### 数学代写|随机图论代写Random Graph代考|CSL866

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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

## 数学代写|随机图论代写Random Graph代考|Generalized Random Intersection Graphs

Godehardt and Jaworski [ 389 ] introduced a model which generalizes both the binomial and uniform models of random intersection graphs. Let $P$ be a probability measure on the set ${0,1,2, \ldots, m}$. Let $V={1,2, \ldots, n}$ be the vertex set. Let $M=$ ${1,2, \ldots, m}$ be the set of attributes. Let $S_1, S_7, \ldots, S_n$ be independent random subsets of $M$ such that for any $v \in V$ and $S \subseteq M$ we have $\mathbb{P}\left(S_v=S\right)=P(|S|) /\left(\begin{array}{l}m \ |S|\end{array}\right)$. If we put an edge between any pair of vertices $i$ and $j$ when $S_i \cap S_j \neq \emptyset$, then we denote such a random intersection graph as $G(n, m, P)$, while if the edge is inserted if $\left|S_i \cap S_i\right| \geq s, s \geq 1$, the respective graph is denoted as $G_s(n, m, P)$. Bloznelis [99] extends these definitions to random intersection digraphs.
The study of the degree distribution of a typical vertex of $G(n, m, P)$ is given in [464], [242] and [97], see also [465]. Bloznelis ( see [98] and [100]) shows that the order of the largest component $L_1$ of $G(n, m, P)$ is asymptotically equal to $n \rho$, where $\rho$ denotes the non-extinction probability of a related multi-type Poisson branching process. Kurauskas and Bloznelis [541] study the asymptotic order of the clique number of the sparse random intersection graph $G_s(n, m, P)$.
Finally, a dynamic approach to random intersection graphs is studied by Barbour and Reinert [63], Bloznelis and Karoński [107], Bloznelis and Goetze [104] and Britton, Deijfen, Lageras and Lindholm [166].
One should also notice that some of the results on the connectivity of random intersection graphs can be derived from the corresponding results for random hyperghraphs, see for example [519], [707] and [390].

## 数学代写|随机图论代写Random Graph代考|Random Geometric Graphs

McDiarmid and Müller [588] gives the leading constant for the chromatic number when the average degree is $\Theta(\log n)$. The paper also shows a “surprising” phase change for the relation between $\chi$ and $\omega$. Also the paper extends the setting to arbitrary dimensions. Müller [618] proves a two-point concentration for the clique number and chromatic number when $n r^2=o(\log n)$.
Blackwell, Edmonson-Jones and Jordan [96] studied the spectral properties of the adjacency matrix of a random geometric graph (RGG). Rai [672] studied the spectral measure of the transition matrix of a simple random walk. Preciado and Jadbabaie [665] studied the spectrum of RGG’s in the context of the spreading of viruses.
Sharp thresholds for monotone properties of RGG’s were shown by McColm [582] in the case $d=1$ viz. a graph defined by the intersection of random subintervals. And for all $d \geq 1$ by Goel, Rai and Krishnamachari [391].
First order expressible properties of random points
$\mathscr{X}=\left{X_1, X_2, \ldots, X_n\right}$ on a unit circle were studied by McColm [581]. The graph has vertex set $\mathscr{X}$ and vertices are joined by an edge if and only if their angular distance is less than some parameter $d$. He showed among other things that for each fixed $d$, the set of a.s. FO sentences in this model is a complete noncategorical theory. McColm’s results were anticipated in a more precise paper [388] by Godehardt and Jaworski, where the case $d=1$, i.e., the evolution a random interval graph, was studied.
Diaz, Penrose, Petit and Serna [256] study the approximability of several layout problems on a family of RGG’s. The layout problems that they consider are bandwidth, minimum linear arrangement, minimum cut width, minimum sum cut, vertex separation, and edge bisection. Diaz, Grandoni and Marchetti-Spaccemela [255] derive a constant expected approximation algorithm for the $\beta$-balanced cut problem on random geometric graphs: find an edge cut of minimum size whose two sides contain at least $\beta n$ vertices each.
Bradonjić, Elsässer, Friedrich, Sauerwald and Stauffer [162] studied the broadcast time of RGG’s. They study a regime where there is likely to be a single giant component and show that w.h.p. their broadcast algorithm only requires $O\left(n^{1 / 2} / r+\log n\right)$ rounds to pass information from a single vertex, to every vertex of the giant. They show on the way that the diameter of the giant is $\Theta\left(n^{1 / 2} / r\right)$ w.h.p. Friedrich, Sauerwald and Stauffer [334] extended this to higher dimensions.

