This thesis investigates multiple-input-multiple-output (MIMO) channel modelling for a wideband indoor environment. Initially the theoretical basis of geometric modelling for a typical indoor environment is looked at, and a space-time model is formulated. The transmit and receive antenna correlation is then separated and is expressed in terms of antenna element spacing, the scattering parameter, mean angle of arrival and number of antenna elements employed. These parameters are used to analyze their effect on the capacity for this environment. Then the wideband indoor channel operating at center frequencies of 2.4 GHz and 5.2 GHz is investigated. The concept of MIMO frequency scaling is introduced and applied to the data obtained in the measurement campaign undertaken at the University of Pretoria. Issues of frequency scaling of capacity, spatial correlation and the joint RX/TX double direction channel response for this indoor environment are investigated. The maximum entropy (ME) approach to MIMO channel modelling is investigated and a new basis is developed for the determination of the covariance matrix when only the RX/TX covariance is known. Finally, results comparing this model with the established Kronecker model and its application for the joint RX/TX spatial power spectra, using a beamformer, are evaluated. Conclusions are then drawn and future research opportunities are highlighted. / Thesis (PhD)--University of Pretoria, 2008. / Electrical, Electronic and Computer Engineering / unrestricted

We map stock market interactions to spin models to recover their hierarchical structure using a simulated annealing based Super-Paramagnetic Clustering (SPC) algorithm. This is directly compared to a modified implementation of a maximum likelihood approach to fast-Super-Paramagnetic Clustering (f-SPC). The methods are first applied standard toy test-case problems, and then to a dataset of 447 stocks traded on the New York Stock Exchange (NYSE) over 1249 days. The signal to noise ratio of stock market correlation matrices is briefly considered. Our result recover approximately clusters representative of standard economic sectors and mixed clusters whose dynamics shine light on the adaptive nature of financial markets and raise concerns relating to the effectiveness of industry based static financial market classification in the world of real-time data-analytics. A key result is that we show that the standard maximum likelihood methods are confirmed to converge to solutions within a Super-Paramagnetic (SP) phase. We use insights arising from this to discuss the implications of using a Maximum Entropy Principle (MEP) as opposed to the Maximum Likelihood Principle (MLP) as an optimization device for this class of problems.

In large observational studies, data are often highly multivariate with many discrete and continuous variables measured on each observational unit. One often derives subpopulations to facilitate analysis. Traditional approaches suggest modeling such subpopulations with a compilation of interaction effects. However, when many interaction effects define each subpopulation, it becomes easier to model membership in a subpopulation rather than numerous interactions. In many cases, subjects are not complete members of a subpopulation but rather partial members of multiple subpopulations. Grade of Membership scores preserve the integrity of this partial membership. By generalizing an analytic chemistry concept related to chromatography-mass spectrometry, we obtain a method that can identify latent subpopulations and corresponding Grade of Membership scores for each observational unit.

The use of moment-closure methods to predict continuum and moderately rarefied flow offers many modelling and numerical advantages over traditional methods. The maximum-entropy family of moment closures offers models described by hyperbolic systems of balance laws. In particular, the twenty-one moment model of the maximum-entropy hierarchy offers a hyperbolic treatment of viscous flows exhibiting heat transfer. This twenty-one moment model has the ability to provide accurate solutions where the Navier-Stokes equations lose physical validity due to the solution being too far from local equilibrium. Furthermore, its first-order hyperbolic nature offers the potential for improved numerical accuracy as well as a decreased sensitivity to mesh quality. Unfortunately, higher-order maximum-entropy closures cannot be expressed in closed form. The only known affordable option is to propose approximations. Previous approximations to the fourteen-moment maximum-entropy model have been proposed [McDonald and Torrilhon, 2014]. Although this fourteen-moment model also predicts viscous flow with heat transfer, the necessary moments to close the system renders it more difficult to approximate accurately than the twenty-one moment model. The proposed approximation for the fourteen-moment model also has realizable states for which hyperbolicity is lost. Unfortunately, the velocity distribution function associated with the twenty-one moment model is an exponential of a fourth-order polynomial. Such a function cannot be integrated in closed form, resulting in closing fluxes that can only be obtained through complex numerical methods. The goal of this work is to present a new approximation to the closing fluxes that respect the maximum-entropy philosophy as closely as possible. Preliminary results show that a proposed approximation is able to provide shock predictions that are in good agreement with the Boltzmann equation and surpassing the prediction of the Navier-Stokes equations. Furthermore, Couette flow results as well as lid-driven cavity flows are computed using a novel approach to Knudsen layer boundary conditions. A dispersion analysis as well as an investigation of the hyperbolicity of the model is also shown. The Couette flow results are compared against Navier-Stokes and the free-molecular analytical solutions for a varying Knudsen number, for which the twenty-one moment model show good agreement over the domain. The shock-tube problem is also computed for different Knudsen numbers. The results are compared with the one obtained by directly solving the BGK equation. Finally, the lid-driven cavity flow computed with the twenty-one moment model shows good agreement with the direct simulation Monte-Carlo (DSMC) solution.

