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## 数据科学代写|复杂网络代写Complex Network代考|Graph Partitioning Using the Cavity Method

The statistical mechanics formulation of the q-partitioning problem is done via the following ferromagnetic Potts Hamiltonian:
$$\mathcal{H}F({\sigma})=-\sum{i \neq j} J_{i j} \delta\left(\sigma_i, \sigma_j\right),$$
where $J_{i j}$ is the ${0,1}$ adjacency matrix of the graph and $\sigma_i$ denotes the Potts spin variable with $\sigma_i \in{1,2, \ldots, q}$. Once one finds the ground state under the constraint $\sum_i \delta\left(\sigma_i, \tau\right)=N / q$ for all $\tau \in{1,2, \ldots, q}$, one can write the total number of cut edges $C$ in the system using the ground state energy $E_g$ of the above Hamiltonian (6.1):
$$C_q=M+E_g=M\left(\frac{q-1}{q}-Q_q\right) .$$
Note the difference to (5.5). Also note that the modularity of the q-partition $Q_q$ can be expressed via Hamiltonian (6.1) as
$$Q_q=-\frac{\mathcal{H}_F}{M}-\frac{1}{q} .$$
This expression is only valid for magnetization zero, i.e., an exact q-partition.

## 数据科学代写|复杂网络代写Complex Network代考|Cavity Method at Zero Temperature

The ground state energy of (6.1) can be calculated by applying the cavity method at zero temperature following the approach presented by Mezard and Parisi [8] in the formulation for a Potts model as presented by Braunstein et al. $[9,10]$ for coloring random graphs. The energy of a system of $N$ spins is written as dependent on a “cavity spin” $\sigma_1$ via the “cavity field” $\boldsymbol{h}1$ : $$E^N\left(\sigma_1\right)=A-\sum{\tau=1}^q h_1^\tau \delta\left(\tau, \sigma_1\right)$$
Note that $h_1^\tau$ takes only integer values, if $J_{i j}$ is composed of only ${0,1}$. The components of the cavity field $\boldsymbol{h}i$ denote the change in energy of the system with a change in spin $i$. In general, these are different from the “effective fields” $\sum_j J{i j} \sigma_j$ acting on spin $\sigma_i$, which are used to calculate the magnetization. Adding a new spin $\sigma_0$ connected to $\sigma_1$, the energy of the now $N+1$ spin system is a function of both $\sigma_1$ and $\sigma_0$ :
$$E^{N+1}\left(\sigma_1, \sigma_0\right)=A-\sum_{\tau=1}^q h_1^\tau \delta\left(\tau, \sigma_1\right)-J_{10} \delta\left(\sigma_1, \sigma_0\right) .$$
One can now write this expression in such a way that it only depends on the newly added cavity spin $\sigma_0$ :
$$E^{N+1}\left(\sigma_0\right)=\min {\sigma_1} E^{N+1}\left(\sigma_1, \sigma_0\right) \equiv A-w\left(\boldsymbol{h}_1\right)-\sum{\tau=1}^q \hat{u}^\tau\left(J_{10}, \boldsymbol{h}_1\right) \delta\left(\tau, \sigma_0\right) .$$
The functions $w$ and $\hat{u}$ take the following form:
\begin{aligned} w(\boldsymbol{h}) & =\max \left(h^1, \ldots, h^q\right), \ \hat{u}^\tau(J, \boldsymbol{h}) & =\max \left(h^1, \ldots, h^\tau+J, \ldots, h^q\right)-w(\boldsymbol{h}) . \end{aligned}
From (6.8) one sees that $\hat{u}^\tau(\boldsymbol{h})$ is one, whenever the $\tau$ th component of $\boldsymbol{h}$ is maximal with respect to all other components in $\boldsymbol{h}$ and zero otherwise. Due to possible degeneracy in the components of $\boldsymbol{h}$, the vector $\hat{u}(\boldsymbol{h})$ may have more than one non-zero entry and is never completely zero.

