With the rapid development of emerging information technology, biometric information has become an important part of today’s information society [1]. The acquisition, dissemination and utilisation of biometric information have become simpler and more convenient with the development of information technology, but this has also led to an increasing number of violations of biometric information [2]. At present, the crime of infringing biometric information in the criminal law is more reflected in the relevant provisions of Article 253 of the Criminal Law on the crime of infringing on citizens’ personal information. The current crime of infringing citizens’ personal information has relatively vague provisions on acts of infringing biometric information. Information is generally identified as general personal information [3]. As a result, it is difficult for the conviction and punishment of acts related to infringing citizens’ biometric information to be adapted to the culpability and punishment, and it is also not conducive to the protection of citizens’ information and the safety of life and property. At present, the theoretical circles have not yet reached a consensus on the number of crimes of infringing biometric information, mainly focussing on the legal interests protected by the crime of infringing on citizens’ personal information [4, 5]. The determination of the number of crimes for infringing biometric information needs to be combined with the analysis of specific behaviours. Based on two types of biometric information violations, this article discusses the criminal law imputation path under different types of behaviour patterns.

The development of biometric identification will bring new breakthroughs and changes to human life research. Its development has played a role in promoting related disciplines and will definitely have a huge impact on industries such as health, medicine and food, with huge economic benefits [6, 7]. Developed countries abroad started relatively early in this regard, and some institutions have already taken the lead in the field of biometric identification, and they all have developed relevant databases and systems. In the study mentioned in Popov et al. [8], it is proposed that the National Center for Biotechnology Information of the United States has developed the Entrez system, which includes a number of large databases, such as biological information databases. The European Bioinformatics Institute is proposed in the study mentioned in Yeo et al. [9], which provides a series of biometric identification databases and analysis tools. These institutions are not isolated; they have very close cooperation so that users can easily obtain information. There are also some major scientific research institutions on biometric identification in China. The ‘centrality–lethality’ rule proposed in the study mentioned in Zhang et al. [10] points out that the criticality of biological information is closely related to the topological structure of the biological information interaction network, which is manifested in the fact that the missing biological information nodes with more neighbours are more easily affected. network structure, resulting in a lethal effect on the body. Sabharwal [11], it is proposed that in the biological information network, there are many nodes with high betweenness but low degree that play a key role in the network. Based on this finding, the betweenness centrality (BC) is proposed. In the study mentioned in Zhang et al. [12], eigenvector centrality (EC) and subgraph centrality (SC) are proposed to consider the importance of biological information nodes from the global and local aspects of the network, respectively. It can be seen that researchers at home and abroad have conducted a lot of research on biometric identification, but they have never researched the integration of biometric identification technology with national criminal law.

This work studies the criminal law imputation path of biometric information. First, a minimum uncertainty neural network (MUNN) model is constructed. Through this model, the classification and identification of citizens’ biometric information can be realised. The resulting criminal law issues should find a suitable entry point, determine the path of criminal law attribution, and realise the judgement of criminal responsibility for the relevant subjects of infringing citizens’ biometric information so that the criminal law can effectively participate in the governance activities of biometric information.

The criminal principle of classifying and identifying biometric information through the MUNN model has been pointed out previously. What needs to be discussed next is what criminal law needs to use the MUNN model to identify biometric information. Such subjects should be held accountable, and what kind of entry point should be used to impute relevant subjects should be found.

In the discussion on infringing the criminal subject status of citizens’ biometric information, many views theoretically believe that the criminal subject qualification of units in criminal law of China is the result of the fiction of the criminal law. There are obstacles. However, the unit is essentially a collection of natural persons’ rights and obligations, and the discussion of the unit’s criminal responsibility is also carried out through the will and behaviour of specific natural persons in the unit [21]. Similarly, imposing a penalty on a unit actually deprives the specific natural person in the unit of the rights, thus having the effect of punishment to prevent crimes. Therefore, the fiction of the unit subject in the criminal law cannot be used to support the independent criminal subject status of citizens’ biometric information. Based on the tool attributes of the current biometric information, the damage caused by the infringement of citizens’ biometric information is in the final analysis the damage caused by the behaviour of the relevant subject. In order to realise the prevention of crimes through punishment, the technical tool of biometric information needs to be used to find the attributable subject behind it.