# 随机图论代写

## 数学代写|随机图论代写Random Graph代考|Generalized Random Intersection Graphs

Godehardt 和 Jaworski [389] 引入了一个模型，该模型概括了随机相交图的二项式模型和均匀模型。让P是集合上的概率测度0,1,2,…,米. 让在=1,2,…,n是顶点集。让米= 1,2,…,米是属性集。让小号1,小号7,…,小号n是独立的随机子集米这样对于任何在∈在和小号⊆米我们有P(小号在=小号)=P(|小号|)/(米 |小号|). 如果我们在任意一对顶点之间放置一条边一世和j什么时候小号一世∩小号j≠∅，那么我们将这样的随机交叉图表示为G(n,米,P), 而如果边被插入如果|小号一世∩小号一世|≥秒,秒≥1，相应的图表示为G秒(n,米,P). Bloznelis [99] 将这些定义扩展到随机相交有向图。

## 数学代写|随机图论代写Random Graph代考|Random Geometric Graphs

McDiarmid 和 Müller [588] 给出了当平均度数为日(日志⁡n). 该论文还显示了两者之间关系的“令人惊讶”的相变H和哦. 该论文还将设置扩展到任意维度。Müller [618] 证明了团数和色数的两点集中，当nr2=欧(日志⁡n).
Blackwell、Edmonson-Jones 和 Jordan [96] 研究了随机几何图 (RGG) 的邻接矩阵的谱特性。Rai [672] 研究了简单随机游走的转移矩阵的谱测度。Preciado 和 Jadbabaie [665] 在病毒传播的背景下研究了 RGG 的谱。
McColm [582] 在案例中展示了 RGG 的单调特性的尖锐阈值d=1即。由随机子区间的交集定义的图。对于所有人d≥1Goel、Rai 和 Krishnamachari [391]。

\mathscr{X}=\left{X_1, X_2, \ldots, X_n\right}\mathscr{X}=\left{X_1, X_2, \ldots, X_n\right}McColm [581] 在单位圆上进行了研究。该图有顶点集X当且仅当它们的角距离小于某个参数时，顶点才由边连接d. 他表明，除其他外，对于每个固定的d, 该模型中的 as FO 句子集是一个完整的非分类理论。McColm 的结果在 Godehardt 和 Jaworski 的更精确的论文 [388] 中得到了预期，其中案例d=1，即随机区间图的演化，进行了研究。
Diaz、Penrose、Petit 和 Serna [256] 研究了 RGG 族上几个布局问题的近似性。他们考虑的布局问题是带宽、最小线性排列、最小切割宽度、最小和切割、顶点分离和边缘平分。Diaz、Grandoni 和 Marchetti-Spaccemela [255] 为b- 随机几何图上的平衡切割问题：找到最小尺寸的边切割，其两侧至少包含bn每个顶点。
Bradonjić、Elsässer、Friedrich、Sauerwald 和 Stauffer [162] 研究了 RGG 的广播时间。他们研究了一个可能存在单个巨大组件的机制，并表明他们的广播算法只需要欧(n1/2/r+日志⁡n)rounds 将信息从单个顶点传递到巨人的每个顶点。他们在路上表明巨人的直径是日(n1/2/r)whp Friedrich、Sauerwald 和 Stauffer [334] 将其扩展到更高的维度。

## 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。