- Detalles de la revista
- Formato
- Revista
- eISSN
- 2444-8656
- Primera edición
- 01 Jan 2016
- Calendario de la edición
- 2 veces al año
- Idiomas
- Inglés
With the development of human information technology and the increasing speed of network information exchange, the information data generated by human society keeps expanding. Big data with multiple features emerge as required by the needs of the times [1, 2, 3, 4]. Artificial intelligence is a technical science that studies the theories, methods, technologies and application systems used to simulate and expand human intelligence [5]. The realisation of artificial intelligence (AI) must be supported by massive data; otherwise, there will be no data source for machine learning [6]. As a social science, the law is increasingly connected with modern science and technology such as big data and AI in terms of research objects [7].
Artificial intelligence and big data technology have had a profound impact on the whole process of criminal litigation both in terms of technology and value [8]. Technological progress cannot deny the dominant position of human beings. At least in the era of weak AI, it is not feasible to replace human beings with machines [9]. The original intention of research and invention of big data and AI is to rely on technology to liberate human labour and replace human beings in simple and repetitive work [10]. Artificial intelligence intervention in criminal litigation can effectively help improve the efficiency of litigation and reduce the pressure of fewer cases.
The traditional legal training link has many shortcomings [11, 12, 13, 14]. For example, legal documents have a wide range of types and are difficult to be systematically grasped. The simulated trial performance is too much and the simulation degree is insufficient. The cases that students encounter in practice base have randomness and repetition. In order to make up for the shortcomings of these real-life training links, law schools in many colleges and universities now use Legal Experimental Teaching System (LETS) [15, 16, 17, 18].
Relying on the experimental teaching platform developed by Zhongnan University of Economics and Law, LETS aims at cultivating legal personnel's professional quality and practicing ability. It explores the informatisation, integration and intelligence of legal experiment teaching, and the use of computer simulation technology [19, 20]. The content covers legislation, law enforcement, litigation and non-litigation. It is used to build a comprehensive system incorporating the legal experiment teaching software platform. Supported by the powerful background of AI and computer application technology, LETS fully simulates a variety of legal work experiment scenarios. The experimenters play different roles in the legal business in the simulation and interact with each other on a networked work interface. The combination of professional knowledge and practical problems improves the practical ability and fills the gap between theory and practice in the process of legal education and training.
Artificial intelligence was introduced to alleviate the unbearable weight of traditional legal experiment teaching [21]. In the process of teaching experiments in law, it is necessary to make full use of modern information technology methods to carry out teaching reforms [22]. It is also necessary to expand the time and space of legal experimental training, optimise the process of legal experimental training and enrich the resources of legal experimental training. The forms of legal experimental training are more flexible and diverse. The LETS in the context of AI solves the problem of separation between theoretical teaching and practice in legal education [23]. The characteristics of the LETS system also show that its effectiveness needs to be fully utilised to enable the full realisation of its potential. The system integrity of LETS fosters presupposed thinking among law students [24]. LETS's open space-time and project autonomy foster generative thinking among law students. LETS's storage stability, retrieval convenience, comparison intuitiveness and variable simplicity can cultivate the experimental thinking of natural science students in the natural science style of law students [25]. LETS also enables the discovery of real social relations in the combination of elements, and optimises the path of real social relations.
Drawing from the above considerations, this paper proposes a framework based on the deep integration of LETS software and criminal litigation in the context of AI. The main innovations are as follows:
First of all, the process and specific system composition of LETS software in law teaching are introduced in detail. Then, the new opportunities and development prospects arising from the combination of criminal proceedings in the context of AI are introduced. At the same time, a set of deep integration frameworks based on LETS software and criminal litigation under the background of AI is designed. It is also applied to a university law school for experiments, and at the same time uses different AI deep learning to personalise and recommend criminal procedure learning courses. Finally, personalised recommendations are compared with traditional LETS systems and different deep learning models. Experiments show that LETS software can push personalised criminal procedure learning courses more matched by using algorithms in the AI environment.
The scale of legal education has expanded rapidly in recent years, and it has shown the characteristics of a multi-level and multi-channel approach. Traditional methods of social science experimentation are less realistic. In order to solve this problem, the scientific research team led by Zhongnan University of Economics and Law proposed the concept of using modern information technology to build a holographic simulation experiment of legal science. In 2010, they successfully developed the LETS. At present, dozens of law schools and departments across the country have signed agreements with Zhongnan University of Economics and Law to introduce the LETS system to carry out experimental teaching of law. It is also necessary to gain a deeper understanding of the strengths and weaknesses of the experimental teaching mode provided by the LETS informatisation system.
