We study the problem of communicating a discrete time analog source over a channel such that the resulting distortion is minimized. For ergodic channels, Shannon showed that separate source and channel coding is optimal. In this work we study this problem for non-ergodic channels. Although not much can be said about the general problem of transmitting any analog sources over any non-ergodic channels with any distortion metric, for many practical problems like video broadcast and voice transmission, we can gain insights by studying the transmission of a Gaussian source over a wireless channel with mean square error as the distortion measure. Motivated by different applications, we consider three different non-ergodic channel models - (1) Additive white Gaussian noise (AWGN) channel whose signal-to-noise ratio (SNR) is unknown at the transmitter; (2) Rayleigh fading multiple-input multiple-output MIMO channel whose SNR is known at the transmitter; and (3) Rayleigh fading MIMO channel whose SNR is unknown at the transmitter. The traditional approach to study these problems has been to fix certain SNRs of interest and study the corresponding achievable distortion regions. However, the problems formulated this way have not been solved even for simple setups like 2 SNRs for the AWGN channel. We are interested in performance over a wide range of SNR and hence we use the distortion SNR exponent metric to study this problem. Distortion SNR exponent is defined as the rate of decay of distortion with SNR in the high SNR limit. We study several layered transmissions schemes where the source is first compressed in layers and then the layers are transmitted using channel codes that provide variable error protection. Results show that in several cases such layered transmission schemes are optimal in terms of the distortion SNR exponent. Specifically, if the band- width expansion (number of channel uses per source sample) is b, we show that the optimal distortion SNR exponent for the AWGN channel is b and it is achievable using a superposition based layered scheme. For the L-block Rayleigh fading M x N MIMO channel the optimal exponent is characterized for b < (|N - M|+1)= min(M;N) and b > MNL2. This corresponds to the entire range of b when min(M;N) = 1 and L = 1. The results also show that the exponents obtained using layered schemes which are a small subclass of joint source channel coding (JSCC) schemes are, surprisingly, as good as and better in some cases than achievable exponent of all other JSCC schemes reported so far.

Voltage flicker limitation of electric utilities has been discussed in the past three decades. Arc furnace is one of the most disturbing loads that cause flicker problems in the power network. If displeasing flicker levels are predictable, then corrective solution such as static var compensation or furnace controls could be developed in cooperation between the utility and the customer. In the past, the electric fluctuations in the arc furnace voltage have been proven to be chaotic in nature. This thesis proposes a phase space approach based on nonlinearity chaotic techniques to analyze and predict voltage flicker. The determination of the phase space dimension and the application of Lyapunov exponent for flicker prediction are described. Test results have shown that accurate prediction results are obtainable for short term flicker prediction based on chaos theory.

The Greenland ice sheet (GIS) is a key component of the warming Arctic climate, having the potential to dramatically influence sea level through melting. Light-absorbing aerosols are thought to be significant contributors to warming in the Arctic, because of their effect on the radiation balance through both aerosol absorption in the atmosphere as well as absorption in surface snow after particulate deposition. At this time it is not possible to estimate the impact of aerosol absorption on the radiation balance over Greenland due to the lack of in-situ measurements. Here, we present time series and estimates of key aerosol optical properties in order to better understand the seasonality and sources of aerosols over central Greenland, and compare their values with other Arctic sites. In-situ measurements made at Summit, Greenland from May 8, 2011 to December 31, 2014 include aerosol light absorption coefficient (σap) and light scattering coefficient (σsp); calculated parameters include absorption Ångström exponent (AAE), and single scattering albedo (ωo). The light absorption and scattering coefficients were found to be low in the winter and highest in the spring and summer. Spring-summer means of σap and σsp were 0.15 ± 0.15 Mm-1 and 2.35 ± 2.80 Mm-1, respectively. Mean AAE was 0.97 ± 0.29 in the spring and summer, indicating that black carbon (BC), and not dust and/or organic brown carbon (BrC), is the main aerosol light absorber. Mean ωo was 0.93 ± 0.03, which is similar to values measured at Barrow, Alaska, USA (0.94 ± 0.05) and Ny-Ålesund, Svalbard, Norway (0.95 ± 0.06). Summit exhibits ωo as low as Barrow and Ny-Ålesund although it is an isolated high-altitude site indicating the importance of aerosol light absorption over the most remote Arctic locations.

