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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|密码学与网络安全代写cryptography and network security代考|Constructing a Binary Huffman Code

Given a discrete source, a Huffman code can be constructed along the following steps:

1. The source symbols are arranged in decreasing probability. The least probable symbols receive the assignments 0 and 1 .
2. Both symbols are combined to create a new source symbol, whose probability is the sum of the original ones. The list is reduced by one symbol. The new symbol is positioned in the list according to its probability.
3. This procedure continues until the list has only two symbols, which receive the assignments 0 and 1 .
4. Finally, the binary codeword for each symbol is obtained by a reverse process.
In order to explain the algorithm, consider the source of Table 4.9.
The first phase is to arrange the symbols in a decreasing order of probability. Assign the values 0 and 1 to the symbols with the smallest probabilities. They are, then, combined to create a new symbol. The probability associated with the new symbol is the sum of the previous probabilities. The new symbol is repositioned in the list, to maintain the same decreasing order for the probabilities. The procedure is shown in Figure 4.2.
The procedure is repeated until only two symbols remain, which are assigned to 0 and 1, as shown in Figure 4.3.

The procedure is repeated to obtain all codewords, by reading the digits in inverse order, from Phase IV to Phase I, as illustrated in Figure 4.4. Following the arrows, for symbol $x_4$, one finds the codeword 011 .

计算机代写|密码学与网络安全代写cryptography and network security代考|Information Transmission and Channel Capacity

Claude Elwood Shannon (1916-2001) is considered the father of information theory. In 1948, he published a seminal article on the mathematical concept of information, which is one of the most cited for decades. Information left the Journalism field to occupy a more formal area, as part of probability theory.

The entropy, in the context of information theory, was initially defined by Ralph Vinton Lyon Hartley (1888-1970), in the article “Transmission of Information,” published by the Bell System Technical Journal, in July 1928, ten years before the formalization of the concept by Claude Shannon.

Shannon’s development was also based on Harry Nyquist’s work (Harry Theodor Nyquist, 1889-1976), which determined the sampling rate as a function of frequency necessary to reconstruct an analog signal using a set of discrete samples.

In an independent way, Andrei N. Kolmogorov developed his complexity theory, during the 1960 decade. It was a new information theory based on the length of an algorithm developed to describe a certain data sequence. He used Alan Turing’s machine in this new definition. Under certain conditions, Kolmogorov’s and Shannon’s definitions are equivalent.

The idea of relating the number of states of a system with a physical measure, although, dates back to the XIX century. Rudolph Clausius proposed the term entropy for such a measure in 1895.

Entropy comes from the Greek word for transformation and, in physics, is related to the logarithm of the ratio between the final and initial temperature of a system or to the ratio of the heat variation and the temperature of the same system.

Shannon defined the entropy of an alphabet at the negative of the mean value of the logarithm of the symbols’ probability. This way, when the symbols are equiprobable, the definition is equivalent to Nyquist’s.

But, as a more generic definition, Shannon’s entropy can be used to compute the capacity of communication channels. Most part the researchers’ work is devoted to either compute the capacity or to develop error correcting codes to attain that capacity.

Shannon died on February 24, 2001, as a victim of a disease named after the physician Aloysius Alzheimer. According to his wife, he lived a quiet life but had lost his capacity to retain information.

密码学与网络安全代考

计算机代写|密码学与网络安全代写cryptography and network security代考|构造二进制霍夫曼码

1. 源符号按递减概率排列。
2. 这两个符号被组合起来创建一个新的源符号，其概率是原符号的和。这个列表减少了一个符号。新符号根据其概率在列表中定位。
3. 此过程继续进行，直到列表中只有两个符号，它们接受赋值0和1。
4. 最后，通过反向过程获得每个符号的二进制码字。为了解释算法，考虑表4.9的来源。第一个阶段是将符号按概率递减顺序排列。将0和1赋值给概率最小的符号。然后，它们结合在一起形成一个新的符号。与新符号相关的概率是先前概率的和。新的符号在列表中重新定位，以保持相同的概率递减顺序。该过程如图4.2所示。
重复这个过程，直到只剩下两个符号，它们被赋值为0和1，如图4.3所示

重复这个过程，从第IV阶段到第I阶段，通过倒序读取数字，得到所有的码字，如图4.4所示。沿着箭头，对于符号$x_4$，可以找到码字011 .
计算机代写|密码学与网络安全代写cryptography and network security代考|信息传输和通道容量 . name
克劳德·埃尔伍德·香农(1916-2001)被认为是信息论之父。1948年，他发表了一篇关于信息的数学概念的开创性文章，这是几十年来被引用最多的文章之一。作为概率论的一部分，信息离开了新闻领域，占据了一个更正式的领域

在信息论的背景下，熵最初是由拉尔夫·文顿·里昂·哈特利(1888-1970)在1928年7月《贝尔系统技术杂志》发表的文章《信息的传输》中定义的，比克劳德·香农的概念正式形成早了十年

Shannon的发展也是基于Harry Nyquist的工作(Harry Theodor Nyquist, 1889-1976)，该工作确定了使用一组离散样本重构模拟信号所需的频率函数的采样率

Andrei N. Kolmogorov在1960年代以一种独立的方式发展了他的复杂性理论。它是一种新的信息理论，基于描述特定数据序列的算法的长度。他在这个新的定义中使用了艾伦·图灵的机器。在一定条件下，Kolmogorov和Shannon的定义是等价的

将系统的状态数与物理度量联系起来的想法可以追溯到19世纪。鲁道夫·克劳修斯(Rudolph Clausius)在1895年提出了熵一词来表示这种度量

熵来自希腊单词“变换”，在物理学中，它与一个系统的最终温度与初始温度之比的对数有关，或与同一系统的热变化与温度之比有关

Shannon定义了字母的熵为符号概率对数的均值的负值。这样，当符号是等概率时，定义等价于Nyquist的。

但是，作为一个更通用的定义，香农熵可以用来计算通信信道的容量。研究人员的大部分工作都致力于计算容量或开发错误纠正代码以达到该容量

香农于2001年2月24日去世，死于一种以医生阿洛伊修斯·阿尔茨海默命名的疾病。据他的妻子说，他过着平静的生活，但已经失去了记忆的能力

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。

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