The maximum entropy principle, pioneered by Jaynes, provides a method for finding the least biased probability distribution for the description of a system or process, given as prior information the expectation values of a set (in general, a small number) of relevant quantities associated with the system. The maximum entropy method was originally advanced by Jaynes as the basis of an information theory inspired foundation for equilibrium statistical mechanics. It was soon realised that the method is very useful to tackle several problems in physics and other fields. In particular it constitutes a powerful tool for obtaining approximate and sometimes exact solutions to several important partial differential equations of theoretical physics. In Chapter 1 a brief review of Shannon’s information measure and Jaynes’ maximum entropy formalism is provided. As an illustration of the maximum entropy principle a brief explanation of how it can be used to derive the standard grand canonical formalism in statistical mechanics is given. The work leading up to this thesis has resulted in the following publications in peer-review research journals: • J.-H. Schönfeldt and A.R. Plastino, Maximum entropy approach to the collisional Vlasov equation: Exact solutions, Physica A, 369 (2006) 408-416, • J.-H. Schönfeldt, N. Jimenez, A.R. Plastino, A. Plastino and M. Casas, Maximum entropy principle and classical evolution equations with source terms, Physica A, 374 (2007) 573-584, • J.-H. Schönfeldt, G.B. Roston, A.R. Plastino and A. Plastino, Maximum entropy principle, evolution equations, and physics education, Rev. Mex. Fis. E, 52 (2)(2006) 151-159. Chapter 2 is based on Schönfeldt and Plastino (2006). Two different ways for obtaining exact maximum entropy solutions for a reduced collisional Vlasov equation endowed with a Fokker-Planck like collision term are investigated. Chapter 3 is based on Schönfeldt et al. (2007). Most applications of the maximum entropy principle to time dependent scenarios involved evolution equations exhibiting the form of a continuity equations and, consequently, preserving normalization in time. In Chapter 3 the maximum entropy principle is applied to evolution equations with source terms and, consequently, not preserving normalization. We explore in detail the structure and main properties of the dynamical equations connecting the time dependent relevant mean values , the associated Lagrange multipliers, the partition function, and the entropy of the maximum entropy scheme. In particular, we compare the H-theorems verified by the maximum entropy approximate solutions with the Htheorems verified by the exact solutions. Chapter 4 is based on Schönfeldt et al. (2006). In chapter 4 it is discussed how the maximum entropy principle can be incorporated into the teaching of aspects of theoretical physics related to, but not restricted to, statistical mechanics. We focus our attention on the study of maximum entropy solutions to evolution equations that exhibit the form of continuity equations (eg. Liouville equation, the diffusion equation the Fokker-Planck equation, etc.). / Dissertation (MSc (Physics))--University of Pretoria, 2008. / Physics / MSc / unrestricted

Textiles and apparel trade has been governed by the Multi-Fiber Arrangement (MFA) for three decades. Trade restrictions have generated substantial welfare losses and price wedges in exporting and importing countries through trade distortions. Beginning in 1995, textiles and apparel trade underwent fundamental changes in trade flows and patterns. The World Trade Organization’s Agreement on Textiles and Clothing (ATC) aimed to remove all MFA quotas by January 2005. This study established an equilibrium displacement model to investigate the impact on textile and cotton sectors of different countries and country-groups of removing the MFA quota. The model specifies the basic linkages of textile and cotton markets in the United States, China and four other country-groups. With different assumptions about U.S. textile supply elasticity, foreign cotton exporters’ reaction and changes in the U.S. farm program payments, alternative scenarios are simulated to predict changes in domestic and import demand for textiles and apparel, import demand for U.S. cotton, domestic and import price of textiles and apparel, U.S. cotton price and adjusted world cotton price. Uniform distribution was imposed for selected parameters involved in the model to overcome the deficiency of equilibrium displacement models of assuming certainty of known related parameters. Results indicate increased import demand for U.S. cotton by China, higher U.S. cotton supply, more textile and apparel supply from China, decreased domestic demand for U.S. cotton, and lower U.S. domestic demand for textiles and apparel. However, prices of both textile and cotton markets experience both positive and negative changes under different scenarios. Holding other assumptions unchanged, when farm program payments increase, U.S. cotton price and adjusted world cotton price declined. When farm program payments are held constant, prices rise. The changes expected in U.S. cotton price are, in absolute value, greater than those of the adjusted world price.

