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In recent years, the scalar auxiliary variable based (SAV-based) approach has become very popular and hot in the design of linear, high-order and unconditional energy stable schemes of dissipative systems. However, the nature of SAV-based numerical schemes preserving modified energy dissipation limits its wider application. A relaxation technique to correct the modified energy for the baseline SAV method (RSAV) was proposed by Jiang et al. (J. Comput. Phys. 456:110954, 2022) and general SAV method (R-GSAV) by Zhang and Shen et al. (J. Comput. Phys. 464:111311, 2022). The RSAV/R-GSAV approaches are unconditionally energy stable with respect to a modified energy that is closer to the original free energy when compared with the SAV/GSAV approaches. In this paper, inspired by the RSAV/R-GSAV approaches, we propose a novel technique to correct the modified energy of the SAV/GSAV approaches, which can be proved to be an optimal energy approximation. We construct new high-order implicit-explicit schemes based on the proposed energy-optimized SAV-based (EOP-SAV) approaches. The constructed EOP-SAV schemes not only provide an improved accuracy but also simplify calculation, and can be viewed as the optimal relaxation. We also prove that the numerical schemes based on the EOP-SAV approaches are unconditionally energy stable. Compared with the RSAV approach, the proposed EOP-SAV approaches do not need introduce any relaxed factors and can share the similar procedure for error estimates. Several interesting numerical examples have been presented to demonstrate the accuracy and effectiveness of the proposed methods.

Based on the big data algorithm, this paper provides a detailed description of the SVM model, optimizes the algorithmic process of SVM with the GWO algorithm, and constructs the GWO-SVM classification model. The GWO-SVM is used for data mining analysis of image perception of tourism scenic planning and development, and three factors affecting image perception, namely image perception attributes, emotional image, and exploratory variables, are mined with the example of a city tourism scenic area. Regarding image perception attributes, the average percentages of functionality, wholeness, psychology, and uniqueness are 79%, 81.97%, 59.35%, and 17.95%, respectively. The perfect tourism facility function and good tourism atmosphere are the tools to enhance tourists’ image perception of tourist attractions. In terms of emotional image data, the percentage of “excited” and “pleasant” emotions are 25.66% and 27.06%, respectively, while the percentage of “frustrated” emotions is only 2.93%. In the exploratory variables, the percentage of “excited” and “happy” emotions were 25.66% and 27.06%, respectively, while the percentage of “frustrated” emotions was only 2.93%. Among the exploratory variables, the approval rates of tourism facilities, natural and humanistic landscapes, and scenic activities are 65.09%, 48.29%, and 47.52%, respectively, which means that play facilities, various landscapes, and preferential activities are good ways to enhance the image recognition, of scenic spots. The reasonable use of big data analysis technology can make the goal of planning and developing tourist attractions clearer and also help to improve the image recognition of tourist attractions and increase the economic benefits of tourist attractions.

In recent years, with the improvement of computers, automation, and communication technologies, autonomous driving has developed rapidly and has become a research hotspot in transportation. In order to optimize the existing autonomous driving scheme, this paper investigates the key technologies in 5G-based Telematics autonomous driving, mainly including the millimeter wave communication method and automatic obstacle avoidance strategy design, and tests and analyzes them through simulation experiments. In the simulation experiment, the synchronization rate of rear vehicle 1 of lane is 97.56%, that of rear vehicle is 98.43%, and that of rear vehicle is 97.82%, with an average synchronization rate of 97.94%. The synchronization rates of rear vehicle , and of lane 2 are 98.27%, 97.84%, and 96.89%, respectively, with an average synchronization rate of 97.67%. For the local observation latency in Telematics, the 5G Big Data-based scheme reduces 10.22% on average compared to the F-DDQL scheme and 9.76% on average compared to the IF-DDQL scheme. Regarding system latency, the 5G Big Data-based scheme reduces 8.67% and 9.21% on average compared to the other two schemes, respectively. The 5G Big Data-based Telematics autopilot can significantly improve the synchronization rate of vehicles and effectively reduce network latency. The research on the key technologies of 5G big data-based connected vehicle autonomous driving in this paper can overcome the shortcomings of traditional autonomous driving technology with unstable networking and help reduce the reliance on high-precision sensors, thus further improving autonomous driving performance.

Under the background of big data development, students have diverse and multi-level demands for music aesthetic education teaching. This paper studies the implementation strategy of aesthetic education in college music teaching under the threshold of big data, mainly through data analysis, predictive modeling and simulation, multi-faceted analysis, and the design of personalized music teaching intervention. By training DNN model experimental conclusion and analysis, the DNN model in the original set R-squared reached 0.8037, the largest performance among all models, compared to multiple linear regression, in multi-level multi-neuron activation, through the sigmoid activation of each level and linear calculation between levels, in backpropagation to update the weights and bias, trained to be able to more The DNN is finally selected as the best model for music learners’ performance prediction. The DNN is finally selected as the best model for music learners’ performance prediction. The advantages of big data mining music aesthetic education resources are exploited to create an open aesthetic education teaching space for students.

