MATH 303 - 统计代写答疑辅导

标签： MATH 303

数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Modeling and Computer Languages

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

计算复杂性理论computational complexity theory的重点是根据资源使用情况对计算问题进行分类，并将这些类别相互联系起来。计算问题是一项由计算机解决的任务。一个计算问题是可以通过机械地应用数学步骤来解决的，比如一个算法。

statistics-lab™ 为您的留学生涯保驾护航在代写计算复杂性理论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性理论computational complexity theory代写方面经验极为丰富，各种代写计算复杂性理论相关的作业也就用不着说。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Modeling and Computer Languages

数学代考|计算复杂性理论代写computational complexity theory代考|Types of Computer Languages

A ‘computer language’ is a method of noting directives for computers. ‘Computer programming languages,’ or ‘programming languages,’ are an important category of computer languages. A programming language is a computer language that allows any computable activity to be expressed. This article focuses on computer programming languages rather than the more general computer languages since virtually all agent-based modeling systems require the power of programming languages. This article sometimes uses the simpler term ‘computer languages’ when referring to computer programming languages. According to Watson [47]:
Programming languages are used to describe algorithms, that is, sequences of steps that lead to the

solution of problems … A programming language can be considered to be a ‘notation’ that can be used to specify algorithms with precision.
Watson [47] goes on to say that “programming languages can be roughly divided into four groups: imperative languages, functional languages, logic programming languages, and others”. Watson [47] states that in imperative languages “there is a fundamental underlying dependence on the assignment operation and on variables implemented as computer memory locations, whose contents can be read and altered”. However, “in functional languages (sometimes called applicative languages) the fundamental operation is function application” [47]. Watson cites LISP as an example. Watson [47] continues by noting that “in a logic programming language, the programmer needs only to supply the problem specification in some formal form, as it is the responsibility of the language system to infer a method of solution”.

A useful feature of most functional languages, many logic programming languages, and some imperative languages is higher-order programming. According to Reynolds [35]:
In analogy with mathematical logic, we will say that a programming language is higher-order if procedures or labels can occur as data, i. e., if these entities can be used as arguments to procedures, as results of functions, or as values of assignable variables. A language that is not higher-order will be called first-order.
Watson [47] offers that “another way of grouping programming languages is to classify them as procedural or declarative languages”. Elaborating, Watson [47] states that:
Procedural languages … are those in which the action of the program is defined by a series of operations defined by the programmer. To solve a problem, the programmer has to specify a series of steps (or statements) which are executed in sequence.

数学代考|计算复杂性理论代写computational complexity theory代考|Requirements of Computer Languages for Agent-Based Modeling

The requirements of computer languages for agent-based modeling and simulation include the following:

There is a need to create well defined modules that correspond to agents. These modules should bind together agent state data and agent behaviors into integrated independently addressable constructs. Ideally these mod-

ules will be flexible enough to change structure over time and to optionally allow fuzzy boundaries to implement models that go beyond methodological individualism [20].

There is a need to create well defined containers that correspond to agent environments. Ideally these containers will be recursively nestable or will otherwise support sophisticated definitions of containment.
There is a need to create well defined spatial relationships within agent environments. These relationships should include notions of abstract space (e.g., lattices), physical space (e.g., maps), and connectedness (e.g. networks).
There is a need to easily setup model configurations such as the number of agents; the relationships between agents; the environmental details; and the results to be collected.
There is a need to conveniently collect and analyze model results.

Each of the kinds of programming languages namely, unstructured languages, structured languages, object-oriented languages, logic-based languages, and functional languages can address these requirements.

Unstructured languages generally support procedure definitions which can be used to implement agent behaviors. They also sometimes support the collection of diverse data into independently addressable constructs in the form of data structures often called ‘records’. However, they generally lack support for binding procedures to individual data items or records of data items. This lack of support for creating integrated constructs also typically limits the language-level support for agent containers. Native support for implementing spatial environments is similarly limited by the inability to directly bind procedures to data.
As discussed in the previous section, unstructured languages offer statements to implement execution jumps. The use of jumps within and between procedures tends to reduce module cohesion and increase module coupling compared to structured code. The result is reduced code maintainability and extensibility compared to structured solutions. This is a substantial disadvantage of unstructured languages.

数学代考|计算复杂性理论代写computational complexity theory代考|Domain-Specific Languages

Domain-specific languages (DSL’s) are computer languages that are highly customized to support a well defined application area or ‘domain’. DSL’s commonly include a substantial number of keywords that are nouns and verbs in the area of application as well as overall structures and execution patterns that correspond closely with the application area. DSL’s are intended to allow users to write in a language that is closely aligned with their area of expertise.

DSL’s often gain their focus by losing generality. For many DSL’s there are activities that can be programmed in most computer languages that cannot be programmed in the given DSL. This is consciously done to simplify the DSL’s design and make it easier to learn and use. If a DSL is properly designed then the loss of generality is often inconsequential for most uses since the excluded activities are chosen to be outside the normal range of application. However, even the best designed DSL’s can occasionally be restrictive when the bounds of the language are encountered. Some DSL’s provide special extension points that allow their users to program in a more general language such as C or Java when the limits of the DSL are reached. This feature is extremely useful, but requires more sophistication on the part of the user in that they need to know and simultaneously use both the DSL and the general language.

DSL’s have the potential to implement specific features to support ‘design patterns’ within a given domain. Design patterns form a “common vocabulary” describing tried and true solutions for commonly faced software design problems (Coplien [6]). Software design patterns were popularized by Gamma et al. [13]. North and Macal [29] describe three design patterns for agent-based modeling itself.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Types of Computer Languages

“计算机语言”是一种记录计算机指令的方法。“计算机编程语言”或“编程语言”是计算机语言的一个重要类别。编程语言是一种允许表达任何可计算活动的计算机语言。本文重点关注计算机编程语言，而不是更通用的计算机语言，因为几乎所有基于代理的建模系统都需要编程语言的强大功能。在提及计算机编程语言时，本文有时会使用更简单的术语“计算机语言”。根据 Watson [47]：
编程语言用于描述算法，即导致

问题的解决方案……编程语言可以被认为是一种“符号”，可以用来精确地指定算法。
Watson [47] 继续说“编程语言可以大致分为四组：命令式语言、函数式语言、逻辑编程语言等”。Watson [47] 指出，在命令式语言中“存在对赋值操作和实现为计算机内存位置的变量的基本潜在依赖，其内容可以被读取和更改”。然而，“在函数式语言（有时称为应用程序语言）中，基本操作是函数应用程序”[47]。Watson 以 LISP 为例。Watson [47] 继续指出“在逻辑编程语言中，程序员只需要以某种形式提供问题规范，因为推断解决方法是语言系统的责任”。

大多数函数式语言、许多逻辑编程语言和一些命令式语言的一个有用特性是高阶编程。根据 Reynolds [35]：
类似于数学逻辑，如果过程或标签可以作为数据出现，即如果这些实体可以用作过程的参数，作为函数的结果，我们将说编程语言是高阶的，或作为可分配变量的值。不是高阶语言将被称为一阶语言。
Watson [47] 提出“对编程语言进行分组的另一种方法是将它们分类为过程性或声明性语言”。详细说明，Watson [47] 指出：
过程语言……是那些程序的动作由程序员定义的一系列操作定义的语言。为了解决一个问题，程序员必须指定一系列按顺序执行的步骤（或语句）。

数学代考|计算复杂性理论代写computational complexity theory代考|Requirements of Computer Languages for Agent-Based Modeling

基于代理的建模和仿真对计算机语言的要求包括：

需要创建与代理相对应的定义良好的模块。这些模块应该将代理状态数据和代理行为绑定到集成的独立可寻址结构中。理想情况下，这些 mod-

规则将足够灵活，可以随着时间的推移改变结构，并可选择允许模糊边界来实现超越方法论个人主义的模型[20]。

需要创建与代理环境相对应的定义良好的容器。理想情况下，这些容器将是递归可嵌套的，或者将支持复杂的包含定义。
需要在代理环境中创建明确定义的空间关系。这些关系应该包括抽象空间（例如格子）、物理空间（例如地图）和连通性（例如网络）的概念。
需要轻松设置模型配置，例如代理数量；代理人之间的关系；环境细节；以及要收集的结果。
需要方便地收集和分析模型结果。

每种编程语言，即非结构化语言、结构化语言、面向对象语言、基于逻辑的语言和函数式语言都可以满足这些要求。

非结构化语言通常支持可用于实现代理行为的过程定义。它们有时还支持以通常称为“记录”的数据结构形式将各种数据收集到可独立寻址的结构中。但是，它们通常缺乏对将过程绑定到单个数据项或数据项记录的支持。缺乏对创建集成构造的支持通常也限制了对代理容器的语言级支持。对实现空间环境的本机支持同样受到无法将过程直接绑定到数据的限制。
如上一节所述，非结构化语言提供语句来实现执行跳转。与结构化代码相比，在过程内部和过程之间使用跳转往往会降低模块内聚并增加模块耦合。与结构化解决方案相比，结果是降低了代码的可维护性和可扩展性。这是非结构化语言的一大缺点。

数学代考|计算复杂性理论代写computational complexity theory代考|Domain-Specific Languages

领域特定语言 (DSL) 是高度定制以支持明确定义的应用领域或“领域”的计算机语言。DSL 通常包括应用领域中大量的名词和动词关键字，以及与应用领域密切对应的整体结构和执行模式。DSL 旨在允许用户使用与其专业领域密切相关的语言进行编写。

DSL 经常通过失去通用性来获得他们的关注。对于许多 DSL，有一些活动可以用大多数计算机语言进行编程，而这些活动不能用给定的 DSL 进行编程。有意识地这样做是为了简化 DSL 的设计并使其更易于学习和使用。如果 DSL 设计得当，那么对于大多数用途来说，一般性的损失通常是无关紧要的，因为被排除的活动被选择在正常的应用范围之外。然而，即使是设计最好的 DSL 有时也会在遇到语言边界时受到限制。一些 DSL 提供了特殊的扩展点，允许用户在达到 DSL 的限制时使用更通用的语言（例如 C 或 Java）进行编程。这个功能非常有用，

DSL 有可能实现特定功能以支持给定域内的“设计模式”。设计模式形成了一个“通用词汇”，描述了针对常见软件设计问题的经过验证的真实解决方案（Coplien [6]）。Gamma 等人推广了软件设计模式。[13]。North 和 Macal [29] 描述了基于代理的建模本身的三种设计模式。

数学代考|计算复杂性理论代写computatiknal complexity theory代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|Adaptation and Learning in Agent-Based Models

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|Adaptation and Learning in Agent-Based Models

Adaptation and Learning in Agent-Based Models Biologists consider adaptation to be an essential part of the process of evolutionary change. Adaptation occurs at two levels: the individual level and the population level. In parallel with these notions, agents in an ABM adapt by changing their individual behaviors or by changing their proportional representation in the population. Agents adapt their behaviors at the individual level through learning from experience in their modeled environment.

With respect to agent-based modeling, theories of learning by individual agents or collectives of agents, as well as algorithms for how to model learning, become important. Machine learning is a field consisting of algorithms for recognizing patterns in data (such as data mining) through techniques such as supervised learning, unsupervised learning and reinforcement learning [3,10]. Genetic algorithms [34] and related techniques such as learning classifier systems [38] are commonly used to represent agent learning in agent-based models. In $\mathrm{ABM}$ applications, agents learn through interactions with the simulated environment in which they are embedded as the simulation precedes through time, and agents modify their behaviors accordingly.

Agents may also adapt collectively at the population level. Those agents having behavioral rules better suited to their environments survive and thrive, and those agents not so well suited are gradually eliminated from the population.

数学代考|计算复杂性理论代写computational complexity theory代考|Future Directions

Agent-based modeling continues to be inspired by ALife in the fundamental questions it is trying to answer, in the algorithms that it employs to model agent behaviors and

solve agent-based models, and in the computational architectures that are employed to implement agent-based models. The future of the fields of both ALife and ABM will continue to be intertwined in essential ways in the coming years.

Computational advances will continue at an ever-increasing pace, opening new vistas for computational possibilities in terms of expanding the scale of models that are possible. Computational advances will take several forms, including advances in computer hardware including new chip designs, multi-core processors, and advanced integrated hardware architectures. Software that take advantage of these designs and in particular computational algorithms and modeling techniques and approaches will continue to provide opportunities for advancing the scale of applications and allow more features to be included in agent-based models as well as ALife applications. These will be opportunities for advancing applications of ABM to ALife in both the realms of scientific research and in policy analysis.

Real-world optimization problems routinely solved by business and industry will continue to be solved by ALifeinspired algorithms. The use of ALife-inspired agentbased algorithms for solving optimization problems will become more widespread because of their natural implementation and ability to handle ill-defined problems.
Emergence is a key theme of ALife. ABM offers the capability to model the emergence of order in a variety of complex and complex adaptive systems. Inspired by ALife, identifying the fundamental mechanisms responsible for higher order emergence and exploring these with agentbased modeling will be an important and promising research area.

Advancing social sciences beyond the genotype/ phenotype framework to address the generative nature of social systems in their full complexity is a requirement for advancing computational social models. Recent work has treated culture as a fluid and dynamic process subject to interpretation of individual agents, more complex in many ways than that provided by the genotype/phenotype framework.

Agent-based modeling will continue to be the avenue for exploring new constructs in ALife. If true artificial life is ever developed in silico, it will most likely be done using the methods and tools of agent-based modeling.

数学代考|计算复杂性理论代写computational complexity theory代考|Primary Literature

Adami C (1998) Introduction to Artificial Life. TELOS, Santa Clara

Alber MS, Kiskowski MA, Glazier JA, Jiang Y (2003) On Cellular Automaton Approaches to Modeling Biological Cells. In: Rosenthal J, Gilliam DS (eds) Mathematical Systems Theory in Biology, Communication, and Finance, IMA Volume. Springer, New York, pp 1-39
Alpaydın $E$ (2004) Introduction to Machine Learning. MIT Press, Cambridge
Axelrod R (1984) The Evolution of Cooperation. Basic Books, New York
Axelrod R (1997) The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. Princeton University Press, Princeton
Azzedine B, Renato BM, Kathia Rப, Joao Bosco MS, Mirela SMAN (2007) An Agent Based and Biological Inspired RealTime Intrusion Detection and Security Model for Computer Network Operations. Comp Commun 30(13):2649-2660
Back T (1996) Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, New York
Berlekamp ER, Conway JH, Guy RK (2003) Winning Ways for Your Mathematical Plays, 2nd edn. AK Peters, Natick
Bernaschi $M$, Castiglione $F$ (2001) Design and Implementation of an Immune System Simulator, Computers in Biology and Medicine 31(5):303-331
Bishop CM (2007) Pattern Recognition and Machine Learning. Springer, New York
Bobashev GV, Goedecke DM, Yu F, Epstein JM (2007) A Hybrid Epidemic Model: Combining the Advantages of Agent-Based and Equation-Based Approaches. In: Henderson SG, Biller B, Hsieh M-H, Shortle J, Tew JD, Barton RR (eds) Proc. 2007 Winter Simulation Conference, Washington, pp 1532-1537
Bonabeau $E$ (1997) From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation. Artif Life 3:191-211
Bonabeau E, Dorigo M, Theraulaz G (1999) Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, New York
Carley KM, Fridsma DB, Casman E, Yahja A, Altman N, Chen LC, Kaminsky B, Nave D (2006) Biowar: Scalable Agent-Based Model of Bioattacks. IEEE Trans Syst Man Cybern Part A: Syst Hum 36(2):252-265
Celada F, Seiden PE (1992) A Computer Model of Cellular Interactions in the Immune System. Immunol Today 13(2):56-62
Clerc M (2006) Particle Swarm Optimization. ISTE Publishing Company, London
Dawkins R (1989) The Selfish Gene, 2nd edn. Oxford University Press, Oxford
DeAngelis DL, Gross $\sqcup$ (eds) (1992) Individual-Based Models and Approaches in Ecology: Populations, Communities and Ecosystems. Proceedings of a Symposium/Workshop, Knoxville, 16-19 May 1990. Chapman \& Hall, New York. ISBN $0-412-03171-X$
Dorigo M, Stūtzle T (2004) Ant Colony Optimization. MIT Press, Cambridge
Dreyfus HL (1979) What Computers Can’t Do: The Limits of Artificial Intelligence. Harper \& Row, New York
Eiben $A E$, Smith JE (2007) Introduction to Evolutionary Computing, 2nd edn. Springer, New York
Eigen M, Schuster P (1979) The Hypercycle: A Principle of Natural Self-Organization. Springer, Berlin

