, que são notórios pelo comportamento não-estacionário e não-Gaussiano. As análises são focadas na forma do decaimento exponencial e na convergência assintótica dos quatro primeiros cumulantes considerando os retornos logarítmicos dos preços diários de ações. Mostramos que o modelo proposto oferece uma boa melhora em relação ao modelo OU clássico. ______________________________________________________________________________ ABSTRACT / We generalize the Ornstein-Uhlenbeck (OU) process using the Doob's theorem. We relax the Gaussian and stationary conditions, assuming a linear and time- homogeneous process. The proposed generalization retains much of the simplicity of the original stochastic process, while exhibiting a somewhat richer behavior. Analytical results are obtained using transition probability and the characteristic function formalism and compared with empirical stock market daily data, which are notorious for the non-stationary and non-Gaussian behavior. The analysis focus on the decay patterns and the convergence study of the rst four cumulants considering the logarithmic returns of stock prices. It is shown that the proposed model o ers a good improvement over the classical OU model.

En el modelo del oscilador armónico se analiza la posibilidad de que se originen ecuaciones estocásticas en la mecánica cuántica. Para ello se hace extensión analítica en el tiempo real hacia el eje imaginario de la probabilidad de transición correspondiente al proceso de Ornstein - Uhlenbeck; como resultado se obtiene el producto de la función de estado básico y la función de Creen de la ecuación de Schrodinger para el oscilador armónico. También se estudia la posibilidad de que se originen ecuaciones estocásticas en problemas con funciones propias superiores del hamiltoniano. Se muestra que la mecánica cuántica, a diferencia de la teoría euclidiana, no puede ser interpretada en términos de procesos estocásticos.

