Genetic Operators and MATLAB Code for Numerical Analysis
3.2 Genetic Operators
(1) Crossover Operator
The crossover operator randomly pairs individuals from the parent population for crossover operations, generating ( m ) offspring individuals to form the next generation. Two types of crossover are employed: single-point crossover and two-point crossover. Given two individuals for crossover ( P = {p_1, p_2, p_3, \dots, p_n} ) and ( Q = {q_1, q_2, q_3, \dots, q_n} ), a random crossover point ( b_1 ) is chosen from the range [1, n] for single-point crossover. The elements before ( b_1 ) in ( P ) are copied to offspring individual ( \text{new Individual1} ), while the remaining elements are copied from ( Q ). Similarly, a second offspring ( \text{new Individual2} ) is generated by swapping the roles of ( P ) and ( Q ). In two-point crossover, two random crossover points ( b_1 ) and ( b_2 ) are chosen, and the elements between ( b_1 ) and ( b_2 ) in ( P ) are copied to the offspring, with the remaining elements taken from ( Q ).
(2) Mutation Operator
After the crossover operation, two mutation operators are applied to the offspring individuals. The first is rotation mutation, where a random position ( \text{bit} ) is chosen, and with probability ( p_m1 ), the portion of the individual after ( \text{bit} ) is rotated. The second is position mutation, with a smaller probability ( p_m2 ), two integers ( \text{bit1} ) and ( \text{bit2} ) are randomly chosen from the range [1, n], and the corresponding parts of the individual are swapped.
(3) Selection Operator
The fitness of the mutated offspring individuals is evaluated using the lowest level line method. The parent and offspring individuals are ranked by their fitness in descending order, and the top ( m ) individuals are selected as the next generation's parents.
3.3 Termination Criteria
The steps in sections 3.2(1), 3.2(2), and 3.2(3) are repeated until the fitness of the best solution meets the required threshold or the pre-defined number of generations is reached. At this point, the optimal solution is output.
4. Case Study
To test the performance of the algorithm, two cases from literature [3] are solved. In Case 1, a large rectangle of size ( 15 \times 40 ) is divided into 25 smaller rectangles. Based on the lowest level line method, the corresponding coding sequence is ( \text{Opt} = {1, -9, 11, -15, 17, -24, -25, -10, -14, -22, -23, -2, -3, -5, 18, 7, -8, -12, 19, -20, 21, 6, 13, 4} ). The width is set at 40, and height considerations follow suit for the genetic algorithm implementation.
Matlab
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2024-11-06
Hierarchical Analysis MATLAB Code-Cancer
该存储库包含我们题为“用于从整个幻灯片图像中提取格里森组织并分级前列腺癌的扩张式残留分层分割框架”的论文的实现。拟议框架的框图所提出的框架是使用TensorFlow 2.3.1和Keras API与Python 3.7.8开发的。此外,一些预处理步骤和结果汇编也通过MATLAB R2020a执行。下面显示了安装和运行代码的详细步骤:
安装
要运行代码库,需要以下库。虽然该框架是使用Anaconda开发的,但它应该与其他平台兼容。- TensorFlow 2.3.1- Keras 2.3.1- OpenCV 4.4.0- tqdm- Matplotlib
另外,我们还提供了一个yml文件,其中包含所有这些软件包。
数据集
请下载所需的数据集,并按照以下提到的层次结构来训练和测试建议的框架:
├── trainingDataset
│ ├── train_images
│ │ └── tr_image_1.png
│ │ └── tr_image_2.png
Matlab
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2024-11-06
IEEG_Data_Analysis_with_Matlab_Code.zip
使用分散的数据点来插入头部图像的像素值。此函数使用GRIDDATA从头部图像上的散点插入像素值。参考图像可用于从10/20国际系统(脑电图电极位置)中交互式选择点位置。插值选项包括线性、三次和最近。输入是对应于每个选定位置的值。包括示例。
Matlab
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2024-11-03
Fourier Inverse Transform Matlab Code-Quantarhei Molecular Open Quantum Systems Theory
Quantarhei 是一个主要用 Python 编写的 分子系统开放量子系统模拟器。它的名字来源于希腊哲学家赫拉克利特的著名格言“潘塔·瑞”(Panta rhei),意指“一切都在流动”或“一切都在变化中”。这一名称非常符合模拟的主题,尤其是在处理 量子系统 时,当‘Panta’替换为‘Quanta’,则显示了其量子性质。在 Quantarhei 中,最后四个字母(‘rhei’)使用希腊文书写,符合 LateX 约定,即(‘\rho \epsilon \iota’)。该框架不断发展,并已经提供了用于定义分子及其聚集体与外部环境相互作用的辅助类。Quantarhei 支持通过各种 Redfield 和 Förster 理论来计算单个分子和其聚集体的吸收光谱及激发能量传递动力学。所有实现的方法和理论都提供了 Python 代码,并允许通过使用 C、Fortran 或其他低级语言编写的优化例程来扩展和替换这些代码。最初开发阶段,重点放在为分子系统的模拟提供有效的 傅里叶反变换 方法和工具。
Matlab
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2024-11-06
Simulating Vibration Dynamics in MATLAB
In this article, we explore how to conduct vibration simulation using MATLAB. MATLAB provides a powerful set of tools for modeling vibration dynamics in various engineering fields. Here’s a step-by-step guide to effectively simulate vibrations:
Step 1: Define the System
Start by defining the mass, spring, and damping parameters for your vibration system. These parameters are crucial for creating a reliable simulation.
