Posted on Categories:Complex Network, 复杂网络, 数据科学代写, 物理代写

# 物理代写|复杂网络代写Complex Network代考|COMP5313 Random recursive trees

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 物理代写|复杂网络代写Complex Network代考|Random recursive trees

Networks with large number of triangles are particularly interesting. The Strauss model of clustering is an exponential model with two soft constraints, for the number of edges and for the number of triangles (Strauss, 1975, 1986). The grand canonical ensemble of the Strauss model is described by the network Hamiltonian
$$\mathcal{H}(G)=-\mu_2 \frac{1}{2} \operatorname{Tr} A^2-\mu_3 \frac{1}{6} \operatorname{Tr} A^3$$
whose second term favours triangles (high clustering). This Hamiltonian can be processed similarly to standard spin models, if we treat the elements of the adjacency matrix as ‘spin variables’, like in matrix models. Then a usual mean-field theory can be applied to this ‘spin system’. The mean-field solution of the problem reveals two phases: normal phase, in which triangles are spread uniformly over the network, and the condensation phase, in which a fraction of vertices have large degrees and clustering about 1, stealing triangles and connections from the remaining vertices. ${ }^{37}$ The phase transition between them is of the first order, and so there is a large region on the phase diagram of this system, where these two phases co-exist. ${ }^{38}$ In simulations, in this region, networks rapidly fall into the condensation phase. At first sight, this is a drawback of the Strauss model originally aimed at real-world network systems with strong though uniform clustering. In other words, it seems that the Strauss model can be either in a uniform state with a uniform state with high clustering. Intrigued by this controversy, Burda, Jurkiewicz, and Krzywicki (2004) explored the dynamics of the transition of this system from the metastable normal state to the stable condensation one in this model, asking, how long does it take to pass the barrier separating the states? It turned out that the height of the barrier rapidly diverges with $N$. Therefore in the metastability region of large networks, it is actually impossible to approach the condensation state, starting from the homogeneous configuration, even with high clustering, and they stay homogeneous virtually for ever.

## 物理代写|复杂网络代写Complex Network代考|Preferential attachment

The preferential attachment process is probably the simplest way to get growing scale-free networks. Vertices for attachment are selected with probability proportional to some function of their degrees:
$$\operatorname{Prob}(i) \propto \mathcal{F}\left(q_i\right),$$
where $f(q)$ is called the preference function. When the preference function is monotonously increasing, ‘popular’ vertices with many connections have a better chance to get new connections than poorly connected vertices’popularity is attractive’. Specifically, a linear preference function
$$\mathcal{F}(q)=q+A,$$
where the constant $A$ is an additional (or initial) attractiveness, generates scale-free networks.

## 物理代夛|笝杂网络代写Complex Network代考|Random recursive trees

$$\mathcal{H}(G)=-\mu_2 \frac{1}{2} \operatorname{Tr} A^2-\mu_3 \frac{1}{6} \operatorname{Tr} A^3$$

## 物理代写|复杂网络代写Complex Network代考|Preferential attachment

$$\operatorname{Prob}(i) \propto \mathcal{F}\left(q_i\right)$$

$$\mathcal{F}(q)=q+A$$

## 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。