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Adaptation and Learning in Agent-Based Models

基于代理的模型中的适应和学习生物学家认为适应是进化变化过程的重要组成部分。适应发生在两个层面：个体层面和群体层面。与这些概念并行的是，ABM 中的代理人通过改变他们的个人行为或通过改变他们在人口中的比例代表来适应。代理通过从其建模环境中的经验中学习来调整他们的个人行为。

对于基于代理的建模，个体代理或代理集体的学习理论以及如何对学习进行建模的算法变得很重要。机器学习是一个由算法组成的领域，用于通过监督学习、无监督学习和强化学习等技术识别数据中的模式（如数据挖掘）[3,10]。遗传算法 [34] 和学习分类器系统 [38] 等相关技术通常用于表示基于代理的模型中的代理学习。在一种乙米在应用程序中，代理通过与嵌入它们的模拟环境的交互来学习，因为模拟随着时间的推移而进行，并且代理相应地修改它们的行为。

代理人也可以在人口水平上集体适应。那些具有更适合其环境的行为规则的智能体生存并茁壮成长，而那些不太适合的智能体则逐渐从人群中淘汰。

数学代考|计算复杂性理论代写computational complexity theory代考|Future Directions

基于代理的建模继续受到 ALife 的启发，在它试图回答的基本问题中，在它用来模拟代理行为的算法和

解决基于代理的模型，以及用于实现基于代理的模型的计算架构。ALife 和 ABM 领域的未来将在未来几年继续以重要的方式交织在一起。

计算的进步将以越来越快的速度继续发展，在扩大可能的模型规模方面为计算可能性开辟新的前景。计算进步将采取多种形式，包括计算机硬件的进步，包括新芯片设计、多核处理器和先进的集成硬件架构。利用这些设计，特别是计算算法和建模技术和方法的软件将继续为提升应用程序的规模提供机会，并允许在基于代理的模型以及 ALife 应用程序中包含更多功能。这些将是推动 ABM 在科学研究和政策分析领域应用到 ALife 的机会。

商业和行业常规解决的实际优化问题将继续由 ALife 启发算法解决。使用受 ALife 启发的基于代理的算法来解决优化问题将变得更加普遍，因为它们的自然实现和处理不明确问题的能力。
Emergence 是 ALife 的一个重要主题。ABM 提供了对各种复杂和复杂自适应系统中出现的秩序进行建模的能力。受 ALife 的启发，识别导致高阶出现的基本机制并使用基于代理的建模来探索这些机制将是一个重要且有前途的研究领域。

推动社会科学超越基因型/表型框架，以解决社会系统在其完全复杂性中的生成性质，是推进计算社会模型的必要条件。最近的工作将文化视为一个流动和动态的过程，受个体代理的解释，在许多方面比基因型/表型框架提供的更复杂。

基于代理的建模将继续成为探索 ALife 新结构的途径。如果真正的人造生命是在计算机上开发出来的，那很可能会使用基于代理的建模方法和工具来完成。

数学代考|计算复杂性理论代写computational complexity theory代考|Primary Literature

Adami C (1998) 人工生命导论。TELOS, 圣克拉拉

Alber MS、Kiskowski MA、Glazier JA、Jiang Y（2003 年）关于对生物细胞建模的元胞自动机方法。在：Rosenthal J，Gilliam DS（编辑）生物学、通信和金融中的数学系统理论，IMA 卷。施普林格，纽约，第 1-39 页
高山和(2004) 机器学习简介。麻省理工学院出版社，剑桥
Axelrod R (1984) 合作的演变。基础书籍，纽约
Axelrod R (1997) 合作的复杂性：基于代理的竞争和合作模型。普林斯顿大学出版社，普林斯顿
Azzedine B、Renato BM、Kathia Rப、Joao Bosco MS、Mirela SMAN (2007) 一种基于代理和受生物启发的计算机网络操作实时入侵检测和安全模型。比较通信 30(13):2649-2660
Back T (1996) 理论与实践中的进化算法：进化策略、进化规划、遗传算法。牛津大学出版社，纽约
Berlekamp ER、Conway JH、Guy RK（2003 年）为您的数学游戏赢得胜利，第 2 版。AK 彼得斯，内蒂克
贝尔纳斯基米, 卡斯蒂廖内F(2001) 免疫系统模拟器的设计和实现，生物学和医学计算机 31(5):303-331
Bishop CM (2007) 模式识别和机器学习。纽约斯普林格
Bobashev GV, Goedecke DM, Yu F, Epstein JM (2007) 混合流行病模型：结合基于代理和基于方程的方法的优势。在：Henderson SG、Biller B、Hsieh MH、Shortle J、Tew JD、Barton RR (eds) Proc。2007 年冬季模拟会议，华盛顿，第 1532-1537 页
博纳博和(1997) 从形态发生的经典模型到基于代理的模式形成模型。人工生活 3:191-211
Bonabeau E、Dorigo M、Theraulaz G (1999) 群体智能：从自然系统到人工系统。牛津大学出版社，纽约
Carley KM, Fridsma DB, Casman E, Yahja A, Altman N, Chen LC, Kaminsky B, Nave D (2006) Biowar: Scalable Agent-Based Model of Bioattacks。IEEE Trans Syst Man Cybern Part A: Syst Hum 36(2):252-265
Celada F, Seiden PE (1992) 免疫系统中细胞相互作用的计算机模型。今日免疫学 13(2):56-62
Clerc M (2006) 粒子群优化。ISTE 出版公司，伦敦
Dawkins R (1989) 自私的基因，第二版。牛津大学出版社，牛津
DeAngelis DL，毛⊔(eds) (1992) 基于个体的生态模型和方法：人口、社区和生态系统。研讨会/研讨会论文集，诺克斯维尔，1990 年 5 月 16 日至 19 日。Chapman \& Hall，纽约。国际标准书号0−412−03171−X
Dorigo M, Stūtzle T (2004) 蚁群优化。麻省理工学院出版社，剑桥
Dreyfus HL (1979) 计算机不能做什么：人工智能的极限。哈珀\&罗，纽约
紫杉树一种和, Smith JE (2007) 进化计算导论，第 2 版。纽约斯普林格
Eigen M, Schuster P (1979) 超循环：自然自组织的原理。施普林格，柏林

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非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

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MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|ALife Summary

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|ALife Summary

Based on the previous discussion, the essential features of an ALife program can be summarized as follows:

Population: A population of organisms or individuals is considered. The population may be diversified, and individuals may vary their characteristics, behaviors, and accumulated resources, in both time and space.
Interaction: Interaction requires sensing of the immediate locale, or neighborhood, on the part of an individual. An organism can simply become “aware” of other organisms in its vicinity or it may have a richer set of interactions with them. The individual also interacts with its (non-agent) environment in its immediate locale. This requirement introduces spatial aspects into the problem, as organisms must negotiate the search for resources through time and space.
Sustainment and renewal: Sustainment and renewal requires the acquisition of resources. An organism needs to sense, find, ingest, and metabolize resources, or nourishment as an energy source for processing into other forms of nutrients. Resources may be provided by the environment, i. e., outside of the agents themselves, or by other agents. The need for sustainment leads to competition for resources among organisms. Competition could also be a precursor to cooperation and more complex emergent social structures if this proves to be a more effective strategy for survival.
Self-reproduction and replacement: Organisms reproduce by following instructions at least partially embedded within themselves and interacting with the environment and other agents. Passing on traits to the next generation implies a requirement for trait transmission. Trait transmission requires encoding an organism’s traits in a reduced form, that is, a form that contains less than the total information representing the entire organism. It also requires a process for transforming the organism’s traits into a viable set of possible new traits for a new organism. Mutation and crossover operators enter into such a process. Organ-

isms also leave the population and are replaced by other organisms, possibly with different traits. The organisms can be transformed through changes in their attributes and behaviors, as in, for example, learning or aging. The populations of organisms can be transformed through the introduction of new organisms and replacement, as in evolutionary adaptation.

As we will see in the section that follows, many of the essential aspects of ALife have been incorporated into the development of agent-based models.

数学代考|计算复杂性理论代写computational complexity theory代考|Agent-Based Modeling Topologies

Agent-based modeling owes much to artificial life in both form and substance. Modeling a population of heterogeneous agents with a diverse set of characteristics is a hallmark of agent-based modeling. The agent perspective is unique among simulation approaches, unlike the process perspective or the state-variable approach taken by other simulation approaches.

As we have seen, agents interact with a small set of neighbor agents in a local area. Agent neighborhoods are defined by how agents are connected, the agent interaction topology. Cellular automata represent agent neighborhoods by using a grid in which the agents exist in the cells, one agent per cell, or as the nodes of the lattice of the grid. The cells immediately surrounding an agent comprise the agent’s neighborhood and the agents that reside in the neighborhood cells comprise the neighbors. Many agent-based models have been based on this cellular automata spatial representation. The transition from a cellular automata, such as the game of Life, to an agent-based model is accomplished by allowing agents to be distinct from the cells on which they reside and allowing the agents to move from cell to cell across the grid. Agents move according to the dictates of their behaviors, interacting with other agents that happen to be in their local neighborhoods along the way.

Agent interaction topologies have been extended beyond cellular automata to include networks, either pre-

defined and static as in the case of autocatalytic chemical networks, or endogenous and dynamic, according to the results of agent interactions that occur in the model. Networks allow an agent’s neighborhood to be defined more generally and flexibly, and in the case of social agents, more accurately describe social agents’ interaction patterns. In addition to cellular automata grids and networks, agent interaction topologies have also been extended across a variety of domains. In summary, agent interaction topologies include:

Cellular automata grids (agents are cells or are within in cells) or lattices (agents are grid points),
Networks, in which agents of vertices and agent relationships are edges,
Continuous space, in one, two or three dimensions;
Aspatial random interactions, in which pairs of agents are randomly selected; and
Geographical Information Systems (GIS), in which agents move over geographically-defined patches, relaxing the one-agent per cell restriction.

数学代考|计算复杂性理论代写computational complexity theory代考|Social Agent-Based Modeling

Early social agent-based models were based on ALife’s cellular automata approach. In applications of agent-based modeling to social processes, agents represent people or groups of people, and agent relationships represent processes of social interaction [33].

Social Agents Sakoda [61] formulated one of the first social agent-based models, the Checkerboard Model, which had some of the key features of a cellular automaton. Following a similar approach, Schelling developed a model of housing segregation in which agents represent homeowners and neighbors, and agent interactions represent agents’ perceptions of their neighbors [62]. Schelling studied housing segregation patterns and posed the question of whether it is it possible to get highly segregated settlement patterns even if most individuals are, in fact, “colorblind? The Schelling model demonstrated that segregated housing areas can develop spontaneously in the sense that system-level patterns can emerge that are not necessarily implied by or consistent with the objectives of the individual agents (Fig. 6). In the model, agents operated according to a fixed set of rules and were not adaptive.

Identifying the social interaction mechanisms for how cooperative behavior emerges among individuals and groups has been addressed using agent-based modeling and evolutionary game theory. Evolutionary game theory accounts for how the repeated interactions of players in a game-theoretic framework affect the development and evolution of the players’ strategies. Axelrod showed, using a cellular automata approach, in which agents on the grid employed a variety of different strategies, that a simple TitFor-Tat strategy of reciprocal behavior toward individuals is enough to establish sustainable cooperative behavior $[4,5]$. In addition, Axelrod investigated strategies that

were self-sustaining and robust in that they reduced the possibility of invasion by agents having other strategies.
Epstein and Axtell introduced the notion of an external environment that agents interact with in addition to other agents. In their groundbreaking Sugarscape model of artificial societies, agents interacted with their environment depending on their location in the grid [26]. This allowed agents to access environmental variables, extract resources, etc., based on location. In numerous computational experiments, Sugarscape agents emerged with a variety of characteristics and behaviors, highly suggestive of a realistic, although rudimentary and abstract, society (Fig. 7). They observed emergent processes that they interpreted as death, disease, trade, wealth, sex and reproduction, culture, conflict and war, as well as externalities such as pollution. As agents interacted with their neighbors as they moved around the grid, the interactions resulted in a contact network, that is, a network consisting of nodes and links. The nodes are agents and the links indicate the agents that have been neighbors at some point in the course of their movements over the grid. Contact networks were the basis for studying contagion and epidemics in the Sugarscape model. Understanding the agent rules that govern how networks are structured and grow, how quickly information is communicated through networks, and the kinds of relationships that networks embody are important aspects of modeling agents.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|ALife Summary

基于前面的讨论，ALife 程序的基本特征可以总结如下：

种群：考虑生物体或个体的种群。人口可能是多样化的，个人可能会在时间和空间上改变他们的特征、行为和积累的资源。
交互：交互需要感知个人的直接区域或邻域。一个有机体可以简单地“意识到”它附近的其他有机体，或者它可能与它们有更丰富的相互作用。个人还在其直接区域中与其（非代理）环境进行交互。这一要求将空间方面引入了问题，因为生物必须通过时间和空间来协商寻找资源。
维持和更新：维持和更新需要获取资源。有机体需要感知、发现、摄取和代谢资源，或将营养物作为能量来源，以加工成其他形式的营养物。资源可以由环境提供，即在代理本身之外，或由其他代理提供。维持的需要导致生物之间对资源的竞争。如果证明是一种更有效的生存策略，竞争也可能是合作和更复杂的新兴社会结构的前兆。
自我繁殖和替换：生物通过遵循至少部分嵌入自身的指令并与环境和其他代理相互作用进行繁殖。将性状传递给下一代意味着对性状传递的要求。特征传递需要以简化形式编码有机体的特征，即包含少于代表整个有机体的全部信息的形式。它还需要一个将有机体的特征转化为新有机体的一组可行的新特征的过程。突变和交叉算子进入这样的过程。器官-

主义也离开人口并被其他生物取代，可能具有不同的特征。有机体可以通过其属性和行为的变化来改变，例如学习或衰老。有机体的种群可以通过引入新的有机体和替换来改变，就像在进化适应中一样。

正如我们将在接下来的部分中看到的，ALife 的许多基本方面已被纳入基于代理的模型的开发中。

数学代考|计算复杂性理论代写computational complexity theory代考|Agent-Based Modeling Topologies

基于代理的建模很大程度上归功于形式和实质上的人造生命。对具有多种特征的异构代理群体进行建模是基于代理的建模的标志。代理视角在模拟方法中是独一无二的，与其他模拟方法所采用的过程视角或状态变量方法不同。

正如我们所看到的，代理与本地区域中的一小组相邻代理进行交互。代理邻域由代理如何连接、代理交互拓扑定义。元胞自动机通过使用一个网格来表示代理邻域，其中代理存在于单元中，每个单元一个代理，或者作为网格点阵的节点。直接围绕代理的单元包括代理的邻域，并且驻留在邻域单元中的代理包括邻居。许多基于代理的模型都基于这种元胞自动机空间表示。从元胞自动机（例如生命游戏）到基于代理的模型的过渡是通过允许代理与其所在的单元不同并允许代理在网格中从一个单元移动到另一个单元来完成的。

代理交互拓扑已经扩展到元胞自动机之外，包括网络，无论是预

根据模型中发生的代理相互作用的结果，定义和静态的，如自催化化学网络的情况，或内生的和动态的。网络允许更广泛和灵活地定义代理的邻域，并且在社交代理的情况下，更准确地描述社交代理的交互模式。除了元胞自动机网格和网络之外，代理交互拓扑也已扩展到各种领域。总之，代理交互拓扑包括：

元胞自动机网格（代理是细胞或在细胞内）或格子（代理是网格点），
网络，其中顶点的代理和代理关系是边，
连续空间，一维、二维或三维；
空间随机交互，其中随机选择代理对；和
地理信息系统 (GIS)，其中代理在地理定义的块上移动，放宽了每个单元一个代理的限制。

数学代考|计算复杂性理论代写computational complexity theory代考|Social Agent-Based Modeling

早期的基于社交代理的模型基于 ALife 的元胞自动机方法。在将基于代理的建模应用于社会过程中，代理代表人或人群，代理关系代表社会互动的过程[33]。

社交代理 Sakoda [61] 制定了第一个基于社交代理的模型，即棋盘模型，它具有元胞自动机的一些关键特征。遵循类似的方法，谢林开发了一种住房隔离模型，其中代理人代表房主和邻居，代理人互动代表代理人对其邻居的看法[62]。谢林研究了住房隔离模式并提出了一个问题，即即使大多数人实际上是“色盲”，是否有可能获得高度隔离的居住模式？Schelling 模型表明，隔离住宅区可以自发发展，因为系统级模式可能会出现，这些模式不一定由个体代理人的目标暗示或与个体目标一致（图 6）。在模型中，

