The compositions of Steve Reich and György Ligeti both contain periodic rhythmic structures. Although periods are not usually easily perceived, the listener may perceive their combinations in a hierarchy of rhythmic structures. This document is an attempt to develop an analytical method that can account for this hierarchy in periodic music. I begin with an overview of the features of Reich's and Ligeti's music that contribute to the property of periodicity. I follow with a discussion of the music and writings of Olivier Messiaen as a precedent for the periodic structures in the music of Reich and Ligeti. I continue by consulting the writings of the Israeli musicologist Simha Arom and describing the usefulness of his ideas and terminology in the development of my method. I explain the working process and terminology of the analytical method, and then I apply it to Reich's Six Pianos and Ligeti's Désordre.

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This social history of science policy development emphasizes the impact on the agricultural community of federal policies regarding release of recombinant DNA (rDNA) organisms into the environment. The history also demonstrates that the U.S. Coordinated Framework for Biotechnology Regulation (1986) is based principally in political criteria, not solidly based in science as its proponents claimed. The power struggle among policy negotiators with incompatible belief systems resulted in a political correction of biotechnology. I also demonstrate that episodes in the rDNA controversy occur in repetitive and periodic patterns. During the 1980s, the first rDNA microbial pesticide, Ice-Minus, struggled through a policy gauntlet of federal agency approval processes, a Congressional hearing, and many legal actions before it was finally released into the environment. At the height of the controversy (1984-1986), the Reagan Administration would admit no new laws or regulations to slow the development of technologies or hinder American international competitiveness. At the same time, Jeremy Rifkin, a radical activist representing a green world view, used the controversy to agitate for social and economic reform. Meanwhile, a group of Congressional aides who called themselves the "Cloneheads" used the debate to fight for more public participation in the science policy-making process. Conflicting perspectives regarding biotechnology originated, not in level of understanding of the science involved, but in personal perspectives that were outwardly expressed as political group affiliations. The direction of federal biotechnology policy was influenced most successfully by politically best-positioned individuals (what I call a "hierarchy effect") who based decisions on how biotechnology harmonized with their pre-existing beliefs. The success of their actions also depended on timing. Historical events during the rDNA controversy followed the same periodic pattern--gestation, threshold, crisis/conflict, and quasi-quiescence--through two consecutive eras--the Containment Era (1970s) and the Release Era (1980s). These periods are modeled after Fletcher's stages through which ethical issues evolve (1990). However, an agricultural perspective on the debate reveals that such stages also occur in finer detail on repeating, overlapping, and multi-level scales. Knowledge of this periodicity may be useful in predicting features of future episodes of the rDNA controversy. / Ph. D.

Les biocapteurs sont utilisés quotidiennement pour déterminer la présence de molécules biologiques dans une matrice complexe, comme l’urine pour les tests de grossesses ou le sang pour les glucomètres. Les techniques courantes pour la détection des autres maladies nécessitent fréquemment le marquage de l’analyte avec une autre molécule, ce qui est à éviter pour fin de simplicité d’analyse. Ces travaux ont pour but la maximisation de la sensibilité d’une surface d’or ou d’argent nanotrouée, afin de permettre la détection de la liaison de molécules biologiques par résonance des plasmons de surface localisés (LSPR), en utilisant la spectroscopie de transmission. Un biocapteur portable, rapide et sans marquage pour quantifier des analytes d’intérêt médical ou environnemental pourrait être construit à partir de ces travaux. Dans l’objectif d’étudier de nombreuses configurations pour maximiser la sensibilité, le temps et le coût des méthodes de fabrication de nanostructures habituelles auraient limité le nombre de surfaces nanotrouées pouvant être étudiées. Un autre objectif du projet consiste donc au développement d’une technique de fabrication rapide de réseaux de nanotrous, et à moindres coûts, basée sur la lithographie de nanosphères (NSL) et sur la gravure au plasma à l’oxygène (RIE). La sensibilité à la variation d’indice de réfraction associée aux liaisons de molécules sur la surface du métal noble et la longueur d’onde d’excitation du plasmon de surface sont influencées par les caractéristiques des réseaux de nanotrous. Dans les travaux rapportés ici, la nature du métal utilisé, le diamètre ainsi que la périodicité des trous sont variés pour étudier leur influence sur les bandes LSPR du spectre en transmission pour maximiser cette sensibilité, visant la fabrication d’un biocapteur. Les surfaces d’argent, ayant un diamètre de nanotrous inférieur à 200 nm pour une périodicité de 450 nm et les nanotrous d’une périodicité de 650 nm démontre un potentiel de sensibilité supérieur. / Biosensors are used daily to determine the presence of biomolecules in a complex matrix, like urine for pregnancy test or blood with a glucometer. The usual biodetection methods require the addition of a tag on the analyte, which is to be avoided to design a simple analytical method. The objective of this work is to maximize the sensitivity of a gold or silver nanohole arrays to detect the biomolecules liaisons close to the metal surface by localized surface plasmon resonance (LSPR) in transmission spectroscopy. A portable and effective biosensor to quantify analytes could be built based on this work, without a tagging step. To achieve the objective of evaluating numerous configurations for maximal sensitivity, the time and cost of the usual nanostructures fabrication methods would have limited the number of nanohole arrays in metal surface that could have been studied in this project. This fact motivated another objective of this project, the development of a fast and low cost fabrication method for nanohole arrays using nanospheres lithography (NSL) followed by reactive ions etching (RIE). The plasmon sensitivity and wavelength excitation are influenced by the nanohole arrays characteristics. In the work presented here, the chemical composition of the metal surface, the diameter and the periodicity of the nanohole arrays are shown to the influence the LSPR bands. The transmission maximum and minimum position of some LSPR bands are sensitive to refractive index change, which can be exploited in a biosensor format to detect biomolecules. The optimization of these nanohole arrays characteristics allows the maximization of this sensitivity to build a biosensor. The best index refraction sensitive results were with silver surfaces, with nanohole diameters smaller than 200 nm for a periodicity of 450 nm and the nanoholes with a periodicity of 650 nm show a potential for an increased sensitivity.