## 数据科学代写|复杂网络代写Complex Network代考|Graph Partitioning Using the Cavity Method

q划分问题的统计力学公式是通过以下铁磁波茨哈密顿量来完成的:
$$\mathcal{H}F({\sigma})=-\sum{i \neq j} J_{i j} \delta\left(\sigma_i, \sigma_j\right),$$

$$C_q=M+E_g=M\left(\frac{q-1}{q}-Q_q\right) .$$

$$Q_q=-\frac{\mathcal{H}_F}{M}-\frac{1}{q} .$$

## 数据科学代写|复杂网络代写Complex Network代考|Cavity Method at Zero Temperature

(6.1)的基态能量可以按照Mezard和Parisi[8]在Braunstein等人$[9,10]$为随机图上色提出的Potts模型公式中提出的方法，在零温度下应用空腔法计算。一个$N$自旋系统的能量被写成依赖于“腔自旋”$\sigma_1$通过“腔场”$\boldsymbol{h}1$: $$E^N\left(\sigma_1\right)=A-\sum{\tau=1}^q h_1^\tau \delta\left(\tau, \sigma_1\right)$$

$$E^{N+1}\left(\sigma_1, \sigma_0\right)=A-\sum_{\tau=1}^q h_1^\tau \delta\left(\tau, \sigma_1\right)-J_{10} \delta\left(\sigma_1, \sigma_0\right) .$$

$$E^{N+1}\left(\sigma_0\right)=\min {\sigma_1} E^{N+1}\left(\sigma_1, \sigma_0\right) \equiv A-w\left(\boldsymbol{h}1\right)-\sum{\tau=1}^q \hat{u}^\tau\left(J{10}, \boldsymbol{h}_1\right) \delta\left(\tau, \sigma_0\right) .$$
$w$和$\hat{u}$函数的形式如下:
\begin{aligned} w(\boldsymbol{h}) & =\max \left(h^1, \ldots, h^q\right), \ \hat{u}^\tau(J, \boldsymbol{h}) & =\max \left(h^1, \ldots, h^\tau+J, \ldots, h^q\right)-w(\boldsymbol{h}) . \end{aligned}

## 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。

Posted on Categories:Complex Network, 复杂网络, 数据科学代写, 统计代写, 统计代考

## avatest™帮您通过考试

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## 数据科学代写|复杂网络代写Complex Network代考|Theoretical Limits of Community Detection

With the results of the last section it is now possible to start explaining Fig. 4.5 and to give a limit to which extent a designed community structure in a network can be recovered. As was shown, for any random network one can find an assignment of spins into communities that leads to a modularity $Q>0$. For the computer-generated test networks with $\langle k\rangle=16$ one has a value of $p=\langle k\rangle /(N-1)=0.126$ and expects a value of $Q=0.227$ according to (4.15) and $Q=0.262$ according to (4.22). The modularity of the community structure built in by design is given by
$$Q\left(\left\langle k_{i n}\right\rangle\right)=\frac{\left\langle k_{i n}\right\rangle}{\langle k\rangle}-\frac{1}{4}$$
for a network of four equal sized groups of 32 nodes. Hence, below $\left\langle k_{i n}\right\rangle=8$, one has a designed modularity that is smaller than what can be expected from a random network of the same connectivity! This means that the minimum in the energy landscape corresponding to the community structure that was designed is shallower than those that one can find in the energy landscape defined by any network. It must be understood that in the search for the builtin community structure, one is competing with those community structures that arise from the fact that one is optimizing for a particular quantity in a very large search space. In other words, any network possesses a community structure that exhibits a modularity at least as large as that of a completely random network. If a community structure is to be recovered reliably, it must be sufficiently pronounced in order to win the comparison with the structures arising in random networks. In the case of the test networks employed here, there must be more than $\approx 8$ intra-community links per node. Figure 4.12 again exemplifies this. Observe that random networks with $\langle k\rangle=16$ are expected to show a ratio of internal and external links $k_{\text {in }} / k_{\text {out }} \approx 1$. Networks which are considerably sparser have a higher ratio while denser networks have a much smaller ratio. This means that in dense networks one can recover designed community structure down to relatively smaller $\left\langle k_{i n}\right\rangle$. Consider for example large test networks with $\langle k\rangle=100$ with four built-in communities. For such networks one expects a modularity of $Q \approx 0.1$ and hence the critical value of intra-community links to which the community structure could reliably be estimated would be $\left\langle k_{i n}\right\rangle_c=35$ which is much smaller in relative comparison to the average degree in the network.

