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To analyze a communication system without the aid of simulation, the channel noise for the simulation must be assumed to be normal. The assumption is often valid, but the normal distribution may not be able to model the channel noise adequately in some environments. This thesis will explore the generalized exponential distribution for better noise modeling and robustness testing in communication system. When using the generalized exponential distribution for the channel noise, the analysis will become analytically intractable, and simulation becomes mandatory. To generate the noise with the distribution, the rejection method can be used. However, since the distribution can take on different shapes, finding the appropriate Upper Bounding Function (UBF) for the method is very difficult. Thus, two modified versions of the rejection method will be examined. They are the Transformed Density Rejection (TDR) and Ratio-of-Uniform (RoU) method; their quality, efficient, trade-offs, etc will be discussed. Choosing TDR, a simulation of a BPSK communication system will be performed. With the simulation, it can further ascertain that the random variates generated by TDR can be used to model the channel noise and to test the robustness of a communication system. / Master of Science

Generating a single order statistic without generating the full sample can be an important task for simulations. If the density and the CDF of the distribution are given it is no problem to compute the density of the order statistic. In the main theorem it is shown that the concavity properties of that density depend directly on the distribution itself. Especially for log-concave distributions all order statistics have log-concave distributions themselves. So recently suggested automatic transformed density rejection algorithms can be used to generate single order statistics. This idea leads to very fast generators. For example for the normal and gamma distribution the suggested new algorithms are between 10 and 60 times faster than the algorithms suggested in the literature. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

In this study, Window-based computer program, named Synthesis Software, is developed for designing filters with equal-ripple or maximally flat passbands and general stopbands by using cascade synthesis technique in transformed frequency domain. Synthesis technique is applicable to lumped element and commensurate line distributed element filters with Lowpass, Highpass or Bandpass characteristics. Singly or Doubly terminated filters can be synthesized. friendly environment for typing in the parameters of the filter to be designed. This part uses Synthesis and Plot parts as modules. This software is based on the previous softwares developed in EEE Department of Middle East Technical University. All the previous softwares were gathered in the well-known software Filpro, which is in DOS environment, in Pascal. Thus, the new software is actually a conversion of Synthesis part of Filpro from DOS environment into Windows environment in the language C#, with some improvements in root finding algorithms for numerical conditioning. Synthesis Software is has three parts. The first and main part is the implementation of synthesis technique by using object oriented programming technique. In this way, synthesis technique implementation is isolated from other parts of Synthesis Software and it can be used by other filter design programs as a module. The second part of the program is responseplotting section. In this part Insertion Loss, Return Loss, Time Delay, Phase and Smith Chart responses are calculated and displayed. The last part is User Interface, which provides user

Microarray technology permit us to study the expression levels of thousands of genes simultaneously. The technique has a wide range of applications including identification of genes that change their expression in cells due to disease or drug stimuli. The dissertation is addressing statistical methods for the selection of differentially expressed genes in two experimental conditions. We propose two different methods for the selection of differentially expressed genes. The first method is a classical approach, where we consider a common distribution for the summary measure of equally expressed genes. To estimate this common distribution, the Johnson system of distribution is used. The advantage of using Johnson system is that, there is no need of a parametric assumption for gene expression data. In contrast to other classical methods, in the proposed method, there is a sharing of information across the genes by the assumption of a common distribution for the summary measure of equally expressed genes. The second method is the gene selection using a mixture model approach and Baye's theorem. This approach also uses the Johnson System of distribution for the estimation of distribution of summary measure. Johnson system of distribution has the flexibility of covering a wide variety of distributional shapes. This system provides a unique distribution corresponding to each pair of mathematically possible values of skewness and kurtosis. The significant flexibility of Johnson system is very useful in characterizing the complicated data set like microarray data. In this dissertation we propose a novel algorithm for the estimation of the four parameters of the Johnson system.

