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Indiana University-Purdue University Indianapolis (IUPUI) / Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points. We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.

In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables/functionals over such sections, i.e. appropriate smooth functions on them. The kinematic will be further specified by means of Peierls brackets, which in turn are defined via the causal propagators of linearized field equations. In the second part we implement deformation quantization of the algebras obtained previously in the simpler setting of scalar field theory. Wick powers and time ordered products for quantum field theories in curved spacetimes are defined by giving a set of axioms which, when implemented, defines uniquely, up to some classifiable ambiguities, the aforementioned quantities. Those ambiguities are known to be tightly restrained by locality, covariance and other regularity conditions. One of the additional constraints used was to require continuous and analytic dependence on the metric and coupling parameters. It was recently shown that this rather strong requirement could be weakened, in the case of Wick powers, to the so-called parametrized microlocal spectrum condition. We therefore show the existence of Wick powers satisfying the above condition and extend this axiom to time ordered products, while reestablishing the usual uniqueness and existence results in light of the new constraint.

Much of the hypermedia literature instructs developers to "Use a map to prevent users from becoming lost." However, there is very little empirical evidence that maps are effective. In addition, no one has examined how to design the maps to make them most helpful to the users. This research evaluates both issues for information retrieval tasks with a fairly small hypermedia application (about 175 nodes). This study evaluates the overall effectiveness of maps by comparing the subjects' performance using hypermedia without a map to performance with one of four maps. Then, it reveals the relative effectiveness of the different types of maps by comparing the results of the subjects' performance with four variations of a map. In addition, this research evaluates (1) the effects of the experimental conditions on the subjects' mental models of the application and (2) the effects of the subjects' spatial abilities on their performance with hypermedia. The results reveal that there is generally no difference between the subjects' performance with a map and performance without a map. In addition, users who had to navigate using the links within the application rather than selecting nodes from the map (using a "passive" map) viewed more extra nodes, but spent less time on each node and completed the tasks in less time than those who could select nodes directly from the map (using an "active" map). However, many of the subjects using the passive map would have preferred to use an active map. Also, subjects who always had a map available to them (using a "present" map) performed as well as subjects who had to call up a map to use it (a "called" map). In addition, there is no difference in the accuracy of the subjects' mental models. All the subjects understood the application fairly well. A few of the spatial abilities test results are correlated with performance, and all of significant correlations indicate that higher spatial abilities leads to improved performance with hypermedia. It is believed that the lack of differences among the conditions is due to a number of factors, including the simplicity of the application the subjects used and the tasks they performed. / Master of Science

This thesis discusses an algorithm for mapping conceptual graphs to primitive VHDL processes. The behavior of each primitive process is stored in the form of a schema. The algorithm identifies concepts in the input referring to MODAS (Modeler's Assistant) process primitives and maps their schemata to the input conceptual graph. The results of the mapping are used to modify the primitive process's VHDL and instantiate a new process. A library of schemata for the primitive processes in MODAS has been developed. This algorithm has been implemented in the CGVHDL Linker program. It has improved the capability of the CGVHDL Linker to handle more complex design specifications. The algorithm provides the CGVHDL Linker with the ability to interpret a structure in the input conceptual graph. It also eases the burden on the designer who can refer to some components without giving details of their behavior. / Master of Science

<p dir="ltr">In this thesis, we provide an application of a Bochner type formula of Siu and Sampson; our main result is as follows [1]: If { M_t } t∈∆ is a polarized family of compact Kähler manifolds over the open unit disk ∆, if N is a Riemannian manifold satisfying the curvature condition: R^N (X, Y, X, Y) ≤ 0 for X, Y ∈ T_C N, and if { φ_t: M_t → N } t∈∆ is a smooth family of pluriharmonic maps, then the Dirichlet energy E( φ_t ) is a subharmonic function of t ∈ ∆. We also investigate the two natural questions: Under what conditions is the energy E( φ_t ) strictly subharmonic? What type of families { φ_t } t∈∆ have constant energy? Some of our answers generalize the results of Tromba [2] and Toledo [3], which concern the case where M_t are compact Riemann surfaces. We conclude this thesis with a discussion of examples of subharmonicity of the energy.</p>

Le travail présenté dans cette thèse s'inscrit à la fois dans le domaine de l'informatique musicale et dans celui de la réalité virtuelle. Nous présentons tout d'abord les avantages des environnements virtuels immersifs et de l'interaction graphique 3D pour les instruments multi-processus et en particulier pour le live-looping hiérarchique, un nouveau modèle d'instrument que nous définissons. Nous proposons ensuite des solutions pour la visualisation et la manipulation des processus sonores dans ces environnements virtuels. Afin de représenter les processus sonores, nous introduisons les widgets réactifs 3D qui s'appuient sur des mappings audiovisuels que nous évaluons. Nous développons un nouveau dispositif d'interaction 3D adapté à l'interaction musicale, appelé Piivert, ainsi que des techniques associées, dont les tunnels afin de manipuler les widgets réactifs 3D. Finalement, nous mettons en œuvre le live-looping hiérarchique avec l'instrument immersif Drile, en utilisant les techniques développées précédemment, et nous étudions plusieurs scènes pour les performances musicales immersives.

