Neste trabalho apresentamos uma nova abordagem para a exploração de fibras neurais a partir de imagens de tensores de difusão. A estratégia combina técnicas de visualização de informação e visualização científica para obter uma rápida e precisa interpretação das fibras. Para isto fazemos uma transformação das fibras para vetores, e utilizamos uma nova técnica de projeção multi-dimensional (P-LSP), para trabalhar com conjuntos grandes de dados. A exploração do espaço das fibras é feita através desta projeção. Além disso, é apresentada a extensão das técnicas LSP e P-LSP para criar projeções em 3D, assim como estratégias que permitem interagir com pontos em 3D. Outra contribuição deste trabalho é a modificação de um método apresentado para criar superfícies de densidade fechadas sobre pontos esparsos. Esta modificação torna possível criar superfícies sobre conjuntos de pontos maiores com uma qualidade aceitável, o que é utilizado para representar conjunto de fibras como uma superfície. Esta nova abordagem é comparada com trabalhos similares mostrando nossas vantagens em termos de tempo de processamento, qualidade e funcionalidades para analisar esta categoria de dados / This work presents a novel approach for the exploration of neural fibers extracted from Diffusion Tensor Images. The developed strategy combines techniques from information and scientific visualization in order to attain a fast and precise interpretation of fiber sets. The approach transforms fibers into vectors from which a new multidimensional projection technique (PLSP) capable of handling large data sets. The fiber space is explored through the projection. Additionally this work extends P-LSP and LSP projections to 3D, and defines strategies to interact with 3D sparse points. Another contribution of this work is the extension of a method to create close density surfaces over the sparse space generated by the projections. The visualization approach is compared with other similar work showing advantages in processing time, quality and exploration capability to analyze this type of data sets

The majority of current multi-label classification research focuses on learning dependency structures among output labels. This paper provides a novel theoretical view on the purported assumption that effective multi-label classification models must exploit output dependencies. We submit that the flurry of recent dependency-exploiting, multi-label algorithms may stem from the deficiencies in existing datasets, rather than an inherent need to better model dependencies. We introduce a novel categorization of multi-label metrics, namely, evenly and unevenly weighted label metrics. We explore specific features that predispose datasets to improved classification by methods that model label dependence. Additionally, we provide an empirical analysis of 15 benchmark datasets, 1 real-life dataset, and a variety of synthetic datasets. We assert that binary relevance (BR) yields similar, if not better, results than dependency-exploiting models for metrics with evenly weighted label contributions. We qualify this claim with discussions on specific characteristics of datasets and models that render negligible the differences between BR and dependency-learning models.

Problems in the demodulation of one, two, and three-dimensional signals are investigated. In one-dimensional linear systems the analytic signal and the Hilbert transform are central to the understanding of both modulation and demodulation. However, it is shown that an efficient nonlinear algorithm exists which is not explicable purely in terms of an approximation to the Hilbert transform. The algorithm is applied to the problem of finding the envelope peak of a white light interferogram. The accuracy of peak location is then shown to compare favourably with conventional, but less efficient, techniques. In two dimensions (2-D) the intensity of a wavefield yields to a phase demodulation technique equivalent to direct phase retrieval. The special symmetry of a Helmholtz wavefield allows a unique inversion of an autocorrelation. More generally, a 2-D (non-Helmholtz) fringe pattern can be demodulated by an isotropic 2-D extension of the Hilbert transform that uses a spiral phase signum function. The range of validity of the new transform is established using the asymptotic method of stationary phase. Simulations of the algorithm confirm that deviations from the ideal occur where the fringe pattern curvature is larger than the fringe frequency. A new self-calibrating algorithm for arbitrary sequences of phase-shifted interferograms is developed using the aforementioned spiral phase transform. The algorithm is shown to work even with discontinuous fringe patterns, which are known to seriously hamper other methods. Initial simulations of the algorithm indicate an accuracy of 5 milliradians is achievable. Previously undocumented connections between the demodulation techniques are uncovered and discussed.