Macroscopic properties of rocks are functions of pore-scale geometry and can be determined from laboratory experiments using rock samples. Macroscopic properties can also be determined from computer simulations using 3D pore geometries derived from various imaging techniques. Using 3D imagery and computer simulations, we can calculate the porosity, permeability, formation resistivity factor and cementation exponent in reservoir drill cores. The objective of this thesis was to develop a workflow using Synchrotron X-ray Computed Microtomography (CMT) images and commercially available software in order to determine the macroscopic properties in reservoir drill cores for Midale Marly (M0) and Vuggy Shoal (V6) rocks. The workflow started by using CMT data that provided three-dimensional images of the reservoir rocks taken from drill cores in the Weyburn oil field. The resulting CMT grey scale images were used to isolate the pore space in the rock image. A three-dimensional mesh, representing the pore space, was then used to obtain the solution of the Navier-Stokes equations for an incompressible fluid and Laplace's equation for electrical current flow. Solutions of the Navier-Stokes equations were computed with different inlet pressures for the same pore geometry in order to confirm a direct proportionality between the mass fluid flux and pressure gradient as Darcy’s Law specifies. Previously measured laboratory transport properties were compared with my calculated transport properties on a smaller sub-volume of the same rock core imaged using 0.78 µm resolution CMT images. For the Midale Marly rock, the calculated permeability ranged from 0.01 to 3.53 mD. The formation resistivity factor ranged from 29.3 to 309.43 and the cementation exponent ranged from 1.99 to 2.10. The sample was verified to be nearly isotropic as the permeability was similar for three orthogonal fluid flow directions. Even though the sub-volume analyzed was smaller than a Representative Elementary Volume (REV), the results are within an order of magnitude of the previously calculated laboratory results as completed by Glemser (2007) and fall on the same power law trend. A Vuggy (V6) sample was investigated after the sample had been exposed to CO2, and dissolution within the rock matrix resulted in large visible pore spaces. Using 7.45 µm resolution CMT images, the permeability for a large isolated pore could not be calculated using the previous workflow due to computer memory limitations. Resampling enabled the data to fit into the available computer memory. The permeability values ranged from 2.66x10^5 to 8.59x10^5 mD for resampling the CMT images from 2x to 10x.

Submitted by Suelen Reis (suziy.ellen@gmail.com) on 2013-05-08T16:09:26Z No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) / Rejected by Alda Lima da Silva(sivalda@ufba.br), reason: Documento de Física on 2013-05-08T18:28:33Z (GMT) / Submitted by Suelen Reis (suziy.ellen@gmail.com) on 2013-05-09T16:49:27Z No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) / Approved for entry into archive by Rodrigo Meirelles(rodrigomei@ufba.br) on 2013-05-09T17:10:10Z (GMT) No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) / Made available in DSpace on 2013-05-09T17:10:10Z (GMT). No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) Previous issue date: 2009 / Nos últimos anos, buscando melhorar os diagnósticos em imagens biomédicas, foram desenvolvidos diversos métodos de filtragem das imagens de forma a facilitar a detecção de padrões estruturais associados aos tumores. Por outro lado, a geometria fractal pode ser aplicada para descrever a hierarquia das irregularidades dos fenômenos naturais. As propriedades de um fractal podem ser caracterizadas por um conjunto de expoentes que descrevem um padrão no comportamento das flutuações. Esse conjunto de expoentes representa uma descrição mais completa da medida fractal e é definida como multifractal. Os parâmetros obtidos através da caracterização multifractal contêm informações que podem relacionar as propriedades observadas em diferentesescalas com os diferentes padrões de ocupação das células no tecido. Tais parâmetros oferecem, portanto, um aprofundamento na compreensão da dinâmica de formação de tais padrões. O objetivo geral desta dissertação é avaliar o formalismo multifractal como uma ferramenta útil para a caracterização de padrões espaciais de tumores hepáticos e até onde nos sabemos trata-se de um trabalho original no tema. Nele discutimos um refinamento sobre os métodos de caracterização de tumores embasados na teoria fractal de forma a considerar o espectro de dimensões fractais mediante uma análise multifractal. As imagens de tumores utilizadas foram consideradas como superfícies multi-afins. Foi feito um estudo de casos a partir de três amostras de exames médicos tomográficos com o objetivo de se testar o método na obtenção do grau de heterogeneidade das imagens. O método de cálculo do espectro multifractal foi validado de maneira a avaliar o efeito das diferentes resoluções nas imagens e os diferentes valores dos expoentes de rugosidade para o caso de superfícies monofractais. As características multifractais foram analisadas por duas abordagens. Primeiro em relação às imagens lesadas pelo tumor e segundo, pela comparação desses resultados com as imagens não atingidas pela lesão. Com esta análise pôde-se verificar que nos casos analisados as imagens apresentam um comportamento multifractal, o que indica um padrão de heterogeneidade maior do que se supunham os métodos fractais. / Salvador

