### 数学代写|数学建模代写math modelling代考|Find2022

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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|数学建模代写math modelling代考|MATHEMATICS

The most basic mathematical concept in modeling is that of the function. A relationship between an input $t$ and an output $x(t)$ is called a function if and only if the value of the output $x(t)$ is completely determined by the input $t$. Symbolically, $x(t)$ is a function if and only if
$$t_1=t_2 \Longrightarrow x\left(t_1\right)=x\left(t_2\right),$$
where the double arrow means “implies.” In words, if the inputs are the same, then the outputs must be the same. Said another way, you can’t get two different outputs from the same input. Algebra students learn this as the “vertical line test.” Functions are deterministic. (By contrast, a relation in which you can get two different outputs from the same input is called stochastic; we will turn our attention to stochasticity in the next section.)

In modeling dynamical systems, we are interested in the state of the system (call it $x$ ) as a function of time $t$. That is, we are interested in the behavior of $x(t)$ as $t$ changes. We can list the corresponding values of $x$ and $t$ in a table, and we can also graph $x$ vs. $t$. This list of pairs of numbers (or its graph) is called a time series. You will see many times series graphs in later chapters (e.g., Figures $4.2$ and 8.2). If there are two state variables for the system of interest, say $x(t)$ and $y(t)$, we must show two time series graphs together: $x$ vs. $t$ and $y$ vs. $t$.

In general, the two state variables $x$ and $y$ may be coupled, that is, may depend on each other, so the two time series graphs must be interpreted together. This is a visually difficult task. A better visual tool in this case is that of state space, or phase space, in which the state variables are graphed against each other in the $x-y$ plane. The current state of the system is represented by a point $(x(t), y(t))$ that moves around in the plane as time progresses, tracing out an orbit. You can see an example of orbits in a state space graph in Figure 9.1. The arrows indicate the movement of the point $(x(t), y(t))$ in time. Calculus provides us with many powerful tools for studying systems whose state changes more or less continuously throughout time. The main tool, of course, is the derivative $d x / d t$, which is the instantaneous rate of change of $x(t)$ with respect to time $t$.

## 数学代写|数学建模代写math modelling代考|STATISTICS

Deterministic models are approximations of real systems; a good model captures the signal (main deterministic trend) in the data. Nevertheless, the data likely will deviate somewhat from the model prediction. This deviation from the signal is called noise or stochasticity. The two main types of noise in biological data are process error and measurement error (observational error). The process error occurs because the real system is more complicated than the mathematical model. The measurement error occurs because the real system cannot be measured exactly. Stochasticity in ecological data can be handled with statistical methods, several of which will be addressed in this book.

There are two main types of process error in ecology: environmental stochasticity and demographic stochasticity. Stochastic events in a population can be likened to the toss of a fair coin. Imagine that a single coin is tossed for a population of animals. The outcome of the toss, although random, is the same for each individual member of the population. This is environmental stochasticity. Such extrinsic events as weather cause this type of noise. Now imagine that each animal in the population tosses its own coin. This time there is a random outcome for each individual. This is demographic stochasticity. Individual variability in intrinsic parameters such as birth and death rates cause this type of noise.

Systems in classical physics may have relatively little stochasticity, and their mathematical models can be so precise that some people call them “laws.” Some social science systems, on the other hand, may have a lot of stochasticity – so much so that the signal may be swamped out by noise and mathematical modeling may be impossible. In ecology, deterministic and stochastic forces are more or less equally important. Therefore, noise should-ideally-be incorporated explicitly into a deterministic model to produce a stochastic version of the model. The interaction of deterministic and stochastic forces can give rise to a rich class of emergent dynamic phenomena that cannot occur in purely deterministic or purely random systems.

## 数学代写|数学建模代写math modelling代考|MATHEMATICS

$$t_1=t_2 \Longrightarrow x\left(t_1\right)=x\left(t_2\right),$$

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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。