### 数学代写|matlab代写|CSC113

MATLAB是一个编程和数值计算平台，被数百万工程师和科学家用来分析数据、开发算法和创建模型。

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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

## 数学代写|matlab代写|Neural Nets

Neural networks, or neural nets, are a popular way of implementing machine “intelligence.” The idea is that they behave like the neurons in a brain. In this section, we will explore how neural nets work, starting with the most fundamental idea with a single neuron and working our way up to a multi-layer neural net. Our example for this will be a pendulum. We will show how a neural net can be used to solve the prediction problem. This is one of the two uses of a neural net, prediction and classification. We’ll start with a simple classification example.

Let’s first look at a single neuron with two inputs. This is shown in Figure 1.2. This neuron has inputs $x_1$ and $x_2$, a bias $b$, weights $w_1$ and $w_2$, and a single output $z$. The activation function $\sigma$ takes the weighted input and produces the output. In this diagram, we explicitly add icons for the multiplication and addition steps within the neuron, but in typical neural net diagrams such as Figure 1.1, they are omitted.
$$z=\sigma(y)=\sigma\left(w_1 x_1+w_2 x_2+b\right)$$
Let’s compare this with a real neuron as shown in Figure 1.3. A real neuron has multiple inputs via the dendrités. Some of thẻse branchẻs mean thăt multiplé inputś cản connect to the cell body through the same dendrite. The output is via the axon. Each neuron has one output. The axon connects to a dendrite through the synapse.
There are numerous commonly used activation functions. We show three:
\begin{aligned} \sigma(y) & =\tanh (y) \ \sigma(y) & =\frac{2}{1-e^{-y}}-1 \ \sigma(y) & =y \end{aligned}
The exponential one is normalized and offset from zero so it ranges from $-1$ to 1 . The last one, which simply passes through the value of $\mathrm{y}$, is called the linear activation function. The following code in the script OneNeuron . m computes and plots these three activation functions for an input q. Figure $1.4$ shows the three activation functions on one plot.

## 数学代写|matlab代写|Types of Deep Learning

There are many types of deep learning networks. New types are under development as you read this book. One deep learning researcher joked that you will have the name for an existing deep learning algorithm if you randomly put together four letters.
The following sections briefly describe some of the major types.

A CNN has convolutional layers. It convolves a feature with the input matrix so that the output emphasizes that feature. This effectively finds patterns. For example, you might convolve an $\mathrm{L}$ pattern with the incoming data to find corners. The human eye has edge detectors, making the human vision system a convolutional neural network of sorts.

Recurrent neural networks are a type of recursive neural network. Recurrent neural networks are often used for time-dependent problems. They combine the last time step’s data with the data from the hidden or intermediate layer, to represent the current time step. A recurrent neural net has a loop. An input vector at time $k$ is used to create an output which is then passed to the next element of the network. This is done recursively in that each stage is identical to external inputs and inputs from the previous stage. Recurrent neural nets are used in speech recognition, language translation, and many other applications. One can see how a recurrent network would be useful in translation. The meaning of the latter part of an English sentence can be dependent on the beginning. Now, this presents a problem. Suppose we are translating a paragraph. Is the output of the first stage necessarily relevant to the 100 th stage? In standard estimation, old data is forgotten using a forgetting factor. In neural networks, we can use Long Short-Term Memory (LSTM) networks that have this feature.

## 数学代写|matlab代写|Neural Nets

$$z=\sigma(y)=\sigma\left(w_1 x_1+w_2 x_2+b\right)$$

$$\sigma(y)=\tanh (y) \sigma(y) \quad=\frac{2}{1-e^{-y}}-1 \sigma(y)=y$$

## 数学代写|matlab代写|Types of Deep Learning

CNN 具有卷积层。它将特征与输入矩阵进行卷积，以便输出强调该特征。这有效地找到了模式。例如，您可能会卷积一个大号模式与传入的数据来寻找角落。人眼具有边缘检测器，使人类视觉系统成为一种卷积神经网络。

## 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。