## 数据科学代写|复杂网络代写Complex Network代考|Analytical Developments

Let us recall the modularity Hamiltonian:
$$\mathcal{H}=-\sum_{i<j}\left(A_{i j}-\gamma p_{i j}\right) \delta\left(\sigma_i, \sigma_j\right) .$$
For convenience, instead of a Potts model with $q$ different spin states, the discussion is limited to only two spin states as in the Ising model, namely $S_i \in-1,1$. The delta function in (5.1) can be expressed as
$$\delta\left(S_i, S_j\right)=\frac{1}{2} S_i S_j+\frac{1}{2},$$
which leads to the new Hamiltonian
$$\mathcal{H}=-\sum_{i<j}\left(A_{i j}-\gamma p_{i j}\right) S_i S_j .$$
Note that (5.3) differs from (5.1) only by an irrelevant constant which even vanishes for $\gamma=1$ due to the normalization of $p_{i j}$. Because of the factor $1 / 2$ in (5.2), the modularity of the partition into two communities is now and for the remainder of this chapter
$$Q_2=-\frac{\mathcal{H}}{2 M},$$
where $\mathcal{H}$ now denotes the Hamiltonian (5.3). For the number of cut edges of the partition one can write
$$\mathcal{C}=\frac{1}{2}\left(M+E_g\right)=\frac{M}{2}\left(1-2 Q_2\right),$$
with $E_g$ denoting the ground state energy of (5.3) and it is clear that $Q_2$ measures the improvement of the partition over a random assignment into groups.

Formally, (5.3) corresponds to a Sherrington-Kirkpatrick (SK) model of a spin glass [3]
$$\mathcal{H}=-\sum_{i<j} J_{i j} S_i S_j,$$
with couplings of the form
$$J_{i j}=\left(A_{i j}-\gamma p_{i j}\right) .$$

## 数据科学代写|复杂网络代写Complex Network代考|Theoretical Limits of Community Detection

$$Q\left(\left\langle k_{i n}\right\rangle\right)=\frac{\left\langle k_{i n}\right\rangle}{\langle k\rangle}-\frac{1}{4}$$

## 数据科学代写|复杂网络代写Complex Network代考|Analytical Developments

$$\mathcal{H}=-\sum_{i<j}\left(A_{i j}-\gamma p_{i j}\right) \delta\left(\sigma_i, \sigma_j\right) .$$

$$\delta\left(S_i, S_j\right)=\frac{1}{2} S_i S_j+\frac{1}{2},$$

$$\mathcal{H}=-\sum_{i<j}\left(A_{i j}-\gamma p_{i j}\right) S_i S_j .$$

$$Q_2=-\frac{\mathcal{H}}{2 M},$$

$$\mathcal{C}=\frac{1}{2}\left(M+E_g\right)=\frac{M}{2}\left(1-2 Q_2\right),$$
$E_g$表示(5.3)的基态能量，很明显，$Q_2$测量了随机分配到组上的分区的改进。

$$\mathcal{H}=-\sum_{i<j} J_{i j} S_i S_j,$$

$$J_{i j}=\left(A_{i j}-\gamma p_{i j}\right) .$$

## 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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## avatest™帮您通过考试

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## 数据科学代写|复杂网络代写Complex Network代考|A New Error Function

We already said that we would like to use a statistical mechanics approach. The problem of finding a block structure which reflects the network as good as possible is then mapped onto finding the solution of a combinatorial optimization problem. Trying to approximate the adjacency matrix $\mathbf{A}$ of rank $r$ by a matrix $\mathbf{B}$ of rank $q<r$ means approximating $\mathbf{A}$ with a block model of only full and zero blocks. Formally, we can write this as $\mathbf{B}_{i j}=B\left(\sigma_i, \sigma_j\right)$ where $B(r, s)$ is a ${0,1}^{q \times q}$ matrix and $\sigma_i \in{1, \ldots, q}$ is the assignment of node $i$ from A into one of the $q$ blocks. We can view $B(r, s)$ as the adjacency matrix of the blocks in the network or as the image graph discussed in the previous chapter and its nodes represent the different equivalence classes into which the vertices of $\mathbf{A}$ may be grouped. From Table 3.1, we see that our error function can have only four different contributions. They should

reward the matching of edges in $\mathbf{A}$ to edges in $\mathbf{B}$,

penalize the matching of missing edges (non-links) in $\mathbf{A}$ to edges in $\mathbf{B}$,

penalize the matching of edges in $\mathbf{A}$ to missing edges in $\mathbf{B}$ and

reward the matching of missing edges in $\mathbf{A}$ to edges in $\mathbf{B}$

## 数据科学代写|复杂网络代写Complex Network代考|Fitting Networks to Image Graphs

The above-defined quality and error functions in principle consist of two parts. On one hand, there is the image graph $\mathbf{B}$ and on the other hand, there is the mapping of nodes of the network to nodes in the image graph, i.e., the assignment of nodes into blocks, which both determine the fit. Given a network $\mathbf{A}$ and an image graph $\mathbf{B}$, we could now proceed to optimize the assignment of nodes into groups ${\sigma}$ as to optimize (3.6) or any of the derived forms. This would correspond to “fitting” the network to the given image graph. This allows us to compare how well a particular network may be represented by a given image graph. We will see later that the search for cohesive subgroups is exactly of this type of analysis: If our image graph is made of isolated vertices which only connect to themselves, then we are searching for an assignment of nodes into groups such that nodes in the same group are as densely connected as possible and nodes in different groups as sparsely as possible. However, ultimately, we are interested also in the image graph which best fits to the network among all possible image graphs B. In principle, we could try out every possible image graph, optimize the assignment of nodes into blocks ${\sigma}$ and compare these fit scores. This quickly becomes impractical for even moderately large image graphs. In order to solve this problem, it is useful to consider the properties of the optimally fitting image graph $\mathbf{B}$ if we are given the networks plus the assignment of nodes into groups ${\sigma}$.