使用基于代理的建模和进化博弈论已经解决了识别个人和群体之间如何出现合作行为的社会互动机制。进化博弈论解释了博弈论框架中参与者的重复交互如何影响参与者策略的发展和演变。Axelrod 表明，使用元胞自动机方法，其中网格上的代理采用各种不同的策略，一个简单的针对个人的互惠行为的 TitFor-Tat 策略足以建立可持续的合作行为[4,5]. 此外，Axelrod 还研究了以下策略：

是自我维持和强大的，因为它们减少了具有其他策略的特工入侵的可能性。
Epstein 和 Axtell 引入了代理与其他代理交互的外部环境的概念。在他们开创性的人工社会 Sugarscape 模型中，代理根据其在网格中的位置与环境进行交互 [26]。这允许代理根据位置访问环境变量、提取资源等。在众多的计算实验中，Sugarscape 代理出现了具有各种特征和行为的各种特征和行为，高度暗示了一个现实的社会，尽管是基本的和抽象的社会（图 7）。他们观察到了被他们解释为死亡、疾病、贸易、财富、性和繁殖、文化、冲突和战争的紧急过程，以及污染等外部因素。当代理在网格周围移动时与他们的邻居互动时，这些交互产生了一个联系网络，即一个由节点和链接组成的网络。节点是代理，链接指示代理在其在网格上的移动过程中的某个时间点是邻居。联系网络是在 Sugarscape 模型中研究传染和流行病的基础。了解管理网络如何构建和增长的代理规则、信息通过网络传递的速度以及网络体现的关系类型是建模代理的重要方面。联系网络是在 Sugarscape 模型中研究传染和流行病的基础。了解控制网络如何构建和增长的代理规则、信息通过网络传递的速度以及网络体现的关系类型是建模代理的重要方面。联系网络是在 Sugarscape 模型中研究传染和流行病的基础。了解控制网络如何构建和增长的代理规则、信息通过网络传递的速度以及网络体现的关系类型是建模代理的重要方面。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|ALife and Computing

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|ALife and Computing

Creating life-like forms through computation is central to Artificial Life. Is it possible to create life through computation? The capabilities and limitations of computation constrain the types of artificial life that can be created. The history of ALife has close ties with important events in the history of computation.

Alan Turing [65] investigated the limitations of computation by developing an abstract and idealized computer, called a Universal Turing Machine (UTM). A UTM has an infinite tape (memory) and is therefore an idealization of any actual computer that may be realized. A UTM is capable of computing anything that is computable, that is, anything that can be derived via a logical, deductive series of statements. Are the algorithms used in today’s computers, and in ALife calculations and agent-based models in particular, as powerful as universal computers?

Any system that can effectively simulate a small set of logical operations (such as AND and NOT) can effectively produce any possible computation. Simple rule systems in cellular automata were shown to be equivalent to universal computers $[67,72]$, and in principal able to compute anything that is computable – perhaps, even life!

Some have argued that life, in particular human consciousness, is not the result of a logical-deductive or algorithmic process and therefore not computable by a Universal Turing Machine. This problem is more generally referred to as the mind-body problem [48]. Dreyfus [20] argues against the assumption often made in the field of artificial intelligence that human minds function like general purpose symbol manipulation machines. Penrose [56] argues that the rational processes of the human mind transcend formal logic systems. In a somewhat different view, biological naturalism contends [63] that human behavior might be able to be simulated, but human consciousness is outside the bounds of computation.

Such philosophical debates are as relevant to agentbased modeling as they are to artificial intelligence, for they are the basis of answering the question of what kind of systems and processes agent-based models will ultimately be able, or unable, to simulate.

数学代考|计算复杂性理论代写computational complexity theory代考|Artificial Life Algorithms

ALife use several biologically-inspired computational algorithms [53]. Bioinspired algorithms include those based on Darwinian evolution, such as evolutionary algorithms,

those based on neural structures, such as neural networks, and those based on decentralized decision making behaviors observed in nature. These algorithms are commonly used to model adaptation and learning in agent-based modeling or to optimize the behaviors of whole systems.
Evolutionary Computing Evolutionary computing includes a family of related algorithms and programming solution techniques inspired by evolutionary processes, especially the genetic processes of DNA replication and cell division [21]. These techniques are known as evolutionary algorithms and include the following [7]:

Genetic algorithms $[34,35,36,38,51]$
Evolution strategies [60]
Learning classifier systems [38]
Genetic programming [40]
Evolutionary programming [28]
Genetic algorithms (GA) model the dynamic processes by which populations of individuals evolve to improved levels of fitness for their particular environment over repeated generations. GAs illustrate how evolutionary algorithms process a population and apply the genetic operations of mutation and crossover (see Fig. 5). Each behavior is represented as a chromosome consisting of a series of symbols, for example, as a series of 0 s and 1 s. The encoding process establishing correspondence between behaviors and their chromosomal representations is part of the modeling process.

The general steps in a genetic algorithm are as follows:

Initialization: Generate an initial population of individuals. The individuals are unique and include specific encoding of attributes in chromosomes that represents the characteristics of the individuals.
Evaluation: Calculate the fitness of all individuals according to a specified fitness function.
Checking: If any of the individuals has achieved an acceptable level of fitness, stop, the problem is solved. Otherwise, continue with selection.
Selection: Select the best pair of individuals in the population for reproduction according to their high fitness levels.
Crossover: Combine the chromosomes for the two best individuals through a crossover operation and produce a pair of offspring.
Mutation: Randomly mutate the chromosomes for the offspring.
Replacement: Replace the least fit individuals in the population with the offspring.
Continue at Step 2

数学代考|计算复杂性理论代写computational complexity theory代考|Biologically Inspired Computing

Biologically Inspired Computing Artificial neural networks (ANN) are another type of commonly used biologically inspired algorithm [50]. An artificial neural network uses mathematical models based on the structures observed in neural systems. An artificial neuron contains a stimulus-response model of neuron activation based on thresholds of stimulation. In modeling terms, neural networks are equivalent to nonlinear, statistical data modeling techniques. Artificial neural networks can be used to model complex relationships between inputs and outputs and to find patterns in data that are dynamically changing. An ANN is adaptive in that changes in its structure are based on external or internal information that flows through the network. The adaptive capability makes ANN an important technique in agent-based models.

Swarm intelligence refers to problem solving techniques, usually applied to solving optimization problems that are based on decentralized problem solving strategies that have been observed in nature. These include:

Ant colony optimization [19].
Particle swarm optimization [16].
Swarm intelligence algorithms simulate the movement and interactions of large numbers of ants or particles over a search space. In terms of agent-based modeling, the ants or particles are the agents, and the search space is the environment. Agents have position and state as attributes. In the case of particle swarm optimization, agents also have velocity.

Ant colony optimization (ACO) mimics techniques that ants use to forage and find food efficiently $[13,24]$. The general idea of ant colony optimization algorithms is as follows:

In a typical ant colony, ants search randomly until one of them finds food.
Then they return to their colony and lay down a chemical pheromone trail along the way.
When other ants find such a pheromone trail, they are more likely to follow the trail rather than to continue to search randomly.
As other ants find the same food source, they return to the nest, reinforcing the original pheromone trail as they return.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|ALife and Computing

通过计算创造类似生命的形式是人工生命的核心。是否有可能通过计算创造生命？计算的能力和局限性限制了可以创造的人造生命的类型。ALife 的历史与计算史上的重要事件有着密切的联系。

Alan Turing [65] 通过开发一种称为通用图灵机 (UTM) 的抽象和理想化计算机来研究计算的局限性。UTM 具有无限的磁带（内存），因此是可以实现的任何实际计算机的理想化。UTM 能够计算任何可计算的东西，也就是说，任何可以通过逻辑、演绎的语句系列推导出的东西。当今计算机中使用的算法，特别是在 ALife 计算和基于代理的模型中使用的算法，是否与通用计算机一样强大？

任何可以有效模拟一小组逻辑运算（例如 AND 和 NOT）的系统都可以有效地产生任何可能的计算。元胞自动机中的简单规则系统被证明等同于通用计算机[67,72]，并且原则上能够计算任何可计算的东西——也许，甚至是生命！

一些人认为，生命，尤其是人类意识，不是逻辑演绎或算法过程的结果，因此无法由通用图灵机计算。这个问题通常被称为身心问题[48]。Dreyfus [20] 反对人工智能领域经常做出的假设，即人类思维的功能类似于通用符号操作机器。Penrose [56] 认为，人类思维的理性过程超越了形式逻辑系统。在另一种观点中，生物自然主义认为 [63] 人类行为可能可以被模拟，但人类意识超出了计算的范围。

这种哲学辩论与基于代理的建模和与人工智能一样相关，因为它们是回答基于代理的模型最终能够或无法模拟什么样的系统和流程的问题的基础。

数学代考|计算复杂性理论代写computational complexity theory代考|Artificial Life Algorithms

ALife 使用几种受生物启发的计算算法 [53]。仿生算法包括那些基于达尔文进化论的算法，例如进化算法，

那些基于神经结构的算法，例如神经网络，以及基于自然界观察到的分散决策行为的算法。这些算法通常用于在基于代理的建模中对适应和学习进行建模或优化整个系统的行为。
进化计算进化计算包括一系列受进化过程启发的相关算法和编程解决方案技术，特别是DNA复制和细胞分裂的遗传过程[21]。这些技术被称为进化算法，包括以下 [7]：

遗传算法[34,35,36,38,51]
进化策略 [60]
学习分类系统 [38]
遗传编程 [40]
进化编程 [28]
遗传算法 (GA) 对个体种群在重复世代中进化到提高其特定环境的适应度水平的动态过程进行建模。GA 说明了进化算法如何处理种群并应用变异和交叉的遗传操作（见图 5）。每个行为都表示为由一系列符号组成的染色体，例如一系列 0 和 1。在行为与其染色体表示之间建立对应关系的编码过程是建模过程的一部分。

遗传算法的一般步骤如下：

初始化：生成初始个体群体。个体是独一无二的，并且包括代表个体特征的染色体中属性的特定编码。
评估：根据指定的适应度函数计算所有个体的适应度。
检查：如果任何人的健康水平达到了可接受的水平，停下来，问题就解决了。否则，继续选择。
选择：根据他们的高适应度水平选择种群中最好的一对个体进行繁殖。
交叉：通过交叉操作将两个最佳个体的染色体组合并产生一对后代。
突变：随机突变后代的染色体。
替换：用后代替换种群中最不适合的个体。
继续第 2 步

数学代考|计算复杂性理论代写computational complexity theory代考|Biologically Inspired Computing

仿生计算人工神经网络（ANN）是另一种常用的仿生算法[50]。人工神经网络使用基于神经系统中观察到的结构的数学模型。人工神经元包含基于刺激阈值的神经元激活的刺激反应模型。在建模方面，神经网络相当于非线性的统计数据建模技术。人工神经网络可用于模拟输入和输出之间的复杂关系，并在动态变化的数据中找到模式。ANN 是自适应的，因为其结构的变化基于流经网络的外部或内部信息。自适应能力使 ANN 成为基于代理的模型中的一项重要技术。

群体智能是指解决问题的技术，通常应用于解决基于自然界观察到的分散问题解决策略的优化问题。这些包括：

蚁群优化[19]。
粒子群优化[16]。
群体智能算法模拟大量蚂蚁或粒子在搜索空间中的运动和相互作用。在基于代理的建模方面，蚂蚁或粒子是代理，搜索空间是环境。代理具有位置和状态作为属性。在粒子群优化的情况下，代理也有速度。

蚁群优化 (ACO) 模仿蚂蚁用于有效觅食和寻找食物的技术[13,24]. 蚁群优化算法的总体思路如下：

在典型的蚁群中，蚂蚁随机搜索，直到其中一只找到食物。
然后他们回到他们的殖民地并沿途铺设化学信息素踪迹。
当其他蚂蚁发现这样的信息素踪迹时，它们更有可能跟随踪迹而不是继续随机搜索。
当其他蚂蚁找到相同的食物来源时，它们会返回巢穴，在它们返回时加强原始的信息素踪迹。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Modeling and Artificial Life

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Modeling and Artificial Life

数学代考|计算复杂性理论代写computational complexity theory代考|Definition of the Subject

Agent-based modeling began as the computational arm of artificial life some 20 years ago. Artificial life is concerned with the emergence of order in nature. How do systems self-organize themselves and spontaneously achieve a higher-ordered state? Agent-based modeling then, is concerned with exploring and understanding the processes that lead to the emergence of order through computational means. The essential features of artificial life models are translated into computational algorithms through agent-based modeling. With its historical roots in artificial life, agent-based modeling has become a distinctive form of modeling and simulation. Agent-based modeling is a bottom-up approach to modeling complex systems by explicitly representing the behaviors of large numbers of agents and the processes by which they interact. These essential features are all that is needed to produce at least rudimentary forms of emergent behavior at the systems level. To understand the current state of agent-based modeling and where the field aspires to be in the future, it is necessary to understand the origins of agent-based modeling in artificial life.

数学代考|计算复杂性理论代写computational complexity theory代考|Introduction

The field of Artificial Life, or ${ }^{\alpha}$ ALife, $”$ is intimately connected to Agent-Based Modeling, or “ABM.” Although one can easily enumerate some of life’s distinctive properties, such as reproduction, respiration, adaptation, emergence, etc., a precise definition of life remains elusive.

Artificial Life had its inception as a coherent and sustainable field of investigation at a workshop in the late 1980 s [43]. This workshop drew together specialists from diverse fields who had been working on related problems in different guises, using different vocabularies suited to their fields.

At about the same time, the introduction of the personal computer suddenly made computing accessible, convenient, inexpensive and compelling as an experimental tool. The future seemed to have almost unlimited possibilities for the development of ALife computer programs to explore life and its possibilities. Thus several ALife software programs emerged that sought to encapsulate the essential elements of life through incorporation of ALife-related algorithms into easily usable software packages that could be widely distributed. Computational programs for modeling populations of digital organisms, such as Tierra, Avida, and Echo, were developed along with more general purpose agent-based simulators such as Swarm.

Yet, the purpose of ALife was never restricted to understanding or re-creating life as it exists today. According to Langton:
Artificial systems which exhibit lifelike behaviors are worthy of investigation on their own right, whether or not we think that the processes that they mimic have played a role in the development or mechanics of life as we know it to be. Such systems can help us expand our understanding of life as it could be. (p. xvi in [43])

The field of ALife addresses life-like properties of systems at an abstract level by focusing on the information content of such systems independent of the medium in which they exist, whether it be biological, chemical, physical or in silico. This means that computation, modeling, and simulation play a central role in ALife investigations.

The relationship between ALife and ABM is complex. A case can be made that the emergence of ALife as a field was essential to the creation of agent-based modeling. Computational tools were both required and became possible in the 1980 s for developing sophisticated models of digital organisms and general purpose artificial life simulators. Likewise, a case can be made that the possibility for creating agent-based models was essential to making ALife a promising and productive endeavor. ABM made it possible to understand the logical outcomes and implications of ALife models and life-like processes. Traditional analytical means, although valuable in establishing baseline information, were limited in their capabilities to include essential features of ALife. Many threads of ALife are still intertwined with developments in $\mathrm{ABM}$ and vice verse. Agent-based models demonstrate the emergence of lifelike features using ALife frameworks; ALife algorithms are widely used in agent-based models to represent agent behaviors. These threads are explored in this article. In ALife terminology, one could say that ALife and ABM have $C O-$ evolved to their present states. In all likelihood they will continue to do so.

数学代考|计算复杂性理论代写computational complexity theory代考|Self-Replication and Cellular Automata

Self-Replication and Cellular Automata Artificial Life traces its beginnings to the work of John von Neumann in the 1940 s and investigations into the theoretical possibilities for developing a self-replicating machine [64]. Such a self-replicating machine not only carries instructions for its operations, but also for its replication. The issue concerned how to replicate such a machine that contained the instructions for its operation along with the instructions for its replication. Did a machine to replicate such a machine need to contain both the instructions for the machine’s operation and replication, as well as instructions for replicating the instructions on how to replicate the original machine? (see Fig. 1). Von Neumann used the abstract mathematical construct of cellular automata, originally conceived in discussions with Stanislaw Ulam, to prove that such a machine could be designed, at least in theory. Von Neumann was never able to build such a machine due to the lack of sophisticated computers that existed at the time.