With the direct goal of cultivating the professionalism and ability of legal professionals, let us base our training on the principles of the interactive and participatory experience teaching method. Using legal business simulation technology, a series of legal experiment modules have been developed, covering five aspects: legislation, law enforcement, litigation, non-litigation business and legal thinking training. It has a highly integrated organisational feature for users, experimental projects, experimental classrooms, experimental tasks, experimental reports and experimental results. Administrators, teachers and students can use the system to easily develop and organise a variety of legal experiments.
LETE consists of five subsystems: the public administration subsystem, the legislative experiment subsystem, the law enforcement experiment subsystem, the litigation experiment subsystem and the non-litigation experimental subsystem. Each system consists of several functional modules, the specific structure of which is illustrated in Figure 1.
According to the framework provided by the system, a large number of experimental teaching projects in law can be freely created. You can quickly create teacher users and student users, and register for each experimental teaching classroom. Students conduct simulation experiments on legislation, law enforcement, litigation and non-litigation in small groups under the guidance of teachers or independently. Teachers can easily evaluate experiments and manage experiment results. Automatic generation of a series of statistical reports can be programmed, and these reports would allow system administrators to gauge the effectiveness of the experimental teaching mode provided by the LETS informatisation system.
Fig. 1
LETS software. LETS, Legal experiment teaching system
Jurisprudence is a discipline that attaches equal importance to theory and practice, and it not only pursues fairness and justice as the supreme good, but also takes it as its mission to resolve major or trivial disputes in reality. On the one hand, legal education should pay full attention to the transmission of legal theoretical knowledge, and on the other hand, efforts should be made to cultivate the legal practice skills of law students. The fusion of legal theory and legal skills is not an easy task. As a law student who has not yet directly experienced the complicated social life, it is important to examine how we can identify and evaluate these legal provisions and legal doctrines in order to successfully establish our legal position and legal thinking. Legal education always assists students in ‘generating’ legal thinking and the concept of fairness and justice through various practical training sessions (legal document writing, moot court trial, clinic-style case study, professional internship, social investigation of legal issues, etc.).
Since AI is used in criminal proceedings, the advantage of evidence collection is that it is highly consistent with the requirements of ‘credible and sufficient evidence’ for evidence collection and acceptance. AI-powered judicial cases are handled based on a huge database and with specific algorithms. It has the characteristics of high-speed processing of information, grasping key vocabulary and integration of data resources. Combining it with criminal proceedings, first of all, can effectively solve the problems of high-tech crimes that are difficult to detect and for which it is difficult to collect evidence. Then, we can alleviate the shortcomings of ‘fewer cases’ in criminal cases in China. At the same time, it can effectively alleviate the pressure on the people's courts to handle cases under the reform of the personnel ratio system for judges. It mainly includes the following aspects:
Smart courts improve judicial efficiency. Big data pushes similar cases and laws and regulations through the analysis of case input information. The time for legal search has been shortened, the efficiency of case handling has been improved and the trial results of similar cases that are very different have been reduced as much as possible. Innovative investigative methods for smart policing. New forms of crime, such as Internet fraud, theft and trafficking of personal privacy information, are emerging one after another. The use of AI to improve detection methods also requires constant updating and creation. Wisdom in case handling narrows the difference in case handling. The new trial support mechanism of judicial reform requires the judge undertaking the case to conduct a search on the China judgement documents network, trial case database and so forth, and is responsible for the authenticity and accuracy of the search results. Artificial intelligence technology can effectively reduce the judge's wilful use of legal provisions, and arbitrary adjudication, and ultimately lead to the embarrassing situation of different judgements in the same case.