We have already seen that the two terms of (3.7) are extremized by the same $B\left(\sigma_i, \sigma_j\right)$. It is instructive to introduce the abbreviations
\begin{aligned} m_{r s} & =\sum_{i j} w_{i j} A_{i j} \delta\left(\sigma_i, r\right) \delta\left(\sigma_j, s\right) \text { and } \ {\left[m_{r s}\right]{p{i j}} } & =\sum_{i j} p_{i j} \delta\left(\sigma_i, r\right) \delta\left(\sigma_j, s\right), \end{aligned}
and write two equivalent formulations for our quality function:
\begin{aligned} & Q^1({\sigma}, \mathbf{B})=\sum_{r, s}\left(m_{r s}-\gamma\left[m_{r s}\right]{p{i j}}\right) B(r, s) \text { and } \ & Q^0({\sigma}, \mathbf{B})=-\sum_{r, s}\left(m_{r s}-\gamma\left[m_{r s}\right]{p{i j}}\right)(1-B(r, s)) . \end{aligned}

## 数据科学代写|复杂网络代写Complex Network代考|Fitting Networks to Image Graphs

\begin{aligned} m_{r s} & =\sum_{i j} w_{i j} A_{i j} \delta\left(\sigma_i, r\right) \delta\left(\sigma_j, s\right) \text { and } \ {\left[m_{r s}\right]{p{i j}} } & =\sum_{i j} p_{i j} \delta\left(\sigma_i, r\right) \delta\left(\sigma_j, s\right), \end{aligned}

\begin{aligned} & Q^1({\sigma}, \mathbf{B})=\sum_{r, s}\left(m_{r s}-\gamma\left[m_{r s}\right]{p{i j}}\right) B(r, s) \text { and } \ & Q^0({\sigma}, \mathbf{B})=-\sum_{r, s}\left(m_{r s}-\gamma\left[m_{r s}\right]{p{i j}}\right)(1-B(r, s)) . \end{aligned}

## 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。

Posted on Categories:Complex Network, 复杂网络, 数据科学代写, 统计代写, 统计代考

## avatest™帮您通过考试

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## 数据科学代写|复杂网络代写Complex Network代考|Positions, Roles and Equivalences

By investigating data from a wide range of sources encompassing the life sciences, ecology, information and social sciences as well as economics, researchers have shown that an intimate relation between the topology of a network and the function of the nodes in that network indeed exists [1-9]. A central idea is that nodes with a similar pattern of connectivity will perform a similar function. Understanding the topology of a network will be a first step in understanding the function of individual nodes and eventually the dynamics of any network.
As before, we can base our analysis on the work done in the social sciences. In the context of social networks, the idea that the pattern of connectivity is related to the function of an agent in the network is known as playing a “role” or assuming a “position” $[10,11]$. Here, we will endorse this idea.
The nodes in a network may be grouped into equivalence classes according to the role they play. Two basic concepts have been developed to formalize the assignments of roles individuals play in social networks: structural and regular equivalence. Both are illustrated in Fig. 2.1. Two nodes are called structurally equivalent if they have the exact same neighbors [12]. This means that in the adjacency matrix of the network, the rows and columns of the corresponding nodes are exactly equal. The idea behind this type of equivalence is that two nodes which have the exact same interaction partners can only perform the exact same function in the network. In Fig. 2.1, only nodes $A$ and $B$ are structurally equivalent while all other nodes are structurally equivalent only to themselves.
To relax this very strict criterion, regular equivalence was introduced $[13$, 14]. Two nodes are regularly equivalent if they are connected in the same way to equivalent others. Clearly, all nodes which are structurally equivalent must also be regularly equivalent, but not vice versa. The seemingly circular definition of regular equivalence is most easily understood in the following way: Every class of regularly equivalent nodes is represented by a single node in an “image graph”. The nodes in the image graph are connected (disconnected), if connections between nodes in the respective classes exist (are absent) in the original network. In Fig. 2.1, nodes $A$ and $B, C$ and $D$ as well as $E$ and $F$ form three classes of regular equivalence. If the network in Fig. 2.1 represents the trade interactions on a market, we may interpret these three classes as producers, retailers and consumers, respectively. Producers sell to retailers, while retailers may sell to other retailers and consumers, which in turn only buy from retailers. The image graph (also “block” or “role model”) hence gives a bird’s-eye view of the network by concentrating on the roles, i.e., the functions, only. Note that no two nodes in the image graph may be structurally equivalent, otherwise the image graph is redundant.