This thesis explores the multi-dimensional aspects of space by engaging three primary “modes of knowing”: the corporeal, the virtual and the spiritual. The crossings of these modes are investigated through the development of three characters in a film; Kira is the earth-worshipping goddess; Kisho is the cyborg, a permanently uploaded information-seeker; and the Shaman is a shape-shifting lightworker. These characters evolve from the distillation of specific readings related to each of the aforementioned modes as well as from interviews and experiences that assist in their development. These readings range from Novalis and Ashley Montagu on corporeal knowledge, Donna Harraway and Neil Spiller on technologically enhanced trans-human states and Fritjof Capra and Alex Grey on the intersection of ancient mystical teaching with recent findings in quantum physics. This exploration is followed by the design portion of the thesis: a short film where each character occupies a separate world in the dystopian future. The radical and regenerative possibilities of their crossings are what the film initiates.

This thesis explores the multi-dimensional aspects of space by engaging three primary “modes of knowing”: the corporeal, the virtual and the spiritual. The crossings of these modes are investigated through the development of three characters in a film; Kira is the earth-worshipping goddess; Kisho is the cyborg, a permanently uploaded information-seeker; and the Shaman is a shape-shifting lightworker. These characters evolve from the distillation of specific readings related to each of the aforementioned modes as well as from interviews and experiences that assist in their development. These readings range from Novalis and Ashley Montagu on corporeal knowledge, Donna Harraway and Neil Spiller on technologically enhanced trans-human states and Fritjof Capra and Alex Grey on the intersection of ancient mystical teaching with recent findings in quantum physics. This exploration is followed by the design portion of the thesis: a short film where each character occupies a separate world in the dystopian future. The radical and regenerative possibilities of their crossings are what the film initiates.

Usage of simulation models is an essential part in many modern engineering disci- plines. Computer models of complex physical systems can be used to expedite the design of control systems and reduce the number of physical tests. Model valida- tion tries to answer the question if the model is a good enough representation of the physical system. This thesis describes techniques to visualize multi-dimensional validation results and the search for an automated validation process. The work is focused on a simulation model of the Primary Environmental Control System of Gripen E, but can be applied on validation results from other simulation models. The result from the thesis can be divided into three major components, static validation, dynamic validation and model coverage. To present the results from the static validation different multi-dimensional visualization techniques are in- vestigated and evaluated. The visualizations are compared to each other and to properly depict the static validation status of the model, a combination of visual- izations are required. Two methods for validation of the dynamic performance of the model are examined. The first method uses the singular values of an error model estimated from the residual. We show that the singular values of the error model relay important information about the model’s quality but interpreting the result is a considerable challenge. The second method aims to automate a visual inspection procedure where interesting quantities are automatically computed. Coverage is a descriptor of how much of the applicable operating conditions that has been validated. Two coverage metrics, volumetric coverage and nearest neigh- bour coverage, are examined and the strengths and weaknesses of these metrics are presented. The nearest neighbour coverage metric is further developed to account for validation performance, resulting in a total static validation quantity.

Core-collapse supernovae are some of the most energetic events in the Universe, they herald the birth of neutron stars and black holes, are a major site for nucleosynthesis, influence galactic hydrodynamics, and trigger further star formation. As such, it is important to understand the mechanism of explosion. Moreover, observations imply that asymmetries are, in the least, a feature of the mechanism, and theory suggests that multi-dimensional hydrodynamics may be crucial for successful explosions. In this dissertation, we present theoretical investigations into the multi-dimensional nature of the supernova mechanism. It had been suggested that nuclear reactions might excite non-radial g-modes (the ε-mechanism) in the cores of progenitors, leading to asymmetric explosions. We calculate the eigenmodes for a large suite of progenitors including excitation by nuclear reactions and damping by neutrino and acoustic losses. Without exception, we find unstable g-modes for each progenitor. However, the timescales for growth are at least an order of magnitude longer than the time until collapse. Thus, the ε-mechanism does not provide appreciable amplification of non-radial modes before the core undergoes collapse. Regardless, neutrino-driven convection, the standing accretion shock instability, and other instabilities during the explosion provide ample asymmetry. To adequately simulate these, we have developed a new hydrodynamics code, BETHE-hydro that uses the Arbitrary Lagrangian-Eulerian (ALE) approach, includes rotational terms, solves Poisson’s equation for gravity on arbitrary grids, and conserves energy and momentum in its basic implementation. By using time dependent arbitrary grids that can adapt to the numerical challenges of the problem, this code offers unique flexibility in simulating astrophysical phenomena. Finally, we use BETHE-hydro to investigate the conditions and criteria for supernova explosions by the neutrino mechanism. We find that a critical luminosity/ mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic 1D and 2D simulations. Importantly, the critical luminosity for 2D simulations is found to be ∼70% of the critical luminosity for 1D simulations. We identify the specifics ofmulti-dimensional hydrodynamic simulations that enable explosions at lower neutrino luminosities in 2D and discuss how these results might foreshadow successful explosions by eventual 3D radiation-hydrodynamic simulations.