In this work we study PhD in general transport properties of and quasi particles-energy particles in one-dimensional systems. We study various models and, through different techniques, we obtained a long spectrum of new results. We did a quick study in a ternary d-1 with electronic distribution site built from a stochastic process known by Ornstein-Uhlenbeck (or). Through exact diagonalizacão we calculate the optical absorption spectrum and distribution of spacing between n ´ levels for this ternary model. Overall, we demonstrated that ´ and can control the position of the absorption peaks by regulating the ternary distribution. In a second moment, we present the results obtained for systems with electronic Dynamics coupled to's vibrations. In this sense, we conducted three separate works: at first, we study the dynamics of an electron in a anarmônica in the presence of electron-interaction network. This anarmônica network was built using the formalism of Fermi-Pasta-Ulam with cubic potential. We made also use of the tight-binding approach to treat the electronic transport, and a classical formalism to describe the longitudinal vibrations. In our studies, electron-interaction network was considered such that the integral of transfer between the neighboring atoms ´ is dependent on the effective distance between neighboring atoms ´ (SuSchrieffer-approach model J. Heeger SSH). Our results suggest a kind of solitônico mode control on electronic Dynamics along the nonlinear network adopted. And, therefore, a kind of State electron moving soliton along the chain. This apparent mobility of electron pair-soliton shown with seemingly constant speed and can be a crucial ingredient in the transport of loads in non-linear chains. In our second approach we investigate the dynamics of electronic State moving in a DNA chain containing N bases, in what we consider beyond the DNA intrinsic disorder distribution, the effect of the vibrations of the DNA. Again, the term electron network was considered such that the electronic hopping energy could depend on the effective distance between the nearest DNA bases. The main results obtained show that the electron-Phonon coupling can transpose the location of Anderson, promoting the emergence of a dynamic sub-difusiva to long. In our work, verificamos also played the role of Atomic coupling type (for 1st gear one cas ˆ nicas, cu ´ Bamford or interac ¸ ' Morse type) within the context of electronic transport in the presence of electron-Phonon coupling. Another point which we investigated was the interaction with acoustic waves pumped throughout the network (an simplificada way to consider acu waves ´ sticas ´ also surface in calls from SAW or Surface Acoustic Waves). In a context we conducted a research on the magnetic dynamics of a magnon in Heisenberg ferromagnetic systems in presence of interactions magnon-fo non ˆ. Our results show that the propagation of spin wave follows a super-difusivo scheme for all values of intensity of magnon-coupling network considered. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho de doutorado estudamos em linhas gerais propriedades de transporte de energia, partículas e quasi-partículas em sistemas unidimensionais. Estudamos diversos modelos e, através de técnicas distintas, obtivemos um longo espectro de novos resultados. Fizemos um rápido estudo em uma cadeia eletrônica ternária 1-d com distribuição on-site construída a partir de um processo estocástico conhecido por Ornstein-Uhlenbeck (OU). Através de diagonalizacão exata calculamos o espectro de absorção ótica e a distribuição de espaçamentos entre n´níveis para este modelo ternário. De modo geral, demonstramos que ´e possível controlar a posição dos picos de absorção regulando a distribuição ternária. Em um segundo momento, apresentamos os resultados obtidos para sistemas com a dinâmica eletrônica acoplada a`s vibrações da rede. Neste sentido, realizamos três trabalhos distintos: a princípio, estudamos a dinâmica de um elétron em uma cadeia anarmônica na presença da interação elétron-rede. Esta rede anarmônica foi construída utilizando o formalismo de Fermi-Pasta-Ulam com o potencial cúbico. Fizemos uso também da aproximação tight-binding para tratar o transporte eletrônico, e um formalismo clássico para descrever as vibrações longitudinais. Em nossos estudos, a interação elétron-rede foi considerada de tal forma que a integral de transferência entre os ´átomos vizinhos seja dependente da distância efetiva entre os ´átomos vizinhos (modelo de aproximação SuSchrieffer-Heeger SSH). Nossos resultados sugerem um tipo de controle do modo solitônico sobre a dinâmica eletrônica ao longo da rede não-linear adotada. Indicando, portanto, um tipo de estado elétron-sóliton se movendo ao longo da cadeia. Esta aparente mobilidade do par elétron-sóliton se mostra com velocidade aparentemente constante e pode ser um ingrediente crucial no transporte de cargas em cadeias não-lineares. Em nossa segunda abordagem investigamos a dinâmica de um estado eletrônico se movendo em uma cadeia de DNA contendo N bases, em que consideramos além da distribuição de desordem DNA intrínseca, o efeito das vibrações do DNA. Novamente, o termo elétron-rede foi considerado de tal forma que a energia de hopping eletrônica pudesse depender da distância efetiva entre as bases mais próximas do DNA. Os principais resultados obtidos revelam que o acoplamento elétron-fônon pode transpor a localização de Anderson, promovendo o aparecimento de uma dinâmica sub-difusiva para tempos longos. Em nosso trabalho, verificamos também o papel do tipo de acoplamento atômico (for¸cas harmoˆnicas, cu´bicas ou interac¸˜ao tipo Morse) dentro do contexto do transporte eletrônico na presença de acoplamento elétron-fônon. Outro ponto que investigamos foi a interação com ondas acústicas bombeadas ao longo da rede (uma maneira simplificada de considerar ondas acu´sticas de superfície tamb´em chamadas de SAW ou Surface Acoustic Waves). Em um contexto magnético realizamos uma investigacão sobre a dinâmica de um magnon em sistemas ferromagnéticos de Heisenberg na presença de interações magnon-foˆnon. Nossos resultados apontam que a propagação da onda de spin segue um regime super-difusivo para todos os valores de intensidade de acoplamento magnon-rede considerados.

Title: Stochastic Differential Equations with Gaussian Noise Author: Josef Janák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Bohdan Maslowski, DrSc., Department of Probability and Mathematical Statistics Abstract: Stochastic partial differential equations of second order with two un- known parameters are studied. The strongly continuous semigroup (S(t), t ≥ 0) for the hyperbolic system driven by Brownian motion is found as well as the formula for the covariance operator of the invariant measure Q (a,b) ∞ . Based on ergodicity, two suitable families of minimum contrast estimators are introduced and their strong consistency and asymptotic normality are proved. Moreover, another concept of estimation using "observation window" is studied, which leads to more families of strongly consistent estimators. Their properties and special cases are descibed as well as their asymptotic normality. The results are applied to the stochastic wave equation perturbed by Brownian noise and illustrated by several numerical simula- tions. Keywords: Stochastic hyperbolic equation, Ornstein-Uhlenbeck process, invariant measure, paramater estimation, strong consistency, asymptotic normality.