abstract: There have been a number of studies that have examined students’ difficulties in understanding the idea of logarithm and the effectiveness of non-traditional interventions. However, there have been few studies that have examined the understandings students develop and need to develop when completing conceptually oriented logarithmic lessons. In this document, I present the three papers of my dissertation study. The first paper examines two students’ development of concepts foundational to the idea of logarithm. This paper discusses two essential understandings that were revealed to be problematic and essential for students’ development of productive meanings for exponents, logarithms and logarithmic properties. The findings of this study informed my later work to support students in understanding logarithms, their properties and logarithmic functions. The second paper examines two students’ development of the idea of logarithm. This paper describes the reasoning abilities two students exhibited as they engaged with tasks designed to foster their construction of more productive meanings for the idea of logarithm. The findings of this study provide novel insights for supporting students in understanding the idea of logarithm meaningfully. Finally, the third paper begins with an examination of the historical development of the idea of logarithm. I then leveraged the insights of this literature review and the first two papers to perform a conceptual analysis of what is involved in learning and understanding the idea of logarithm. The literature review and conceptual analysis contributes novel and useful information for curriculum developers, instructors, and other researchers studying student learning of this idea. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2018

Orientador: José Roberto Campanha / Banca: Anderson Luis Hebling Christofoletti / Banca: Osvaldo Missiato / Os sinais analisados são séries temporais de precipitações pluviométricas ou simplesmente denominadas chuvas, que sofrem influências de outras variáveis atmosféricas, como a temperatura, pressão, vento, relevo, posição geográfica, sazonalidade, dentre outras, constituindo um sistema complexo. Estas séries temporais de chuvas, foram obtidas de 48 postos de coleta de dados, com medidas diária, em (mm), de quantidade de chuva, pertencentes a 38 municípios, localizados nas 9 regiões climáticas do Estado de São Paulo, proposto por Monteiro (1973). Os valores do expoente de Hurst, destas séries temporais, foram estimados com o método conhecido como análise R/S, o método utilizando a transformada de Fourier e o método utilizando a transformada de wavelets. A análise R/S e o método utilizando a transformada de Fourier apresentaram resultados equivalentes, mostrando coerência e grande importância na análise de sistemas complexos, objeto deste estudo. O método utilizando a transformada de wavelets, forneceu alguns resultados coerentes, uma grande parte, com resultados superestimados e uma pequena parte, com resultados subestimados, em relação aos outros dois métodos, mostrando-se inadequado para esta análise. / We analyze temporal series associated to pluvial precipitations, best known as rain, The latter depends on temperature, pressure, landscape, location and season, among many other atmospheric variables, thus qualifying as a complex system. These rain's temporal series were obtained from 48 data collection posts, with daily rain measurements (in mm), associated to 38 counties within the nine climatic regions of the State of São Paulo. The values of the time series Hurst exponent, were computed by three methods namely: the R/S analysis method, a Fourier transform and the wavelet transform method. The first two yield coherent results, showing both the consistency and relevance of these methods when applied to complex systems, the main goal of this work. The wavelet method yielded higher and lower values for the Hurst exponent, thus probing the limitations of this method. / Mestre

This thesis deals with a complex analysis and prediction of foreign exchange markets. It uses advanced artificial intelligence methods, namely neural networks and chaos theory. It introduces unconventional approaches and methods of each of these areas, compares them and uses on a real problem. The core of this thesis is a comparison of several prediction models based on completely different principles and underlying theories. The outcome is then a selection of the most appropriate prediction model called NAR + H. The model is evaluated according to several criteria, the pros and cons are discussed and approximate expected profitability and risk are calculated. All analytical, prediction and partial algorithms are implemented in Matlab development environment and form a unified library of all used functions and scripts. It also may be considered as a secondary main outcome of the thesis.