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In this thesis, I have assessed and modelled invasion of alien plant species in the forest of the southeastern United States. There are over 380 recognized invasive plants in southeastern forests and grasslands with 53 ranked as high-to-medium risk to natural communities. I have focused on ten of these: Chinese lespedeza, tall fescue, Japanese honeysuckle, Chinese privet, autumn olive, princesstree, silktree, chinaberry, tree of heaven, tallowtree. Assessing them at differing scales, locally (Chapter 2 and 3), eco-regionally (Chapter 4 and 5) and regionally (Chapters 6 and 7), using field based measurements integrated with remotely sensed and digital datasets, and applying both parametric and non-parametric modelling approaches. Data from field based measurements as well as digitally available sources was evaluated, bringing together freely available data with time consuming, intensively collected data. Once models were developed application to assessing long term impacts was done by integrating potential climate change scenarios. At the local level Chinese lespedeza and Japanese Honeysuckle were the most prevalent, with models at the local level dominated by remotely sensed variables. At an eco-regional level Japanese honeysuckle was the most prevalent with models primarily dominated by environmental variables. At a regional level, where only trees were assessed, potential distributions of the invasive species ranged from 12 to 33 percent of the southeastern forests under current conditions with this dramatically increasing for chinaberry and tallowtree under most climate change scenarios, up as high as 66 percent of southeastern forest sites. In this thesis information on anthropogenic factors added some value to the models, however it was rarely dominant. Roads and land use (proportion of forest or distance to forest) were the most useful anthropogenic variables. In all models evaluated, only six times did any one anthropogenic variable represent more than 25 percent of the models, four of these were at the local scale. At the regional and eco-regional level, roads had a greater than 25 percent contribution to the silktree models, at a local level, distance to forest and distance roads contributed more than 25 percent to three of the species evaluated, sawtooth oak, Japanese honeysuckle and privet. Human activities have the most influence on invasion progression through dispersal (movement and introduction rate) and disturbance of the landscape (increased resource availability). Anthropogenic variables such as roads are likely to be a mechanism of spread, thus the more a model is driven by anthropogenic variables, the more likely the invasive plant is to be in the early stages of invasion process. Thus our results suggest that many of these species have moved through the first stages of invasion. Environmental characteristics play an important role in determining a site’s vulnerability to invasion. At an eco-region and regional scale, environmental characteristics dominated (>50%) all but one model (silktree at the regional scale). At the eco-region level elevation was the dominant variable, and at a regional level minimum temperature was the dominant variable. These have some correlation, with higher elevation often relating to lower temperatures, particularly at a smaller scale. This confirms the validity of matching the climate ranges of native species with the range of potential invasion, and the approach of integrating elevation, latitude and longitude to estimate potential distribution. It also suggests that climate change will influence the distribution and that variation in climate should be integrated into models. Two different modelling approaches, logistic regression and maximum entropy, were used throughout my thesis, and applied to the same data. Agreement between different modelling types adds strength to conclusions, while disagreement can assist in asking further questions. The inclusion in the models of similar variables with the same direction of relationships gives confidence to any inference about the importance of these variables. The geographical agreement between models adds confidence to the probability of occurrence in the area. Alternatively using the same model but different datasets can give you similar information. Overall for all models created by both logistic regression and MaxEnt, the logistic regression had slightly better omission rates and the MaxEnt model had better AUC’s. Logistic regression models also often predicted larger geographical areas of occurrences when the threshold of maximum sensitivity plus specificity was used, thus the lower omission rates is related to the less stringent model that predicts a larger area. The selection of appropriate data to answer the question was shown to be fundamental in Chapter 7. When data were used outside of the area of interest it generalized the models and increased the potential for invasion significantly. There was more value in the intensive surveyed data but this was less dramatic than in using the defined areas of interest to select the data for models.

