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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|网络分析代写Network Analysis代考|Traversing a graph

Despite the existence of many algorithms for graph analysis, it should be noted that a large class of them employs graph traversal algorithms. Graph traversal, also known as graph search, refers to the process of enumerating (or visiting, or checking, or modifying), all the nodes of the graph. There exist two ways of performing traversals, which differ by the order in which vertices are visited.

Graph traversal algorithms start by visiting a node of the graph, termed as source or initial node (initial or source node). Next, it explores all the nodes of the graph (assuming that the graph is connected) and returning the list of visited nodes. Once a node has been traversed, that node is marked or coloured as visited (to guarantee the termination of the algorithm). Then the algorithm selects one of its adjacent ones, and the algorithm ends when all the nodes have been visited. The selection of the adjacent one will define the properties of the traversal, and based on this selection, two different techniques have been developed, namely breadth first search and depth first search, as depicted in Fig. 3.1.

Graph traversal techniques have been developed both for ordered and unordered graphs. In the following discussions, we assume that the graphs are unordered. If the graph has many connected components, then the traversal will return to the list of the nodes of the connected component to which the start node belong. Consequently, a generic algorithm for graph traversal is represented in Fig. 3.2. The algorithm is based on three main concepts: a collection of visited nodes, a collection of unvisited nodes and the choice of a node from this list. The algorithm initially marks all nodes unvisited. Then it starts from the starting node. After that starting node has been visited, it considers its adjacent the collection tovisitNodes determines the characteristics of the graph traversal.

A possible choice may be the first-in-first-out by using a queue while implementing BFS. In queue based implementation after visiting a node, all the adjacent ones are added to the queue. Then a first adjacent is visited, and its adjacent are added to the queue. Before visiting these nodes, all the adjacent nodes of the first node is visited. It is obvious that all the nodes that are a distance $k$ from it are visited before any node at a distance $k+1$. This traversal is called breadth-first search and is depicted in Fig. 3.3.

The time complexity can be expressed as $\mathcal{O}(|\mathcal{V}|+|\mathcal{E}|)$, where $|\mathcal{V}|$ is the number of the nodes, and $|\mathcal{E}|$ is the number of the edges. In the worst-case, every vertex and every edge will be explored. The formula clearly shows that the time complexity may vary depending on the sparsity of the input graph (see [10] for a deep discussion of the complexity in many different cases). This algorithm requires the building of the queue, then it requires the space for storing the graph, and a supplementary space $\mathcal{O}(|\mathcal{V}|)$ for the queue.

The possibility of speed-up of BFS through parallel algorithms has been explored in the past [24]. BFS is used in many other algorithms such as the following:

• Finding the shortest path between two nodes (see next sections);Computing the maximum flow in a flow network (FordFulkerson algorithm [16]);
• Testing bipartiteness;
• Cheney’s algorithm [8] for managing garbage collection in shared memory.

# 网络分析代考

## 统计代写|网络分析代写Network Analysis代考|Breadth first search

• 寻找两个节点之间的最短路径（见下一节）；计算流网络中的最大流量（FordFulkerson 算法 [16]）；
• 测试二分性；
• Cheney 的算法 [8] 用于管理共享内存中的垃圾收集。

## 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。

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