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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|信息论作业代写information theory代考|Transformation Operators and Introduction to the Theory of Info-dynamics

It must be analytically clear that socio-natural transformation is the production of information through the conversions of varieties and categorial varieties of systems. This is another way of seeing the concept of systems dynamics in the most complex form. The dynamics is about a continual production and storage of information. The complexity is about the size of the variety space that presents a multiplicity of problems of variety identification over an expansive fuzziness in information processing. The study of information is, thus, the study of systemicity in either automatic control or non-automatic control framework at both static and dynamic conditions. The theory of static systemicity is embedded in the theory of info-statics

which has been presented in [R17.17]. The theory of dynamic systemicity is embedded in the theory of info-dynamics which is currently under development.
Central to the study and development of the theory of systems dynamics and complexity are time $t$ with time set $(t \in \mathbb{T})$ and (time-transformation processor) categorial-conversion operator $\pi(t)$ with a set of time-transformation processors or categorial-conversion operators $\pi(t) \in(\Pi, \mathbb{T})$ that act on the elements of the key definitional building blocks of the information. The categorial-conversion operator is a function of the internal technologies that have been discussed above such that $\pi(t) \in(\Pi, \mathbb{T}) \subset \mathbb{E}$. Every time set has special properties that allow any time-processor to belong to the set of time-processors. Few questions may be asked that will provide entry and exist points to the development of the theory of info-dynamics in support of the theory of info-statics. What is the structural relation between the set of conditions of info-statics and those of info-dynamics? Is the structure of the evolving transformation isomorphic to the structure of info-dynamics? Is the cost-benefit structure involved in this info-dynamic process? If cost-benefit is involved, what is its time-processor? If the costs and benefits are involved, then what are the relationships of costs to benefits in transformations? The results of the systems dynamics will be shown to generate an organic information enveloping $\mathbb{Z}{\Omega}(t)$ of stock-flow conditions where $(t \in \mathbb{T})$. At any time-point $(t \in \mathbb{T})$, the organic information $\mathbb{Z}{\Omega}$ is a static structure of the set of the form:
$$\mathbb{Z}{\Omega}=(\mathbb{X} \otimes \mathbb{S})=\left{\mathbb{Z}_v=\left(\mathbb{X}_v \otimes \mathbb{S}{\mathrm{v}}\right) \mid v \in \mathbb{V}, \mathbb{X}v \subset \mathbb{X}, \& \mathbb{S}_v \subset \mathbb{S}\right}$$ The organic information enveloping is a set of individual variety-information enveloping $\mathbb{Z}_v$ of a particular variety $(v \in \mathbb{V})$ such that $\mathbb{Z}{\Omega}=\bigcup_{v \in \mathbb{V}} \mathbb{Z}v$ and $\mathbb{Z}{\Omega}=$ $\bigcup_{\mathrm{v} \in \mathrm{V}}\left(\mathbb{X}{\mathrm{v}} \otimes \mathbb{S}{\mathrm{v}}\right)$ which describes the total information space of all available varieties at any given time point. The space of varieties is the collection of all the individual varieties of the form $\mathbb{V}=\left{v_i \mid i \in \mathbb{I}^{\infty}\right.$ for any $\left.t \in \mathbb{T}\right}$. This is the conditions of info-statics, the inner structure of which must be examined. The info-statics presents a general information definition which is made up by characteristics that define the contents of the varieties. The characteristics of the varieties send signals that reveal their inner structures and hence their identities.

## 数学代写|信息论作业代写information theory代考|The Structural Analytics of Characteristic-Signal

To construct a theory of info-dynamics as a theory of the dynamic behavior on a system of transformation of varieties in its general form, it is useful to initialize the definitional conditions of the space of varieties that establishes the universal object set $\Omega$, where every $\omega \in \Omega$ is a variety $v \in \mathbb{V}$. Each variety has a corresponding characteristic-signal disposition $\mathbb{Z}{\mathrm{v}}=\left(\mathbb{X}{\mathrm{v}} \otimes \mathbb{S}_{\mathrm{v}}\right)$ and corresponding phenomenon $\phi_{\mathrm{v}} \in \Phi$. The definitional conditions of information at the static state must be the same and must hold for each element in the space. The inner structure of each variety will vary in accord with the information content $\mathbb{X}v$ and corresponding signals $\mathbb{S}{\mathrm{v}}$. Every categorial variety is a collection of the same varieties which is defined by a characteristic set $\mathbb{X}{\mathbb{C}}$ referred to as a categorial characteristic disposition, where $\mathbb{C}_v$ is the home category of $v \in \mathbb{V}$. Corresponding to each categorial characteristic disposition is a categorial signal disposition $\mathbb{S}{\mathbb{C}}$. The two together define information on the category of the same varieties $\mathbb{V}_{\mathrm{C}}$. The internal conditions of these categorial varieties are under plenum of forces from opposing forces that are generated under the principle of opposites composed of infinite set of socio-natural dualities which supports an infinite set of socio-natural polarities to produce energy from within and to generate internal self-motions of varieties and categorial varieties. Here, the universe is considered as a unit composed of internal opposing parts for conflicts with relation destruction and creation. The theory of info-dynamics is a general theory of dynamics of elements in the universal object info-dynamics is a general theory of dynamics.