Cellular automata (CA) have been central to the development of computing Artificial Life models. Virtually all of the early agent-based models that required agents to be spatially located were in the form of von Neumann’s original cellular automata. A cellular automata is a finitestate machine in which time and space are treated as discrete rather than continuous, as would be the case, for example in differential equation models. A typical CA is a two-dimensional grid or lattice consisting of cells. Each cell assumes one of a finite number of states at any time. A cell’s neighborhood is the set of cells surrounding a cell, typically, a five-cell neighborhood (von Neumann neighborhood) or a nine-cell neighborhood (Moore neighborhood), as in Fig. $2 .$

A set of simple state transition rules determines the value of each cell based on the cell’s state and the states of neighboring cells. Every cell is updated at each time according to the transition rules. Each cell is identical in terms of its update rules. Cells differ only in their initial states. A CA is deterministic in the sense that the same state for a cell and its set of neighbors always results in the same updated state for the cell. Typically, CAs are set up with periodic boundary conditions, meaning that the set of cells on one edge of the grid boundary are the neighbor cells to the cells on the opposite edge of the grid boundary. The space of the CA grid forms a surface on a toroid, or donut-shape, so there is no boundary per se. It is straightforward to extend the notion of cellular automata to two, three, or more dimensions.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Definition of the Subject

大约 20 年前，基于代理的建模开始作为人工生命的计算臂。人工生命关注的是自然界秩序的出现。系统如何自我组织并自发达到更高的有序状态？那么，基于代理的建模关注的是通过计算手段探索和理解导致秩序出现的过程。通过基于代理的建模将人工生命模型的基本特征转化为计算算法。凭借其在人工生命中的历史渊源，基于代理的建模已成为建模和模拟的一种独特形式。基于代理的建模是一种自下而上的复杂系统建模方法，它通过显式表示大量代理的行为以及它们交互的过程。这些基本特征是在系统层面产生至少基本形式的紧急行为所需要的。要了解基于代理的建模的当前状态以及该领域未来的目标，有必要了解基于代理的建模在人工生命中的起源。

数学代考|计算复杂性理论代写computational complexity theory代考|Introduction

人工生命领域，或一种生命，”与基于代理的建模或“ABM”密切相关。尽管人们可以很容易地列举出生命的一些独特属性，例如繁殖、呼吸、适应、出现等，但对生命的精确定义仍然难以捉摸。

人工生命在 1980 年代后期的一次研讨会上作为一个连贯且可持续的研究领域开始兴起 [43]。本次研讨会汇集了来自不同领域的专家，他们以不同的形式使用适合其领域的不同词汇来解决相关问题。

大约在同一时间，个人计算机的引入突然使计算成为一种易于使用、方便、廉价和引人注目的实验工具。未来似乎拥有开发 ALife 计算机程序以探索生命及其可能性的几乎无限可能。因此，出现了几个 ALife 软件程序，它们试图通过将与 ALife 相关的算法合并到可以广泛分发的易于使用的软件包中来封装生活的基本要素。用于模拟数字生物种群的计算程序（例如 Tierra、Avida 和 Echo）与更通用的基于代理的模拟器（例如 Swarm）一起开发。

然而，ALife 的目的从未局限于理解或重新创造当今存在的生活。根据兰顿的说法：
表现出逼真行为的人工系统本身就值得研究，无论我们是否认为它们模仿的过程在我们所知的生命发展或机制中发挥了作用。这样的系统可以帮助我们扩大对生命的理解。（第 xvi 页，[43]）

ALife 领域通过关注此类系统的信息内容，在抽象层面解决系统的类生命属性，而这些信息内容独立于它们存在的介质，无论是生物、化学、物理还是计算机。这意味着计算、建模和模拟在 ALife 调查中发挥着核心作用。

ALife 和 ABM 之间的关系很复杂。可以证明，ALife 作为一个领域的出现对于创建基于代理的建模至关重要。在 1980 年代，计算工具既是必需的，也是可能的，用于开发复杂的数字生物模型和通用人工生命模拟器。同样，可以证明创建基于代理的模型的可能性对于使 ALife 成为有前途和富有成效的努力至关重要。ABM 使理解 ALife 模型和栩栩如生的过程的逻辑结果和含义成为可能。传统的分析手段，虽然在建立基线信息方面很有价值，但在包含 ALife 基本特征的能力方面受到限制。ALife 的许多主线仍然与一种乙米反之亦然。基于代理的模型使用 ALife 框架展示了栩栩如生的特征的出现；ALife 算法广泛用于基于代理的模型中来表示代理行为。本文探讨了这些线程。在 ALife 术语中，可以说 ALife 和 ABM 具有C这−进化到现在的状态。他们很可能会继续这样做。

数学代考|计算复杂性理论代写computational complexity theory代考|Self-Replication and Cellular Automata

自我复制和元胞自动机人工生命可以追溯到约翰·冯·诺依曼在 1940 年代的工作以及对开发自我复制机器的理论可能性的研究[64]。这样一台自我复制的机器不仅携带着它的操作指令，而且还携带着它的复制指令。问题涉及如何复制这样的机器，该机器包含其操作指令及其复制指令。复制这样一台机器的机器是否需要同时包含机器操作和复制的指令，以及如何复制原始机器的复制指令？（见图 1）。Von Neumann 使用了元胞自动机的抽象数学结构，最初是在与 Stanislaw Ulam 的讨论中构思的，证明可以设计这样的机器，至少在理论上是这样。由于当时缺乏复杂的计算机，冯·诺依曼永远无法制造出这样的机器。

元胞自动机 (CA) 一直是计算人工生命模型开发的核心。几乎所有需要代理在空间上定位的早期基于代理的模型都是冯诺依曼最初的元胞自动机的形式。元胞自动机是一种有限状态机，其中时间和空间被视为离散的而不是连续的，例如在微分方程模型中就是这种情况。典型的 CA 是由单元组成的二维网格或点阵。每个单元在任何时候都假定为有限数量的状态之一。一个单元的邻域是一个单元周围的一组单元，通常是一个五单元邻域（冯诺依曼邻域）或一个九单元邻域（摩尔邻域），如图 1 所示。2.

一组简单的状态转换规则根据单元的状态和相邻单元的状态确定每个单元的值。每个单元格每次都根据转换规则进行更新。每个单元格的更新规则都是相同的。细胞的不同之处仅在于它们的初始状态。CA 是确定性的，即一个小区及其邻居集的相同状态总是导致该小区相同的更新状态。通常，CA 设置有周期性边界条件，这意味着网格边界一个边缘上的一组单元格是网格边界另一边上的单元格的相邻单元格。CA 网格的空间在环形或甜甜圈形状上形成一个表面，因此本身没有边界。将元胞自动机的概念扩展到两个、三个或更多维度是很简单的。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|Full Spectrum of EMB Investors

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|Full Spectrum of EMB Investors

Full Spectrum of EMB Investors Up to this point we have analyzed markets with at most three different subpopulations (one RII population and two EMB populations). The market dynamics we found displayed the empirically observed market anomalies, but they were unrealistic in the magnitude, frequency, and semi-predictability of booms and crashes. In reality, we would expect not only two or three investor types, but rather an entire spectrum of investors. In this section we consider a model with a full spectrum of different EMB investors. It turns out that more is different. When there is an entire range of investors, the price dynamics become realistic: booms and crashes are not periodic or predictable, and they are also less frequent and dramatic. At the same time, we still obtain all of the market anomalies described before.

In this model each investor has a different number of ex-post observations which he utilizes to estimate the exante distribution. Namely, investor $i$ looks at the set of the $m^{i}$ most recent returns on the stock, and we assume that $m^{i}$ is distributed in the population according to a trun-

cated normal distribution with average $\tilde{m}$ and standard deviation $\sigma_{m}$ (as $m \leq 0$ is meaningless, the distribution is truncated at $m=0$ ).

Figure 8 shows the price pattern of a typical simulation of this model. In this simulation $90 \%$ of the investors are RII, and the remaining $10 \%$ are heterogeneous EMB investors with $\bar{m}=40$, and $\sigma_{m}=10$. The price pattern seems very realistic with “smoother” and more irregular cycles. Crashes are dramatic, but infrequent and unpredictable.

The heterogeneous EMB population model generates the following empirically observed market phenomena:
Return Autocorrelation: Momentum and Mean-Reversion In the heterogeneous EMB population model trends are generated by the same positive feedback mechanism that generated cycles in the homogeneous case: high (low) returns tend to make the EMB investors more (less) aggressive, this generates more high (low) returns, etc. The difference between the two cases is that in the heterogeneous case there is a very complicated interaction between all the different investor sub-populations and as a result there are no distinct regular cycles, but rather, smoother and more irregular trends. There is no single cycle length the dynamics are a combination of many different cycles. This makes the autocorrelation pattern also smoother and more continuous. The return autocorrelations in the heterogeneous model are shown in Fig. 9. This autocorrelation pattern conforms with the empirical findings. In the short-run (lags 1-4) the autocorrelation is positive – this is the empirically documented phenomena known as momentum: in the short-run, high returns tend to be fol-lowed by more high returns, and low returns tend to be followed by more low returns. In the longer-run (lags 5-13) the autocorrelation is negative, which is known as meanreversion. For even longer lags the autocorrelation eventually tends to zero. The short-run momentum, longerrun mean-reversion, and eventual diminishing autocorrelation creates the general “U-shape” which is found in empirical studies $[7,13,31]$ and which is seen in Fig. $9 .$

数学代考|计算复杂性理论代写computational complexity theory代考|Discussion of the LLS Results

Discussion of the LLS Results The LLS model is an Agent Based Simulation model of the stock market which incorporates some of the fundamental experimental findings regarding the behavior of investors. The main nonstandard assumption of the model is that there is a small minority of investors in the market who are uninformed about the dividend process and who believe in market efficiency. The investment decision of these investors is reduced to the optimal diversification between the stock and the bond.

The LLS model generates many of the empirically documented market phenomena which are hard to explain in the analytical rational-representative-agent framework. These phenomena are:

Short term momentum;
Longer term mean reversion;
Excess volatility;
Heavy trading volume;
Positive correlation between volume and contemporaneous absolute returns;
Positive correlation between volume and lagged absolute returns;
Endogenous market crashes.
The fact that so many “puzzles” are explained with a simple model built on a small number of empirically documented behavioral elements leads us to suspect that these behavioral elements are very important in understanding the workings of the market. This is especially true in light of the observations that a very small minority of the nonstandard bounded-rational investors can have a dramatic influence on the market, and that these investors are not wiped out by the majority of rational investors.

数学代考|计算复杂性理论代写computational complexity theory代考|Summary and Future Directions

Standard economic models typically describe a world of homogeneous rational agents. This approach is the foundation of most of our present day knowledge in economic theory. With the Agent Based Simulation approach we can investigate a much more complex and “messy” world with different agent types, who employ different strategies to try to survive and prosper in a market with structural uncertainty. Agents can learn over time, from their own experience and from their observation about the performance of other agents. They co-evolve over time and as they do so, the market dynamics change continuously. This is a world view closer to biology, than it is to the “clean” realm of physical laws which classical economics has aspired to.
The Agent Based approach should not and can not replace the standard analytical economic approach. Rather, these two methodologies support and complement each other: When an analytical model is developed, it should become standard practice to examine the robustness of the model’s results with agent based simulations. Similarly, when results emerge from agent based simulation, one should try to understand their origin and their generality, not only by running many simulations, but also by trying to capture the essence of the results in a simplified analytical setting (if possible).

Although the first steps in economic agent based simulations were made decades ago, economics has been slow and cautious to adopt this new methodology. Only in recent years has this field begun to bloom. It is my belief and hope that the agent based approach will prove as fruitful in economics as it has been in so many other branches of science.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Full Spectrum of EMB Investors

EMB 投资者的全谱到目前为止，我们已经分析了最多包含三个不同子群体（一个 RII 群体和两个 EMB 群体）的市场。我们发现的市场动态显示了经验观察到的市场异常，但它们在繁荣和崩溃的幅度、频率和半可预测性方面是不切实际的。实际上，我们预计的不仅是两种或三种投资者类型，而是整个范围的投资者。在本节中，我们考虑一个包含各种不同 EMB 投资者的模型。事实证明，更多是不同的。当有一个完整的投资者范围时，价格动态变得现实：繁荣和崩溃不是周期性的或可预测的，而且它们也不那么频繁和剧烈。同时，我们仍然获得了之前描述的所有市场异常。

在这个模型中，每个投资者都有不同数量的事后观察，他利用这些观察来估计事前分布。也就是说，投资者 $i$ 查看股票最近收益 $m^{i}$ 的集合，我们假设 $m^{i}$ 在总体中按照 trun-

具有平均 $\tilde{m}$ 和标准偏差 $\sigma_{m}$ 的正态分布（由于 $m \leq 0$ 没有意义，分布在 $m=0$ 处被截断）。

图 8 显示了该模型的典型模拟的价格模式。在这个模拟中，$90\%$ 的投资者是 RII，剩下的 $10\%$ 是异构 EMB 投资者，$\bar{m}=40$，$\sigma_{m}=10$。价格模式似乎非常现实，周期“更平滑”且更不规则。崩溃是戏剧性的，但很少发生且不可预测。

异质 EMB 人口模型产生以下经验观察的市场现象：
回报自相关：动量和均值回归在异质 EMB 人口模型中，趋势是由在同质情况下产生周期的相同正反馈机制产生的：高（低）回报往往使 EMB 投资者更（更少）激进，这会产生更高（低）回报等。两种情况之间的区别在于，在异质情况下，所有不同的投资者子群体之间存在非常复杂的相互作用，因此没有明显的规则周期，而是更平滑和更不规则的趋势。没有单一的周期长度，动态是许多不同周期的组合。这使得自相关模式也更平滑和更连续。异构模型中的回归自相关如图 9 所示。这种自相关模式与实证结果一致。在短期（滞后 1-4）中，自相关是正的——这是经验证明的现象，称为动量：在短期内，高回报往往会跟随更高的回报，而低回报往往会跟随更高的回报。其次是更低的回报。从长远来看（滞后 5-13），自相关是负的，这被称为均值回归。对于更长的滞后时间，自相关最终趋于零。短期动量、长期均值回归和最终递减的自相关创造了一般的“U 形”，这在实证研究 $[7,13,31]$ 中发现，如图 9 所示。$ 在短期内，高回报往往会伴随着更多的高回报，而低回报往往会伴随着更多的低回报。从长远来看（滞后 5-13），自相关是负的，这被称为均值回归。对于更长的滞后时间，自相关最终趋于零。短期动量、长期均值回归和最终递减的自相关创造了一般的“U 形”，这在实证研究 $[7,13,31]$ 中发现，如图 9 所示。$ 在短期内，高回报往往会伴随着更多的高回报，而低回报往往会伴随着更多的低回报。从长远来看（滞后 5-13），自相关是负的，这被称为均值回归。对于更长的滞后时间，自相关最终趋于零。短期动量、长期均值回归和最终递减的自相关创造了一般的“U 形”，这在实证研究 $[7,13,31]$ 中发现，如图 9 所示。$

数学代考|计算复杂性理论代写computational complexity theory代考|Discussion of the LLS Results

LLS 结果的讨论 LLS 模型是一种基于代理的股票市场模拟模型，它结合了一些关于投资者行为的基本实验结果。该模型的主要非标准假设是市场上有少数投资者不了解股息过程并相信市场效率。这些投资者的投资决策被简化为股票和债券之间的最佳多元化。

LLS 模型产生了许多在分析理性-代表-代理框架中难以解释的经验记录的市场现象。这些现象是：

短期动量；
长期均值回归；
过度波动；
交易量大；
成交量与同期绝对收益呈正相关；
交易量与滞后绝对收益呈正相关；
内生市场崩盘。
如此多的“谜题”是用一个建立在少数经验证明的行为元素上的简单模型来解释的，这一事实使我们怀疑这些行为元素对于理解市场运作非常重要。鉴于极少数非标准有限理性投资者可以对市场产生巨大影响，并且这些投资者并未被大多数理性投资者淘汰，这一点尤其正确。

数学代考|计算复杂性理论代写computational complexity theory代考|Summary and Future Directions

标准经济模型通常描述同质理性主体的世界。这种方法是我们当今大多数经济理论知识的基础。使用基于代理的模拟方法，我们可以调查一个更加复杂和“混乱”的世界，其中包含不同的代理类型，他们采用不同的策略试图在结构不确定的市场中生存和繁荣。随着时间的推移，代理可以从他们自己的经验和他们对其他代理表现的观察中学习。它们随着时间的推移共同发展，并且随着时间的推移，市场动态不断变化。这是一种更接近生物学的世界观，而不是古典经济学所追求的“干净”的物理定律领域。
基于代理的方法不应该也不能取代标准的分析经济方法。相反，这两种方法相互支持和互补：当开发分析模型时，应该通过基于代理的模拟来检查模型结果的稳健性，这应该成为标准做法。同样，当基于代理的模拟结果出现时，人们应该尝试理解它们的起源和普遍性，不仅通过运行许多模拟，而且通过尝试在简化的分析设置中捕捉结果的本质（如果可能的话）。

尽管基于经济主体的模拟的第一步是在几十年前进行的，但采用这种新方法的经济学一直缓慢而谨慎。直到最近几年，这个领域才开始开花。我相信并希望基于代理的方法将在经济学中像在许多其他科学分支中一样富有成效。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|The Kim and Markowitz Portfolio Insurers Model

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|The Kim and Markowitz Portfolio Insurers Model

Harry Markowitz is very well known for being one of the founders of modern portfolio theory, a contribution for which he has received the Nobel Prize in economics. It is less well known, however, that Markowitz is also one of the pioneers in employing agent based simulations in economics.

