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Interpretation of three experiments, each in triplicate, where the vectors V 1 , V 2 , V 3 are the mean vectors of w 1,i,j , w 2,i,j and w 3,i,j of the i th gene in the j th experiment with coordinates x 1 (0.0) to
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Microarray experimentation has been widely used for screening and high throughput discovery of mechanisms underlying biological systems. However, there are many factors that need to be taken into account for an effective microarray experimental design. Such factors are the abundance of starting material (RNA), number of replicates or experimental c...
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... represent the interconnection relations. From Eq. (7) to Eq. (10) not only we derive estimations of the third experiment ( v 3 ), but we also can minimize the inference of experimental measurement error. In the aforementioned relations we have not taken into account the possibility of replicates among similar experiments and their respective variance. The above hypotheses are based on the fact that the signal intensities of two different dyes of the same sample are equal (or at least approach equality). This of course is not the case in real experiments, therefore it is necessary to define a way for measuring variance within the approach we describe in the present work. In Figure 3 we present an interpretation of variance in a vector and geometric level. Let w 1,i,j , w 2,i,j , w 3,i,j be the vectors describing the expression intensities of the i th gene in the j th replicate experiment with w 1,i,j (x 1,i,j ,y 1,i,j ) , w 2,i,j (x 2,i,j ,y 2,i,j ) , w 3,i,j (x 3,i,j ,y 3,i,j ) . We can then define three new vectors as V 1 (R 1 ,G 1 ) , V 2 (R 2 ,G 2 ) , V 3 (R 3 ,G 3 ) where R and G are the coordinates of each centroid formed by the three vectors w 1,i,j , w 2,i,j , w 3,i,j . In particular, the three new vectors V 1 , V 2 , V 3 would be defined ...
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High throughput technologies have facilitated the study of thousands of factors simultaneously. A well-known method that has been utilized throughout recent years is microarray technology. Since their advent, microarrays have been used to discover differences between samples, such as those on the level of gene expression or polymorphism detection. This technique has found applications in many areas of life sciences, including forensics. Despite its usefulness, the microarray method is not flawless. Microarray experimentation contains a lot of bias, which makes the use of sophisticated statistical techniques necessary in order to overcome these problems. One basic assumption made from the very first microarray experiments, concerning expression studies, was that samples are homogeneous. This assumption was based on the fact that the biggest part/percentage of a biological sample consists of cells of the same type. For example, tumor biopsies, although considered to be homogeneous, are infiltrated with many other cell types such as macrophages, surrounding fibroblasts and even normal, healthy tissue surrounding tumor cells. As a consequence, forensic samples may consist of tissue mixtures that need to be distinguished.This chapter reviews the microarray technology and deal with the majority of aspects regarding microarrays. It focuses on today’s knowledge of separation techniques and methodologies of complex signal, i.e. samples. Overall, the chapter reviews the current knowledge on the topic of microarrays and presents the analyses and techniques used, which facilitate such approaches. It starts with the theoretical framework on microarray technology; second, the chapter gives a brief review on statistical methods used for microarray analyses, and finally, it contains a detailed review of the methods used for discriminating traces of nucleic acids within a complex mixture of samples.
High throughput technologies have facilitated the study of thousands of factors simultaneously. A wellknown method that has been utilized throughout recent years is microarray technology. Since their advent, microarrays have been used to discover differences between samples, such as those on the level of gene expression or polymorphism detection. This technique has found applications in many areas of life sciences, including forensics. Despite its usefulness, the microarray method is not flawless. Microarray experimentation contains a lot of bias, which makes the use of sophisticated statistical techniques necessary in order to overcome these problems. One basic assumption made from the very first microarray experiments, concerning expression studies, was that samples are homogeneous. This assumption was based on the fact that the biggest part/percentage of a biological sample consists of cells of the same type. For example, tumor biopsies, although considered to be homogeneous, are infiltrated with many other cell types such as macrophages, surrounding fibroblasts and even normal, healthy tissue surrounding tumor cells. As a consequence, forensic samples may consist of tissue mixtures that need to be distinguished. This chapter reviews the microarray technology and deal with the majority of aspects regarding microarrays. It focuses on today's knowledge of separation techniques and methodologies of complex signal, i.e. samples. Overall, the chapter reviews the current knowledge on the topic of microarrays and presents the analyses and techniques used, which facilitate such approaches. It starts with the theoretical framework on microarray technology; second, the chapter gives a brief review on statistical methods used for microarray analyses, and finally, it contains a detailed review of the methods used for discriminating traces of nucleic acids within a complex mixture of samples.