In 1970, Raoul Bott published The Periodicity Theorem for the Classical Groups and Some of Its Applications, in which he uses this famous result as a guideline to present some important areas and tools of Algebraic Topology. This dissertation aims to use the path Bott presented in his article as a guideline to address certain topics on Algebraic Topology. We start this incursion developing important tools used in Homotopy Theory such as spectral sequences and Eilenberg-MacLane spaces, exploring how they can be combined to aid in computation of homotopy groups. We then study important results of Morse Theory, a tool which was in the centre of Botts proof of the Periodicity Theorem. We also develop two extensions: Morse-Bott Theory, and the applications of such results to the loopspace of a manifold. We end by giving an introduction to generalised cohomology theories and K-Theory. / Em 1970, Raoul Bott publicou o artigo The Periodicity Theorem for the Classical Groups and Some of Its Applications no qual usava esse famoso resultado como um guia para apresentar importantes áreas e ferramentas da Topologia Algébrica. O presente trabalho usa o mesmo caminho traçado por Bott em seu artigo como roteiro para explorar tópicos importantes da Topologia Algébrica. Começamos esta incursão desenvolvendo ferramentas importantes da Teoria de Homotopia como sequências espectrais e espaços de Eilenberg-MacLane, explorando como estes podem ser combinados para auxiliar em cálculos de grupos de homotopia. Passamos então a estudar resultados importantes de Teoria de Morse, uma ferramenta que estava no centro da demonstração de Bott do Teorema da Periodicidade. Desenvolvemos ainda, duas extensões: Teoria de Morse-Bott e aplicações destes resultados ao espaço de laços de uma variedade. Terminamos com uma introdução a teorias de cohomologia generalizadas e K-Teoria.

First, the theory of MSG is extended to aperiodic heterogeneous solid structures. Integral constraints are introduced to decompose the displacements and strains of the heterogeneous material into a fluctuating part and a macroscopic part, of which the macroscopic part represents the responses of the homogenized material. One advantage of this theory is that boundary conditions are not required. Consequently, it is capable of handling micro-structures of arbitrary shapes. In addition, periodic constraints can be incorporated into this theory as needed to model periodic or partially periodic materials such as textile composites. In this study, the newly developed method is employed to investigate the finite thickness effect of textile composites.<div><br></div><div>Second, MSG is enabled to deal with Timoshenko beam-like structures with spanwise heterogeneity, which provide higher accuracy than the previous available Euler–Bernoulli beam model. Its reduced form, the MSG beam cross sectional analysis, is found to be able to analyze generalized free-edge problems with arbitrary layups and subjected to general loads. In this method, the only assumption applied is that the laminate is long enough so that the Saint-Venant principle can be adopted. There is no limitation on the cross section of the laminate since no ad hoc assumption is involved with the microstructure geometry. This method solve the free-edge problem from a multiscale simulation point of view.<br></div><div><br></div>