In this paper we present some variants of transformed density rejection (TDR) that provide more flexibility (including the possibility to halve the expected number of uniform random numbers) at the expense of slightly higher memory requirements. Using a synchronized first stream of uniform variates and a second auxiliary stream (as suggested by Schmeiser and Kachitvichyanukul (1990)) TDR is well suited for correlation induction. Thus high positive and negative correlation between two streams of random variates with same or different distributions can be induced. The software can be downloaded from the UNURAN project page. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

This paper presents an overview of the most powerful universal methods. These are based on acceptance/rejection techniques where hat and squeezes are constructed automatically. Although originally motivated to sample from non-standard distributions these methods have advantages that make them attractive even for sampling from standard distributions and thus are an alternative to special generators tailored for particular distributions. Most important are: the marginal generation time is fast and does not depend on the distribution. They can be used for variance reduction techniques, and they produce random numbers of predictable quality. These algorithms are implemented in a library, called UNURAN, which is available by anonymous ftp. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Random variate genration is an important tool in statistical computing. Many programms for simulation or statistical computing (e.g. R) provide a collection of random variate generators for many standard distributions. However, as statistical modeling has become more sophisticated there is demand for larger classes of distributions. Adding generators for newly required distribution seems not to be the solution to this problem. Instead so called automatic (or black-box) methods have been developed in the last decade for sampling from fairly large classes of distributions with a single piece of code. For such algorithms a data about the distributions must be given; typically the density function (or probability mass function), and (maybe) the (approximate) location of the mode. In this contribution we show how such algorithms work and suggest an interface for R as an example of a statistical library. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

