### 数学代写|计算复杂度理论代写Computational complexity theory代考|The Public Goods Game

statistics-lab™ 为您的留学生涯保驾护航 在代写计算复杂度理论Computational complexity theory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。我们的专家在代写计算复杂度理论Computational complexity theory代写方面经验极为丰富，各种代写计算复杂度理论Computational complexity theory相关的作业也就用不着说。

• 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|计算复杂度理论代写Computational complexity theory代考|Cooperation: Motivations and Mechanisms

Cooperation is one of the most interesting phenomena in nature and in societies. Cooperation leads to forms of organization and to the growth of a system. However, at least according to the Game Theory, often is a target very difficult to be reached. Beyond the underlying motivations, and the potential risks, results coming from cooperation require joint efforts. For this reason, cooperation can be viewed as an emergent phenomenon, where an increasing amount of agents becomes cooperator. Martin A. Nowak wrote a very important work, in the field, highlighting and explaining the famous five rules of cooperation, related to the concept of natural selection: kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection. Here, we just limit to mention and to briefly summarize each rule. The kin selection is a principle based on the similarity between the donor and the recipient of an altruistic act. For instance, in case of a parental relation between two individuals, it is very likely to observe cooperation. The direct reciprocity results from the observation that when a game involves many times always the same individuals, cooperation can actually become a promising option. The indirect reciprocity is a mechanism that explains why individuals act as donors, even if they know that the one receiving the benefit is not (will not be) in the condition to exchange the favor. Notably, especially in the human society, we can observe forms of cooperation related to indirect reciprocity, mainly because the donor has the opportunity to gain the respect of other individuals (that, obviously, must see the action). Accordingly, this action might allow to achieve, indirectly, some benefits. The network reciprocity is similar to the direct reciprocity and can be observed in spatially structured populations, where the individuals interact always with the same neighbors. This mechanism is then responsible for the emergence of clusters of cooperators. Then, the group selection indicates forms of cooperation observed within community of people, i.e., among individuals belonging to the same group. Notably, in this case, groups of cooperators can obtain more benefits than groups of defectors. Finally, further mechanisms responsible for the emergence of cooperation have been described in complex networks, in continuous spaces (e.g., random motion, also discussed in the Chap. 3) and in many other conditions.

## 数学代写|计算复杂度理论代写Computational complexity theory代考|Modeling Complex Systems

Statistical Physics deals with a number of topics of absolute relevance in Physics, as phase transitions. Notably, it aims to connect the macroscopic behavior of a system with the local mechanisms of its constituents, e.g., one aims to connect the thermodynamic view of a gas with its mechanical laws (i.e., the kinetic theory). As a result, this approach becomes strongly valuable when dealing with complex systems, also in those cases where the subject of investigation is a nonphysical system, like a social network or a socioeconomic system. Modern Network Theory represents one of the most successful frameworks for dealing with this kind of topics, and its link with Statistical Physics has deep roots uncovered in the early works of A.L. Barabasi, M. Newman, Y. Moreno, S. Boccaletti, A. Arenas, R. Albert, G. Caldarelli, A. Barrat, V. Latora, D. Krioukov, G. Bianconi and many other scientists, now forming the growing community of complex systems (i.e., the Complex Systems Society). Therefore, the scope of this chapter is to provide a very brief presentation of some mathematical and physical method for dealing with Evolutionary Games, focusing both on the mathematical description and on the computational strategies for implementing models and studying their behavior. The reader interested in further details is invited to consult the huge amount of texts on the specific topic (a brief list of reference can be found at the end of the chapter). Here, the material is organized as follows: we start with models related to population dynamics, then we move to a general discussion of phase transitions, introducing the Ising model, the Curie-Weiss model, and the Mean-field approach. Eventually, a section on complex networks ends the chapter.

## 数学代写|计算复杂度理论代写Computational complexity theory代考|Population Dynamics

Population dynamics is an area that sinks its roots in the field of Mathematical Biology, adopted for representing processes like population growth, competitions, aging, and so on and so forth. Beyond the classical models introduced by Malthus, Lotka-Volterra, Verhulst, Ginzburg, and many more who contributed to the early developments of this field, EGT constitutes a further framework for studying the behavior and the dynamics of a population. Here, we present some basic concepts that can be adopted for defining new models both in the area of EGT and in contexts that might benefit from this mathematical approach (e.g., social dynamics). Let us begin with a simple continuous growth, considering a population composed of $N$ individuals living in a system without competitors:
$$\frac{d N}{d t}=r N$$
with $r$ defined as growth rate, or Malthusian parameter. From a mathematical point of view, computing the analytical solution of Eq. (2.1) is quite simple. In particular, we have $N(t)=N_{0} e^{r t}$, with $N_{0}$ initial condition, indicating the population size at $t=0$. As we can observe, Eq. (2.1) does not take under consideration further aspects that can be found in ecological contexts, e.g., processes/mechanisms that can reduce the growth of a population. For instance, we can be interested in analyzing the behavior of a system with two competing populations/species. Obviously, in order to model this occurrence, we have to know the rules underlying the interactions between individuals of the two species. One of the first proposals for representing these scenarios is the Lotka-Volterra model, also named predatorprey model. Notably, it aims to describe the dynamics of interactions between two species, i.e., predators (say $A$ ) and preys (say $B$ ). The mathematical definition of this model reads
$$\left{\begin{array}{l} \frac{d A}{d t}=\alpha A B-\beta A \ \frac{d B}{d t}=\gamma A-\delta A B \end{array}\right.$$
with $\alpha$ and $\gamma$ representing internal processes within the single species (e.g., growth) and $\beta$ and $\delta$ parameters that quantify the interactions between the two species. The values of these parameters can be modified for considering different scenarios.

## 数学代写|计算复杂度理论代写Computational complexity theory代考|Population Dynamics

dñd吨=rñ

$$\left{ d一个d吨=一个一个乙−b一个 d乙d吨=C一个−d一个乙\正确的。$$

## 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。