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This work presents SPOQL, a structured query language for Semistructured Probabilistic Object (SPO) model [4]. The original query language for semistructured probabilistic database management system [20], SP-Algebra [4], has limitations such as complex functional notation and unfamiliarity to application programmers. SPOQL alleviates these problems by providing a user friendly and familiar SQL-like declarative syntax for writing queries against SPDBMS. We show that parsing SPOQL queries is a more involving task than parsing SQL queries. We describe the evaluation algorithm for SPOQL queries that we have implemented.

The aim of this work is to elaborate the metodology of creation of custom add-ins for statistical application SAS Enterprise Guide and create one of these that would enable to simplify the calculation of quantiles, values of probability mass function (probability density function respectively) and cumulative distribution function and further based on user's specifications create an appropriate graph. In connection with content of this add-in, the presented work includes the recherche from background of twenty two probability distributions that are supported by SAS Enterprise Guide. Custom add-in is programmed in Visual Basic.NET language in development environment Visual Studio 2003, its source code and the codes of graphs, used in this work and the module itself, are due to their extent included in the attached CD. Theoretical part containing the recherche mentioned above is assessed in second and third chapter of this work, the methodology of creation of custom add-ins for SAS Enterprise Guide is described in fourth chapter and own add-in is introduced in chapter five.

The thesis examines calculation of the order quantity in case of the stochastic demand. The order quantity is calculated from the cost function and the profit function. In case of the stochastic demand, the exact demand is unknown, but the probability distribution is known. The aim of the thesis is the transformation of the formulas for different probability distributions of the demand. It is necessary to calculate the order quantity so that cost function is minimal. The cost fiction is considered to be bipolar structure where ordering costs are increasing with higher ordering quantity, storage costs are decreasing with higher ordering quantity. In the profit fiction it is examined if it is possible to make higher profits from contracts and how contracts influence the order quantity.

No / Due to the advance of modern computing technology, decisions can be made based on all the existing related data instances scattered across multiple data storages, such that available information has been entirely taken into consideration. Particularly in the predictive toxicology domain, because of the heterogeneity of data sources, multiple data instances with respect to the same endpoint are usually inconsistent, and the quality (or reliability) of the data instances is typically different. Also, the quantity of data instances is often not sufficient to conduct a study using conventional statistics-based methods. This paper presents a novel risk analysis approach for chemical toxicity assessment which considers all the available heterogeneous data instances in the same time, assisted by their quality (or reliability) values. The system is developed on the basis of possibility-probability distribution, where the uncertainty of the approximated probability values based on traditional statistics methods is represented by possibility. The uncertainty considered herein is led not only by the statistics on limited small number of data instances, but also by the poor quality (or reliability) of data instances. The possibility-probability distribution is automatically computed from available data instances by employing a modified diffused-interior-outer-set model (where the reliability of data is considered) based on information diffusion theory. Toxicity value for a given chemical compound is then estimated as the fuzzy expected value based on the resulted possibility-probability distribution. Toxicity risk with respect to regulatory threshold is also introduced, in order to evaluate the probability of which the toxicity may be classified into a certain regulatory range. The proposed approach is applied to a real-world dataset to illustrate the utility and the potential of the approach in risk assessment of chemical toxicity.

No description available.