A partir de extratos aquosos da esponja marinha Axinella corrugata, coletada na costa sul do Brasil (Santa Catarina), foram purificadas duas lectinas, ACL-I e ACL-II, por cromatografia em coluna de afinidade de matriz de estroma de coelhopoliacrilamida, seguida por gel filtração em Ultrogel AcA 44. Os trabalhos se concentraram, especialmente, no estudo da lectina com maior atividade hemaglutinante, ACL-I. Dentre os eritrócitos testados, ACL-I aglutinou, fortemente, eritrócitos de coelho, além de eritrócitos caprinos e caninos. A atividade hemaglutinante foi inibida por N-acetil-D-glicosamina, N-acetil-D-galactosamina e Nacetil- D-manosamina com igual intensidade, além de N, N’, N”-triacetilquitotriose, o melhor inibidor. Por outro lado, ACL-II aglutinou, preferencialmente, eritrócitos de coelho e caninos, tendo sua atividade hemaglutinante inibida por N-acetil-Dglicosamina, N-acetil-D-manosamina, quitina, N, N’, N”-triacetilquitotriose e fetuína, além de D-galactose, mas não por N-acetil-D-galactosamina. Ambas lectinas foram fracamente inibidas por N-acetil-D-lactosamina. A atividade hemaglutinante mostrouse independente de cátions divalentes e foi estável a uma ampla faixa de temperatura e de pH para ACL-I e para ACL-II. ACL-I foi estável frente à ação de enzimas proteolíticas, mas perdeu 50 % de sua atividade na presença de agentes redutores e desnaturantes. ACL-I é uma glicoproteína e sua massa molecular relativa foi estimada em 82.300 por SDS-PAGE em condições redutoras e não redutoras, e sem desnaturação pelo calor. Ainda, mostrou ser constituída por 6 subunidades monoméricas de 13.900, apresentando pontes de dissulfeto entre as mesmas. Por FPLC, a massa molecular estimada foi de 78.500. Da mesma forma como para ACL-I, ACL-II apresentou apenas uma banda em sistema SDS-PAGE, na ausência de agente redutor e sem desnaturação pelo calor, cuja massa molecular relativa foi estimada em 80.000, enquanto que por FPLC foi estimada em 78.000. O pI de ACL-I foi de 6,3, avaliado por focalização isoelétrica, e a sua composição centesimal de aminoácidos exibiu uma prevalência de glicina, seguida de ácido aspártico/asparagina, ácido glutâmico/glutamina e alanina. Dentre as atividades biológicas testadas, a ACL-I demonstrou atividade quimiotáxica, mitogênica e citotóxica, mas não antioxidante. Os ensaios imuno-histoquímicos mostraram que ACL-I se encontra intracelularmente em grânulos celulares, provavelmente no interior de células esferulosas da esponja marinha. A lectina também mostrou ser uma ferramenta útil na marcação de células transformadas de mama, cólon, pulmão, ovário e bexiga. / Two lectins, ACL-I and ACL-II, were purified from aqueous extracts of marine sponge Axinella corrugata, collected at Atlantic coastline of southern Brazil (Santa Catarina) by rabbit stroma-polyacrylamide gel affinity column, followed by size-exclusion chromatography on Ultrogel AcA 44. The analysis were performed, especially, on the study of lectin with greater hemagglutinating activity, ACL-I. Among the erythrocytes tested, ACL-I agglutinated, strongly, native rabbit, goat and dog erythrocytes, whose hemagglutinating activity was inhibited by N-acetyl-D-glucosamine, N-acetyl-Dmannosamine, N-acetyl-D-galactosamine and N, N’, N”- triacetylchitotriose. On the other hand, ACL-II agglutinated, preferentially, rabbit and dog erythrocytes, with its hemagglutinating activity inhibited by D-galactose, N-acetyl-D-glucosamine, N-acetyl- D-mannosamine, chitin, N, N’, N”- triacetylchitotriose and fetuin, but not by N-acetyl- D-galactosamine. Both lectins were weakly inhibited by N-acetyl-D-lactosamine. The hemagglutinating activity was independent of divalent cations and it was stable at large range of temperature and pH to ACL-I and ACL-II. ACL-I was resistent to enzymatic proteolysis, but lost 50 % of its activity in the presence of reducing or denaturant agents. This lectin presented a relative molecular mass of 82,300 estimated by SDS-PAGE in the presence or absence of 2-mercaptoethanol, without pre-heating, and it is constituted by six monomeric subunits of 13,900, showing disulphide bridges among them. By FPLC the relative molecular mass was 78,500. Similar to ACL-I, ACL-II showed one unique protein band by SDS-PAGE, in the absence of 2-mercaptoethanol and without pre-heating, whose relative molecular mass was estimated as 80,000 and by gel filtration as 78,000. The isoelectric focusing of ACL-I revealed the presence of one unique protein band with pI of 6.3 and the amino acid composition showed a prevalence of glycine, followed by aspartic acid/asparagine, glutamic acid/glutamine and alanine. Among the biological activities analysed, the ACL-I demonstrated chemotactic, mitogenic and cytotoxic activities, but not antioxidant. The immunohistochemical assays revealed that ACL-I is stored in vesicles, probably inside of spherulous cells of the marine sponge. The lectin showed to be a useful tool in the labelling of transformed cells of breast, colon, lung, ovary and bladder.