## 数据科学代写|复杂网络代写Complex Network代考|Block Modeling

Let us consider the larger example from Fig. 2.2. The network consists of 18 nodes in 4 designed roles. Nodes of type A connect to other nodes of type A and to nodes of type $\mathrm{B}$. Those of type $\mathrm{B}$ connect to nodes of type $\mathrm{A}$ and $\mathrm{C}$,
acting as a kind of intermediary. Nodes of type $\mathrm{C}$ have connections to nodes of type B, others of type C and of type D. Finally, nodes of type D form a kind of periphery to nodes of type $\mathrm{C}$. An ordering of rows and columns according to the types of nodes makes a block structure in the adjacency matrix apparent. Hence the name “block model”. The image graph effectively represents the 4 roles present in the original network and the 16 blocks in the adjacency matrix. Every edge present in the network is represented by an edge in the image graph and all edges absent in the image graph are also absent in the original network.
Regular equivalence, though a looser concept than structural equivalence, is still very strict as it requires the nodes to play their roles exactly, i.e., each node must have at least one of the connections required and may not have any connection forbidden by the role model. In Fig. 2.2, a link between two nodes of type A may be removed without changing the image graph, but an additional link from a node of type $\mathrm{A}$ to a node of type $\mathrm{C}$ would change the role model completely. Clearly, this is unsatisfactory in situations where the data are noisy or only approximate role models are desired for a very large data set.