The characteristic disposition is the same for all varieties in a fixed category and is composed of two opposite sub-sets of negative characteristics set $\mathbb{X}{\mathbb{C}}^N$ with a corresponding negative signal set $\mathbb{S}{\mathrm{C}}^{\mathrm{N}}$, and positive characteristics set $\mathbb{X}{\mathrm{C}}^{\mathrm{P}}$ with a corresponding positive signal set $\mathbb{S}{\mathbb{C}}^{\mathrm{P}}$. The set conditions are such that the information about each categorial variety of the characteristic-signal disposition $\mathbb{Z}{\Gamma}=\left(\mathbb{X}_C \otimes \mathbb{S}_C\right), \mathbb{X}_C=\left(\mathbb{X}{\mathbb{C}}^{\mathrm{p}} \cup \mathbb{X}{\mathbb{C}}^{\mathrm{N}}\right)$ and $\left(\mathbb{X}{\mathbb{C}}^{\mathrm{p}} \cap \mathbb{X}{\mathbb{C}}^{\mathrm{N}}\right) \neq \varnothing$ with $\left(# \mathbb{X}{\mathbb{C}}^{\mathrm{p}} \leqq # \mathbb{X}{\mathrm{C}}^{\mathrm{N}}\right)$ are supported by $\mathbb{S}{\mathbb{C}}=\left(\mathbb{S}{\mathbb{C}}^{\mathrm{P}} \bigcup \mathbb{S}{\mathbb{C}}^{\mathrm{N}}\right)$ and $\left(\mathbb{S}{\mathbb{C}}^{\mathrm{p}} \cap \mathbb{S}{\mathbb{C}}^{\mathrm{N}}\right) \neq \varnothing$, with $\left(# \mathbb{S}{\mathbb{C}}^{\mathrm{p}} #{\mathrm{C}}^{\mathrm{N}}\right)$, in order to establish its identity and the category to which a variety belongs. Similarly, $\left(\mathbb{X}{\mathbb{C}} \otimes \mathbb{S}{\mathbb{C}}\right)==\left(\left(\mathbb{X}{\mathbb{C}}^{\mathrm{p}} \otimes \mathbb{S}{\mathbb{C}}^{\mathrm{p}}\right) \cup\left(\mathbb{X}{\mathbb{C}}^{\mathrm{N}} \otimes \mathbb{S}{\mathbb{C}}^{\mathrm{N}}\right)\right)$ and $\mathbb{Z}{\mathbb{C}}=\left(\mathbb{Z}{\mathbb{C}}^{\mathrm{P}} \cup \mathbb{Z}_{\mathbb{C}}^{\mathrm{N}}\right)$. The set specifications establish the necessary conditions that create external relations for transformation of varieties and corresponding identities.

# 信息论代写

## 数学代写|信息论作业代写information theory代考|转换算子和信息动力学理论简介

. .

，已在[R17.17]中提出。动态系统性理论是目前发展中的信息动力学理论的一部分。系统动力学和复杂性理论的研究和发展的中心是时间$t$和时间集$(t \in \mathbb{T})$，以及(时间转换处理器)类别转换算符$\pi(t)$和一组时间转换处理器或类别转换算符$\pi(t) \in(\Pi, \mathbb{T})$，它们作用于信息的关键定义构建块的元素。类别转换运算符是上面讨论过的内部技术的函数，例如$\pi(t) \in(\Pi, \mathbb{T}) \subset \mathbb{E}$。每个时间集都有特殊的属性，允许任何时间处理程序属于时间处理程序集。对于信息动力学理论的发展，很少会提出一些问题来为信息静力学理论提供切入点和存在点。信息静力学条件集和信息动力学条件集之间的结构关系是什么?进化转换的结构是否与信息动力学的结构同构?这个信息动态过程是否涉及成本效益结构?如果涉及成本效益，它的时间处理器是什么?如果涉及到成本和收益，那么在转换中成本与收益之间的关系是什么?系统动力学的结果将显示为生成包含$\mathbb{Z}{\Omega}(t)$的库存流动条件的有机信息，其中$(t \in \mathbb{T})$。在任何时间点$(t \in \mathbb{T})$，有机信息$\mathbb{Z}{\Omega}$是一个形式为:
$$\mathbb{Z}{\Omega}=(\mathbb{X} \otimes \mathbb{S})=\left{\mathbb{Z}v=\left(\mathbb{X}_v \otimes \mathbb{S}{\mathrm{v}}\right) \mid v \in \mathbb{V}, \mathbb{X}v \subset \mathbb{X}, \& \mathbb{S}_v \subset \mathbb{S}\right}$$的静态结构集。有机信息包膜是一个单独的品种信息集合，包膜特定品种$(v \in \mathbb{V})$的$\mathbb{Z}_v$，这样$\mathbb{Z}{\Omega}=\bigcup{v \in \mathbb{V}} \mathbb{Z}v$和$\mathbb{Z}{\Omega}=$$\bigcup_{\mathrm{v} \in \mathrm{V}}\left(\mathbb{X}{\mathrm{v}} \otimes \mathbb{S}{\mathrm{v}}\right)$描述了在任何给定时间点所有可用品种的总信息空间。变体空间是任何$\left.t \in \mathbb{T}\right}$形式的$\mathbb{V}=\left{v_i \mid i \in \mathbb{I}^{\infty}\right.$的所有单个变体的集合。这就是信息静力学的条件，必须考察它的内部结构。信息静力学是由定义品种内容的特征组成的一般信息定义。品种的特征发出信号，揭示了它们的内部结构，从而揭示了它们的身份

.

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MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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