A partir de extratos aquosos da esponja marinha Axinella corrugata, coletada na costa sul do Brasil (Santa Catarina), foram purificadas duas lectinas, ACL-I e ACL-II, por cromatografia em coluna de afinidade de matriz de estroma de coelhopoliacrilamida, seguida por gel filtração em Ultrogel AcA 44. Os trabalhos se concentraram, especialmente, no estudo da lectina com maior atividade hemaglutinante, ACL-I. Dentre os eritrócitos testados, ACL-I aglutinou, fortemente, eritrócitos de coelho, além de eritrócitos caprinos e caninos. A atividade hemaglutinante foi inibida por N-acetil-D-glicosamina, N-acetil-D-galactosamina e Nacetil- D-manosamina com igual intensidade, além de N, N’, N”-triacetilquitotriose, o melhor inibidor. Por outro lado, ACL-II aglutinou, preferencialmente, eritrócitos de coelho e caninos, tendo sua atividade hemaglutinante inibida por N-acetil-Dglicosamina, N-acetil-D-manosamina, quitina, N, N’, N”-triacetilquitotriose e fetuína, além de D-galactose, mas não por N-acetil-D-galactosamina. Ambas lectinas foram fracamente inibidas por N-acetil-D-lactosamina. A atividade hemaglutinante mostrouse independente de cátions divalentes e foi estável a uma ampla faixa de temperatura e de pH para ACL-I e para ACL-II. ACL-I foi estável frente à ação de enzimas proteolíticas, mas perdeu 50 % de sua atividade na presença de agentes redutores e desnaturantes. ACL-I é uma glicoproteína e sua massa molecular relativa foi estimada em 82.300 por SDS-PAGE em condições redutoras e não redutoras, e sem desnaturação pelo calor. Ainda, mostrou ser constituída por 6 subunidades monoméricas de 13.900, apresentando pontes de dissulfeto entre as mesmas. Por FPLC, a massa molecular estimada foi de 78.500. Da mesma forma como para ACL-I, ACL-II apresentou apenas uma banda em sistema SDS-PAGE, na ausência de agente redutor e sem desnaturação pelo calor, cuja massa molecular relativa foi estimada em 80.000, enquanto que por FPLC foi estimada em 78.000. O pI de ACL-I foi de 6,3, avaliado por focalização isoelétrica, e a sua composição centesimal de aminoácidos exibiu uma prevalência de glicina, seguida de ácido aspártico/asparagina, ácido glutâmico/glutamina e alanina. Dentre as atividades biológicas testadas, a ACL-I demonstrou atividade quimiotáxica, mitogênica e citotóxica, mas não antioxidante. Os ensaios imuno-histoquímicos mostraram que ACL-I se encontra intracelularmente em grânulos celulares, provavelmente no interior de células esferulosas da esponja marinha. A lectina também mostrou ser uma ferramenta útil na marcação de células transformadas de mama, cólon, pulmão, ovário e bexiga. / Two lectins, ACL-I and ACL-II, were purified from aqueous extracts of marine sponge Axinella corrugata, collected at Atlantic coastline of southern Brazil (Santa Catarina) by rabbit stroma-polyacrylamide gel affinity column, followed by size-exclusion chromatography on Ultrogel AcA 44. The analysis were performed, especially, on the study of lectin with greater hemagglutinating activity, ACL-I. Among the erythrocytes tested, ACL-I agglutinated, strongly, native rabbit, goat and dog erythrocytes, whose hemagglutinating activity was inhibited by N-acetyl-D-glucosamine, N-acetyl-Dmannosamine, N-acetyl-D-galactosamine and N, N’, N”- triacetylchitotriose. On the other hand, ACL-II agglutinated, preferentially, rabbit and dog erythrocytes, with its hemagglutinating activity inhibited by D-galactose, N-acetyl-D-glucosamine, N-acetyl- D-mannosamine, chitin, N, N’, N”- triacetylchitotriose and fetuin, but not by N-acetyl- D-galactosamine. Both lectins were weakly inhibited by N-acetyl-D-lactosamine. The hemagglutinating activity was independent of divalent cations and it was stable at large range of temperature and pH to ACL-I and ACL-II. ACL-I was resistent to enzymatic proteolysis, but lost 50 % of its activity in the presence of reducing or denaturant agents. This lectin presented a relative molecular mass of 82,300 estimated by SDS-PAGE in the presence or absence of 2-mercaptoethanol, without pre-heating, and it is constituted by six monomeric subunits of 13,900, showing disulphide bridges among them. By FPLC the relative molecular mass was 78,500. Similar to ACL-I, ACL-II showed one unique protein band by SDS-PAGE, in the absence of 2-mercaptoethanol and without pre-heating, whose relative molecular mass was estimated as 80,000 and by gel filtration as 78,000. The isoelectric focusing of ACL-I revealed the presence of one unique protein band with pI of 6.3 and the amino acid composition showed a prevalence of glycine, followed by aspartic acid/asparagine, glutamic acid/glutamine and alanine. Among the biological activities analysed, the ACL-I demonstrated chemotactic, mitogenic and cytotoxic activities, but not antioxidant. The immunohistochemical assays revealed that ACL-I is stored in vesicles, probably inside of spherulous cells of the marine sponge. The lectin showed to be a useful tool in the labelling of transformed cells of breast, colon, lung, ovary and bladder.