Šiais laikais vis daugiau domimasi daugiamačių duomenų aproksimavimo teorija. Daugiamatėje erdvėje aproksimavimo teorija palčiai kur taikoma, pavyzdžiui, skaitinių metodų analizėje, bangų analizėje, signalų apdorojime, įvairiose informacinių technologijų sistemose, kompiuterių grafikoje, astronomijoje, naftos klodų tyrinėjime. Ši sritis viliojanti, nes didelė dalis klasikinės matematikos sunkiai pritaikoma daugiamačiams uždaviniams analizuoti. Taigi senoms problemoms spręsti reikalingi nauji įrankiai. Funkcijų aproksimavimo uždavinių gausu įvairiose matematikos, fizikos ir technikos srityse. Gausu ir jų sprendimų būdų bei metodų. Nesunkiai šie uždaviniai sprendžiami, kai funkcija priklauso nuo vieno ar dviejų kintamųjų. Tačiau realiame gyvenime naudojamos funkcijos turi daug daugiau nežinomųjų. Didėjant kintamųjų skaičiui uždavinio sudėtingumas taip pat auga. Pavyzdžiui, kai funkcija priklauso nuo vieno kintamojo, ją galima pavaizduoti plokštumoje kaip kreivę. Dviejų kintamųjų funkciją atitinka paviršius, nubrėžtas trimatėje erdvėje. Funkcijų, kurios priklauso nuo trijų ir daugiau kintamųjų, vaizdavimas jau sukelia problemų, nes žmogus nebegali suvokti didesnio matumo erdvės. Kadangi trimatę erdvę galima pavaizduoti plokštumoje, manoma, kad panašiu principu keturmatę erdvę galima pavaizduoti trimatėje, o šią vėl plokštumoje. Jei pavyktų sugalvoti tokį metodą, erdvės matumas nebesukeltų problemų. Visgi trijų kintamųjų funkciją bandoma vaizduoti dviem būdais: 1. pateikti... [toliau žr. visą tekstą] / This Master‘s work covers a mathematical analysis system which can visualize multivariate data layers, approximate multi-dimensional functions by polynomials, estimate approximation accuracy and present few the most effective aproximation models. Multivariate approximation theory is an increasingly active research area today. It encompasses a wide range of tools for multivariate approximation such as multi-dimensional splines and finite elements, shift-invariant spaces and radial-basis functions. Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. The field is fascinating since much of the mathematics of the classical univariate theory does not straightforwardly generalize to the multivariate setting, so new tools are required. Graphs of one variable functions are frequantly displayed as curves, bivariate functions - as contour plots. In generally it is very hard to display or realize function in the multivariate setting. However, some efforts have been made to render functions of precisely three variables. Two obvious approaches suggest themselves: 1. Display a number of cross sections where one of the variables is held constant, or, 2. display contour surfaces where the value of function equals some constant. We will use the first method modification in this Master‘s work. All function variables except... [to full text]