Environmentally related selective pressures and community interactions are well-documented drivers for niche differentiation, as natural selection acts on adaptive traits best fit for survival. Here, we investigated niche evolution between and within Pinus taeda, Pinus rigida, and Pinus pungens and sought to identify which climate variables contributed to species divergence. We also sought to describe niche differentiation across genetic groupings previously identified for P. taeda and P. rigida. Ecological niche models were produced using Maximum Entropy followed by statistical testing based on a measure of niche overlap, Schoener’s D. Both niche conservatism and niche divergence were detected, thus leading us to conclude that directional or disruptive selection drove divergence of the P. taeda lineage from its ancestor with P. rigida and P. pungens, while stabilizing selection was associated with the divergence of P. rigida and P. pungens. The latter implies that factors beyond climate are important drivers of speciation within Pinus.

A produção de alimentos no mundo está condicionada à oferta e ao consumo de fertilizantes inorgânicos, obtidos de fontes naturais não renováveis. Existe um limite entrópico para o atendimento das necessidades crescentes de alimentos. A sustentabilidade da dinâmica dos sistemas agrícolas dependerá da adequação da produção de alimentos à quantidade de recursos naturais disponíveis. No presente trabalho nós testamos essa sustentabilidade, procurando analisar a eficiência do uso de fertilizantes inorgânicos na produção de soja, um dos alimentos básicos nas cadeias alimentares globais, segundo uma abordagem da bioeconomia fundamentada na termodinâmica. Com base nos dados de produção e área cultivada de soja no Brasil, como disponibilizados pelo Instituto Brasileiro de Geografia e Estatística (IBGE), desenvolveu-se um modelo analítico baseado em programação matemática e no princípio de máxima entropia para estimar o uso de fertilizantes por extrato de área cultivada, bem como os respectivos custos totais de produção. Neste trabalho estimou-se a eficiência termodinâmica do uso de fertilizantes e a eficiência econômica da produção de soja nos diferentes extratos de área de produção. Para avaliar essas eficiências utilizou-se um conceito de retorno constante de produtividade da terra (RCP). Esse indicador define o rendimento relativo por hectare da produção de soja nos diferentes extratos de área. Assim, analisando o caso da produção de soja brasileira, verificou-se que no ano de 2008 o aumento de preços das matérias-primas para produzir fertilizantes levou a uma queda no seu respectivo consumo global. A partir dessa observação, procurou-se identificar os fundamentos da tomada de decisão do produtor de soja relativa ao emprego dos fertilizantes no Brasil. Verificou-se que o produtor de soja brasileiro decide as quantidades de fertilizantes que vai empregar, baseando-se na expectativa do lucro da respectiva safra. Os resultados apontam que essa decisão leva a um emprego ineficiente de fertilizantes inorgânicos entre os diferentes extratos de área, principalmente nos extratos inferiores a 20 hectares, em relação a produtores com área superior a 2500 hectares. Essa ineficiência relativa se dá devido ao fato de que, embora a taxa de aplicação de fertilizantes por hectare apresente diferenças pouco significativas entre os extratos de área, as respectivas produtividades são evidentemente distintas. A produtividade da terra em soja é menor nos extratos até 20 hectares, quando comparada à produtividade nos extratos superiores, ocorrendo casos em que essa diferença venha a ser até de duas toneladas de soja por hectare. No período de 1975 a 2011, anos selecionados para este estudo, outros extratos menores, mas superiores a 20 hectares, também apresentaram menor eficiência em relação ao uso de fertilizantes em comparação aos extratos superiores a 2500 hectares. Em relação à respectiva eficiência econômica, verificou-se que os custos de fertilizantes por tonelada de soja são similares entre os extratos, sugerindo-se uma homogeneidade em termos de estrutura de comercialização dos fertilizantes, o que acaba por impactar na lucratividade relativa da produção de soja. Os custos totais de produção refletem também a estrutura tecnológica adotada em cada extrato de área. Ao utilizar-se o conceito de RCP, verifica-se que extratos abaixo de 500 hectares possuem uma menor eficiência econômica quando comparadas com os extratos acima de 