During the October 1987 crash markets all over the globe plummeted by more than $20 \%$ within a few days. The surprising fact about this crash is that it appeared to be spontaneous – it was not triggered by any obvious event. Following the 1987 crash researchers started to look for endogenous market features, rather than external forces, as sources of price variation. The Kim-Markowitz [15] model explains the 1987 crash as resulting from investors? “Constant Proportion Portfolio Insurance” (CPPI) policy. Kim and Markowitz proposed that market instabilities arise as a consequence of the individual insurers’ efforts to cut their losses by selling once the stock prices are going down.

The Kim Markowitz agent based model involves two groups of individual investors: rebalancers and insurers (CPPI investors). The rebalancers are aiming to keep a constant composition of their portfolio, while the insurers make the appropriate operations to insure that their eventual losses will not exceed a certain fraction of the investment per time period.

The rebalancers act to keep a portfolio structure with (for instance) half of their wealth in cash and half in stocks. If the stock price rises, then the stocks weight in the portfolio will increase and the rebalancers will sell shares until the shares again constitute $50 \%$ of the portfolio. If the stock price decreases, then the value of the shares in the portfolio decreases, and the rebalancers will buy shares until the stock again constitutes $50 \%$ of the portfolio. Thus, the rebalancers have a stabilizing influence on the market by selling when the market rises and buying when the market falls.

A typical CPPI investor has as his/her main objective not to lose more than (for instance) $25 \%$ of his initial wealth during a quarter, which consists of 65 trading days. Thus, he aims to insure that at each cycle $75 \%$ of the initial wealth is out of reasonable risk. To this effect, he assumes that the current value of the stock will not fall in one day by more than a factor of 2 . The result is that he always keeps in stock twice the difference between the present wealth and $75 \%$ of the initial wealth (which he had at the beginning of the 65 days investing period). This determines the amount the CPPI agent is bidding or offering at each stage. Obviously, after a price fall, the amount he wants to keep

in stocks will fall and the CPPI investor will sell and further destabilize the market. After an increase in the prices (and personal wealth) the amount the CPPI agent wants to keep in shares will increase: he will buy, and may support a price bubble.

The simulations reveal that even a relatively small fraction of CPPI investors (i. e. less than $50 \%$ ) is enough to destabilize the market, and crashes and booms are observed. Hence, the claim of Kim and Markowitz that the CPPI policy may be responsible for the 1987 crash is supported by the agent based simulations. Various variants of this model were studied intensively by Egenter, Lux and Stauffer [5] who find that the price time evolution becomes unrealistically periodic for a large number of investors (the periodicity seems related with the fixed 65 days quarter and is significantly diminished if the 65 day period begins on a different date for each investor).

数学代考|计算复杂性理论代写computational complexity theory代考|The Arthur, Holland, Lebaron, Palmer and Tayler Stock Market Model

Palmer, Arthur, Holland, Lebaron and Tayler [30] and Arthur, Holland, Lebaron, Palmer and Tayler 3 construct an agent based simulation model that is focused on the concept of co-evolution. Each investor adapts his/her investment strategy such as to maximally exploit the market dynamics generated by the investment strategies of all others investors. This leads to an ever-evolving market, driven endogenously by the everchanging strategies of the investors.

The main objective of AHLPT is to prove that market fluctuations may be induced by this endogenous coevolution, rather than by exogenous events. Moreover, AHLPT study the various regimes of the system: the regime in which rational fundamentalist strategies are dominating vs. the regime in which investors start developing strategies based on technical trading. In the technical trading regime, if some of the investors follow fundamentalist strategies, they may be punished rather than rewarded by the market. AHLPT also study the relation between the various strategies (fundamentals vs. technical) and the volatility properties of the market (clustering, excess volatility, volume-volatility correlations, etc.).

In the first paper quoted above, the authors simulated a single stock and further limited the bid/offer decision to a ternary choice of: i) bid to buy one share, ii) offer to sell one share, or: iii) do nothing. Each agent had a collection of rules which described how he should behave (i, ii or iii) in various market conditions. If the current market conditions were not covered by any of the rules, the default was to do nothing. If more than one rule applied in a certain

market condition, the rule to act upon was chosen probabilistically according to the “strengths” of the applicable rules. The “strength” of each rule was determined according to the rule’s past performance: rules that “worked” became “stronger”. Thus, if a certain rule performed well, it became more likely to be used again.

The price is updated proportionally to the relative excess of offers over demands. In [3], the rules were used to predict future prices. The price prediction was then transformed into a buy/sell order through the use of a Constant Absolute Risk Aversion (CARA) utility function. The use of CARA utility leads to demands which do not depend on the investor’s wealth.

The heart of the AHLPT dynamics are the trading rules. In particular, the authors differentiate between “fundamental” rules and “technical” rules, and study their relative strength in various market regimes. For instance, $a^{\text {“fundamental }}$ ” rule may require a market conditions of the type:
$$
\frac{\text { dividend }}{\text { current price }}>0.04
$$
in order to be applied. A “technical” rule may be triggered if the market fulfills a condition of the type:
current price $>10$-period moving-average of past prices.
The rules undergo genetic dynamics: the weakest rules are substituted periodically by copies of the strongest rules and all the rules undergo random mutations (or even versions of “sexual” crossovers: new rules are formed by combining parts from 2 different rules). The genetic dynamics of the trading rules represent investors’learning: new rules represent new trading strategies. Investors examine new strategies, and adopt those which tend to work best. The main results of this model are:

For a Few Agents, a Small Number of Rules, and Small Dividend Changes

The price converges towards an equilibrium price which is close to the fundamental value.
Trading volume is low.
There are no bubbles, crashes or anomalies.
Agents follow homogeneous simple fundamentalist rules.

数学代考|计算复杂性理论代写computational complexity theory代考|The Lux and Lux and Marchesi Model

Lux [27] and Lux and Marchesi [28] propose a model to endogenously explain the heavy tail distribution of returns and the clustering of volatility. Both of these phenomena emerge in the Lux model as soon as one assumes that in addition to the fundamentalists there are also chartists in the model. Lux and Marchesi [28] further divide the chartists into optimists (buyers) and pessimists (sellers). The market fluctuations are driven and amplified by the fluctuations in the various populations: chartists converting into fundamentalists, pessimists into optimists, etc.
In the Lux and Marchesi model the stock’s fundamental value is exogenously determined. The fluctuations of the fundamental value are inputted exogenously as a white noise process in the logarithm of the value. The market price is determined by investors’ demands and by the market clearance condition.
Lux and Marchesi consider three types of traders:

Fundamentalists observe the fundamental value of the stock. They anticipate that the price will eventually converge to the fundamental value, and their demand for shares is proportional to the difference between the market price and the fundamental value.
Chartists look more at the present trends in the market price rather than at fundamental economic values; the chartists are divided into
Optimists (they buy a fixed amount of shares per unit time)
Pessimists (they sell shares).
Transitions between these three groups (optimists, pessimists, fundamentalists) happen with probabilities depending on the market dynamics and on the present numbers of traders in each of the three classes:The transition probabilities of chartists depend on the majority opinion (through an “opinion index” measuring the relative number of optimists minus the relative number of pessimists) and on the actual price trend (the current time derivative of the current market price), which determines the relative profit of the various strategies.
The fundamentalists decide to turn into chartists if the profits of the later become significantly larger than their own, and vice versa (the detailed formulae used by Lux and Marchesi are inspired from the exponential transition probabilities governing statistical mechanics physical systems).
The main results of the model are:
No long-term deviations between the current market price and the fundamental price are observed.
The deviations from the fundamental price, which do occur, are unsystematic.
In spite of the fact that the variations of the fundamental price are normally distributed, the variations of the market price (the market returns) are not. In particular the returns exhibit a frequency of extreme events which is higher than expected for a normal distribution. The authors emphasize the amplification role of the market that transforms the input normal distribution of the fundamental value variations into a leptokurtotic (heavy tailed) distribution of price variation, which is encountered in the actual financial data.
clustering of volatility.

The Kim and Markowitz Portfolio Insurers Model 的图像结果 — 数学代考|计算复杂性理论代写computational complexity theory代考|The Kim and Markowitz Portfolio Insurers Model

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|The Kim and Markowitz Portfolio Insurers Model

Harry Markowitz 以现代投资组合理论的创始人之一而闻名，他因此获得了诺贝尔经济学奖。然而，鲜为人知的是，马科维茨也是在经济学中采用基于代理的模拟的先驱之一。

在 1987 年 10 月的崩盘期间，全球市场暴跌超过20%几天之内。关于这次崩溃的令人惊讶的事实是，它似乎是自发的——它不是由任何明显的事件触发的。1987 年崩盘之后，研究人员开始寻找内生的市场特征，而不是外部力量，作为价格变化的来源。Kim-Markowitz [15] 模型将 1987 年的崩盘解释为投资者造成的？“固定比例投资组合保险”（CPPI）政策。Kim 和 Markowitz 提出，市场不稳定是由于个别保险公司在股价下跌时通过出售来减少损失的努力的结果。

基于 Kim Markowitz 代理的模型涉及两组个人投资者：再平衡者和保险公司（CPPI 投资者）。再平衡者的目标是保持其投资组合的恒定组成，而保险公司则进行适当的操作以确保其最终损失不会超过每个时期投资的一定比例。

再平衡者采取行动保持投资组合结构，例如，他们一半的财富是现金，一半是股票。如果股价上涨，则投资组合中的股票权重将增加，再平衡者将出售股票，直到股票再次构成50%的投资组合。如果股价下跌，那么投资组合中股票的价值就会下降，再平衡者将购买股票，直到股票再次构成50%的投资组合。因此，再平衡器通过在市场上涨时卖出并在市场下跌时买入来对市场产生稳定影响。

典型的 CPPI 投资者的主要目标是不损失超过（例如）25%他在一个季度（包括 65 个交易日）内的初始财富。因此，他的目标是确保在每个周期75%的初始财富是出于合理的风险。为此，他假设股票的当前价值不会在一天内下跌超过 2 倍。结果是他的存货总是两倍于现在的财富和75%初始财富（他在 65 天投资期开始时拥有）。这决定了 CPPI 代理在每个阶段的投标或报价金额。显然，在价格下跌之后，他想要保留的数量

股票将下跌，CPPI 投资者将抛售并进一步破坏市场稳定。在价格（和个人财富）上涨之后，CPPI 代理人想要持有的股票数量将会增加：他会购买，并可能支持价格泡沫。

模拟表明，即使是相对较小的 CPPI 投资者（即少于50%) 足以破坏市场的稳定，并观察到崩盘和繁荣。因此，Kim 和 Markowitz 声称 CPPI 政策可能是 1987 年崩溃的原因得到了基于代理的模拟的支持。Egenter、Lux 和 Stauffer [5] 对该模型的各种变体进行了深入研究，他们发现对于大量投资者而言，价格时间演变变得不切实际的周期性（周期性似乎与固定的 65 天季度有关，如果每个投资者的 65 天期限从不同的日期开始）。

数学代考|计算复杂性理论代写computational complexity theory代考|The Arthur, Holland, Lebaron, Palmer and Tayler Stock Market Model

Palmer、Arthur、Holland、Lebaron 和 Tayler [30] 以及 Arthur、Holland、Lebaron、Palmer 和 Tayler 3构建了一个基于代理的仿真模型，该模型专注于协同进化的概念。每个投资者都会调整他/她的投资策略，以最大限度地利用所有其他投资者的投资策略产生的市场动态。这导致了一个不断发展的市场，由投资者不断变化的策略内生驱动。

AHLPT 的主要目标是证明市场波动可能是由这种内生的协同进化引起的，而不是由外生事件引起的。此外，AHLPT 研究了系统的各种制度：理性的原教旨主义策略占主导地位的制度与投资者开始基于技术交易制定策略的制度。在技术交易体系中，如果部分投资者遵循原教旨主义策略，他们可能会受到市场的惩罚而不是奖励。AHLPT 还研究各种策略（基本面与技术面）与市场波动性特性（聚类、过度波动、交易量-波动率相关性等）之间的关系。

在上面引用的第一篇论文中，作者模拟了一只股票，并进一步将买入/卖出决策限制为三元选择：i）买入一股，ii）卖出一股，或：iii）什么都不做。每个代理人都有一组规则，描述了他在各种市场条件下应该如何表现（i、ii 或 iii）。如果任何规则均未涵盖当前的市场状况，则默认为不采取任何行动。如果在某个特定应用中应用了多个规则

在市场条件下，要采取行动的规则是根据适用规则的“优势”概率性地选择的。每个规则的“强度”是根据该规则过去的表现来确定的：“有效”的规则变得“更强”。因此，如果某个规则表现良好，它就更有可能再次被使用。

价格根据报价超过需求的相对过剩比例进行更新。在 [3] 中，这些规则用于预测未来价格。然后通过使用恒定绝对风险厌恶 (CARA) 效用函数将价格预测转换为买入/卖出订单。CARA 公用事业的使用导致了不依赖于投资者财富的需求。

AHLPT 动态的核心是交易规则。特别是，作者区分了“基本”规则和“技术”规则，并研究了它们在各种市场制度中的相对优势。例如，一种“基本的 ”规则可能需要以下类型的市场条件：
股利目前的价格 >0.04
为了被应用。如果市场满足以下类型的条件，则可能会触发“技术”规则：
当前价格>10- 过去价格的周期移动平均线。
规则经历遗传动力学：最弱的规则被最强规则的副本定期替换，所有规则都经历随机突变（甚至是“性”交叉的版本：新规则是通过组合来自 2 个不同规则的部分形成的）。交易规则的遗传动力代表了投资者的学习：新规则代表新的交易策略。投资者检查新策略，并采用那些往往效果最好的策略。该模型的主要结果是：

对于少数代理人、少量规则和少量股息变化

价格趋于接近基本价值的均衡价格。
交易量低。
没有气泡、崩溃或异常。
代理人遵循同质的简单原教旨主义规则。

数学代考|计算复杂性理论代写computational complexity theory代考|The Lux and Lux and Marchesi Model

Lux [27] 和 Lux 和 Marchesi [28] 提出了一个模型来内生地解释收益的重尾分布和波动性的聚类。一旦人们假设除了原教旨主义者之外，模型中还有图表主义者，这两种现象就会出现在勒克斯模型中。Lux 和 Marchesi [28] 进一步将图表分析师分为乐观主义者（买家）和悲观主义者（卖家）。市场波动是由不同人群的波动驱动和放大的：图表主义者转变为原教旨主义者，悲观主义者转变为乐观主义者，等等。
在 Lux 和 Marchesi 模型中，股票的基本价值是外生决定的。基值的波动作为白噪声过程以值的对数形式外生地输入。市场价格由投资者的需求和市场出清情况决定。
Lux 和 Marchesi 考虑了三种类型的交易者：

基本面主义者观察股票的基本价值。他们预计价格最终会收敛到基本价值，他们对股票的需求与市场价格和基本价值之间的差额成正比。
图表专家更多地关注市场价格的当前趋势，而不是基本经济价值；图表专家分为
乐观主义者（他们每单位时间购买固定数量的股票）
悲观主义者（他们出售股票）。
这三组（乐观主义者、悲观主义者、基本面主义者）之间的转变发生的概率取决于市场动态和三个类别中每个类别的当前交易者数量：图表师的转变概率取决于多数意见（通过“意见指数” ”衡量乐观者的相对数量减去悲观者的相对数量）和实际价格趋势（当前市场价格的当前时间导数），这决定了各种策略的相对利润。
如果后者的利润明显大于他们自己的利润，则原教旨主义者决定变成图表主义者，反之亦然（Lux 和 Marchesi 使用的详细公式的灵感来自于管理统计力学物理系统的指数转换概率）。
该模型的主要结果是：
没有观察到当前市场价格与基本价格之间的长期偏差。
确实发生的与基本价格的偏差是非系统性的。
尽管基本价格的变化是正态分布的，但市场价格（市场收益）的变化却不是。特别是回报表现出极端事件的频率高于正态分布的预期。作者强调了市场的放大作用，它将基本价值变化的输入正态分布转换为价格变化的细峰（重尾）分布，这在实际金融数据中会遇到。
波动性的聚类。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Computational Economics

Posted on 2022年5月20日2022年5月20日 by statistics-lab

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我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

Schelling's Segregation Model 的图像结果 — 数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Computational Economics

数学代考|计算复杂性理论代写computational complexity theory代考|Definition of the Subject

Mainstream economic models typically make the assumption that an entire group of agents, e.g. “investors”, can be modeled with a single “rational representative agent”. While this assumption has proven extremely useful in advancing the science of economics by yielding analytically tractable models, it is clear that the assumption is not realistic: people are different one from the other in their tastes, beliefs, and sophistication, and as many psychological studies have shown, they often deviate from rationality in systematic ways.