In the process of the use and development of modern technology, there is often a long causal chain, especially in biometric information technology. The complex software systems used by biometric information often have many developers involved in the development of various parts of the software at different stages. Even in the case of biometric information based on a self-learning algorithm, there is a process of data production, selection and processing. The process also requires the participation of multiple subjects and multiple stages [22]. Whether it is the person who provides the data, the person who collects and processes the data, the person who sells the data, the person who analyses the data, etc., it is possible to affect the process of self-learning of biometric information. At the same time, each participating subject only has knowledge of the specific stage in which the subject participates and cannot predict or control the influence of other subjects on the operation of biometric information in the previous stage or the next stage. The causal chain can also continue to extend to the application stage of the algorithm, and when the algorithm is dominated by the user, it can also produce corresponding damage results. In this causal chain, the damage caused by the violation of citizens’ biometric information may be caused by the superposition of causal relationships in multiple stages, or it may be caused by a certain stage independently, so theoretically, the violation of citizens’ biometric information will be. The characteristics of identification information responsibility judgement are summarised as a kind of ‘the problem of many hands’. How to accurately locate the causal behaviour in the causal chain is of critical significance to the determination of the responsibility of the relevant subjects of biometric information. Article 2 of the ‘Code of Ethics’ stipulates that the applicable subjects of the code include ‘natural persons, legal persons and other relevant institutions engaged in biometric information management, research and development, supply, use and other related activities’, and in Article 2, paragraph 1 to the definition of the relevant subject is clarified in paragraph 4 [23]. This regulation defines a specific scope for the relevant subjects of biometric information and conforms to the characteristics of ‘multi-subject responsibility’ of biometric information. It regulates the behaviour of subjects in ‘management, research and development, supply and use’, which can cover biometric information. Every link from design and development to final use: As far as criminal law is concerned, it is necessary to pay attention to the definition of the scope of relevant subjects of biometric information in the Code of Ethics because in the past, the discussion of biometric information product liability in criminal law theory circles often only focussed on the relationship between producers and users. Division of responsibilities: This division of responsibilities is in line with the requirements of the ‘Development Plan’ in 2017 to ‘implement a two-tier regulatory structure with equal emphasis on design accountability and application supervision’ for biometric information, thereby focussing on both design and application and effectively handling most cases of damage to biometric information products. However, the definition of the scope of relevant subjects in the ‘Code of Ethics’ brings inspiration to criminal law theory: sometimes the cause of biometric information damage does not originate from the producer or user, as well as problems in biometric information management or research and development. It is entirely possible to lead to the occurrence of damage results and then to the issue of criminal liability. If it is required to establish a corresponding artificial intelligence supervision mechanism, the staff of state organs who are legally obliged to supervise activities related to biometric information may constitute a crime of dereliction of duty or abuse of power due to dereliction of duty. This is the principle of negligence in supervision. Conclusion [24]: Another example is that the production activities of biometric information products belong to the supply chain of biometric information according to the definition in Article 2 of the ‘Code of Ethics’, and in the development process of biometric information technology, the producers and developers of biometric information may not the same subject. For example, in the case of superimposed use of disclosed algorithm technology in the production process, the producer cannot control the process of upstream algorithm development, and deviations in the upstream algorithm development process are often the root cause of defects in biometric information. The main body of biometric information ‘management, research and development, supply and use’ can control or intervene in biometric information at different stages, so they need to bear corresponding obligations. This is the conclusion that the principle of business negligence can produce.

Safety in a risk society is one of the basic value orientations that criminal law needs to adhere to, and under certain circumstances, the safety value of criminal law takes priority over other values, that is, sometimes only on the premise of realising safety value, criminal law can pursue other values. Therefore, if we only discuss from the perspective of producers and users, we will ignore the biometric information managers and developers who are also in the causal chain of ‘multi-subject responsibility’, and it is difficult to meet the needs of contemporary criminal law to defend against technological risks. Of course, the damage caused by the biometric information may also exist in which the relevant subjects cannot be held liable. For example, when the R&D, supply, management and use links all meet the requirements of the specification, the algorithm applied to the biometric information may also cause algorithm discrimination and algorithm bias. The reason may be that the algorithm has autonomously learned the discriminatory and prejudicial knowledge that is common on the Internet. This phenomenon is the reflection of the algorithm on the objective existence of the society. It can be said that the entire social group is responsible for this. For such phenomena, the criminal law needs to maintain due humility. Even in order to prevent risks, it cannot be held accountable only based on the results. Otherwise, it is easy to expand the scope of the attack, and the criminal responsibility will be transformed into a pure result responsibility, thus forcing the biometric information. Practitioners are trembling and timid, inappropriately inhibiting the progress of algorithms and the normal development of biometric information business.