2500 hectares. Esses resultados indicam a necessidade de uma escala mínima de produção para o produtor manter-se competitivo do ponto de vista econômico. Desses resultados, e aproveitando-se a modelagem desenvolvida por este estudo, foram derivados alguns cenários pertinentes ao cultivo de soja no Brasil, relativos à produção, área, produtividade e uso de fertilizantes, bem como os custos de produção associados. O modelo desenvolvido para estimar as quantidades de fertilizantes inorgânicos utilizados pelos diferentes extratos de área, relativos à produção de soja, tem como principal característica oferecer a possibilidade de testar-se hipóteses sobre produção, área, produtividade e uso de fertilizantes. Esse modelo pode ser uma ferramenta de apoio à decisão, tanto para gestores de investimentos públicos na agricultura, quanto para a gestão nas unidades de produção agrícola. Os resultados deste presente trabalho sugerem que na produção de soja brasileira o uso de fertilizantes inorgânicos está desconectado de determinantes tecnológicos agronômicos, assim como está dissociado de questões relativas à segurança alimentar ou da sustentabilidade ambiental. Isso porque a tomada de decisão sobre o uso de fertilizantes inorgânicos na agricultura ignora a termodinâmica do processo produtivo como um todo. Para que a produção de soja no Brasil seja efetivamente eficiente e sustentável, do ponto de vista bioeconômico, ou seja, integrador das dimensões econômica, agronômica e termodinâmica, é necessário levar-se em consideração de que são imprescindíveis extratos de produção agrícola de áreas superiores, que contenham uma certa área mínima para a produção de soja, e que se redesenhe com propriedade as tecnologias empregadas nos seus respectivos sistemas de produção, levando-se em conta o limite entrópico da disponibilidade de fertilizantes inorgânicos no mundo. / Food production worldwide is conditioned to supply and consumption of inorganic fertilizers that are obtained from nonrenewable natural sources. The satisfaction of the increasing food needs is limited by an entropic threshold. Therefore, sustainability of the agricultural systems’ dynamics will depend on the adequacy of food production to the amount of available natural resources. In this paper, we examine such sustainability, seeking to analyze the efficiency of the inorganic fertilizers’ use in the production of soybean, one of the basic foods from the global food chain, according to a bioeconomic approach grounded on thermodynamics. Based on data on the soybean production and cultivated areas in Brazil, made available by the Brazilian Institute of Geography and Statistics (IGBE, from the Brazilian Portuguese: “Instituto Brasileiro de Geografia e Estatística”), we have developed an analytical model, which is based on mathematical programing and on the generalized maximum entropy principle, to estimate the use of fertilizers per level of cultivated land, as well as its full production costs. In this paper, we have estimated the efficiency of thermodynamics regarding the use of fertilizers and the economical efficiency of soybean production in different levels of cultivated land. To evaluate such efficiencies, a concept of constant return on land productivity (RCP, from the Brazilian Portuguese: “Retorno Constante de Produtividade”) has been used. This indicator defines the yield per hectare of soybean production in different levels of cultivated land. Thus, analyzing the case of Brazilian soybean production, it’s been asserted that during 2008 the increased price of raw materials used to produce fertilizers lead to a decline in its global consumption. From that observation, we have sought to identify the reasons behind soybean producers’ decision-making regarding the use of fertilizers in Brazil. We’ve discovered that Brazilian soybean producers decide on the amount of fertilizers they will use based on the expectations of profit regarding that particular crop. Results indicate that such decision leads to an inefficient use of inorganic fertilizers per different levels of cultivated land, mainly on portions lower than 20 hectares, from producers holding a field over 2500 hectares. Such relative inefficiency occurs due to the fact that, although the fertilizer’s usage rate per hectare shows little significant differences between producers, their yields are clearly distinct. The soil productivity of soybean is lower in portions up to 20 hectares in comparison to productivity on higher levels of