Problems in the demodulation of one, two, and three-dimensional signals are investigated. In one-dimensional linear systems the analytic signal and the Hilbert transform are central to the understanding of both modulation and demodulation. However, it is shown that an efficient nonlinear algorithm exists which is not explicable purely in terms of an approximation to the Hilbert transform. The algorithm is applied to the problem of finding the envelope peak of a white light interferogram. The accuracy of peak location is then shown to compare favourably with conventional, but less efficient, techniques. In two dimensions (2-D) the intensity of a wavefield yields to a phase demodulation technique equivalent to direct phase retrieval. The special symmetry of a Helmholtz wavefield allows a unique inversion of an autocorrelation. More generally, a 2-D (non-Helmholtz) fringe pattern can be demodulated by an isotropic 2-D extension of the Hilbert transform that uses a spiral phase signum function. The range of validity of the new transform is established using the asymptotic method of stationary phase. Simulations of the algorithm confirm that deviations from the ideal occur where the fringe pattern curvature is larger than the fringe frequency. A new self-calibrating algorithm for arbitrary sequences of phase-shifted interferograms is developed using the aforementioned spiral phase transform. The algorithm is shown to work even with discontinuous fringe patterns, which are known to seriously hamper other methods. Initial simulations of the algorithm indicate an accuracy of 5 milliradians is achievable. Previously undocumented connections between the demodulation techniques are uncovered and discussed.

The present explosion in digital communications and multi-user wireless cellular networks has urged a demand for more effective modulation methods, utilizing the available frequency spectrum more efficiently. To accommodate a large number of users sharing the same available frequency band, one requirement is the availability of large families of spreading sequences with excellent AC and CC properties. Another requirement is the availability of sets of orthogonal basis functions to extend capacity by exploiting all available degrees of freedom (e.g., temporal, frequency and spatial dimesions), or by employing orthogonal multi-code operation in parallel, such as used in the latest 3GPP and 3GPP2 Wide-band Code Division Multiple Access (WCDMA) modulation standards by employing sets of orthogonal Walsh codes to improve the overall data throughput capacity. The generic Direct Sequence Spread Spectrum (DSSS) transmitter developed in this dissertation has originally been designed and implemented to investigate the practicality and usefulness of complex spreading sequences, and secondly, to verify the concept of non-linearly interpolated root-of-unity (NLI-RU) filtering. It was found that both concepts have a large potential for application in point-to-point, and particularly micro-cellular Wireless Local Area Networks (WLANs) and Wireless-Local-Loop (WLL) environments. Since then, several novel concepts and subsystems have been added to the original system, some of which have been patented both locally and abroad, and are outlined below. Consequently, the ultimate goal of this research project was to apply the principles of the generic DSSS transmitter and receiver developed in this study in the implementation of a WLL radio-frequency (RF)-link, and particularly towards the establishment of affordable wireless multimedia services in rural areas. The extended coverage at exceptionally low power emission levels offered by the new design will be particularly useful in rural applications. The proposed WLL concept can for example also be utilized to add a unique mobility feature to for example existing Private Automatic Branch Exchanges (PABXs). The proposed system will in addition offer superior teletraffic capacity compared to existing micro-cellular technologies, e.g., the Digital European Cordless Telephony (DECT) system, which has been consider by Telkom for employment in rural areas. The latter is a rather outdated interim standard offering much lower spectral efficiency and capacity than competitive CDMA-solutions, such as the concept analyzed in this dissertation, which is based on the use of unique large families of spectrally well confined (i.e., band-limited) constant envelope (CE) complex spreading sequences (CSS) with superior correlation properties. The CE characteristic of the new spreading sequences furthermore facilitates the design of systems with superior power efficiency and exceptionally robust performance characteristics (much less spectral re-growth) compared to existing 2G and 3G modulation standards, in the presence of non-linear power amplification. This feature allows for a system with larger coverage for a given performance level and limited peak power, or alternatively, longer battery life for a given maximum communication distance and performance level, within a specified fixed spreading bandwidth. In addition, the possibility to extend the concept to orthogonal multi-code operation provides for comparable capacity to present 3G modulation standards, while still preserving superior power efficiency characteristics in non-linear power amplification. Conventional spread spectrum communication systems employ binary spreading sequences, such as Gold or Kasami sequences. The practical implementation of such a system is relatively simple. The design and implementation of a spread-spectrum communication system employing complex spreading sequences is however considerable more complex and has not been previously presented, nor been implemented in hardware. The design of appropriate code lock loops for CSS has led to a unique design with 3dB performance advantage compared to similar loops designed for binary spreading sequences. The theoretical analysis and simulation of such a system will be presented, with the primary focus on an efficient hardware implementation of all new concepts proposed, in the form of a WLL RF-link demonstrator. / Dissertation (MEng (Electronic Engineering))--University of Pretoria, 2007. / Electrical, Electronic and Computer Engineering / unrestricted