The application of different unit root statistics is by now a standard practice in empirical work. Even when it is a practical issue, these statistics have complex nonstandard distributions depending on functionals of certain stochastic processes, and their derivations represent a barrier even for many theoretical econometricians. These derivations are based on rigorous and fundamental statistical tools which are not (very) well known by standard econometricians. This paper aims to fill this gap by explaining in a simple way one of these fundamental tools: namely, the Functional Central Limit Theorem. To this end, this paper analyzes the foundations and applicability of two versions of the Functional Central Limit Theorem within the framework of a unit root with a structural break. Initial attention is focused on the probabilistic structure of the time series to be considered. Thereafter, attention is focused on the asymptotic theory for nonstationary time series proposed by Phillips (1987a), which is applied by Perron (1989) to study the effects of an (assumed) exogenous structural break on the power of the augmented Dickey-Fuller test and by Zivot and Andrews (1992) to criticize the exogeneity assumption and propose a method for estimating an endogenous breakpoint. A systematic method for dealing with efficiency issues is introduced by Perron and Rodriguez (2003), which extends the Generalized Least Squares detrending approach due to Elliot et al. (1996). An empirical application is provided. / Hoy en día es una práctica estándar de trabajo empírico la aplicación de diferentes estadísticos de contraste de raíz unitaria. A pesar de ser un aspecto práctico, estos estadísticos poseen distribuciones complejas y no estándar que dependen de funcionales de ciertos procesos estocásticos y sus derivaciones representan una barrera incluso para varios econometristas teóricos. Estas derivaciones están basadas en herramientas estadísticas fundamentales y rigurosas que no son (muy) bien conocidas por econometristas estándar. El presente artículo completa esta brecha al explicar en una forma simple una de estas herramientas fundamentales la cual es el Teorema del Límite Central Funcional. Por lo tanto, este documento analiza los fundamentos y la aplicabilidad de dos versiones del Teorema del Límite Central Funcional dentro del marco de una raíz unitaria con un quiebre estructural. La atención inicial se centra en la estructura probabilística de las series de tiempo propuesta por Phillips (1987a), la cual es aplicada por Perron (1989) para estudiar los efectos de un quiebre estructural (asumido) exógeno sobre la potencia de las pruebas Dickey-Fuller aumentadas y por Zivot y Andrews (1992) para criticar el supuesto de exogeneidad y proponer un método para estimar un punto de quiebre endógeno. Un método sistemático para tratar con aspectos de eficiencia es introducido por Perron y Rodríguez (2003), el cual extiende el enfoque de Mínimos Cuadrados Generalizados para eliminar los componentes determinísticos de Elliot et al. (1996). Se presenta además una aplicación empírica.

Leo Ornstein's most significant piano oeuvre, the Seventeen Waltzes, stand out as a unique example of a pianism as a foundation for the composer's musical thoughts. The purpose of this document is to provide musical and technical suggestions based on Ornstein's pianistic patterns, which will help pianists understand the composer's complex writing and form a coherent interpretation. The guide covers the main avant-garde musical devices used by Ornstein such as tone clusters, polymeter, and polyrhythm. A comparison process within the collection will help performers to address Ornstein's unmarked waltzes by underlining the composer's similar ideas and traits.

In the Thesis the problem of estimating an unknown parameter in a stochastic dif- ferential equation is studied. Linear equations with Volterra process as the source of noise are considered. Firstly, the properties of Volterra processes and the properties of stochastic integral with respect to a Volterra process are presented. Secondly, the prop- erties of the solution to the equation under consideration are discussed. This includes the existence of the strictly stationary solution, the properties of such solution and ergodic results. These results are then generalized to equations with a mixed noise. Ergodic results are used to derive strongly consistent estimators of the unknown parameter. 1