cultivated land and there are instances where such difference is up to two tons of soybean per hectare. From 1975 to 2011, the period selected for this particular study, other smaller levels of cultivated land which were higher than 20 hectares, also evidenced a lower efficiency with regard to the use of fertilizers in comparison to levels higher than 2500 hectares. Regarding their economic efficiency, evidence showed that the costs of fertilizers per ton are similar between levels of cultivated land, suggesting homogeneity in terms of the fertilizers trading structure, resulting in an impact on the relative yielding of soybean production. Total production costs also reflect the technological structure adopted in each level of cultivated land. By applying the concept of RCP, it’s been ascertained that levels lower than 500 hectares have a lower economic efficiency when compared to levels higher than 2500 hectares. Such results indicate the need for a minimal production scale in order for the producer to keep their competitiveness, from an economic perspective. From these results, and taking advantage of the modeling developed for this study, some sceneries pertaining the soybean culture in Brazil have been derived that relate to production, area, yield, and use of fertilizers, as well as related production costs. The model developed to estimate the amounts of inorganic fertilizers used in soybean production, in different levels of cultivated land, holds as its main feature the fact that it allows for the testing of hypothesis on production, area, yield, and use of fertilizers. Such a model can be used as a decision-making supporting tool, both for public agricultural investment managers and for managing the agricultural production units (farms). This paper’s results suggest that, in Brazilian soybean production, the use of inorganic fertilizers is disconnected from agronomic technological determiners and dissociated from food safety and environmental sustainability issues. That happens because decision-making on agricultural use of fertilizers overlooks the thermodynamics of the productive process as a whole. In order for the soybean production in Brazil to be effectively efficient and sustainable, from the bioeconomic point of view, i.e., integrating the economic, agricultural, and thermodynamic dimensions, it is necessary to consider that they are fundamental portions of agricultural production in bigger areas, which contain a minimal area for the production of soybean, and to properly redesign the technologies applied in their production systems, taking into account the entropic threshold of availability of inorganic fertilizers in the world.

Accounts of species’ range shifts in response to climate change, most often as latitudinal shifts towards the poles or upslope shifts to higher elevations, are rapidly accumulating. These range shifts are often attributed to species ‘tracking’ their thermal niches as temperatures in their native ranges increase. Our objective was to estimate the degree to which climate change-driven shifts in water temperature may increase the exposure of West Virginia’s native freshwater fishes to mountaintop removal surface coal mining. Mid-century shifts in habitat suitability for nine non-game West Virginia fishes were projected via Maximum Entropy species distribution modeling, using a combination of physical habitat, historical climate conditions, and future climate data. Modeling projections for a high-emissions scenario (Representative Concentration Pathway 8.5) predict that habitat suitability will increase in high elevation streams for eight of nine species, with marginal increases in habitat suitability ranging from 46-418%. We conclude that many West Virginia fishes will be at risk of increased exposure to mountaintop removal surface coal mining if climate change continues at a rapid pace.

This thesis identifies and extends techniques that can be linked to the principle of maximum entropy (maxent) and applied to parameter estimation in machine learning and statistics. Entropy functions based on deformed logarithms are used to construct Bregman divergences, and together these represent a generalization of relative entropy. The framework is analyzed using convex analysis to charac- terize generalized forms of exponential family distributions. Various connections to the existing machine learning literature are discussed and the techniques are applied to the problem of non-negative matrix factorization (NMF).