Agent Based Computational Economics is a framework allowing economics to expand beyond the realm of the “rational representative agent”. By modeling and simulating the behavior of each agent and the interaction among agents, agent based simulation allows us to investigate the dynamics of complex economic systems with many heterogeneous and not necessarily fully rational agents.

The agent based simulation approach allows economists to investigate systems that can not be studied with the conventional methods. Thus, the following key questions can be addressed: How do heterogeneity and systematic deviations from rationality affect markets? Can these elements explain empirically observed phenomena which are considered “anomalies” in the standard economics literature? How robust are the results obtained with the analytical models? By addressing these questions the agent based simulation approach complements the traditional analytical analysis, and is gradually becoming a standard tool in economic analysis.

数学代考|计算复杂性理论代写computational complexity theory代考|Introduction

For solving the dynamics of two bodies (e.g. stars) with some initial locations and velocities and some law of attraction (e.g. gravitation) there is a well-known analytical solution. However, for a similar system with three bodies there is no known analytical solution. Of course, this does not mean that physicists can’t investigate and predict the behavior of such systems. Knowing the state of the system (i. e. the location, velocity, and acceleration of each body)

at time $t$, allows us to calculate the state of the system an instant later, at time $t+\Delta t$. Thus, starting with the initial conditions we can predict the dynamics of the system by simply simulating the “behavior ” of each element in the system over time.

This powerful and fruitful approach, sometimes called “Microscopic Simulation”, has been adopted by many other branches of science. Its application in economics is best known as “Agent Based Simulation” or “Agent Based Computation”. The advantages of this approach are clear they allow the researcher to go where no analytical models can go. Yet, despite of the advantages, perhaps surprisingly, the agent based approach was not adopted very quickly by economists. Perhaps the main reason for this is that a particular simulation only describes the dynamics of a system with a particular set of parameters and initial conditions. With other parameters and initial conditions the dynamics may be different. So economists may ask: what is the value of conducting simulations if we get very different results with different parameter values? While in physics the parameters (like the gravitational constant) may be known with great accuracy, in economics the parameters (like the risk-aversion coefficient, or for that matter the entire decision-making rule) are typically estimated with substantial error. This is a strong point. Indeed, we would argue that the “art” of agent based simulations is the ability to understand the general dynamics of the system and to draw general conclusions from a finite number of simulations. Of course, one simulation is sufficient as a counterexample to show that a certain result does not hold, but many more simulations are required in order to convince of an alternative general regularity.

This manuscript is intended as an introduction to agent-based computational economics. An introduction to this field has two goals: (i) to explain and to demonstrate the agent-based methodology in economics, stressing the advantages and disadvantages of this approach relative to the alternative purely analytical methodology, and (ii) to review studies published in this area. The emphasis in this paper will be on the first goal. While Sect. “Some of the Pioneering Studies” does provide a brief review of some of the cornerstone studies in this area, more comprehensive reviews can be found in $[19,24,32,39,40]$, on which part of Sect. “Some of the Pioneering Studies” is based. A comprehensive review of the many papers employing agent based computational models in economics will go far beyond the scope of this article. To achieve goal (i) above, in Sect. “Illustration with the LLS Model” we will focus on one particular model of the stock market in some detail. Section “Summary and Future Directions” concludes with some thoughts about the future of the field.

数学代考|计算复杂性理论代写computational complexity theory代考|Schelling’s Segregation Model

Schelling’s [36] classical segregation model is one of the earliest models of population dynamics. Schelling’s model is not intended as a realistic tool for studying the actual dynamics of specific communities as it ignores economic, real-estate and cultural factors. Rather, the aim of this very simplified model is to explain the emergence of macroscopic single-race neighborhoods even when individuals are not racists. More precisely, Schelling found that the collective effect of neighborhood racial segregation results even from individual behavior that presents only a very mild preference for same-color neighbors. For instance, even the minimal requirement by each individual of having (at least) one neighbor belonging to ones’ own race leads to the segregation effect.

The agent based simulation starts with a square mesh, or lattice, (representing a town) which is composed of cells (representing houses). On these cells reside agents which are either “blue” or “green” (the different races). The crucial parameter is the minimal percentage of same-color neighbors that each agent requires. Each agent, in his turn, examines the color of all his neighbors. If the percentage of neighbors belonging to his own group is above the “minimal percentage”, the agent does nothing. If the percentage of neighbors of his own color is less then the minimal percentage, the agent moves to the closest unoccupied cell. The agent then examines the color of the neighbors of the new location and acts accordingly (moves if the number of neighbors of his own color is below the minimal percentage and stays there otherwise). This goes on until the agent is finally located at a cite in which the minimal percentage condition holds. After a while, however, it might happen that following the moves of the other agents, the minimal percentage condition ceases to be fulfilled and then the agent starts moving again until he finds an appropriate cell. As mentioned above, the main result is that even for very mild individual preferences for same-color neighbors, after some time the entire system displays a very high level of segregation.

A more modern, developed and sophisticated reincarnation of these ideas is the Sugarscape environment described by Epstein and Axtell [6]. The model considers a population of moving, feeding, pairing, procreating, trading, warring agents and displays various qualitative collective events which their populations incur. By employing agent based simulation one can study the macroscopic results induced by the agents’ individual behavior.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Definition of the Subject

主流经济模型通常假设整个代理组，例如“投资者”，可以用单个“理性代表代理”建模。虽然这一假设已被证明通过产生易于分析的模型在推进经济学科学方面非常有用，但很明显，该假设是不现实的：人们在品味、信仰和成熟度方面与其他人不同，并且与许多心理学研究一样已经表明，他们经常以系统的方式偏离理性。

基于代理的计算经济学是一个允许经济学扩展到“理性代表代理”领域之外的框架。通过对每个代理的行为以及代理之间的交互进行建模和模拟，基于代理的模拟使我们能够研究具有许多异构且不一定完全理性的代理的复杂经济系统的动态。

基于代理的模拟方法允许经济学家研究无法用传统方法研究的系统。因此，可以解决以下关键问题：异质性和对理性的系统性偏差如何影响市场？这些要素能否解释在标准经济学文献中被视为“异常”的经验观察现象？使用分析模型获得的结果有多稳健？通过解决这些问题，基于代理的模拟方法补充了传统的分析分析，并逐渐成为经济分析的标准工具。

数学代考|计算复杂性理论代写computational complexity theory代考|Introduction

为了求解具有一些初始位置和速度以及一些吸引力法则（例如万有引力）的两个物体（例如恒星）的动力学，有一个众所周知的解析解。但是，对于具有三个主体的类似系统，没有已知的解析解。当然，这并不意味着物理学家无法调查和预测此类系统的行为。了解系统的状态（即每个物体的位置、速度和加速度）

有时吨, 允许我们稍后计算系统的状态吨+Δ吨. 因此，从初始条件开始，我们可以通过简单地模拟系统中每个元素随时间的“行为”来预测系统的动态。

这种强大而富有成效的方法，有时被称为“微观模拟”，已被许多其他科学分支采用。它在经济学中的应用以“基于代理的模拟”或“基于代理的计算”而闻名。这种方法的优点很明显，它们允许研究人员去没有分析模型可以去的地方。然而，尽管有这些优势，也许令人惊讶的是，基于代理的方法并没有很快被经济学家采用。造成这种情况的主要原因可能是特定的模拟仅描述了具有一组特定参数和初始条件的系统的动力学。对于其他参数和初始条件，动态可能会有所不同。所以经济学家可能会问：如果我们用不同的参数值得到非常不同的结果，那么进行模拟的价值是什么？虽然在物理学中可以非常准确地知道参数（如引力常数），但在经济学中，参数（如风险规避系数，或就此而言，整个决策规则）的估计通常存在很大误差。这是一个强项。事实上，我们认为基于代理的模拟的“艺术”是能够理解系统的一般动态并从有限数量的模拟中得出一般结论的能力。当然，一个模拟作为反例足以表明某个结果不成立，但需要更多的模拟才能说服另一种一般规律。

这份手稿旨在介绍基于代理的计算经济学。对该领域的介绍有两个目标：（i）解释和展示经济学中基于代理的方法，强调这种方法相对于替代纯分析方法的优缺点，以及（ii）回顾发表在这片区域。本文的重点将放在第一个目标上。虽然教派。“一些开创性研究”确实提供了对该领域的一些基石研究的简要回顾，更全面的回顾可以在[19,24,32,39,40]，在教派的哪个部分。“一些开创性研究”是根据。对经济学中使用基于代理的计算模型的许多论文进行全面回顾将远远超出本文的范围。为了实现上述目标 (i)，在 Sect. 在“LLS 模型的说明”中，我们将重点关注一种特定的股票市场模型。“总结和未来方向”部分总结了对该领域未来的一些想法。

数学代考|计算复杂性理论代写computational complexity theory代考|Schelling’s Segregation Model

Schelling 的 [36] 经典隔离模型是最早的种群动态模型之一。Schelling 的模型并非旨在作为研究特定社区实际动态的现实工具，因为它忽略了经济、房地产和文化因素。相反，这个非常简化的模型的目的是解释宏观单一种族社区的出现，即使个人不是种族主义者。更准确地说，谢林发现，邻里种族隔离的集体效应甚至来自对同色邻居仅表现出非常温和的偏好的个人行为。例如，即使每个人（至少）有一个属于自己种族的邻居的最低要求也会导致隔离效应。

基于代理的模拟从由单元（代表房屋）组成的方形网格或格子（代表城镇）开始。在这些细胞上驻留“蓝色”或“绿色”（不同种族）的代理。关键参数是每个代理所需的同色邻居的最小百分比。每个代理人轮流检查他所有邻居的颜色。如果属于他自己组的邻居的百分比高于“最小百分比”，则代理什么也不做。如果他自己颜色的邻居的百分比小于最小百分比，则代理移动到最近的未占用单元格。然后代理检查新位置的邻居的颜色并采取相应的行动（如果他自己颜色的邻居的数量低于最小百分比，则移动，否则保持在那里）。这种情况一直持续到代理最终位于满足最小百分比条件的引用处。然而，一段时间后，可能会发生以下情况：随着其他智能体的移动，最小百分比条件不再满足，然后智能体再次开始移动，直到找到合适的单元格。如上所述，主要结果是即使对于同色邻居的非常温和的个人偏好，一段时间后整个系统也会显示出非常高的隔离水平。

Epstein 和 Axtell [6] 描述的 Sugarscape 环境是这些想法的更现代、更发达和更复杂的转世。该模型考虑了移动、喂养、配对、繁殖、交易、交战代理的群体，并显示了他们的群体发生的各种定性集体事件。通过采用基于代理的模拟，可以研究由代理的个体行为引起的宏观结果。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|Transient Lengths and Cycle Periods

Posted on 2022年5月20日2022年5月20日 by statistics-lab

如果你也在怎样代写计算复杂性理论computational complexity theory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。

我们提供的计算复杂性理论computational complexity theory及其相关学科的代写，服务范围广, 其中包括但不限于:

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

数学代考|计算复杂性理论代写computational complexity theory代考|Transient Lengths and Cycle Periods

For any cellular automata acting on a finite state space, every state eventually maps to a fixed point or cycle. If a rule is injective, it is reversible and every state is a fixed point, or is on a cycle. If not injective, there will be states without predecessors, Garden-of-Eden states. As indicate, however, if a rule is additive its Garden-of-Eden states are spurious in the sense that they do have predecessors if the state space is enlarged.

The following theorem lists several significant properties of cellular automata rules acting on $\mathcal{E}(\mathcal{A}, \mathcal{Z})$ or $\mathcal{E}\left(\mathcal{A}, \mathcal{Z}^{+}\right)$with left justified neighborhoods.

Theorem 3 ([81]) Let $\mathcal{X}$ be a $k$-site cellular automata rule acting on $\mathcal{E}(\mathcal{A}, \mathcal{Z})$ or on $\mathcal{E}\left(\mathcal{A}, Z^{+}\right)$with left justified neighborhoods. Then the following statements are equivalent: (a) $X$ is surjective, (b) $\chi$ has an empty Garden-ofEden, (c) Every finite sequence $\mu_{0} \ldots \mu_{n-1}$ has exactly $p^{k-1}$ pre-images and every state $\mu$ has at most $p^{k-1}$ predecessors, (d) $\mathcal{X}$ maps eventually periodic states to eventually periodic states and non-periodic states to non-periodic states, (e) as a map of the interval $[0,1] X$ maps rationals to rationals and irrationals to irrationals.

If $\mathcal{X}: \mathcal{E}\left(\mathcal{A}, \mathcal{Z}{n}\right) \mapsto \mathcal{E}\left(\mathcal{A}, \mathcal{Z}{n}\right)$ is a $k$-site rule with $|\mathcal{A}|=p$ and either periodic or null boundary conditions, the state transition diagram, $\operatorname{STD}(\mathcal{X})$ is a graph with $p^{n}$ vertices labeled by the set of $p$-adic numbers $\left{i_{0}, \ldots, i_{n-1} \mid 0 \leq i_{r} \leq p-1\right}$. An edge is directed from the vertex $i_{0}, \ldots, i_{n-1}$ to the vertex $j_{0}, \ldots, j_{n-1}$ if and only if $\chi\left(i_{0}, \ldots, i_{n-1}\right)=j_{0}, \ldots, j_{n-1}$. Each state $\mu$ maps to a unique state $\mathcal{X}(\mu)$ so $\operatorname{STD}(\mathcal{X})$ consists of a set of trees rooted on fixed points or cycles. States at the top of trees are Garden-of-Eden states.

If $h(\mathcal{X}, n)$ is the maximum tree height, states at heights $h \leq h(\mathcal{X}, n)$ cannot appear after $h(\mathcal{X}, n)-h+1$ iterations and after $h(\mathcal{X}, n)$ iterations only fixed points and states on cycles remain. Thus, iteration of a non-injective rule on $\mathcal{E}\left(\mathcal{A}, \mathcal{Z}{n}\right)$ decreases the number of available states with a corresponding reduction in entropy. On the other hand, non-injective additive rules acting on $\mathcal{E}\left(\mathcal{A}, Z^{+}\right)$ do not reduce entropy [117] even though the do so on $\mathcal{E}\left(\mathcal{A}, Z{n}\right)$ for all $n$. The explanation for this apparent paradox is that the Garden-of-Eden states that appear in $\mathcal{E}\left(\mathcal{A}, Z_{n}\right)$ are artifacts of the finite length of states in this space. When embedded in $Z^{+}$, states in $Z_{n}$ correspond to periodic configurations, hence to rational numbers in $[0,1]$ and the set of all rationals has measure 0 in the reals.

