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

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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|Fundamentals

This Chapt. presents the necessary mathematical background and the fundamental formalisms of the work that will be introduced and further developed in the next Chapts. This includes the main reversible decompositions in Chapt. 5 that will be used to construct reversible primitives, from which reversible structures are built in Chapts. 6, 7 and 8 , respectively. Also, the foundations that are introduced in this Chapt. will be used to construct the quantum gates and their associated quantum circuits and computing in Chapt. $11 .$
Spectral transforms play an important role in synthesis, analysis, testing, classification, formal verification, and simulation of logic circuits. Dyadic families of discrete transforms: Reed-Muller and Green-Sasao hierarchy, Walsh, Arithmetic, Adding, and Haar wavelet transforms and their generalizations to p-adic (multi-valued) transforms, have found a fruitful use in digital system design $[120,125]$. In this Chapt., we present a specialized framework for the creation, classification, and counts of new non-singular generalized Reed-Muller-like families of expansions for an arbitrary radix of Galois field.

Reed-Muller-like spectral transforms [240] have found a variety of useful applications in minimizing Exclusive Sum-Of-Products (ESOP) and Galois field SOP (GFSOP) expressions $[9,76,77,79,80,171,264]$, creation of new forms $[4,78,104,173,265,266]$, binary decision diagrams $[2,45,142]$, spectral decision diagrams $[82,238,239]$, regular structures $[5,7,13,18,50,51,84,177]$, besides their well-known uses in digital communications $[125]$, digital signal processing $[89,257,260]$, digital image processing $[90]$, and fault detection (testing) $[99,124,147,198,199,204,218]$. Ternary Reduced Post Galois field Sum-Of-Products (RP-GFSOPs), their generalized Green/Sasao hierarchies, and the extensions of such hierarchies to the case of quaternary Galois field hierarchy were recently developed $[4,9]$.

## 计算机代写|量子计算代写Quantum computing代考|Normal Galois Forms in Logic Synthesis

Normal canonical forms play an important role in the synthesis of logic circuits $[113,213,217,219]$. This role includes testing, synthesis, and optimization. The main algebraic structure which is used in this work for developing the canonical normal forms is the Galois field (GF) algebraic structure, which is a fundamental algebraic structure in the theory of algebras $[56,67,87,146,160,166]$.
Galois field has proven high efficiency in various applications such as in logic synthesis and computer engineering, communications, information systems and computer science, and mathematics. This includes items like: design for test [124], reversible logic synthesis (cf. Sect. $5.4$ in Chapt. 5) [6], error correction codes [48], cryptography, number theory, and proving Fermat’s last theorem [251]. The importance of Galois field results from the fact that every finite field is isomorphic to a Galois field [146]. In general, the attractive properties of GF-based circuits, such as the high testability of such circuits, are due to the fact that the GF operators exhibit the Cyclic Group (Latin Square) Property [67]. This property can be explained, for example, using the four-valued (quaternary) GF operators as shown in Figs. 2.1e and 2.1f, respectively. Note that in any row and column of the addition table (Fig. 2.1e), the elements are all different, which is cyclic, and that the elements have a different order in each row and column. Another cyclic group can be observed in the multiplication table; if the zero elements are removed from the multiplication table (Fig. 2.1f), then the remaining elements form a cyclic group. In binary, for example, the $\mathrm{GF}(2)$ addition operator, EXOR, has the cyclic group property.

## 计算机代写|量子计算代写Quantum computing代考|2 Invariant Multi-Valued Families of Generalized

In this Sect. we present the invariant multiple-valued Galois field based spectral transforms, and their generalized notation. The new scaled expansions can be used to produce minimal size circuits for the three-dimensional lattice structures which will be presented in Chapt. 4. Also, the new scaled expansions will be used for the construction of a new type of logic primitives (as will be shown in Fig. 2.4) that implement “weights” into their inputs. Such new primitives can be useful in technological implementations where weighted inputs are used to realize logic functionalities.

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

Reed-Muller-like 谱变换 [240] 已经发现了各种有用的应用来最小化独家乘积 (ESOP) 和伽罗瓦域 SOP (GFSOP) 表达式[9,76,77,79,80,171,264], 创造新形式[4,78,104,173,265,266], 二元决策图[2,45,142], 谱决策图[82,238,239], 规则结构[5,7,13,18,50,51,84,177]，除了它们在数字通信中的众所周知的用途[125]， 数字信号处理[89,257,260], 数字图像处理[90], 和故障检测（测试）[99,124,147,198,199,204,218]. 最近开发了三元缩减后伽罗瓦域乘积和 (RP-GFSOP)，它们的广义 Green/Sasao 层次结构，以及这种层次结构对四元伽罗瓦域层次结构的扩展[4,9].

## 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。