Based on the AI background, the deep integration framework of LETS software and criminal litigation is a comprehensive simulation system, as shown in Figure 2. The framework includes several parts, such as the legislative experimental system, the law enforcement experimental system, the litigation experimental system, the non-litigation experimental system and the public management system. Finally, the deep learning of AI will be used to predict the results and in the experimental analysis. Criminal procedure experiment in the context of AI is one of the components of the litigation experiment system, and its specific operation process is as follows:
Group classes and create tasks. After the system administrator gives the classroom teacher permission, law teachers can import the class list into the system, and after importing, they can group students. The students can be grouped according to the number of roles in the criminal proceedings. In the event of a mismatch or a disaggregated role assignment, multiple non-conflicting roles can be held by the same classmate, such as witnesses and victims, expert evaluators and clerks. Once grouped, you can create the appropriate task, that is, select the experimental case. At present, the number of cases in the system is pre-implanted, and thus the number is still relatively limited, with only 14 criminal cases. Teachers can select appropriate cases based on the progress of the theoretical course teaching, and create the same or different case tasks for each student experimental group. Let students enter the experimental system and understand the basic situation of the case. Subsequently, let them read the system's given materials to understand the case handling process and to ensure that the specific content and requirements of the experiment are clearly registered in their comprehension. The LETS system provides some materials in advance for each case, such as basic facts, interrogation records, litigation documents, etc. Students serve as reference samples; otherwise, they lose the significance of the experiment. To be capable of working with these materials, students are required to be familiar with them in advance. However, in the specific experimental process, the case process should be handled according to the changes in the situation. Students follow the procedure for experiments. The experimental cases in the system are designed as a step-by-step process according to the complete process of criminal proceedings, and there is a process guidance diagram. Students are assigned roles in sequence. The responsible person of the public security organ approves the filing of the case, and after filing the case, the investigation is selected for investigation based on the circumstances of the case. Criminal suspects are interrogated, witnesses and victims are questioned, etc. These investigations are conducted online. At each stage, the case processing will form some materials, which are the basis for judging the results of the experiment. Legal documents are filled in by students in the given format and in combination with the facts of the case. In the aspects of questioning, interrogation, court investigation, debate, etc., students are encouraged to expand the content according to the specific circumstances of the case to make the experimental situation more realistic. Teachers judge the results of the experiment. After students complete the lab process, teachers can log in to view the progress of each lab group and the materials students have completed at each stage. The results of the experiment are comprehensively evaluated, that is, the completion of the entire experiment and its related data are scored. Each student's performance in the group experiment is then scored. However, this is because the experiments are conducted in groups, and each group of students has a different division of litigation roles. Teachers have difficulty grasping the specific performance of each student and may only be able to judge their performance based on the material they have completed in the system.
Fig. 2
Framework of deep integration of LETS software and criminal litigation based on. AI, artificial intelligence; LETS, legal experimental teaching system
In this paper, the experimental data of a university law school are selected from the semesters 2021.9 to 2022.6. Students and faculty use the LETS system to study the criminal procedure course. First, teachers select courses for students. Students study according to the course selected by the teacher, and collect a questionnaire of after-class learning feedback after learning. Artificial intelligence conducts data analysis to make algorithm recommendations, recommending students to master and learn the corresponding criminal procedure courses. Finally, based on the results obtained at the end of the semester, the student's satisfaction with the course and the accuracy of the criminal procedure course based on the personalised study recommended by LETS are analysed.
The present study experiments with a LETS system and a computer with Linux, Python 3.6.1, TensorFlow 2.0, 32 GB of memory and GTX 1080Ti graphics card in the experimental software platform. The specific parameters are shown in Table 1.
Hyperparameters setting
| N | 6 | Attention layer number |
| Heads | 8 | Number of multi-layer heads |
| Batch size | 32 | Batch processing steps |
| Hidden | 512 | Hidden layer |
| Dropout | 0.1 | Prevent overfitting |
| Learning rate | 1 × 1−4 | Learning rate |
Since model parameter settings have a great impact on the accuracy and robustness of the model, this paper obtains better continuous model training and updated model parameters, personalised recommendation accuracy (P), recall rate® and F1 value as evaluation indicators.
In order to verify the effectiveness of the proposed method, not only the traditional LETS system but also the traditional neural network is discussed. Five sets of comparative experiments were set up. The inputs are all weight-matching vectors. To verify the effect of feature extraction and the impact on the model during vector processing, the experimental results were recoded, and are shown in Table 2.
Experimental results
| LETS | 87.93 | 88.23 | 87.31 |
| LETS + LSTM | 89.15 | 90.61 | 89.24 |
| LETS + BiLSTM | 92.19 | 92.56 | 91.79 |
| LETS + CRF | 95.20 | 94.08 | 93.52 |
| LETS + LSTM + CRF | 95.12 | 93.32 | 92.29 |
| LETS + Transformer | 94.24 | 92.34 | 93.24 |
| LETS + Transformer + CRF | 97.89 | 97.46 | 96.85 |
LETS, legal experimental teaching system
After several rounds of experiments and cross-verification of experimental results, the evaluation results of various baseline models and fusion models are derived, and these are shown in Table 2, while the model execution time is shown in Table 3. In order to further visually demonstrate the superiority of the proposed framework, the training process of each model is analysed, and the accuracy change process of the set is verified for the training process of each model.