## 数据科学代写|复杂网络代写Complex Network代考|Positions, Roles and Equivalences

\begin{aligned}
\Delta \alpha_i(t+1)=\alpha_i(t+1)-\alpha_i(t) & =\frac{d_i(t)}{2 t}\left(\frac{s_i(t)+m}{d_i(t)+1}-\frac{s_i(t)}{d_i(t)}\right)+ \
\frac{s_i(t)}{2 t}\left(\frac{s_i(t)+1}{d_i(t)}-\frac{s_i(t)}{d_i(t)}\right) & =\frac{m}{2 t}-\frac{1}{2 t\left(d_i(t)+1\right)}+\alpha_i(t) \frac{1}{2 t\left(d_i(t)+1\right)}
\end{aligned}
$$## 数据科学代写|复杂网络代写Complex Network代考|Triadic Closure Model Analysis Holme和Kim研究了一种利用三元闭合机制的问责模型[7]。它是优先依恋Barabási-Albert模型的扩展[3]，并使用了先前在论文[10,17]中指定的三元闭包思想。该模型生成的网络具有重尾度分布(以及BA模型)，但具有与现实世界网络相似的更高的聚类。 Holme和Kim[7]的三元闭包模型生成了如下的增长网络。在每次迭代t: 合并一个新生节点t; m 连接到网络现有节点的链接如下: (a)第一条链路使用优先连接机制将节点t与节点i连接起来(即连接到节点i的概率与其程度\left.d_i(t)\right)成正比); (b)剩余的m-1边连接新节点t如下: (b1)以固定的概率0<p<1，链路附着到节点i的任意邻居(所谓三元形成); (b2)的概率为1-p，链路以优先依附的方式依附于现有节点之一。 文献[7]表明，通过选择p和m，模型可以产生具有不同聚类水平的网络。另一方面，对于任何p，它们的度分布遵循指数为\gamma=-3的幂律，即与BA模型相同。在本节的其余部分中，我们将假设为p \neq 0和m \geq 2。 设节点j和i为邻居，即(j, i) \in E(t)。文献[7]表明，随着迭代次数的增加t，聚类系数趋向于某个恒定值\theta=\theta(p, m)。然后，随机选择的节点j的邻居也是节点i的邻居的概率可以用平均聚类系数\theta(t)的值来近似，而平均聚类系数可以用常数\theta来近似。 数据科学代写|复杂网络代写Complex Network代考 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。 ## 微观经济学代写 微观经济学是主流经济学的一个分支，研究个人和企业在做出有关稀缺资源分配的决策时的行为以及这些个人和企业之间的相互作用。my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论代写Graph Theory代写方面经验极为丰富，各种图论代写Graph Theory相关的作业也就用不着 说。 ## 线性代数代写 线性代数是数学的一个分支，涉及线性方程，如：线性图，如：以及它们在向量空间和通过矩阵的表示。线性代数是几乎所有数学领域的核心。 ## 博弈论代写 现代博弈论始于约翰-冯-诺伊曼（John von Neumann）提出的两人零和博弈中的混合策略均衡的观点及其证明。冯-诺依曼的原始证明使用了关于连续映射到紧凑凸集的布劳威尔定点定理，这成为博弈论和数学经济学的标准方法。在他的论文之后，1944年，他与奥斯卡-莫根斯特恩（Oskar Morgenstern）共同撰写了《游戏和经济行为理论》一书，该书考虑了几个参与者的合作游戏。这本书的第二版提供了预期效用的公理理论，使数理统计学家和经济学家能够处理不确定性下的决策。 ## 微积分代写 微积分，最初被称为无穷小微积分或 “无穷小的微积分”，是对连续变化的数学研究，就像几何学是对形状的研究，而代数是对算术运算的概括研究一样。 它有两个主要分支，微分和积分；微分涉及瞬时变化率和曲线的斜率，而积分涉及数量的累积，以及曲线下或曲线之间的面积。这两个分支通过微积分的基本定理相互联系，它们利用了无限序列和无限级数收敛到一个明确定义的极限的基本概念 。 ## 计量经济学代写 什么是计量经济学？ 计量经济学是统计学和数学模型的定量应用，使用数据来发展理论或测试经济学中的现有假设，并根据历史数据预测未来趋势。它对现实世界的数据进行统计试验，然后将结果与被测试的理论进行比较和对比。 根据你是对测试现有理论感兴趣，还是对利用现有数据在这些观察的基础上提出新的假设感兴趣，计量经济学可以细分为两大类：理论和应用。那些经常从事这种实践的人通常被称为计量经济学家。 ## 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。 Posted on Categories:Complex Network, 复杂网络, 数据科学代写, 统计代写, 统计代考 ## 数据科学代写|复杂网络代写Complex Network代考|Triple-Tuple Motif 如果你也在 怎样代写复杂网络Complex Network 这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。复杂网络Complex Network在网络理论的背景下，复杂网络是指具有非微观拓扑特征的图（网络）–这些特征在简单的网络（如格子或随机图）中不会出现，但在代表真实系统的网络中经常出现。复杂网络的研究是一个年轻而活跃的科学研究领域（自2000年以来），主要受到现实世界网络的经验发现的启发，如计算机网络、生物网络、技术网络、大脑网络、气候网络和社会网络。 复杂网络Complex Network大多数社会、生物和技术网络显示出实质性的非微观拓扑特征，其元素之间的连接模式既不是纯粹的规则也不是纯粹的随机。这些特征包括学位分布的重尾、高聚类系数、顶点之间的同态性或异态性、社区结构和层次结构。在有向网络的情况下，这些特征还包括互惠性、三联体重要性概况和其他特征。相比之下，过去研究的许多网络的数学模型，如格子和随机图，并没有显示这些特征。最复杂的结构可以由具有中等数量相互作用的网络实现。这与中等概率获得最大信息含量（熵）的事实相对应。 复杂网络Complex Network代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。最高质量的复杂网络Complex Network作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此复杂网络Complex Network作业代写的价格不固定。通常在专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。 ## 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！ 在不断发展的过程中，avatest™如今已经成长为论文代写，留学生作业代写服务行业的翘楚和国际领先的教育集团。全体成员以诚信为圆心，以专业为半径，以贴心的服务时刻陪伴着您， 用专业的力量帮助国外学子取得学业上的成功。 •最快12小时交付 •200+ 英语母语导师 •70分以下全额退款 想知道您作业确定的价格吗? 免费下单以相关学科的专家能了解具体的要求之后在1-3个小时就提出价格。专家的 报价比上列的价格能便宜好几倍。 我们在统计Statistics代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在复杂网络Complex Network代写方面经验极为丰富，各种复杂网络Complex Network相关的作业也就用不着说。 ## 数据科学代写|复杂网络代写Complex Network代考|Triple-Tuple Motif In the third step, we wonder the occurrence frequency of 5 sorts of triads based on the concept of T B P s, which can effectively and simply reflect the microstructure of GVC. If we compare the GVC to DNA, the TBPs will be its base pairs. As we mentioned above, TBP1 stands for inland trade (for instance, AUSS1 \rightarrow AUSS3 \rightarrow AUSS4), TBP2 for international trade I (AUSS1 \rightarrow AUTS3 \rightarrow AUSS4), TBP3 for import trade (AUSS1 \rightarrow AUTS3 \rightarrow AUTS3), TBP4 for export trade (AUSS1 \rightarrow AUSS3 \rightarrow AUTS3), TBP5 for international trade II (AUSS1 \rightarrow AUSS3 \rightarrow BELS3). In detail, all the consecutive-three-strings fragments on all the SRPLs are first identified according to the concept of T B P s, and then statistics of triple-tuple motifs are examined according to the names of industrial sectors and economies. For instance, we can get \mathrm{S} 1 \rightarrow \mathrm{S} 3 \rightarrow \mathrm{S} 4 and AUS \rightarrow AUS \rightarrow AUS from AUSS1 \rightarrow AUSS3 \rightarrow AUSS4, \mathrm{S} 1 \rightarrow \mathrm{S} 3 \rightarrow \mathrm{S} 4 and AUS \rightarrow AUT \rightarrow AUS from AUSS1 \rightarrow AUTS3 \rightarrow AUSS4, etc. The frequency for all the possible combinations of triad on both the national level and sectoral level can be obtained under the circumstances of five TBPs. At last, we add up the same sort of T B P to produce new indicators named Cumulative Trade Brokerage Property (CTBP). Notice that, due to this cumulation process, only one set of CTBPs is obtainable. The most obvious feature in Fig. 3.7 is the proportion of CTBP2, indicating it is rare that countries provide value-added services of intermediate goods for another one (i.e., they import intermediate goods from other countries and then export them to the same one after further processing). In contrast, it is the trend that countries also acquire industrial resources on the GVC through import and export trade (the ratio of both CTBP3 and CTBP4 is basically stable in one-third), and cooperate with upstream and downstream countries on the GVC (the ratio of CTBP5 is 23.44\%, which shows a downward tendency during 15 years) to ensure the sustainable development of the global economic system (although there has been a certain degree of anti-globalization in recent years). From the statistics of triads on the sectoral level (see Table 3.2), the most frequent triple-tuple motifs are based on the top 5 manufacturing and services, which once again certify that the manufacturing-related IVC links constitute the GVC as the most important microstructural basis. Since the year of 2000 , the top 3 triple-tuple motifs are always SC3 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 3, \mathrm{SC} 3 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 4, and SC4 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 3 However, it is scarcely seen that three industrial sectors of a triad all belong to manufacturing appears less and less, reducing from 26,105 times in 2000 to 20,633 times in 2014. The rankings of the following triple-tuple motifs are constantly changing, and the overall frequency is higher than that in 2000 . It is thus crystal clear that the global industrial structure has been in an ongoing process of adjustment. It will be further analyzed in subsequent research according to the classification of 56 sectors. ## 数据科学代写|复杂网络代写Complex Network代考|Average/Maximum Strongest Relevance Degree In non-weighted networks, the Average Path Length (APL) of the whole network can be calculated via FWA, depicting the degree of separation of nodes. As a counterpart in GIVCN model, the average of S R P L^{\prime} matrix is chosen to measure the overall flow efficiency of the economic system, i.e., the Connectedness of Industrial Value Chain. The Average Strongest Relevance Degree (ASRD) is proposed, namely:$$
A S R D=\frac{\sum_{i=1}^N \sum_{j=1}^N S R P L_{i j}^{(N)}}{N}