Parameters of interest for characterizing state transition diagrams of rules acting on $\mathcal{E}\left(\mathcal{A}, Z_{n}\right)$ are the maximum tree height $h(\mathcal{X}, n)$ and the cycle periods $c_{s}(\mathcal{X}, n)$

数学代考|计算复杂性理论代写computational complexity theory代考|Computing Predecessor States

A problem of general interest for cellular automata is computation of predecessor states. For a rule $\mathcal{X}: \mathbb{E}(\mathcal{A}, \mathcal{L}) \mapsto \mathcal{E}(\mathcal{A}, \mathcal{L})$ with a state $\beta$ given this requires solution of the equation $\mathcal{X}(\mu)=\beta$. It is always possible to construct solutions for this equation, or to show that none exist by a method of backward reconstruction based on the rule table.

Example 7 (Rule 60 Acting on $Z_{4}$ With Periodic Boundary Conditions) Rule 60 is a 2 -site rule, defined by $(00,11) \mapsto 0,(01,10) \mapsto 1$. Given the state 0110 the predecessors of this state can be computed as follows:

The initial 0 in 0110 can arise from either 00 or 11 .
Starting with a 00, the next symbol in 0110 is a 1 and this can arise from a 01 or a 10 , but this must also connect to the original 00 so only 01 is allowed, giving 001 . Starting from a 11, on the other hand, the same reasoning requires 110 .
The third symbol in 0110 is also a 1 . To be consistent with 001 requires that 10 be selected, and to be consistent with 110 requires that 01 be selected, thus giving the two partially constructed possibilities as 0010 and 1101 .
Finally, the fourth symbol must be a 0 . This requires that the predecessor string conclude with either 00 or 11. Since the strings are in $Z_{4}$ with periodic boundary conditions, the final symbol in the predecessor string must also be the first symbol in that string. Thus, both 0010 and 1101 are seen to be predecessors of 0110 .
Other ways of computing predecessor states for finite strings is through the construction of a rule matrix [81] or the use of de Bruijn diagrams $[81,113]$. Backward reconstruction, the rule matrix, and use of a de Bruijn diagram are valid methods for computing predecessor states for all one-dimensional rules. For additive rules, how ever, there is an analytic means for computing predecessor states, starting from left justified neighborhoods defined on $\mathcal{E}\left(\mathcal{A}, \mathcal{Z}{n}\right)$ or $\mathcal{E}\left(\mathcal{A}, Z^{+}\right)[81,128]$. This can be illustrated for rules defined on $\mathcal{E}\left({0,1}, Z^{+}\right)$. This method also works for rules defined on $\mathcal{E}\left({0,1}, Z{n}\right)$ if it is embedded in $\mathcal{E}\left({0,1}, Z^{+}\right)$as the subset of halfinfinite periodic sequences with periods that divide $n$. Define operators $\mathcal{B}: \mathcal{E}\left({0,1}, Z^{+}\right) \mapsto \mathcal{E}\left({0,1}, Z^{+}\right)$and $\sigma^{-1}: \mathcal{E}\left({0,1}, Z^{+}\right) \mapsto \mathcal{E}\left({0,1}, Z^{+}\right)$by
$$
\begin{gathered}
{[B(\mu)]{s}=\sum{i=0}^{s} \mu_{i} \bmod (2)} \
{\left[\sigma^{-1}(\mu)\right]{s}= \begin{cases}0 & s=0 \ \mu{s-1} & s>0\end{cases} }
\end{gathered}
$$

数学代考|计算复杂性理论代写computational complexity theory代考|$d$-Dimensional Rules

Both $[102,105]$ discuss the extension from one-dimensional to $d$-dimensional rules defined on tori. In [102] this discussion uses a formalism of multinomials defined over finite fields. In [105], the one-dimensional analysis based on circulant matrices is generalized. The matrix formulism of state transitions is retained by defining a $d$-fold “circulant of circulants,” which is not, of itself, necessarily a circulant. Computation of the the non-zero eigenvalues of this matrix yields results on transient lengths and cycle periods.

More recently, an extensive analysis of additive rules defined on multi-dimensional tori has appeared [129]. A $d$-dimensional integer vector $\vec{n}=\left(n_{1}, \ldots, n_{d}\right)$ defines a discrete toridal lattice $\mathcal{L}(\vec{n})$. Every $d$-dimensional matrix of size $\vec{n}$ with entries in $\mathcal{A},|\mathcal{A}|=p$ (prime), defines an additive rule acting on $\mathcal{E}(\mathcal{A}, \mathcal{L}(\vec{n}))$ as follows: Let $\mathcal{T}$ and $\mu(t)$ be elements of $\mathcal{E}(\mathcal{A}, \mathcal{L}(\vec{n}))$ with $X$ the rule defined by $\mathcal{T}$ and $\mu(t)$ a state at time $t$. The state transition defined by $\mathcal{X}$ is $\mu(t+1)=\mathcal{X}(\mu(t))$ and this is given by
$$
\begin{array}{r}
{[\mu(t+1)]{i{1} \ldots i_{d}}=\sum_{k_{1}, \ldots, k_{d}}[C(\mathcal{T})]{i{1} \ldots i_{d}}^{k_{1} \ldots k_{d}}[\mu(t)]{k{1} \ldots k_{d}}} \
{[C(\mathcal{T})]{i{1} \ldots i_{d}}^{k_{1} \ldots k_{d}}=\mathcal{T}{j{1} \ldots j_{d}} \quad j_{s}=k_{s}-i_{s} \bmod \left(n_{s}\right)}
\end{array}
$$

The matrix $C(T)$ is the $d$-dimensional generalization of a circulant matrix with $T$ as the equivalent of its first row. For example, if $d=1$ and $p=2$ with $\mathcal{T}=(0,1,0,0,0,1)$ this defines the additive rule $\sigma+\sigma^{5}$ (rule 90 ) and the matrix $C(T)$ is given in Eq. (10a).

Let $S$ and $\mathcal{T}$ be elements of $\mathcal{E}(\mathcal{A}, \mathcal{L}(\vec{n}))$ and define the binary operation $\psi: \mathcal{E}(\mathcal{A}, \mathcal{L}(\vec{n})) \times \mathcal{E}(\mathcal{A}, \mathcal{L}(\vec{n}))$ $\mapsto \mathcal{E}(\mathcal{A}, \mathcal{C}(\vec{n}))$ by
$$
\begin{aligned}
{[\psi(S, \mathcal{T})]{i{1} \ldots i_{d}}=} & \sum_{k_{1}, \ldots, k_{d}} S_{k_{1} \ldots k_{d}} \mathcal{T}{i{1}-k_{1} \ldots i_{d}-k_{d}} \
& 0 \leq k_{s}<n_{s}
\end{aligned}
$$
with all sums taken $\bmod (p)$.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Transient Lengths and Cycle Periods

对于任何作用于有限状态空间的元胞自动机，每个状态最终都会映射到一个固定点或循环。如果一个规则是单射的，那么它是可逆的，并且每个状态都是一个不动点，或者是一个循环。如果不是单射的，就会有没有前人的国家，伊甸园国家。然而，正如所表明的那样，如果一个规则是可加的，那么它的伊甸园状态是虚假的，因为如果状态空间被扩大，它们确实有前辈。

以下定理列出了元胞自动机规则的几个重要性质E(A,Z)或者E(A,Z+)与左对齐的社区。

定理 3 ([81]) 令X做一个k- 站点元胞自动机规则作用于E(A,Z)或开E(A,Z+)与左对齐的社区。那么下面的语句是等价的： (a)X是满射的，(b)χ有一个空的伊甸园，(c) 每个有限序列μ0…μn−1正好有pk−1前图像和每个状态μ最多有pk−1前辈，(d)X将最终周期性状态映射到最终周期性状态，将非周期性状态映射到非周期性状态，(e) 作为区间的映射[0,1]X将理性映射到理性，将非理性映射到非理性。

如果X:E(A,Zn)↦E(A,Zn)是一个k- 现场规则|A|=p以及周期性或空边界条件，状态转移图，STD⁡(X)是一个图pn由一组标记的顶点p-进数\left{i_{0}, \ldots, i_{n-1} \mid 0 \leq i_{r} \leq p-1\right}\left{i_{0}, \ldots, i_{n-1} \mid 0 \leq i_{r} \leq p-1\right}. 一条边从顶点指向i0,…,in−1到顶点j0,…,jn−1当且仅当χ(i0,…,in−1)=j0,…,jn−1. 每个州μ映射到一个独特的状态X(μ)所以STD⁡(X)由一组植根于固定点或循环的树组成。树顶的州是伊甸园州。

如果h(X,n)是树的最大高度，高度为 $ h \leq h(\mathcal{X}, n)cannotappearafterh(\mathcal{X}, n)- h +1iterationsandafterh(\mathcal{X}, n)iterationsonlyfixedpointsandstatesoncyclesremain.Thus,iterationofanon−injectiveruleon\mathcal{E}\left(\mathcal{A}, \mathcal{Z}{n}\right)decreasesthenumberofavailablestateswithacorrespondingreductioninentropy.Ontheotherhand,non−injectiveadditiverulesactingon\mathcal{E}\left(\mathcal{A}, Z^{+}\right)donotreduceentropy[117]eventhoughthedosoon\mathcal{E}\left(\mathcal{A}, Z{n}\right)foralln.TheexplanationforthisapparentparadoxisthattheGarden−of−Edenstatesthatappearin\mathcal{E}\left(\mathcal{A}, Z_{n}\right)areartifactsofthefinitelengthofstatesinthisspace.WhenembeddedinZ ^ {+},statesinZ_{n}correspondtoperiodicconfigurations,hencetorationalnumbersin[0,1]$ 并且所有有理数的集合在实数中的度量为 0。

用于表征规则的状态转移图的感兴趣参数E(A,Zn)是最大树高h(X,n)和周期cs(X,n)

数学代考|计算复杂性理论代写computational complexity theory代考|Computing Predecessor States

元胞自动机普遍感兴趣的一个问题是前驱状态的计算。对于一个规则X:E(A,L)↦E(A,L)有状态β鉴于这需要方程的解X(μ)=β. 总是可以为这个方程构造解，或者通过基于规则表的反向重构方法来证明不存在。

示例 7（规则 60 作用于Z4具有周期性边界条件）规则 60 是 2 点规则，定义为(00,11)↦0,(01,10)↦1. 给定状态 0110，该状态的前身可以计算如下：

0110 中的初始 0 可以来自 00 或 11 。
从 00 开始，0110 中的下一个符号是 1，这可以从 01 或 10 产生，但这也必须连接到原始 00，因此只允许 01，给出 001。另一方面，从 11 开始，同样的推理需要 110 。
0110 中的第三个符号也是 1 。与 001 一致需要选择 10，而与 110 一致则需要选择 01，因此给出了 0010 和 1101 两种部分构造的可能性。
最后，第四个符号必须是 0 。这要求前导字符串以 00 或 11 结尾。由于字符串在Z4在周期性边界条件下，前导字符串中的最后一个符号也必须是该字符串中的第一个符号。因此， 0010 和 1101 都被视为 0110 的前身。
计算有限字符串的前驱状态的其他方法是通过构建规则矩阵 [81] 或使用 de Bruijn 图[81,113]. 后向重构、规则矩阵和使用 de Bruijn 图是计算所有一维规则的先行状态的有效方法。然而，对于加法规则，有一种用于计算先行状态的分析方法，从定义的左对齐邻域开始E(A,Zn)或者E(A,Z+)[81,128]. 这可以用定义的规则来说明E(0,1,Z+). 此方法也适用于定义的规则E(0,1,Zn)如果它嵌入E(0,1,Z+)作为半无限周期序列的子集，其周期为n. 定义运算符B:E(0,1,Z+)↦E(0,1,Z+)和σ−1:E(0,1,Z+)↦E(0,1,Z+)经过
[B(μ)]s=∑i=0sμimod(2) [σ−1(μ)]s={0s=0 μs−1s>0

数学代考|计算复杂性理论代写computational complexity theory代考|d-Dimensional Rules

[ 102,105都讨论了从一维到维规则的扩展，定义在 tori 上。在[102]中，这个讨论使用了在有限域上定义的多项式的形式。在[105]中，基于循环矩阵的一维分析得到了推广。状态转换的矩阵公式通过定义一个倍的“循环的循环”来保留，它本身不一定是循环的。计算该矩阵的非零特征值会产生瞬态长度和循环周期的结果。[102,105]dd

最近，出现了对多维环上定义的加法规则的广泛分析[129]。一个维整数向量定义了一个离散的环形点阵。每个具有维矩阵定义了一个作用于如下：设和是与定义的规则dn→=(n1,…,nd)L(n→)dn→A,|A|=pE(A,L(n→))Tμ(t)E(A,L(n→))XT和在时间的状态。定义的状态转换是并且这是由μ(t)tXμ(t+1)=X(μ(t))
[μ(t+1)]i1…id=∑k1,…,kd[C(T)]i1…idk1…kd[μ(t)]k1…kd [C(T)]i1…idk1…kd=Tj1…jdjs=ks−ismod(ns)

矩阵是循环矩阵的维推广，其中相当于其第一行。例如，如果和且这定义了加法规则（规则 90）和矩阵在方程式中给出。(10a)。C(T)dTd=1p=2T=(0,1,0,0,0,1)σ+σ5C(T)

设和是的元素并定义二元运算由$$ \begin{aligned} {[\psi(S, \mathcal{T})] {i {1} \ldots i_{d}}=} & \sum_{k_{1}, \ldots, k_{d}} S_{k_{1} \ldots k_{d}} \mathcal{T} {i {1}- k_{1} \ldots i_{d}-k_{d}} \ & 0 \leq k_{s}<n_{s} \end{aligned} $$取所有总和。STE(A,L(n→))ψ:E(A,L(n→))×E(A,L(n→)) ↦E(A,C(n→))
mod(p)

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非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

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EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代考|计算复杂性理论代写computational complexity theory代考|Additive Cellular Automata

Posted on 2022年5月20日2022年5月20日 by statistics-lab

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Statistical Inference 统计推断
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数学代考|计算复杂性理论代写computational complexity theory代考|Additive Cellular Automata

数学代考|计算复杂性理论代写computational complexity theory代考|Notation and Formal Definitions

Let $S(\mathcal{L})=\left{s_{i}\right}$ be the set of lattice sites of a $d$-dimensional lattice $\mathcal{L}$ with $n_{r}$ equal to the number of lattice sites on dimension $r$. Denote by $\mathcal{A}$ a finite symbols set with $|\mathcal{A}|=p$ (usually prime). An $\mathcal{A}$-configuration on $\mathcal{L}$ is a surjective map $v: \mathcal{A} \mapsto S(\mathcal{L})$ that assigns a symbol from $\mathcal{A}$ to each site in $S(\mathcal{L})$. In this way, every $\mathcal{A}$-configuration defines a size $n_{1} \times \cdots \times n_{d}, d$-dimensional matrix $\mu$ of symbols drawn from $\mathcal{A}$. Denote the set of all $\mathcal{A}$-configurations on $\mathcal{L}$ by $\mathcal{E}(\mathcal{A}, \mathcal{L})$.

Each $s_{i} \in S(\mathcal{L})$ is labeled by an integer vector $\vec{i}=$ $\left(i_{1}, \ldots, i_{d}\right)$ where $i_{r}$ is the number of sites along the $r$ th dimension separating $s_{i}$ from the assigned origin in $\mathcal{L}$. The shift operator on the $r$ th dimension of $\mathcal{L}$ is the map $\sigma_{r}: \mathcal{L} \mapsto \mathcal{L}$ defined by
$$
\sigma_{r}\left(s_{i}\right)=s_{j}, \quad \vec{j}=\left(i_{1}, \ldots, i_{r}-1, \ldots, i_{d}\right)
$$
Equivalently, the shift maps the value at site $\vec{i}$ to the value at site $\vec{j}$.

Let $\mu\left(s_{i} ; t\right)=\mu\left(i_{1}, \ldots, i_{d} ; t\right) \in \mathcal{A}$ be the entry of $\mu$ corresponding to site $s_{i}$ at iteration $t$ for any discrete dynamical system having $\mathcal{E}(\mathcal{A}, \mathcal{L})$ as state space. Given a finite set of integer $d$-tuples $\mathcal{N}=\left{\left(k_{1}, \ldots, k_{d}\right)\right}$, define the

$$
N\left(s_{i}\right)=\left{s_{j} \mid \vec{j}=\vec{i}+\vec{k}, \vec{k} \in \mathcal{N}\right}
$$
A neighborhood configuration is a surjective map $y$ : $\mathcal{A} \mapsto N\left(s_{0}\right)$. Denote the set of all neighborhood configurations by $\mathcal{E}_{\mathcal{N}}(\mathcal{A})$.