Step 2: Set Up the Differential Equations
Use MATLAB’s symbolic math toolbox to define the differential equations governing the vibration behavior. This step ensures accurate simulation results.
Step 3: Simulate Using MATLAB Functions
Utilize MATLAB’s ode45 or ode23 functions for solving ordinary differential equations. These functions help simulate the vibration responses over time.
Step 4: Visualize Results
Use MATLAB’s plotting tools to visualize displacement, velocity, and acceleration. Graphs provide clear insights into the vibration characteristics of the system.
Note: Fine-tuning parameters like damping ratio and stiffness constant can significantly affect the simulation’s accuracy.
This guide should help you achieve precise and practical vibration simulations using MATLAB, improving your understanding of dynamic responses in mechanical systems.
Matlab
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2024-11-05
MATLAB Code for DEM Noise Analysis using 2D DFT
DFT的matlab源代码标题日期作者使用FFT测试DEM中的高频噪声2017年1月本·普林顿(purinton@uni-potsdam.de)代码迁移到PYTHON :) 注意:截至2020年5月,此分析已迁移到Python:如果要使用MATLAB TM,请继续下面的操作。使用2D DFT进行DEM噪声分析的Matlab代码。该MATLAB TM函数用于栅格化地形数据(DEM)的频谱分析,以分析高频,低波长噪声,如以下所示: Purinton,B.,and Bookhagen,B .:验证中部安第斯高原南部的数字高程模型(DEM)和地貌指标,《地球表面动力学》,2017年。)运行它在分析之前,用户必须下载并设置一些必需功能的路径: T. Perron的2DSpecTools软件包可用。有关此光谱分析程序的背景以及引起该分析的论文,请参见:Perron,JT,Kirchner,JW和Dietrich,WE:景观中特征空间尺度和非分形结构的光谱特征,地球物理研究杂志,113,2008年。 W.Schwangh
Matlab
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2024-11-06
MATLAB Code for Cross Sectional Area Analysis from Time Series Data in Excel
This MATLAB code imports time-series data related to riverbank and water depth coordinates in XY format, sampled every 10 minutes. The code calculates the cross-sectional area for each water depth and writes the following data to an Excel file: Date/Time, Water Depth, and the cross-sectional area for each water depth.
Matlab
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2024-11-06
MATLAB_Import_Excel_Code_RPD_PLoSOne_Resistor_Disruption_Distance_Analysis
MATLAB导入Excel代码 核机器测试脑网络与表型之间的关联
作者:亚历山大·詹森(MS),杰森·特雷格拉斯(Jason R Tregellas)博士,Brianne Sutton博士,邢福永博士,Debashis Ghosh博士
摘要:在过去的十年中,由于定量网络分析能够描述大脑网络的一般拓扑原理,因此在其功能上的应用已广受欢迎。然而,将标准统计分析技术应用于功能磁共振成像(fMRI)连接图时,会出现许多问题。通常,这些映射的摘要度量(例如全局效率和聚类系数)使图拓扑不断变化的结构从多个比例崩溃为一个比例。这可能会导致全脑时空模式信息的丢失,这在关联和预测分析中可能很重要。从电气工程领域来看,电阻扰动距离是对同一顶点集上的图之间相似度的量化,已显示该图可识别动态图的变化(例如来自fMRI的变化),而不会造成计算上的昂贵或导致损失信息。
这项工作提出了一种新颖的基于核的回归方案,该方案结合了阻力扰动距离,可以使用模拟和真实数据集更好地了解与fMRI的生物表型的关联。
真实数据集:COBRE随附手稿中使用的真实数据集来自卓越生物医学研究中心(COBRE)通过新墨西哥大学神经科学中心提供。
Matlab
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2024-11-05
Multiple Correlation Coefficient Homogeneity Test in MATLAB
在本脚本中,多个相关系数之间的比较将被测试。该脚本用于检验k个相关系数的样本是否相等,以便可以用平均相关系数表示。相关系数可以从具有不同样本大小的样本n1, n2,...,nk中计算得出。
Matlab
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2024-11-03