Orientador: Manoel Ferreira Borges Neto / Banca: Masoyoshi Tsuchida / Banca: José Arnaldo Frutuoso Roveda / Resumo: Nesta dissertação, estuda-se estruturas matemáticas relacionadas à álgebra dos sedenions de Cayley-Dickson. O conceito de funções sedeniônicas do tipo f(z) = zn, z 2 S e n 2 N, é desenvolvido a partir da distância jf(y)¡f(x)j, com o objetivo de obter-se uma generalização. A este tipo de mapeamentos trata-se por funções quaseconformes, ou seja, mapeamentos que não preservam a magnitude dos ângulos. Em particular, através de métodos de resolução, apresenta-se e discute-se polinômios de 2n graus com coeficientes sedeniônicos com o intuito de enfatizar o valor da k-dilatação causada quando trabalha-se com o número sedeniônico em coordenadas esféricas. Por fim, ilustra-se geometricamente os cortes produzidos em hiperesferas B(x; r) quando submetidas às transformações do tipo z2 e z3. / Abstract: In this work, we propose to study the mathematical construction related with algebra of Cayley-Dickson sedenions. We will present the concept of sedenions functions of f(z) = zn type, z 2 S and n 2 N, developing jf(y) ¡ f(x)j distance, with the objective of creating a generalization. This type of mappings is known as quasiconformal functions, that is, mapping that don't preserve the magnitude of angles. Specially, by means of resolution methods, we will discuss polynomials of 2n degrees with sedenions coefficients focused on highlighting the value of the k-dilation caused when we work with the sedenion number in spherical coordinates. Finally, it is illustrated geometrically the cuts produced in hiperspheres B(x; r) when submitted to the transformations of the type z2 and z3. / Mestre

Nesse trabalho introduzimos e desenvolvemos a teoria de hiper-ideais de aplicações multilineares contínuas e polinômios homogêneos contínuos entre espaços de Banach. A ideia central é refinar os conceitos de multi-ideais e de ideais de polinômios com o objetivo de explorar de forma mais aprofundada a natureza não-linear das aplicações envolvidas. Para isso tomamos a teoria de ideais de operadores lineares, aplicações multilineares e polinômios homogêneos, desenvolvida a partir dos trabalhos de Pietsch, tanto no caso linear como no caso multilinear, como referencial. Provamos resultados gerais para hiper-ideais, damos muitos exemplos ilustrativos, e desenvolvemos métodos para gerar hiper-ideais, tanto no caso multilinear como no caso polinomial. / In this work we introduce and develop the theory of hyper-ideals of multilinear mappings and homogeneous polynomials between Banach spaces. The main idea is to refine the concepts of multi-ideal and of ideal of polynomials with the purpose of exploring deeply the nonlinear nature of the underlying mappings. To do this we take the ideal theory of linear operators, multilinear mappings and homogeneous polynomials, developed from the works of Pietsch, both in the linear and nonlinear cases, as a reference. We prove general results for hyper-ideals, provide a number of illustrative examples, and develop methods to generate hyper-ideals of multilinear mappings, as well as of hyper-ideals of homogeneous polynomials.

Orientador: Rosângela Doin de Almeida / Banca: Alfredo Pereira de Queiroz Filho / Banca: Belarmino Cesar Guimarães da Costa / Resumo: A emergência das novas tecnologias de comunicação e informação tem transformado profundamente o modo de produzir mapas. As recentes ferramentas de mapeamento online abriram o mundo dos mapas para as pessoas em geral, permitindo que não cartógrafos criassem, individualmente ou colaborativamente, suas próprias representações espaciais. A presente pesquisa busca investigar as mudanças culturais introduzidas pelas tecnologias do ciberespaço nas práticas de mapeamento e nas representações criadas por elas. Desse modo, iremos apresentar uma discussão teórica sobre os caminhos que a cartografia contemporânea vem tomando nesse novo contexto técnico-cultural / Abstract: The emergence of new technologies of communication and information has deeply transformed the way of making maps. The recently online mapping tools opened the world of maps to people in general, allowing non-cartographers to create, individually or collaboratively, their own spatial representation. This work searches to investigate the cultural changes introduced by cyberspace technologies in the practices of mapping and in the representations resulted from them. Then, we will present a theoretical discussion about the paths that contemporary cartography has been taking in this new technical-cultural context / Mestre