Two standard graph representations for linear codes are the Tanner graph and the tailbiting trellis. Such graph representations allow the decoding problem for a code to be phrased as a computational problem on the corresponding graph and yield graph theoretic criteria for good codes. When a Tanner graph for a code is used for communication across a binary erasure channel (BEC) and decoding is performed using the standard iterative decoding algorithm, the maximum number of correctable erasures is determined by the stopping distance of the Tanner graph. Hence the computational problem of determining the stopping distance of a Tanner graph is of interest. In this thesis it is shown that computing stopping distance of a Tanner graph is NP hard. It is also shown that there can be no (1 + є ) approximation algorithm for the problem for any є > 0 unless P = NP and that approximation ratio of 2(log n)1- є for any є > 0 is impossible unless NPCDTIME(npoly(log n)). One way to construct Tanner graphs of large stopping distance is to ensure that the graph has large girth. It is known that stopping distance increases exponentially with the girth of the Tanner graph. A new elementary combinatorial construction algorithm for an almost regular LDPC code family with provable Ώ(log n) girth and O(n2) construction complexity is presented. The bound on the girth is close within a factor of two to the best known upper bound on girth. The problem of linear time exact maximum likelihood decoding of tailbiting trellis has remained open for several years. An O(n) complexity approximate maximum likelihood decoding algorithm for tail-biting trellises is presented and analyzed. Experiments indicate that the algorithm performs close to the ideal maximum likelihood decoder.

一般而言財務資料具有高峰(High Kurtosis)及厚尾(Heavy Tail)的特性，極值理論(Extreme Value Theorem)即是著重於尾部極端事件發生的機率，描繒出尾部極端值的機率分配，以捕捉財務資料中具厚尾的現象，利用估算尾部指數(Tail Index) α值判斷尾部分配的厚、薄程度。一般在估算α值時均是假設α值是不會隨著時間而變動的穩定值，然而在我們所選取的樣本期間內，可能伴隨著一些重大事件，如金融風暴、或是制度面的改變等，均有可能造成尾部極端值發生機率的增加或減少，因此在其樣本期間所估算的α值不應假設為一不變的常數。本文即是針對亞洲四小龍的匯率資料做”尾部參數是否發生結構變化(Structural Change)”之假設檢定，並且找出發生結構變化的時點。 實証結果發現，在1993~2004年間，亞洲四小龍的匯率報酬率其尾部參數確實有發生結構變化的情形。此結論對於風險管理者而言，必須注意到尾部參數α值應該是一個會隨著時間而改變的值，也就是在估算 值時應該要避開發生結構變化的可能時點，或許應於所要估計的樣本期間先執行尾部參數是否有結構變化的檢定，如此才能更準確的估算α值。

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This diploma thesis deals with design methods and optimization techniques of dynamic latched comparators. It compares latched and continuous comparators and describes their principle. Then it analyses three popular latched comparator structures with respect to offset, speed and kickback noise. It shows practical comparator design focused on offset precision.

It is of great importance to find an analytical copula that will represent the empirical lower tail dependence. In this study, the pairwise empirical copula are estimated using data of the S&P 500 stocks during the period 2007-2010.Different optimization methods and measures of dependence have been used to fit Gaussian, t and Clayton copula to the empirical copulas, in order to represent the empirical lower tail dependence. These different measures of dependence and optimization methods with their restrictions, point at different analytical copulas being optimal. In this study the t copula with 5 degrees of freedom is giving the most fulfilling result, when it comes to representing lower tail dependence. The t copula with 5 degrees of freedom gives the best representation of empirical lower tail dependence, whether one uses the 'Empirical maximum likelihood estimator', or 'Equal Ƭ' as an approach.