Training time (/s)
| LETS | 1089 |
| LETS + LSTM | 1834 |
| LETS + BiLSTM | 1227 |
| LETS + CRF | 652 |
| LETS + LSTM + CRF | 451 |
| LETS + Transformer | 320 |
| LETS + Transformer + CRF | 289 |
LETS, legal experimental teaching system
The experimental results of Table 3 show that the LETS software framework proposed in this paper has achieved the best results in personalised criminal procedure learning, with an accuracy rate of 97.89%. Compared with other models, the overall effect is increased by 4%–5%, which demonstrates the superiority of the model used in this paper. Experiments also prove that the accuracy rate of various deep learning models and LETS systems in the training process changes trends due to the characteristics of the data. Concerning the suitability of various models for the application of LETS software to enable students to learn criminal procedures, it is ascertained that the Transformer + CRF model demonstrates greater suitability. The LSTM and BiLSTM models as baselines have a turbulent trend as a whole before converging. The accuracy of the verification set of this model is the most excellent, reaching the convergence state after 289s, and the accuracy convergence rate is 97.89%, which is significantly higher than those of the other models in the comparative experiment, thus further verifying the effectiveness and robustness of the model proposed in this paper.
The present research studies the experimental principle of deep integration of LETS software and criminal procedure under the background of AI, and has as its chief aim the cross-convergence of AI and LETS software with criminal prosecution. The LETS software is used to form a personalised criminal procedure learning system for college law students. Personalised recommendations are made through AI algorithm learning, forming a big data platform, and providing an important basis for learning-related criminal procedure laws. Based on the above problems, this paper proposes a framework for the deep integration of LETS software and criminal litigation under the background of AI. First, the paper introduces the situation currently prevailing concerning the development of criminal proceedings in the context of AI. Then, a deep integration framework based on LETS software and criminal litigation in the context of AI is designed. At the same time, the framework is used to facilitate the LETS system to intelligently learn criminal proceedings. Experimental results show that LETS software can push personalised criminal procedure learning courses more matched by using algorithms in an AI environment. There are also some problems with the experiments conducted as part of this study, and they are as follows:
Algorithmic bias leads to judicial injustice. The application of AI is based on algorithms. An algorithm is an inexhaustible set of rules. An algorithm specifies a series of operations to solve a particular type of problem and is an accurate and complete description of the method of solving the problem. Capture of shallow information is mainly carried out by large databases. Pre-designed algorithms are inherently hysterical. Subjective discrimination by people leads to algorithmic bias. The algorithmic system may cause the program to end. Putting sufficiently objective proof criteria into AI is a reasonable and legal operation of input algorithm rules, but its inherent drawbacks are also huge and obvious.
In future work, the systematic research proposed in this paper will be improved in relation to the aspects of increasing the transparency of AI technology, determining the scope of work of AI justice and establishing the working principles of AI justice.
Fig. 1
Fig. 2
Hyperparameters setting
| N |
6 | Attention layer number |
| Heads | 8 | Number of multi-layer heads |
| Batch size | 32 | Batch processing steps |
| Hidden | 512 | Hidden layer |
| Dropout | 0.1 | Prevent overfitting |
| Learning rate | 1 × 1−4 | Learning rate |
Training time (/s)
| LETS | 1089 |
| LETS + LSTM | 1834 |
| LETS + BiLSTM | 1227 |
| LETS + CRF | 652 |
| LETS + LSTM + CRF | 451 |
| LETS + Transformer | 320 |
| LETS + Transformer + CRF | 289 |
Experimental results
| LETS | 87.93 | 88.23 | 87.31 |
| LETS + LSTM | 89.15 | 90.61 | 89.24 |
| LETS + BiLSTM | 92.19 | 92.56 | 91.79 |
| LETS + CRF | 95.20 | 94.08 | 93.52 |
| LETS + LSTM + CRF | 95.12 | 93.32 | 92.29 |
| LETS + Transformer | 94.24 | 92.34 | 93.24 |
| LETS + Transformer + CRF | 97.89 | 97.46 | 96.85 |
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Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsResearch on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network