The typical preparation plant producing coal for the utility market targets a relative separation density in the plant of around 1.60 whereas plants generating metallurgical coal use relative cut point density values approaching 1.50. In some cases, achieving the specified coal quality requires operating at lower cut point values, which results in a significant loss of valuable coal. In these situations, a middlings stream can be produced using a secondary separator or a three-product unit, which would allow crushing of the middlings for liberation purposes and re-introduction into the plant feed. In this manner, higher quality coal can be produced while maximizing plant yield. A detailed laboratory analysis was conducted to study the liberation characteristics resulting from the crushing of middlings at different top sizes. The experimental data were later used as input for modeling and simulation of plant flowsheet in LIMN. Simulations were run for several regrinding cases. The results of the current study investigating the economic benefits of middlings liberation and re-treatment are presented and discussed in this thesis. Improvement up to 6% in plant yield with 16-21% reduction in ash and 14-18% sulfur reductions can be achieved by crushing the +1/2 inch middlings to a ½-inch top size.

Youden index, a main summary index for the Receiver Operating Characteristic (ROC) curve, is a comprehensive measurement for the effectiveness of a diagnostic test. For a continuous-scale diagnostic test, the optimal cut-point for the positive of disease is the cut-point leading to the maximization of the sum of sensitivity and specificity. Finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. In this thesis, we propose a new non-parametric confidence interval for the Youden index. Extensive simulation studies are conducted to compare the relative performance of the new interval with the existing intervals for the index. Our simulation results indicate that the newly developed non-parametric method performs as well as the existing parametric method but it has better finite sample performance than the existing non-parametric methods. The new method is flexible and easy to implement in practice. A real example is also used to illustrate the application of the proposed interval.

Der Inhalt dieser Arbeit sind jedoch nicht Quantencomputer im Allgemeinen, sondern hauptsächlich Quantenautomaten. Dies führt zu den Begriffen der „endlichen Quantenautomaten“ und der „quantenregulären“ oder „quantenerkennbaren Sprachen“, die Hauptgegenstand der vorliegenden Arbeit sind.

Lorsqu'un biomarqueur est mesuré de façon répétée au cours du suivi de patients, il est d'abord nécessaire d'établir un critère, issu du profil d'évolution longitudinal du marqueur, afin de détecter la survenue d'un événement, ou d'en prédire la gravité. Nous avons développé une méthode de modélisation robuste de données longitudinales, afin de calculer les différents critères pour les patients, et d'en comparer les performances diagnostiques ou pronostiques. Dans un second temps, il faut déterminer un seuil de ce critère quantitatif au dessus ou en dessous duquel le test diagnostique est considéré comme positif. Une méthode Bayésienne d'estimation de ce seuil et de son intervalle de crédibilité a été développée. Ce travail a été appliqué au diagnostic de persistance locale de cellules cancéreuses après traitement par ultrasons d'un cancer de la prostate. Ce diagnostic est effectué à partir des mesures répétées d'antigène spécifique de la prostate (PSA), dont le nadir a été retenu, avec différents seuils, comme meilleur critère diagnostique. Ceci permet de n'effectuer des biopsies que lorsqu'il y a de fortes chances qu'elles soient positives. / For the early diagnosis or prognosis of an event in presence of repeated measurements of a biomarker over time, it is necessary to define a criterion, stemming from the longitudinal profiles of that marker. A method was developed for a robust modelling of marker measurements, to calculate the various criteria for the patients, and compare their diagnostic or prognostic accuracies. Using the continuous criterion as a diagnostic test requires the specification of a threshold. A Bayesian method was developed to estimate this threshold and its credible interval. This method was applied to the diagnosis of local prostate cancer persistence after an ultrasound treatment. The diagnosis relies on serial measurements of prostate specific antigen (PSA), whose nadir (along with several thresholds) was found to be the best diagnostic criterion. This allows to trigger biopsy only when this biopsy is likely to be positive.

時間數列分析過程，常常發現其走勢，隨著時間過程而演變，應用傳統的線性模式來配適，往往很難獲得合適預測值。因此近幾年來，非線性時間數列結構性改變的研究越來越受到重視，也一直是時間數列及計量經濟學學者所熱衷的研究主題之一。本文利用模糊理論的觀念，以模糊炳找出配適ARCH模式數列之轉折區間，分別以轉折區問起始點及結束點作為截取點，去配適ARCH(1)模式，稱之為截取式自迴歸條件變異數分析法(Trimmed ARCH(1) model)。針對台幣對美元銀行間每日收盤匯率，分別以單變量ARIMA、ARCH(1)、Trtmmed ARCH(1)來建構模式，並做比較分析。比較結果發現，以轉折區間結束點作為截取點之Trimmed ARCH(1)模式，其預測值最為準確，大為改善了原來ARCH(1)模式之預測水準。 / In time series analysis, we often find the trend of which changing with time. Using the traditional model fitting can't get a good prediction. Hence the research of structure change of non-linear time series is attentive in recent years, and non-linear time series analysis is a research topic which the scholars of time series and econometrics are intent on. This article tries to use the theory of fuzzy ,to recognize the structure change period by the fuzzy classification, let the first point and the last point of the structure change period be the cute points, to fit ARCH(1) mod ie which we called the Trimmed ARCH(1) model. We use the data of the exchange rate between N.T dol liars and U.S dollars to compare the ARIMAwith ARCH(1) and Trimmed ARCH(1), the forcasting performance shows that Trimmed ARCH(1) model takes a better prediction result.