After determining the scope of the subjects to be held accountable, we can further examine the specific path to confirm the criminal responsibility of the relevant subjects.

Obtaining biometric information for the purpose of committing a crime for oneself should be punished as a crime by the absorption theory. Take the perpetrator’s conduct of extortion after stealing a large number of citizens’ biometric information as an example. Although individually, the perpetrator committed two acts, the first act constituted the crime of infringing on citizens’ personal information, and the second act constituted the crime of extortion, but between these two crimes, there is a relationship similar to dependence. It is precisely because of this special state that there is an absorption relationship between the crime of infringing on citizens’ personal information and the crime of extortion. In this relationship, the criminal act of infringing on citizens’ personal information does not have strong independence, and the act is absorbed by the more independent crime of extortion. On the whole, it should also take the initiative in the final conviction and punishment. Absorption of racketeering convictions and penalties, it seems that the crime of violating citizens’ personal information and the crime of extortion are two separate crimes, but there is an extremely close connection between these two crimes, and this connection also provides the possibility for the absorption of crimes.

Compared with the implicated crime theory, the absorption crime theory is more reasonable. The final result of the implicated offender and the absorbing offender is similar, that is, they are both punished as one crime, but the absorbing offence theory is more applicable to the case of illegally obtaining biometric information for their own crime in the connection between the subjective intention and the punishment result. Illegal acquisition of biometric information for one’s own crime involves both homogeneous and heterogeneous behaviours, and implicated offenders cannot be applied to implicated in heterogeneous acts. Absorbing offenders have a wider scope of application and are more suitable for infringing on biometric information in this case. Behavioural regulatory needs [25]: In summary, in the case of illegally obtaining biometric information for one’s own crime, the identification of infringing biometric information and other acts through the theory of absorption is more in line with the principle of adapting the crime and punishment. The complex and difficult-to-judgement situation provides a clearer judgement. Under this theory, whether the act of obtaining biometric information is legal or illegal can be reasonably explained if it is absorbed by subsequent crimes.

Obtaining biometric information for others to commit crimes should be punishable by multiple offences. The term ‘obtaining biometric information for others to commit a crime’ as mentioned here refers to the act of providing biometric information to others after knowing that another person uses the biometric information provided by him to commit a crime after obtaining the biometric information legally or illegally. Obtaining biometric information for others to commit crimes, from a stand-alone perspective, if the perpetrator first illegally obtains citizens’ biometric information or legally obtains citizens’ biometric information and then illegally provides it to others without consent, it shall be subject to the ‘Supreme People’s Court and Supreme People’s Procuratorate Regulations on Handling Infringement’. The relevant provisions of the interpretation on several issues concerning the application of law in criminal cases of citizens’ personal information (hereinafter referred to as ‘interpretation’) have constituted the crime of infringing upon citizens’ personal information. Secondly, if the perpetrator knowingly uses the citizen’s biometric information to commit other crimes and still intentionally provides the biometric information for him, he is a helper of other criminal acts and should also bear criminal responsibility. In this case, if the theory of absorbing crime is used, it is necessary to emphasise behaviour and absorb light behaviour, and which one is more important, whether it is the principal and the accomplice, or the sentencing result, the judgement standard is difficult to determine, and the result will be inconsistent. At the same time, it cannot be judged that there is a necessary implicated relationship between the two acts. To sum up, obtaining biometric information for other people’s crime-related behaviours and punishing them for multiple crimes conform to the principle of adapting guilt and punishment and also meet the needs of judicial practice.

Infringement of criminal tool-type biometric information is divided into obtaining biometric information for one’s own crime and obtaining biometric information for others to commit crimes, which are determined according to different situations, which avoid the traditional single-crime model or the combination of multiple crimes. There are flaws in the standards on which the penalty model is based. Specifically, the absorbing offender theory is used, instead of the implicated offender theory, in obtaining biometric information for the determination of one’s own crime. Although the final presentation results are all treated as one crime and have similarities, the theory of absorbing crime does not require that the perpetrator must have only one criminal intent, and it can also be applied to homogeneous acts objectively. Both subjective and objective aspects are more rational. In the determination of obtaining biometric information for others to commit crimes, different behaviours are identified separately, and finally, multiple crimes are punished. Compared with obtaining biometric information for oneself to commit crimes, obtaining biometric information for others to commit crimes involves more complex subjects. In addition, it is more difficult to determine when the criminal intent occurred subjectively. Obtaining biometric information for others to commit multiple crimes in a crime is reasonable in the determination of responsibility and punishment and the determination of criminal behaviour.

