### 统计代写|主成分分析代写Principal Component Analysis代考|STAT6020

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|主成分分析代写Principal Component Analysis代考|Lymphoma data sets

The lymphoma data set comes from a study of gene expression of three prevalent lymphoid malignancies: B-cell chronic lymphocytic leukemia (B-CLL), follicular lymphoma (FL) and diffuse large B-cell lymphoma (DLCL). Among 96 samples we took 62 samples 4026 genes in three classes: 11 cases of B-CLL, 9 cases of FL and 42 cases of DLCL. Gene expression levels were measured using 2-channel cDNA microarrays.

After preprocessing, all gene expression profiles were base 10 log-transformed and, in order to prevent single arrays from dominating the analysis, standardized to zero mean and unit variance. Finally, we complete the preprocessing of the gene expression data with gene centring.

In this example we perform the KPCA, as detailed in the previous section, we compute the kernel matrix with using the radial basis kernel with $c=0.01$, this value is set heuristically. The resulting plot is given in Figure 6. It shows the projection onto the two leading kernel principal components of microarrays. In this figure we can see that KPCA detect the group structure in reduced dimension. DLCL, FL and B-CLL are fully separated by KPCA.

To validate our procedure we select a list of genes differentially expressed proposed by (Reverter et al. (2010)) and a list of genes that are not differentially expressed. In particular, in Figures 7, 8,9 and 10 we show the results in the case of genes: $139009,1319066,1352822$ and 1338456 , respectively. The three first genes belong to the list of genes differentially expressed and the last gene is not differentially expressed.

Figure 7 (top) shows the tangent vectors associated with 139009 gene attached at each sample point. This vector field reveals upper expression towards DLCL cluster as is expected from references above mentioned. This gene is mainly represented by the first principal component. The length of the arrows indicate the influence strength of the gene on the sample position despite the dimension reduction. Figure 7 (bottom) shows the expression profile of 139009 gene. We can observe that 139009 gene is up regulated in DLCL cluster. This profile is agree with our procedure because the direction in which the expression of the 139009 gene increases points to the DLCL cluster.

## 统计代写|主成分分析代写Principal Component Analysis代考|Definitions of major «omics» in molecular biology and their goals

The nomicsm era, also called classically the post-genomic era, is described as the period of time which extends the first publication of the human genome sequence draft in 2001 (International Human Genome Sequencing Consortium, 2001; Venter et al., 2001). Ten years after that milestone, extensive use of high-throughput analytical technologies, high performance computing power and large advances in bioinformatics have been applied to solve fundamental molecular biology questions as well as to find clues concerning human diseases (cancers) and aging. Principal nomicsw, such as Gen-omics, Transcript-omics, Proteomics and Metabol-omics, are biology disciplines whose main and extremely ambitious objective is to describe as extensively as possible the complete class-specific molecular components of the cell. In the a omics sciences, the catalog of major cell molecular components, respectively, genes, messenger RNAs and small interfering and regulatory RNAs, proteins, and metabolites of living organisms, is recorded qualitatively as well as quantitatively in response to environmental changes or pathological situations. Various research communities, organized in institutions both at the academic and private levels and working in the nomicsm fields, have spent large amounts of effort and money to reach. standardization in the different experimental and data processing steps. Some of these “omics” specific steps basically include the following: the optimal experimental workflow design, the technology-dependent data acquisition and storage, the pre-processing methods and the post-processing strategies in order to extract some level of relevant biological knowledge from usually large data sets. Just like Perl (Practical Extraction and Report Language) has been recognized to have saved the Human Genome project initiative (Stein, 1996), by using accurate rules to parse genomic sequence data, other web-driven. programming languages and file formats such as XML have also facilitated nomics” data dissemination among scientists and helped rationalize and integrate molecular biology data.
Data resulting from different womicsw have several characteristics in common, which are summarized in Figure 1: (a) the number of measured variables $\mathrm{n}$ ( $\mathrm{SNP}$, gene expression, proteins, peptides, metabolites) is quite large in size (from 100 to 10000), (b) the number of samples or experiments $\mathrm{p}$ where these variables are measured associated with factors such as the pathological status, environmental conditions, drug exposure or kinetic points (temporal experiments) is rather large $(10$ to 1000$)$ and (c) the measured variables are organized in a matrix of $\mathrm{n} \times \mathrm{p}$ dimensions. The cell contents of such a matrix usually record a metric (or numerical code) related to the abundance of the measured variables. The observed data are acquired keeping the lowest amount of possible technical and analytical variability. Exploring these womicsw data requires fast computers and state-of-the-art data visualization and statistical multivariate tools to extract relevant knowledge, and among these tools PCA is a tool of choice in order to perform initial exploratory data analysis (EDA).

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。