The rule table for a cellular automata acting on the state space $\mathcal{E}(\mathcal{A}, \mathcal{L})$ with standard neighborhood $N\left(s_{0}\right)$ is defined by a map $x: \mathcal{E}{\mathcal{N}}(\mathcal{A}) \mapsto \mathcal{A}$ (note that this map need not be surjective or injective). The value of $x$ for a given neighborhood configuration is called the (value of the) rule component of that configuration. The map $x: \mathcal{E}{\mathcal{N}}(\mathcal{A}) \mapsto \mathcal{A}$ induces a global map $\mathcal{X}: \mathcal{E}(\mathcal{A}, \mathcal{L}) \mapsto$ $\mathcal{E}(\mathcal{A}, \mathcal{L})$ as follows: For any given element $\mu(t) \in$ $\mathcal{E}(\mathcal{A}, \mathcal{L})$, the set $C\left(s_{i}\right)=\left{\mu\left(s_{j} ; t\right) \mid s_{j} \in N\left(s_{i}\right)\right}$ is a neighborhood configuration for the site $s_{i}$, hence the map $\mu\left(s_{i} ; t\right) \mapsto x\left(C\left(s_{i}\right)\right)$ for all $s_{i}$ produces a new symbol $\mu\left(s_{i} ; t+1\right)$. The site $s_{i}$ is called the mapping site. When taken over all mapping sites, this produces a matrix $\mu(t+1)$ that is the representation of $\mathcal{X}(\mu(t))$. A cellular automaton is indicated by reference to its rule table or to the global map defined by this rule table.

A cellular automaton with global map $\chi$ is additive if and only if, for all pairs of states $\mu$ and $\beta$,
$$
\chi(\mu+\beta)=\chi(\mu)+\chi(\beta)
$$
Addition of states is carried out site-wise $\bmod (p)$ on the matrix representations of $\mu$ and $\beta$; for example, for a onedimensional six-site lattice with $p=3$ the sum of 120112 and 021212 is 111021 .

The definition for additivity given in [52] differs slightly from this standard definition. There, a binary valued cellular automaton is called “linear” if its local rule only involves the XOR operation and “additive” if it involves XOR and/or XNOR. A rule involving XNOR can be written as the binary complement of a rule involving only XOR. In terms of the global operator of the rule, this means that it has the form $1+X$ where $\mathcal{X}$ satisfies Eq. (3) and 1 represents the rule that maps every site to 1 . Thus, $(1+X)(\mu+\beta)$ equals $1 \ldots 1+\mathcal{X}(\mu+\beta)$ while
$$
\begin{aligned}
(1&+X)(\mu)+(1+X)(\beta) \
&=1 \ldots 1+1 \ldots 1+X(\mu)+\chi(\beta) \
&=X(\mu)+\chi(\beta) \bmod (2)
\end{aligned}
$$
In what follows, an additive rule is defined strictly as one obeying Eq. (3), corresponding to rules that are “linear” in [52].

Much of the formal study of cellular automata has focused on the properties and forms of representation of the map $\mathcal{X}: \mathbb{E}(\mathcal{A}, \mathcal{L}) \mapsto \mathcal{E}(\mathcal{A}, \mathcal{L})$. The structure of the state transition diagram $(\operatorname{STD}(\mathcal{X}))$ of this map is of particular interest.

数学代考|计算复杂性理论代写computational complexity theory代考|Boundary Conditions and Additivity

In the case of one-dimensional cellular automata, the lattice $\mathcal{L}$ can be isomorphic to the integers; to the nonnegative integers; to the finite set ${0, \ldots, n-1} \in Z$; or to the integers modulo an integer $n$. In the first case, there are no boundary conditions; in the remaining three cases, different boundary conditions apply. If $\mathcal{L}$ is isomorphic to $Z_{n}$, the integers $\bmod (n)$, the boundary conditions are periodic and the lattice is circular (it is a $p$-adic necklace). This is called a cylindrical cellular automata [77] because evolution of the rule can be represented as taking place on a cylinder. If the lattice is isomorphic to ${0, \ldots, n-1}$, null, or Dirchlet boundary conditions are set $[78,79,80]$. That is, the symbol assigned to all sites in $\mathcal{L}$ outside of this set is the null symbol. When the lattice is isomorphic to the non-negative integers $Z^{+}$, null boundary conditions are set at the left boundary. In these latter two cases, the neighborhood structure assumed may influence the need for null conditions.

Example 4 (Elementary Rule 90) Let $\delta$ represent the global map for the elementary cellular automata rule 90 , with rule table
$\begin{array}{cccccccc}000 & 001 & 010 & 011 & 100 & 101 & 110 & 111 \ 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0\end{array}$
For a binary string $\mu$ in $Z$ or $Z_{n}$ the action of rule 90 is defined by $[\delta(\mu)]{i}=\mu{i-1}+\mu_{i+1} \bmod (2)$, where all indices are taken $\bmod (n)$ in the case of $Z_{n}$. In the remaining cases,
$$
\begin{aligned}
{[\delta(\mu)]{i} } &= \begin{cases}\mu{1} & i=0 \
\mu_{i-1}+\mu_{i+1} & 0<i< \
\mu_{n-2} & i=n\end{cases} \
{[\delta(\mu)]{i} } &= \begin{cases}\mu{1} & i=0 \
\mu_{i-1}+\mu_{i+1} & 0<i\end{cases}
\end{aligned}
$$
half-infinite conditions
Note that $\mathcal{L}$ and $Z_{n}$ are representations of the intervals $[-1,1]$ and $[0,1]$ respectively. Cellular automata rules are not quite functions on these intervals, however, since they are generally double valued on rational points having distinct representations as binary strings [81]. For example, both $0 1$ and $1 0$ in $Z^{+}$, where underlining indicates infinite repetition, are numerically $1 / 2$ but $\delta(0 1)=1 0=3 / 4$ while $\delta(10)=01 0=1 / 4$.

The state space $\mathcal{E}({0,1}, \mathcal{L})$ for binary valued one-dimensional cellular automata is just the set of binary sequences over the specified one-dimensional lattice. For the

cases of $Z$ and $Z_{n}$ all such rules commute with the shift operator $\sigma$. When null boundary conditions are involved, however, commutativity fails at the boundary sites. For example, let $\mathcal{X}$ be the global operator for an elementary cellular automata operating on strings $\mu=\mu_{0} \ldots \mu_{n-1}$ of length $n$ with null boundary conditions. Noting that $-1=1 \bmod (2)$, the commutator $[\mathcal{X}, \sigma]$ has components
$$
\begin{aligned}
&{[\mathcal{X}, \sigma]{i}=[\mathcal{X} \sigma(\mu)+\sigma \mathcal{X}(\mu)]{i}} \
&= \begin{cases}\chi\left(0 \mu_{1} \mu_{2}\right)+X\left(\mu_{0} \mu_{1} \mu_{2}\right) \bmod (2) & i=0 \
0 & 0<i<n-1 \
\mathcal{X}\left(\mu_{n-1} 00\right) & i=n-1\end{cases}
\end{aligned}
$$

数学代考|计算复杂性理论代写computational complexity theory代考|Additive Cellular Automata and Fractals

There is a direct connection between the space-time output patterns of additive cellular automata and self-similar fractal patterns $[82,83,84,85,86,87,88]$. The simplest examples are elementary rules 102 and 90 . When acting on a doubly infinite sequence with the initial state $0 1 0$, iteration of these rules yields the space-time output indicated in Fig. 1. In the case of rule 60, this output is the $\bmod (2)$ Pascal triangle while for rule 90 it consists of every other row of this triangle [89].

The pattern generated by rule 60 (or, equivalently, by rule 102) rescales to yield the fractal known as the Sirpinski gasket $[90,91]$. Direct connections between cellular automata outputs and the fractal generation schemes of matrix substitution systems and hierarchical iterated function systems are shown in $[92,93,94,95,96,97,98,99]$. In $[100,101]$ the dimension spectrum associated to the space-time output of additive cellular automata is shown to be equal to the singularity spectrum of an associated multifractal.

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Notation and Formal Definitions

让S(\mathcal{L})=\left{s_{i}\right}S(\mathcal{L})=\left{s_{i}\right}是 a 的格点的集合d维晶格大号和nr等于维度上的格点数r. 表示为一种一个有限符号集|一种|=p（通常是素数）。一个一种-配置开启大号是一个满射图在:一种↦小号(大号)分配一个符号一种到每个站点小号(大号). 这样一来，每一种-configuration 定义一个大小n1×⋯×nd,d维矩阵μ从中提取的符号一种. 表示所有的集合一种- 配置开启大号经过和(一种,大号).

每个s一世∈小号(大号)由整数向量标记一世→= (一世1,…,一世d)在哪里一世r是沿线的站点数量r维分离s一世从指定的原点大号. 移位运算符r第维大号是地图σr:大号↦大号被定义为
σr(s一世)=sj,j→=(一世1,…,一世r−1,…,一世d)
等效地，班次映射了现场的价值一世→到现场的价值j→.

让μ(s一世;吨)=μ(一世1,…,一世d;吨)∈一种成为μ对应站点s一世在迭代吨对于任何具有和(一种,大号)作为状态空间。给定一个有限的整数集d-元组\mathcal{N}=\left{\left(k_{1}, \ldots, k_{d}\right)\right}\mathcal{N}=\left{\left(k_{1}, \ldots, k_{d}\right)\right}，定义N\left(s_{i}\right)=\left{s_{j}\mid\vec{j}=\vec{i}+\vec{k},\vec{k}\in\mathcal{N } \ 对}N\left(s_{i}\right)=\left{s_{j}\mid\vec{j}=\vec{i}+\vec{k},\vec{k}\in\mathcal{N } \ 对}
邻域配置是一个满射图是 : 一种↦ñ(s0). 将所有邻域配置的集合表示为和ñ(一种).

作用于状态空间的元胞自动机规则表和(一种,大号)与标准邻里ñ(s0)由地图定义X:和ñ(一种)↦一种（请注意，此映射不必是满射或单射的）。的价值X对于给定的邻域配置，称为该配置的（值）规则组件。地图X:和ñ(一种)↦一种引出一张全球地图X:和(一种,大号)↦ 和(一种,大号)如下：对于任何给定的元素μ(吨)∈ 和(一种,大号), 集合C\left(s_{i}\right)=\left{\mu\left(s_{j} ; t\right) \mid s_{j} \in N\left(s_{i}\right)\right }C\left(s_{i}\right)=\left{\mu\left(s_{j} ; t\right) \mid s_{j} \in N\left(s_{i}\right)\right }是站点的邻域配置s一世，因此地图μ(s一世;吨)↦X(C(s一世))对全部s一世产生一个新符号μ(s一世;吨+1). 网站s一世称为映射站点。当接管所有映射站点时，这会产生一个矩阵μ(吨+1)那是X(μ(吨)). 元胞自动机通过参考其规则表或由该规则表定义的全局映射来指示。

具有全球地图的元胞自动机χ当且仅当对于所有状态对是可加的μ和b,
χ(μ+b)=χ(μ)+χ(b)
状态的添加是按站点进行的反对(p)关于矩阵表示μ和b; 例如，对于具有p=3120112 和 021212 之和为 111021 。

[52] 中给出的可加性定义与这个标准定义略有不同。在那里，如果局部规则仅涉及 XOR 操作，则二进制值元胞自动机称为“线性”，如果涉及 XOR 和/或 XNOR，则称为“加法”。涉及 XNOR 的规则可以写成只涉及 XOR 的规则的二进制补码。就规则的全局运算符而言，这意味着它具有以下形式1+X在哪里X满足方程。(3) 和 1 表示将每个站点映射到 1 的规则。因此，(1+X)(μ+b)等于1…1+X(μ+b)尽管
(1+X)(μ)+(1+X)(b) =1…1+1…1+X(μ)+χ(b) =X(μ)+χ(b)反对(2)
在下文中，一个加法规则被严格定义为一个服从方程。（3），对应于[52]中的“线性”规则。

许多对元胞自动机的正式研究都集中在地图的属性和表示形式上X:和(一种,大号)↦和(一种,大号). 状态转移图的结构(性病⁡(X))这张地图特别有趣。

数学代考|计算复杂性理论代写computational complexity theory代考|Boundary Conditions and Additivity

在一维元胞自动机的情况下，格大号可以同构于整数；到非负整数；到有限集0,…,n−1∈从; 或以整数模整数n. 在第一种情况下，没有边界条件；在其余三种情况下，适用不同的边界条件。如果大号同构于从n, 整数反对(n)，边界条件是周期性的，晶格是圆形的（它是p-adic 项链）。这被称为圆柱元胞自动机[77]，因为规则的演化可以表示为发生在圆柱体上。如果晶格同构于0,…,n−1、null 或 Dirclet 边界条件已设置[78,79,80]. 也就是说，分配给所有站点的符号大号在这个集合之外是空符号。当晶格与非负整数同构时从+，空边界条件设置在左边界。在后两种情况下，假定的邻域结构可能会影响对零条件的需求。

示例 4（基本规则 90）让d表示基本元胞自动机规则 90 的全局映射，带有规则表
000001010011100101110111 01011010
对于二进制字符串μ在从或者从n规则 90 的动作定义为[d(μ)]一世=μ一世−1+μ一世+1反对(2), 取所有索引反对(n)如果是从n. 在其余情况下，
[d(μ)]一世={μ1一世=0 μ一世−1+μ一世+10<一世< μn−2一世=n [d(μ)]一世={μ1一世=0 μ一世−1+μ一世+10<一世
半无限条件
注意大号和从n是区间的表示[−1,1]和[0,1]分别。然而，元胞自动机规则在这些区间上并不完全是函数，因为它们通常在具有不同表示为二进制字符串的有理点上是双值的 [81]。例如，$0 1一种nd1 0一世nZ ^ {+},在H和r和在nd和rl一世n一世nG一世nd一世C一种吨和s一世nF一世n一世吨和r和p和吨一世吨一世这n,一种r和n在米和r一世C一种ll是1 / 2b在吨\delta(0 1 )=1 0 =3 / 4在H一世l和\delta(10)=01 0 =1 / 4$。

状态空间和(0,1,大号)对于二进制值的一维元胞自动机，它只是指定一维格上的二进制序列集。为了

的案例从和从n所有这些规则都与班次运营商通勤σ. 然而，当涉及零边界条件时，交换性在边界位置失败。例如，让X成为对字符串进行操作的基本元胞自动机的全局操作员μ=μ0…μn−1长度n边界条件为零。注意到−1=1反对(2), 换向器[X,σ]有分量
$$
\begin{aligned}
&{[ \mathcal{X}, \sigma ]{i}=[\mathcal{X} \sigma(\mu)+\sigma \mathcal{X}(\mu)] {i}} \
&={χ(0μ1μ2)+X(μ0μ1μ2)反对(2)一世=0 00<一世<n−1 X(μn−100)一世=n−1
\end{对齐}
$$

数学代考|计算复杂性理论代写computational complexity theory代考|Additive Cellular Automata and Fractals

加性元胞自动机的时空输出模式与自相似分形模式之间存在直接联系[82,83,84,85,86,87,88]. 最简单的例子是基本规则 102 和 90。当作用于具有初始状态 $ 0 1 0的双重无限序列时,一世吨和r一种吨一世这n这F吨H和s和r在l和s是一世和lds吨H和sp一种C和−吨一世米和这在吨p在吨一世nd一世C一种吨和d一世nF一世G.1.一世n吨H和C一种s和这Fr在l和60,吨H一世s这在吨p在吨一世s吨H和\bmod (2)$ 帕斯卡三角形，而对于规则 90，它由该三角形的每隔一行组成 [89]。

由规则 60（或等效地由规则 102）生成的图案重新缩放以产生称为 Sirpinski 垫片的分形[90,91]. 元胞自动机输出与矩阵替换系统和分层迭代函数系统的分形生成方案之间的直接联系显示在[92,93,94,95,96,97,98,99]. 在[100,101]与加法元胞自动机的时空输出相关的维谱被证明等于相关多重分形的奇点谱。

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