## 统计代写|网络分析代写Network Analysis代考|CSE416a

2023年3月23日

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• Statistical Inference 统计推断
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• (Generalized) Linear Models 广义线性模型
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## 统计代写|网络分析代写Network Analysis代考|Inference of expression networks

The limitation of experimental wet lab technologies is that it cannot measure mutual influences among all genes from one organizm’s genome simultaneously, therefore computational methods are applied to infer and reveal mutual gene interactions. Analysis and interpretation of the relationships in biological networks is becoming a major research area of interest in modern computational biology, and its translation to genomic medicine. Several difficulties arise when dealing with large regulatory networks involving thousands of genes/protein interactions. One severe bottleneck is the visual analysis and the interpretation of these regulatory networks. This has led the scientific community, computer engineers, statisticians, and biologist to come together to develop new methodology and algorithm to address these issues by developing open-source reconstruction and visualization tools.

Once the expression is available, it is further preprocessed [57] to remove experimental noise (if persists). Normalization of ex-pression values is another important step before considering the expression matrix fit for further analysis. Expression matrix records relative abundance of mRNA levels in a target sample and scale of levels may vary with experimentation environment, and hence normalization is important. Preprocessed expression data is used directly in differential expression analysis, coexpressed gene clustering or biclustering [55]. However, among them the most important task is to infer computationally the gene interactions, which ultimately forms a graph or network of gene expression levels. Two types of graph are usually inferred using expression data, such as directed and undirected. It is challenging to infer the directed network, termed as causal or gene regulatory network, among genes or proteins, due to lack of sufficient information in the available data sources. Such data are limited in inferring coexpression networks only, as true regulatory information is missing. Inferring undirected graph from expression matrix is relatively easy in comparison to directed graph. The guilt-byassociation in the form of coexpression may be measured in terms of statistical correlations, mutual information, or some other similarity measures between the genes’ expressions. The count for coexpression network inference methods is much higher than regulatory inference methods. If we consider a simplistic view of the network inference, it is a task of computationally converting expression matrix into another matrix, called adjacency matrix. The target is to generate adjacency matrix as close as possible to the actual interactions. However, interestingly, known interactions derived based purely on expression data is missing. Hence, validating any method about its quality of prediction is also equally challenging.

## 统计代写|网络分析代写Network Analysis代考|Inferring causal gene regulatory networks

The graph theoretic formalism of expression network is the common and simplistic way of representing it.

Definition 6.3.1. Gene regulatory network (GRN): A GRN is a graph, $\mathcal{G}=(\mathcal{V}, \mathcal{E})$, where $\mathcal{V}$ is the set of all genes in the network and $\mathcal{E}$ is the set of edges between a pair of genes, say $\left(v_i, v_j\right) \in \mathcal{V}$, representing a strong biomolecular interaction between the two genes.

A directed edge from node $v_i$ to $v_j\left(v_i \rightarrow v_j\right)$ indicates that a causal effect exists from node $v_i$ to $v_j$. Causality provides the direction of influence between the two genes, called cause and effect, respectively. The directed edges in a GRN correspond to causal influences between gene activities (nodes). These may include regulation of transcription by transcription factors, but also less intuitive causal effects between genes, involving signal transduction or metabolism.

A causal effect may be direct or indirect [10]. A gene may influence activities of other genes or gene products directly. It is also possible that a gene may influence activities of other genes, or itself, by coding a transcription factor (TF) that in turn regulates another gene, or itself. Some possible causal relationships within a GRN are shown in Fig. 6.2, which illustrates the following types of causal relationships [2]:

1. One-to-many: A gene can influence the activities of more than one gene. Gene A regulates positively the expression of genes $\mathrm{B}, \mathrm{C}$, and $\mathrm{D}$.
2. Many-to-one: A gene’s activity may be influenced by more than one gene (relationships among B, D, and F).
3. Feedback loop: In a feedback loop, a gene influences the activities of some of its ancestors in its regulatory pathways. For example, E regulates the expression of gene $\mathrm{A}$ negatively.
4. Feed-forward loop: The regulation among $\mathrm{D}, \mathrm{F}$, and $\mathrm{H}$ is called a feed-forward regulatory structure, where $\mathrm{H}$ is directly and indirectly influenced by $D$.
5. Self-loop: A gene can influence its own activity (node B).
6. Inhibition: A gene may inhibit activity of another gene (D inhibits E). Inhibition or negative regulation may take place in many-to-one, one-to-many, and different loop structures.

# 网络分析代考

## 统计代写|网络分析代写Network Analysis代考|Inferring causal gene regulatory networks

1. 一对多：一个基因可以影响多个基因的活动。基因A正向调节基因的表达B,C， 和D.
2. 多对一：一个基因的活性可能受到多个基因的影响（B、D 和 F 之间的关系）。
3. 反馈回路：在反馈回路中，基因会影响其某些祖先在其调节通路中的活动。例如，E调节基因的表达A消极的。
4. 前馈回路：之间的调节D,F， 和H称为前馈调节结构，其中H直接或间接地受到影响D.
5. 自循环：一个基因可以影响它自己的活动（节点 B）。
6. 抑制：一个基因可能会抑制另一个基因的活性（D 抑制 E）。抑制或负调控可能发生在多对一、一对多和不同的循环结构中。

## 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。