### 计算机代写|量子计算代写Quantum computing代考|Novel Reconstructability Analysis Circuits

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 计算机代写|量子计算代写Quantum computing代考|Reversible Realizations

This Chapt. will introduce another new type of reversible structures called Reversible Modified Reconstructability Analysis (RMRA). Reconstructability Analysis (RA) is an important decomposition technique that is used widely in system science area to decompose qualitative data $[133,134,135,138,273,275]$. This kind of decomposition is commonly used in the decomposition of data obtained in the social and system science fields, and overlaps with other decomposition techniques used in the social sciences as well like the Log-Linear (LL) decomposition method [138]. RA decomposition aims at the simplest decomposition of qualitative data using Lattice-Of-Structure (LOS) (cf. Fig. 7.1) as representation (generation) and contingency tables (for probabilistic data) for evaluation (minimization of error).

In lossless decomposition, the aim is to obtain the simplest decomposed model from data (saturated model) without the loss of any information (i.e., error $=0$ ). In lossy decomposition, the aim is to obtain the simplest decomposed model from data (saturated model) with an acceptable amount of error. RA data is typically either a set-theoretic relation [271,272] (or mapping) or it is a probability (or frequency) distribution. The former case is the domain of set-theoretic RA or more precisely crisp possibilistic RA. The latter is the domain of information-theoretic RA, or more precisely probabilistic RA $[133,134,135,138,274]$. The RA framework can apply to other types of data (e.g., fuzzy data) via generalized information theory $[135,223]$. In this work, we are concerned only with crisp possibilistic RA.

## 计算机代写|量子计算代写Quantum computing代考|New Type of Reconstructability Analysis

This Sect. introduces an innovation in set-theoretic RA, which we call “modified” RA (or MRA) as opposed to the conventional settheoretic RA (or CRA). This innovation will be illustrated by Examples $7.1$ and 7.2. The main idea of MRA stems from the following fact: While the conventional RA (CRA) decomposes on the set of all functional values of the corresponding function, the modified RA (MRA) decomposes on the set of minimum functional values from which the function can be totally reconstructed. In general, the procedure for the lossless MRA decomposition follows the following steps:
(1) Using the lattice-of-relations, decompose for one value only of the Boolean function into the simplest error-free decomposed structure:
(1a) Remove one relation between variables from the previous level.
(1b) Add the embedded relation(s) between variables, in the current level, if they are not already present in the new model.
(2) As a result of step 1, one obtains MRA decomposition for value “1” of the Boolean function (denoted as 1-MRA decomposition), and MRA decomposition for value ” 0 ” of the Boolean function (denoted as 0-MRA decomposition). Select the simplest model from

the resulting 1-MRA decomposition and the 0-MRA decomposition, respectively.
(3) In the resulting simplest decomposed data model from step 2, generate the corresponding sub-functional values for each interaction (relation) between the variables that exist in the decomposed model.
(4) Generate the total functional values using the intersection between all possible sub-functional values for 1-MRA, and the union between all possible sub-functional values for 0-MRA.
Example 7.1. Figure $7.2$ illustrates decomposed structures using both CRA and MRA decompositions, respectively for the logic function: $F=x_{1} x_{2}+x_{1} x_{3}$.

## 计算机代写|量子计算代写Quantum computing代考|Multiple-Valued MRA

Real-life data are in general many-valued. Consequently, if MRA can decompose relations between many-valued variables it can have practical applications in machine learning (ML) and data mining (DM). Many-valued MRA is made up of two main steps which are common to two equivalent (intersection-based and union-based) algorithms as follows:
(1) partition the many-valued truth table into sub-tables, each contain only single functional value.
(2) Perform CRA on all sub-tables. Figure $7.5$ illustrates the general pre-processing procedure for the two many-valued MRA algorithms, which will be explained in more detail below.

For an “n”-valued completely specified function one needs (n-1) values to define the function (i.e., to be able to retrieve the completely specified function without any loss of information). We thus do all $\mathrm{n}$ decompositions and use for our MRA model the (n-1) simplest of these. Figure $7.5$ illustrates the general flow diagram of the multiple-valued MRA decomposition using the pre-processing steps that are common to both of the intersection-based and unionbased algorithms.

For example, using the lattice-of-structures, decompose the 3valued function for each individual value. One then obtains the simplest lossless MRA decomposition for value “0” of the function (denoted as the 0-MRA decomposition), for value “1” (1-MRA decomposition), and for value “2” (2-MRA decomposition). By selecting the simplest two models from these 0-MRA, 1-MRA, and 2-MRA decompositions, one can generate the complete function.

## 计算机代写|量子计算代写Quantum computing代考|New Type of Reconstructability Analysis

(1) 使用关系格，仅将布尔函数的一个值分解为最简单的无错误分解结构：
(1a) 删除一个关系上一级的变量之间。
(1b) 在当前级别添加变量之间的嵌入关系，如果它们尚未出现在新模型中。
(2) 作为步骤 1 的结果，得到布尔函数值“1”的 MRA 分解（记作 1-MRA 分解），以及布尔函数值“0”的 MRA 分解（记作 0-MRA分解）。选择最简单的模型

(3) 在从步骤 2 得到的最简单的分解数据模型中，为分解模型中存在的变量之间的每个交互（关系）生成相应的子功能值。
(4) 使用 1-MRA 的所有可能子功能值之间的交集和 0-MRA 的所有可能子功能值之间的并集来生成总功能值。

## 计算机代写|量子计算代写Quantum computing代考|Multiple-Valued MRA

（1）将多值真值表划分为子表，每个子表仅包含单个功能价值。
(2)对所有子表进行CRA。数字7.5图 1 说明了两种多值 MRA 算法的一般预处理过程，这将在下面更详细地解释。

## 有限元方法代写

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## MATLAB代写

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