With more and more cases of crimes using biometric information, many scholars have begun to study how criminals obtain citizens’ biometric information. Neural networks are considered by many researchers to be the most common method for obtaining biometric information about citizens. Therefore, this article proposes a new MUNN model, which combines Bayesian probability and particle swarm optimisation (PSO) to train its parameters. Criminals use this model to complete the classification and identification of citizens’ biometric information so as to achieve criminal purposes.

Inferring the uncertainty of various types of _{j}

Taking the logarithm of both sides, we get

Its form is similar to the general signal transmission equation of the neural network: _{ii}_{i}

Taking the logarithm of both sides, we get

When _{ii′}_{ii′}_{ii′}

The equation for obtaining the threshold can be expressed as follows:

The equation for obtaining the weights can be expressed as follows:

The uncertainty equation can be expressed as follows:

Or normalising π_{j}

Based on the previous equation, the neural network structure can be determined, as shown in Figure 1.

The secondary model is defined as the MUNN model. After obtaining the weight ω_{ji}_{j}

The speech rate usually refers to the pronunciation speed, which is a measure of the speaker’s pronunciation speed. It can be reflected by calculating the number

With an _{1}, _{2}, ... , _{N}_{1}, _{2}, ... , _{N}

So, the equation can be expressed as follows:

Assuming events A_{i} = {_{i} occurs}, _{1}, _{2}, … , _{N} are independent in pairs:

Set event _{1} ∪ _{2} ∪ … ∪ _{N}) from _{1}, _{2}, … , _{N}, we can get

If _{i}_{i}_{i}

π = 1 −

When the classification set _{1}, _{2}, … ,_{m}) and j ∈ [1, 2, … ,_{j}

Therefore, when classifying, select π_{j}

In order to verify the validity of the MUNN model for the classification and identification problem, we conduct a classification and identification test on the two-dimensional signals of the citizen biometric information of 10 people (100 samples for each person, a total of 1000 training samples). Before the signal is input, the two-dimensional signal needs to be preprocessed. According to the characteristics of each dimension of the signal, the continuous value of the signal is divided into 11 and 13 discrete regions at equal distances to meet the MUNN discrete value input requirements. For each iteration, it takes about 20 s, with 1G P3 processor PC, 128M memory, Win2000 system, VC++6.0 language.

The Bayesian probability model, the PSO training model and the MUNN model proposed in this article are used to train these 1000 samples, and the results of the three models in terms of the number of misjudgements, recognition rate and iteration times are analysed. The comparison results are shown in Table 1.

Comparison of training results of different models

Bayesian probability model | 287 | 71.3 | 1 |

PSO model | 429 | 57.1 | 1500 |

Minimum uncertainty neural network model | 65 | 93.50 | 1501 |

PSO, particle swarm optimisation

Table 1 shows that in terms of the number of misjudgements, the MUNN model proposed in this study has the least number of misjudgements, and only 65 samples are misjudged; in terms of recognition rate, the model proposed in this article has the highest recognition rate, reaching 93.5%. In terms of the number of iterations, the number of iterations in this study is the most, so the classification and recognition process are the most stable, and the accuracy is also high. In order to compare the training results more vividly, it is shown in the form of a graph. The specific recognition rate training change curve is shown in Figure 2.

In Figure 2, since the number of iterations of the Bayesian probability model is 1, the curve of the model cannot be reflected. The figure can only reflect the PSO model and the MUNN model proposed in this study. The training change curve of the recognition rate: The identification training curve of the PSO model shows that the initial number of misjudgements is 870, but as the number of iterations continues to increase, the number of misjudgements is also decreases. At the 200th iteration, the number of misjudgements became stable and remained at 429; the training curve of the MUNN model proposed in this article shows that the initial number of misjudgements is 290, but as the number of iterations continued to increase, the number of misjudgements increased. It is also decreasing continuously. At the 200th iteration, the number of misjudgements began to stabilise and remained at 65.