This dissertation thesis is dedicated to the heart rate variability and methods of its evaluation. It mainly focuses on nonlinear methods and especially on the Poincaré plot. First it deals with the principle and nature of the heart rate variability, then the ways of its representation, linear and also nonlinear methods of its analysis and physiological and pathophysiological influence on heart rate variability changes. In particular, there is emphasis on the metabolic syndrome. In the next section of the thesis there are compared and evaluated different ways of representation of the heart rate variability and further are tested selected methods of heart rate variability analysis on unique data from patients with the metabolic syndrome and healthy subjects provided by the Institute of Scientific Instruments, Academy of Sciences of Czech Republic. In particular, they are used the Poincaré plot and its parameters SD1 and SD2, commonly used time domain and frequency domain parameters, parameters evaluating signal entropy and the Lyapunov exponent. SD1 and SD2 combining the advantages of time and frequency domain methods of heart rate variability analysis distinguish successfully between patients with the metabolic syndrome and healthy subjects.

An enormous and urgent energy demand is predicted due to the growing global population, increase in power intensive industries, higher living standards, electrification of remote areas, and globalisation (transportation). Moreover, the global consciousness about the harmful effects of traditional methods of power generation on the environment. That, in turn, has created a need to strategically plan and develop renewable and sustainable energy generation systems. This study presents a wind resource assessment of seven locations proximate to the largest industrial hub in the Middle East, Jubail Industrial City, Kingdom of Saudi Arabia, and a Geographic Information System, GIS based model considering a multi-criteria wind farm site suitability approach for the entire Kingdom of Saudi Arabia and elsewhere. The hourly mean wind speed data at 10, 50 and 90 m above the ground level (AGL) over a period of five years was used for a meteorological station at the Industrial Area (Central) of Jubail. At the remaining six sites, the meteorological data were recorded at 10 m AGL only. Five years of wind data were used for five sites and three years of data were available for the remaining one site. At the Industrial Area (East), the mean wind speeds were found to be 3.34, 4.79 and 5.35 m/s at 10, 50 and 90 m AGL, respectively. At 50 and 90 m AGL, the availability of wind speed above 3.5 m/s was more than 75%. The local wind shear exponent, calculated using measured wind speed values at three heights, was found to be 0.217. The mean wind power density values at measurement heights were 50.92, 116.03 and 168.46 W/m2, respectively. After the assessment and comparison of wind characteristics of all seven sites, the highest annual mean wind speed of 4.52 m/s was observed at Industrial Area (East) and the lowest of 2.52 m/s at the Pearl Beach with standard deviations of 2.52 and 1.1 m/s, respectively. In general, at all sites, the highest monthly mean wind speed was observed in February/June and the lowest in September/October. The period of higher wind availability coincides with a high power demand period in the region attributable to the air conditioning load. The wind rose plots show that the prevailing wind direction for all sites was from the north-west. Weibull parameters for all sites were estimated using maximum likelihood, least-squares regression method (LSRM), and WAsP algorithm. In general, at all sites, the Weibull parameter, c, was the highest in the months of February/June and the lowest in the month of October. The most probable and maximum energy carrying wind speed was determined by all three methods. The highest value of most probable wind speed was found to be in the range of 3.2 m/s to 3.6 m/s at Industrial Area (East) and the highest value of maximum energy carrying wind speed was found to be in the range 8.6 m/s to 9.0 m/s at Industrial Area 2 (South) by three estimation methods. The correlation coefficient (R2), root mean square error (RMSE), mean bias error (MBE), and mean bias absolute error (MAE) showed that all three methods represent wind data at all sites accurately. However, the maximum likelihood method is slightly better than LSRM, followed by WAsP algorithm. The wind power output at all seven sites, from five commercially available wind turbines of rated power ranging from 1.8 to 3.3 MW, showed that Industrial Area (East) is most promising for wind farm development. At all sites, based on percentage plant capacity factor, PCF, the 1.8 MW wind turbine was found to be the most efficient. At Industrial Area (East), this wind turbine was found to have a maximum PCF of 41.8%, producing 6,589 MWh/year energy output. The second best wind turbine was 3 MW at all locations except the Al-Bahar Desalination Plant and Pearl Beach. At both of these locations, 3.3 MW was the next best option. The energy output from the 3 MW wind turbine at Industrial Area (East) was found to be 11,136 MWh/year with a PCF of 41.3%. The maximum duration of rated power output from all selected wind turbines was observed to be between 8 to 16.6% at Industrial Area 2 (South). The minimum duration of rated power output, less than 0.3% for all wind turbines, was observed at Pearl Beach. The maximum duration of zero power output of between 35 to 60% was also observed at Pearl Beach. / Thesis (PhD)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / PhD / Unrestricted