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Les biocapteurs sont utilisés quotidiennement pour déterminer la présence de molécules biologiques dans une matrice complexe, comme l’urine pour les tests de grossesses ou le sang pour les glucomètres. Les techniques courantes pour la détection des autres maladies nécessitent fréquemment le marquage de l’analyte avec une autre molécule, ce qui est à éviter pour fin de simplicité d’analyse. Ces travaux ont pour but la maximisation de la sensibilité d’une surface d’or ou d’argent nanotrouée, afin de permettre la détection de la liaison de molécules biologiques par résonance des plasmons de surface localisés (LSPR), en utilisant la spectroscopie de transmission. Un biocapteur portable, rapide et sans marquage pour quantifier des analytes d’intérêt médical ou environnemental pourrait être construit à partir de ces travaux. Dans l’objectif d’étudier de nombreuses configurations pour maximiser la sensibilité, le temps et le coût des méthodes de fabrication de nanostructures habituelles auraient limité le nombre de surfaces nanotrouées pouvant être étudiées. Un autre objectif du projet consiste donc au développement d’une technique de fabrication rapide de réseaux de nanotrous, et à moindres coûts, basée sur la lithographie de nanosphères (NSL) et sur la gravure au plasma à l’oxygène (RIE). La sensibilité à la variation d’indice de réfraction associée aux liaisons de molécules sur la surface du métal noble et la longueur d’onde d’excitation du plasmon de surface sont influencées par les caractéristiques des réseaux de nanotrous. Dans les travaux rapportés ici, la nature du métal utilisé, le diamètre ainsi que la périodicité des trous sont variés pour étudier leur influence sur les bandes LSPR du spectre en transmission pour maximiser cette sensibilité, visant la fabrication d’un biocapteur. Les surfaces d’argent, ayant un diamètre de nanotrous inférieur à 200 nm pour une périodicité de 450 nm et les nanotrous d’une périodicité de 650 nm démontre un potentiel de sensibilité supérieur. / Biosensors are used daily to determine the presence of biomolecules in a complex matrix, like urine for pregnancy test or blood with a glucometer. The usual biodetection methods require the addition of a tag on the analyte, which is to be avoided to design a simple analytical method. The objective of this work is to maximize the sensitivity of a gold or silver nanohole arrays to detect the biomolecules liaisons close to the metal surface by localized surface plasmon resonance (LSPR) in transmission spectroscopy. A portable and effective biosensor to quantify analytes could be built based on this work, without a tagging step. To achieve the objective of evaluating numerous configurations for maximal sensitivity, the time and cost of the usual nanostructures fabrication methods would have limited the number of nanohole arrays in metal surface that could have been studied in this project. This fact motivated another objective of this project, the development of a fast and low cost fabrication method for nanohole arrays using nanospheres lithography (NSL) followed by reactive ions etching (RIE). The plasmon sensitivity and wavelength excitation are influenced by the nanohole arrays characteristics. In the work presented here, the chemical composition of the metal surface, the diameter and the periodicity of the nanohole arrays are shown to the influence the LSPR bands. The transmission maximum and minimum position of some LSPR bands are sensitive to refractive index change, which can be exploited in a biosensor format to detect biomolecules. The optimization of these nanohole arrays characteristics allows the maximization of this sensitivity to build a biosensor. The best index refraction sensitive results were with silver surfaces, with nanohole diameters smaller than 200 nm for a periodicity of 450 nm and the nanoholes with a periodicity of 650 nm show a potential for an increased sensitivity.

Die transkranielle Magnetstimulation (TMS) ist ein nichtinvasives Hirnstimulationsverfahren, mit welchem sowohl die funktionelle Untersuchung umschriebener kortikaler Regionen als auch die Modulation der Erregbarkeit ebendieser sowie die Induktion neuroplastischer Phänomene möglich ist. Sie wurde in der Vergangenheit insbesondere bei der Erforschung des humanen zentralmotorischen Systems angewandt. Dabei zeigte sich, dass ein einzelner über dem primärmotorischen Areal (M1) applizierter TMS-Puls multiple deszendierende Erregungswellen im Kortikospinaltrakt induzieren kann. Von diesen Undulationen besitzt die D-Welle (direkte Welle) die kürzeste Latenz und sie rekurriert auf eine direkte Aktivierung kortikospinaler Neurone, wohingegen I-Wellen (indirekte Wellen) längere Latenzen besitzen und durch transsynaptische Aktivierung dieser Zellen entstehen. Bemerkenswert ist das periodische Auftreten der letztgenannten Erregungswellen mit einer Periodendauer von etwa 1,5 ms. Zwar sind die genauen Mechanismen noch unbekannt, welche der Entstehung dieser I-Wellen sowie dem Phänomen der I-Wellen-Fazilitierung, das sich in geeigneten TMS-Doppelpulsprotokollen offenbart, zugrunde liegen, jedoch existieren hierzu verschiedene Erklärungsmodelle. Im Mittelpunkt der vorliegenden Arbeit steht die repetitive Anwendung eines TMS-Doppelpulsprotokolls, bei dem das Interpulsintervall (IPI) im Bereich der I-Wellen-Periodizität liegt (iTMS) und das gleichsam durch eine Implementierung der I-Wellen-Fazilitierung in der repetitiven TMS charakterisiert ist. Da gezeigt werden konnte, dass iTMS mit einem IPI von 1,5 ms (iTMS_1,5ms) die kortikospinale Erregbarkeit signifikant intra- und postinterventionell zu steigern vermag, und die I-Wellen-Periodizität interindividuellen Schwankungen unterliegt, wurde in der hier vorgestellten Studie an Normalprobanden der Einfluss einer individuellen Anpassung des IPIs (resultierend in der iTMS_adj) auf die intrainterventionelle kortikospinale Erregbarkeit untersucht. In der Tat stellte sich heraus, dass die iTMS_adj der iTMS_1,5ms diesbezüglich überlegen ist. Dieses Ergebnis unterstreicht das Potential einer Individualisierung der interventionellen TMS für erregbarkeitsmodulierende Effekte und macht dasjenige der ohnehin auf physiologische Prozesse abgestimmten iTMS explizit, was insbesondere für klinische Anwendungen relevant sein mag.