Since September 2020, the defendant Guo Yong violated the robots agreement and other means by adopting high-similarity browser camouflage technology on the Internet, and illegally obtained 108 pieces of motor vehicle information, 79 pieces of company registration information, 101 pieces of passport information, 57 pieces of hotel check-in information, 85 pieces of demographic information, 94 pieces of bank personal credit report information, 86 pieces of personal bank information and 106 pieces of mobile phone information. As of the time of the incident, the defendant Guo Yong used the aforementioned illegally obtained information to defraud the victim, and some pieces of the information were sold at a higher price, and now he has made a profit of more than 100,000 yuan.

Using the criminal law imputation path of biometric information in this study, this case is analysed, and the analysis results are compared with the actual criminal law imputation results of the court, as shown in Table 2.

Comparative analysis of criminal law imputation results

Responsible subject | Suspect Guo Yong | Suspect Guo Yong | Suspect Guo Yong | 100 |

Main charge | The crime of illegally obtaining citizens’ personal information and the crime of fraud | Fraud | The crime of illegally obtaining citizens’ personal information and the crime of fraud | 50 |

Sentence | 7 years | 6 years | 8 years | 75 |

It can be seen from Table 2 that the adopted criminal law imputation path is used to analyse the case, and the analysis results are compared with the actual criminal law imputation results of the court. The subject is the criminal suspect Guo Yong himself, so the consistency in the subject of attribution is 100%; in terms of the main charges, Guo Yong was convicted of illegally obtaining citizens’ personal information and fraud in the first instance, but in the second instance, the prosecutor claimed the crime in this case. For the crime of fraud, the final suspect was convicted of fraud. According to the path of attribution of criminal law in this article, it is believed that the suspect in this case should be punished for the crime of illegally obtaining citizens’ personal information and the crime of fraud, so the consistency of the main crimes is 50%. The main reason for this situation is the insufficient response of the criminal law to biometric information. Violation of citizens’ biometric information includes two types of criminal tools and criminal objects. How should different types of behaviour be convicted and punished? The criminal law does not clearly stipulate the punishment for multiple crimes; there is also a gap in terms of the sentence. The criminal law in this article believes that according to the case of the crime of illegally obtaining citizens’ personal information and the crime of fraud, the sentence should be 8 years. However, the actual court only punished the crime according to the crime of fraud, so the final sentence was 6 years, so the consistency of the sentence was 75%.

Because of the particularity of biometric information, it has been widely used in many fields, playing a unique role beyond general personal information. Faced with the huge commercial value and wide application of biometric information, as well as various chaos in the process, the criminal law must guard the last line of defence and regulate related behaviours. Criminal legislation and criminal law theory need to provide effective solutions for the criminal law governance of biometric information according to the characteristics of biometric information. This article analyses the principle of web crawler technology and, on this basis, criminally imputes the relevant subjects of biometric information. Responsibility determination provides a possible path. This study conducts experiments from two aspects of signal acquisition and processing analysis and criminal law imputation analysis, and arrived at the following implications:

In the process of signal acquisition and processing analysis, this study finds that in terms of the number of misjudgements, the MUNN model proposed in this article has the least number of misjudgements of 65; in terms of recognition rate, the recognition rate of the model proposed in this article is 93.5. In terms of the number of iterations, the number of iterations in this study is 1501, so the model proposed in this article is the most stable in the process of information classification and recognition, and the accuracy is also the highest.

In the analysis of criminal law imputation, the analysis results of the criminal law imputation path in this study are compared with the actual criminal law results, and it is found that although the consistency of the subject of attribution reaches 100%, the criminal law response to biometric information is insufficient, so there are differences in the main charges and sentences, and the agreement is 50% and 75%, respectively.

#### Comparative analysis of criminal law imputation results

Responsible subject | Suspect Guo Yong | Suspect Guo Yong | Suspect Guo Yong | 100 |

Main charge | The crime of illegally obtaining citizens’ personal information and the crime of fraud | Fraud | The crime of illegally obtaining citizens’ personal information and the crime of fraud | 50 |

Sentence | 7 years | 6 years | 8 years | 75 |

#### Comparison of training results of different models

Bayesian probability model | 287 | 71.3 | 1 |

PSO model | 429 | 57.1 | 1500 |

Minimum uncertainty neural network model | 65 | 93.50 | 1501 |

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Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching 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 -groupsStudy on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Research 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 sentiment analysis method based on bidirectional long short-term memory networks 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