With the high development of economic and demand for city research, an issue of detecting city boundaries plays an extremely important role in urbanization that promotes the progress of human civilization. Some critical applications such as land use, urban planning and city sprawl have been constantly discussed, which rely on the acquisition of city areas. For the better acquisition of city areas, choosing a proper method to capture city boundaries becomes significant where it greatly improves the value of city study. Although conventional data can be used to define the city boundaries, some drawbacks still exist when measuring the city boundaries in a global scale. Remote sensing (RS) data of nightlight imagery (2010) by Defense Meteorological Satellite Program’s Operational Linescan System (DMSP/OLS) acquired from National oceanic and atmospheric administration's National Geoscience Data Center (NOAA/NOGA) is applied to extract the city boundaries in fifty countries, of which these countries are chosen followed by the Gross Domestic Product that are ranked in top 50. In this case, the data distribution of nightlight imagery followed by heavy-tailed distribution. Head/tail break algorithm poses a possibility of calculating reasonable threshold and extracting the natural cities with the help of software based on the Geomatics information system (GIS). An extended study of power law is made by using of power law estimator from previous studies to check whether the extracted natural cities can match the power law distribution. Result shows that combination of the nightlight imagery data and the head/tail break is capable of extracting the city boundaries and a set of possible thresholds with visual inspection by using the head/tail break are executed. There is only one country, namely Belgium, cannot be processed due to its data properties. Result also address how well the natural cities of the fifty countries can be extracted in terms of visual inspection, among the chosen cities, 33 of countries boundaries can be better matched and 13 countries can fundamentally match the city boundaries. Meanwhile, an extended study of power law is provided and four countries have to be found that do not follow the power law distribution. From the result obtained, the study expects that integration of support data will efficiently increase the accuracy of extraction and more useful information can be acquired in further study. On the other hand, a comparative study of threshold decision needs to be verified, put it differently, whether using head/tail break with visual inspection on extracted city boundaries is helpful or not.

The boundaries of the cities are not immutable, they can be changed. With the development of the economies and societies, the population and pollution of cities are increasing. Some urban areas are expanding with more population or other dynamics of urbanization, while other urban areas are reducing with the changing of the dynamics. Therefore, detecting urban areas or delineating the boundaries of the cities is one of the most important steps for urban studies, which is closely related to human settlements and human activities. Remote sensing data (RS) is widely used to monitor and detect land use and land cover on the surface of the earth. But the extraction of urban areas from the ordinary RS data is not easy work. The Operational Linescan System (OLS) is the sensors of the Defense Meteorological Satellite Program (DMSP). The nighttime lights from the DMSP/OLS provide worldwide remotely sensed data to analyze long-term light emissions which are closely related to human activities. But the nighttime lights imagery data contains inherent errors. Therefore, the approaches to calibrate the data and extract the urban areas from the data are complicated. The long-term objective of this thesis is to delineate the boundaries of the natural cities of the continental United States of America (USA) from 1992 to 2010 of nightlight imagery data with all the different satellites. In this thesis, the coefficients for the intercalibration of the nightlight imagery data have been calculated based on the method developed by Elvidge, et al. (2009), but the coefficients are new and available. The approach used to determine the most appropriate threshold value is very important to eliminate the possible data error. The method to offset this possible error and delineate the boundaries of the cities from nightlight imagery data is the head/tail breaks classification, which is proposed by Jiang (2012b). The head/tail breaks classification is also useful for finding the ht-index of the extracted natural cities which is developed by Jiang and Yin (2013). The ht-index is an indicator of the underlying hierarchy of the data. The results of this study can be divided into two categories. In the first, the achieved coefficients for the intercalibration of nightlight images of the continental USA are shown in a table, and the achieved data of the urban areas are stored in a data archive. In the second, the different threshold values of the uncalibrated images and the individual threshold value of the calibrated images are shown in tables, and the results of the head/tail breaks classification and power law test are also drawn. The results show that the acquired natural cities obey the power law distribution. And the results also confirm that the head/tail breaks classification is available for finding a suitable threshold value for the nightlight imagery data. Key words: cities’ boundaries; DMSP/OLS; head/tail breaks classification; nighttime lights; power law; urban areas