$$where S R P L_{i j}^{(N)} is the S R P L between nodes i and j within the scope of the whole network. We allow for self-loops, and the denominator thus incorporates two parts, i.e., edges and self-loops.$$
N=N_e+N_s=N_n\left(N_n-1\right)+N_s
$$where N_e stands for the number of normal edges, N_s for self-loops, and N_n for nodes. Furthermore, to observe its impact on the uppermost branch of \mathrm{GVC}, another measuring method named the Maximum Strongest Relevance Degree (MSRD) is here designed, namely:$$
M S R D=\max {i, j \in{1,2, \cdots, N}}\left{S R P L{i j}^{(N)}\right}
$$In a mathematical sense, M S R D is the highest value in S R P L^{\prime} matrix, and there exists a complicated process of intermediate goods propagation behind it. Different from ASRD, MSRD only depends on a single value chain that covers the most significant spreading effect across industrial sectors-just like a threshold value of the Compactness of Industrial Value Chain. Correspondingly, both upstream and downstream sectors are respectively the source and sink nodes of this max-SRPL path. Under normal circumstances, the random small-scale industrial fluctuation is not supposed to shake the closest economic connection in the global or regional economic system, and this kind of special IVC will in turn drive the development of all relevant industrial sectors and even the entire industrial network. ## 复杂网络代写 ## 数据科学代写|复杂网络代写Complex Network代考|Triple-Tuple Motif 第三步，我们根据 T B P s ，可以有效、简单地反映全球价值链的微观结构。如果我们将 GVC 比作 DNA，则 TBP 就是它的碱基对。正如我们上面提到的，TBPI代表内陆贸易（例如，AUSSI \rightarrow A U S S 3 \rightarrow A U S S 4 )，TBP2 用 于国际贸易 I (AUSS1 \rightarrow AUTS 3 \rightarrow AUSS4)， TBP3 用于进口贸易 (AUSSI \rightarrow A \cup T S 3 \rightarrow A U T S 3 ), TBP4 用于出口 贸易 (AUSS1 \rightarrow AUSS3 \rightarrow AUTS3)，TBP5 用于国际贸易 II (AUSS1 \rightarrow A \cup S S 3 \rightarrow B E L S 3 ). 具体而言，所有SRPL上 的所有连续三串片段首先根据以下概念进行识别 T B P s ，然后根据工业部门和经济体的名称检查三元组主题的 统计数据。例如，我们可以得到 \mathrm{S} 1 \rightarrow \mathrm{S} 3 \rightarrow \mathrm{S} 4 和关闭 \rightarrow 在…..之外 \rightarrow 从 OUT1 输出 \rightarrow AUSS3 \rightarrow \mathrm{AUSS4} ， \mathrm{S} 1 \rightarrow \mathrm{S} 3 \rightarrow \mathrm{S} 4 和关闭 \rightarrow 奥特 \rightarrow 从 OUT1 输出 \rightarrow AUTS3 \rightarrow AUSS4等。在5个TBP的情况下，可以得到国家 层面和行业层面所有三元组可能组合的频率。最后，我们加起来是同一种 T B P 产生名为傫积贸易经纪财产 (CTBP) 的新指标。请注意，由于此男积过程，只能获得一组 CTBP。 图 3.7 中最明显的特征是 CTBP2 的比例，表明很少有国家为另一个国家提供中间产品的增值服务（即从其他国 家进口中间产品，然后再出口到同一国家) 进一步处理)。相比之下，趋势是各国也通过进出口贸易获取GVC 上的产业资源 (CTBP3和CTBP4的比例基本稳定在三分之一)，与GVC上下游国家合作 ( CTBP5 比率为 23.44 \% ， 15 年呈下降趋势)，以确保全球经济体系的可持续发展 (尽管近年来出现了一定程度的逆全球化)。 从部门层面的三元组统计 (见表 3.2) 来看，出现频率最高的三元组主题是前 5 位的制造业和服务业，这再次 证明制造业相关的 IVC 环节构成了 GVC 最重要的环节。微观结构基础。自 2000 年以来，前 3 个三元组图案 始終是 \mathrm{SC} 3 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 3, \mathrm{SC} 3 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 4, 和 \mathrm{SC} 4 \rightarrow \mathrm{SC} 3 \rightarrow \mathrm{SC} 3 但很少见三元组的三个工业 部门都属于制造业的出现越来越少，从2000年的26105次减少到2014年的20633次。频率高于2000年。由此 可见，全球产业结构一直处于调整过程中。后续研究将按照 56 个行业分坣进行进一步分析。 ## 数据科学代写|复杂网络代写Complex Network代考|Average/Maximum Strongest Relevance Degree 在非加权网络中，可以通过FWA计算整个网络的平均路径长度 (APL)，描述节点的分离程度。作为 GIVCN 模 型的对应物，平均 S R P L^{\prime} 选择矩阵来衡量经济系统的整体流动效率，即产业价值链的连通性。提出平均最强 相关度 (ASRD)，即：$$
A S R D=\frac{\sum_{i=1}^N \sum_{j=1}^N S R P L_{i j}^{(N)}}{N}
$$在哪里 S R P L_{i j}^{(N)} 是个 S R P L 节点之间 i 和 j 全网范围内。我们允许自环，因此分母包含两部分，即边和自 环。$$
N=N_e+N_s=N_n\left(N_n-1\right)+N_s
$$在哪里 N_e 代表法线边的数量， N_s 对于自循环，和 N_n 对于节点。此外，观察其对最上层分支的影响 \mathrm{GVC} ，这 里设计了另一种称为最大最强相关度 (MSRD) 的测量方法，即：$$
M \text { S R D }=\backslash \max {i, j \backslash \text { in }{1,2, \backslash \text { cdots, } N}} \backslash \text { left }{S R P L{i j} \wedge{(N)} \backslash \text { right }}


## 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。