Os modelos de simulação devem ser ajustados para que os valores dos parâmetros e variáveis de entrada forneçam resultados que melhor representem os valores observados. Assim, face às imprecisões a que estão sujeitos os resultados obtidos a partir do ajuste, há a necessidade de implementar métodos que permitam a avaliação das incertezas, quer seja nos parâmetros de cultura ou nas variáveis de entrada do modelo. Tem-se, para a cana-de-açúcar, que a máxima produtividade de açúcar ocorre no momento em que a Pol e a biomassa de colmos (TCH) são potencializados. Sendo assim, este trabalho objetivou: (i) testar a aderência de três distribuições de probabilidade (normal, gama e Weibull) aos dados diários de temperaturas média do ar e radiação solar global, em Piracicaba, SP; (ii) simular as variáveis temperatura do ar e radiação solar global por intermédio das distribuições normal bivariada, gama e Weibull, e a precipitação por intermédio da distribuição gama; (iii) propor um modelo, utilizando abordagem determinística para a variedade de interesse, para caracterizar a variação temporal do crescimento de biomassa seca de cana-de-açúcar e estimar a ordem de magnitude do período útil de industrialização (PUI), do dia de ocorrência do valor máximo da produtividade de sacarose (expressa em TPH) e das produtividades potencial e deplecionada de cana-de-açúcar, em dois ambientes de produção; (iv) estimar as variações das produtividades potencial, deplecionada por água e TPH (ciclo cana planta) por intermédio de procedimento estocástico para os elementos do clima (temperatura, radiação fotossinteticamente ativa e precipitação). As simulações utilizando as distribuições normal bivariada e gama são apropriadas por representarem melhor os elementos do clima; o modelo para a estimação das produtividades potencial, deplecionada e de sacarose apresentou resultados satisfatórios quanto aos objetivos propostos (abordagem determinística); o desempenho das variações das produtividades ocorreu de forma semelhante, no que se refere a magnitude de valores, para as simulações utilizando as distribuições normal bivariada e gama, e apresentou tendência de superestimar os valores das produtividades, para a simulação utilizando a distribuição Weibull (abordagem estocástica dos elementos do clima). / Simulation models should be adjusted by values of parameters and input variables in order to provide results that best represent the observed values. Thus, due to inaccuracies that are subject the adjustment´s results, it is necessary to implement methods for uncertainties evaluation for either, the parameters of the culture or input variables of the model. For the sugarcane, the maximum productivity of sugar occurs when both, Pol and biomass of stems (TCH) are the maximum. The aims of this study were: (i) to verify the adherence of three probability distributions (normal, gama and Weibull) to the daily data of average air temperature and solar radiation, in Piracicaba, SP; (ii) to simulate the variables air temperature and solar radiation through the bivariate normal, gama and Weibull distributions, and precipitation through the gama distribution; (iii) to propose a model, by using deterministic approach to the genotype of interest, to characterize the temporal variation in dry matter growth of sugarcane estimating the magnitude order of the useful period of industrialization, the date of occurrence in maximum sucrose yield (expressed by TPH) and the sugarcane potential and depleted productivity, in two production environments; (iv) to estimate the variability of potential, depleted by water and TPH (sugarcane plant cycle) through a stochastic procedure for the climate elements (temperature, photosynthetically active radiation and precipitation). The simulations by using bivariate normal and gama distributions are appropriate to better represent the climate elements; the model to estimate potential, depleted and sucrose productivity showed satisfactory results for the proposed objectives (deterministic approach); yield variability was similar, as regard the magnitude of values, for the simulations by using bivariate normal and gama distributions and it presented a tendency to overestimate the productivity for simulations by using Weibull distribution (stochastic approach of climate elements).

In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X1,X2, ..., XN, where each Xi has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where Xi is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for the continuous random variables such as Arcsine, Topp-Leone, and N is chosen to be Geometric or Zipf. Wherever appropriate, we estimate of the parameter in the one-parameter family in question and test the hypotheses about the parameter. In the last section, two permutation distributions are introduced and studied.