## 数学代写|信息论作业代写information theory代考|STA2301

2022年7月21日

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• Statistical Inference 统计推断
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• (Generalized) Linear Models 广义线性模型
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• Foundations of Data Science 数据科学基础
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## 数学代写|信息论作业代写information theory代考|Universal Limits

Information is ultimately limited by the laws of high-energy physics, which preclude it increasing indefinitely. In order to increase the amount of information transported by waves, we need to increase the radiated energy, and this requires packing more and more energy at the source of the radiation. Eventually, this strategy comes to an abrupt stop, and a limiting value for the amount of information that can be transported is reached. This limit is well beyond the capability of any practical communication system and is of purely theoretical interest.

To describe this information bound we recall that according to general relativity any three-dimensional spherical region is characterized by a critical Schwarzschild radius
$$r_{\mathrm{S}}=\frac{2 G m}{c^{2}},$$
where $G$ is Newton’s gravitational constant and $m$ is the mass of the region. If the radius of the region is smaller than its Schwarzschild radius it will collapse into a black hole. The surface at the Schwazschild radius is called the event horizon and it represents the boundary of the black hole. By Einstein’s relation
$$E=m c^{2},$$
increasing the energy inside a volume effectively increases its mass, and eventually causes it to collapse into a black hole.

## 数学代写|信息论作业代写information theory代考|Tour d’Horizon

This chapter has provided a roadmap for the topics addressed in the remainder of the book. A central result is the cut-set area bound on the number of degrees of freedom per radiated frequency, leading to the total number of degrees of freedom of electromagnetic signals, (1.19) and (1.80). A complete derivation of these results appears in Chapters 8 and 9 , where they are also extended to more general cut-set surfaces with rotational symmetry. Chapters $2,3,4$, and 5 build all the necessary background for this derivation and take us on a journey through the theory of functional approximation, decomposition of operators in infinite-dimensional Hilbert spaces, and electromagnetic wave propagation. Chapter 6 provides an analogous description of signals from a stochastic perspective, and Chapter 7 is an intermezzo that precedes the more technically demanding content of Chapters 8 and 9; Chapter 7 describes how the degrees of freedom and the stochastic diversity of electromagnetic waveforms are exploited in current communication technologies. It discusses the principles behind orthogonal frequency division, code division, time division, and multiple-antenna systems, viewing all of these technologies through the lens of the orthogonal representations examined in the previous chapters. It also gives an overview of the methods that have been proposed to operate next-generation communication systems arising in a network setting. The remaining chapters provide an additional in-depth look at some selected topics in wave theory and at their relationship with information theory.

We now provide a brief summary of the contents of the single chapters. In Chapter 2 we introduce the communication problem, define the signals’ space, introduce Slepian’s concentration problem, and discuss how this is related to the number of degrees of freedom of bandlimited functions. We show that the prolate spheroidal wave functions, solving the concentration problem and serving as the optimal representation basis for bandlimited signals, also arise in the context of wave propagation. We also discuss how Slepian’s problem is related to the impossibility of simultaneous localization of signals in time and frequency, which provides the mathematical justification for Heisenberg’s uncertainty principle in quantum mechanics. Thus, the same mathematics of spectral concentration at the basis of information-theoretic results is at the basis of the observational limits of our world.

# 信息论代写

## 数学代写|信息论作业代写information theory代考|Universal Limits

$$r_{\mathrm{S}}=\frac{2 G m}{c^{2}}$$

$$E=m c^{2}$$

## 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。