In medical diagnostic studies, the area under the Receiver Operating Characteristic (ROC) curve (AUC) and Youden index are two summary measures widely used in the evaluation of the diagnostic accuracy of a medical test with continuous test results. The first half of this dissertation will highlight ROC analysis including extension of Youden index to the partial Youden index as well as novel confidence interval estimation for AUC and Youden index in the presence of covariates in induced linear regression models. Extensive simulation results show that the proposed methods perform well with small to moderate sized samples. In addition, some real examples will be presented to illustrate the methods. The latter half focuses on the application of empirical likelihood method in economics and finance. Two models draw our attention. The first one is the predictive regression model with independent and identically distributed errors. Some uniform tests have been proposed in the literature without distinguishing whether the predicting variable is stationary or nearly integrated. Here, we extend the empirical likelihood methods in Zhu, Cai and Peng (2014) with independent errors to the case of an AR error process. The proposed new tests do not need to know whether the predicting variable is stationary or nearly integrated, and whether it has a finite variance or an infinite variance. Another model we considered is a GARCH(1,1) sequence or an AR(1) model with ARCH(1) errors. It is known that the observations have a heavy tail and the tail index is determined by an estimating equation. Therefore, one can estimate the tail index by solving the estimating equation with unknown parameters replaced by Quasi Maximum Likelihood Estimation (QMLE), and profile empirical likelihood method can be employed to effectively construct a confidence interval for the tail index. However, this requires that the errors of such a model have at least finite fourth moment to ensure asymptotic normality with n1/2 rate of convergence and Wilk's Theorem. We show that the finite fourth moment can be relaxed by employing some Least Absolute Deviations Estimate (LADE) instead of QMLE for the unknown parameters by noting that the estimating equation for determining the tail index is invariant to a scale transformation of the underlying model. Furthermore, the proposed tail index estimators have a normal limit with n1/2 rate of convergence under minimal moment condition, which may have an infinite fourth moment, and Wilk's theorem holds for the proposed profile empirical likelihood methods. Hence a confidence interval for the tail index can be obtained without estimating any additional quantities such as asymptotic variance.

Poly(A) tail addition to pre-mRNAs is a highly coordinated and essential step in mRNA maturation involving multiple cis- and trans-acting factors. The trans-acting factor, poly(A) polymerase (PAP) plays an essential role in the polyadenylation of mRNA precursors. The Arabidopsis thaliana genome contains four putative PAP genes. We have found, using in silico analysis and transgenic plants expressing GUS under the control of the four PAP promoters, that each of these genes is expressed in overlapping, yet unique patterns. This gives rise to the possibility that these genes are not redundant and may be essential for plant survival. To further test this, inducible RNAi and T-DNA mutagenized plants were obtained and analyzed. Plants lacking all, or most, of each PAP gene product, due to RNAi induction, were not viable at any of the stages of plant growth tested. Furthermore, T-DNA PCR analysis determined that no plants containing a homozygous mutation, were viable. This data reveals that lack of any of the four PAP gene products has a significant effect on the plants ability of survive, thus indicating that each PAP gene is essential. Finally, transient expression experiments with each of the full length PAP cDNAs fused to GFP showed that the PAP I, PAP II and PAP IV gene products are localized throughout the nucleus and within nuclear speckles. The cellular localization of PAP III could not be determined.

Codes can be represented by edge-labeled directed graphs called trellises, which are used in decoding with the Viterbi algorithm. We will first examine the well-known product construction for trellises and present an algorithm for recovering the factors of a given trellis. To maximize efficiency, trellises that are minimal in a certain sense are desired. It was shown by Koetter and Vardy that one can produce all minimal tail-biting trellises for a code by looking at a special set of generators for a code. These generators along with a set of spans comprise what is called a characteristic pair, and we will discuss how to determine the number of these pairs for a given code. Finally, we will look at trellis dualization, in which a trellis for a code is used to produce a trellis representing the dual code. The first method we discuss comes naturally with the known BCJR construction. The second, introduced by Forney, is a very general procedure that works for many different types of graphs and is based on dualizing the edge set in a natural way. We call this construction the local dual, and we show the necessary conditions needed for these two different procedures to result in the same dual trellis.