Ground-borne vibrations by railway trains are generated at the rail-wheel interface due to the passage of wheels and due to irregularities of wheels and tracks. These vibrations need to be predicted and controlled during the design and service of the railway for the safety and serviceability of the railway to avoid possible vibration-induced problems such as settlement and differential settlement due to their compaction effect, liquefaction, and discomfort of people. While such railway vibrations are modeled by different techniques, only a few studies do exist to analyze them in the case of soil-improved conditions. In this study, we propose a mathematical framework to study the effects of soil improvement on the ground-borne vibrations induced by railway trains. We use an experimentally calibrated model that utilizes the evolutionary random process approach to model the time-varying transfer functions between the axles of the train and the fixed observation point. The railway is modeled as a Winkler foundation with rail pads and corresponding transfer functions are used. The target area of this study is the Eminonu-Alibeykoy Tramway Line in Istanbul, which is under construction. Due to poor soil conditions at the specific stations along the proposed tramway route, soil improvement by the application of geo-synthetics is performed at the site and taken into account in our model. The improvement in soil conditions is modeled as increased vertical soil stiffness in the Winkler foundation of the evolutionary random process model. To model the various tramway loading conditions, both the 5-axle and 6-axle tramway configurations with non-uniform axle spacing are considered. We show that by increasing the vertical soil stiffness [k.sub.sb], the vibration velocity and acceleration levels can be reduced significantly. By implementing the model proposed, we present the reduction of the vibration velocity and acceleration levels as the functions of soil improvement parameters and discuss our findings and the applicability of the model. Keywords: Train Induced Vibrations, Random Vibrations, Soil Improvement. AMS Subject Classification: 65T50, 65Z05

With the national emphasis on vocational education and the reform of the examination and enrollment system of higher vocational education, the scale of students in higher vocational colleges and universities has been expanding, and the enrollment channels and student source types have been diversified, especially the characteristics of student source in local higher vocational colleges and universities are more prominent. The traditional student management mode has been difficult to meet the needs of students’ development and talent training mode. As an important part of education and teaching in colleges and universities, the effectiveness of student management determines the success or failure of ideological and political education of college students and the safety and stability of colleges and universities and is also related to the cultivation of high-quality technical and skilled talents needed by the society. Therefore, taking Jiyuan Vocational and Technical College as an example, this paper finds that 66% of the teachers and students think that the student management concept is backward, 58% think that the student management mode is single, 74% think that the student management system is not perfect, 58% think that the student management mode is rigid, and 59% think that the student management personnel are not of high professional quality in student management. The analysis of the results shows that using the hierarchical student management model based on ISM analysis makes the student management model with reasonable and effective articulation and operation, scientific and smooth implementation, and builds a set of effective student management systems in higher vocational institutions, which has certain theoretical and practical significance for the implementation of student management in higher vocational schools.

The orientation of music teachers’ talent training and the construction of talent training models are the core issues of concern for the reform of music education majors. Facing the new requirements of society for music education professional talents training in the new period, this paper proposes an improved talent training model based on the ADDIE model by studying the current situation of music education professional talents training from the perspective of adapting to the development needs of music curriculum reform in basic education. From the assessment of students’ and teachers’ evaluation and acceptance of the model, the mean value of students’ evaluation scores increased from 64.7 to 75.7 compared with the original training model, an increase of 17.00%. The mean teacher evaluation score increased from 67.0 to 72.7, an increase of 8.51%. It is evident that the talent development model has improved and is accepted by students and teachers. In terms of the acceptance of the training model proposed in this paper, the percentage of students who strongly agree with it has increased by 19.8%, the percentage of students who can accept it has increased by 20.2%, and the percentage of students who cannot adapt to the teaching model has decreased by 6.1 percentage points, with a comparative decrease of 20.3%. Teachers were also more accepting of the new training model, and the percentage of those who could accept it increased by 5.3 percentage points and 7.17% in comparison. In conclusion, the talent cultivation model of music education based on the ADDIE model can be well adapted to the teaching classroom of colleges and universities and also meets the needs of the country and society for music teachers in the new era, which is conducive to the cultivation of composite talents who are highly educated and have a solid theoretical foundation and excellent practical ability.

Higher vocational schools are responsible for training socialist builders and later generations, and they must always take moral education as their development purpose, penetrate ideological and political education into the whole stage of education and teaching, implement the three comprehensive education guidelines, and try their best to cultivate generations of talents who support the leadership of the Communist Party and the Chinese socialist system, and firmly contribute to socialism with Chinese characteristics. In this paper, we analyze the situation of the implementation of Civic Science and Politics in higher education institutions by investigating the implementation of the Civic Science and Politics curriculum in higher education institutions and using a more scientific questionnaire and ISO analysis to analyze the situation of Civic Science and Politics practice in higher education institutions and study the root causes of the slow development of Civic Science and Politics education. There are four main factors influencing the construction process of the development of the college’s curriculum thinking politics: 69.9% believe that there is a siloed model of the college’s thinking politics theory course, 56.7% of the college’s teachers’ ability to educate people in the curriculum is not strong, 73.2% of the professional courses’ thinking politics education resources cannot be fully explored, and 51.3% of the college does not have a mechanism for judging the effectiveness of the curriculum thinking politics. The experimental results of this paper show that the ISO analysis method can be used to know the influencing factors to promote the development of thinking and political education scientifically and to propose strategies based on the problems, which can help to propose the promotion for the reform of the thinking and politics work in Chinese universities and has certain significance to continuously improve the actual effectiveness and validity of the thinking and political education work in higher education institutions, etc.

In artificial intelligence applications, the model training phase is critical and computationally demanding. In the graph neural networks (GNNs) research field, it is interesting to investigate how varying the graph topological and spectral structure impacts the learning process and overall GNN performance. In this work, we aim to theoretically investigate how the topology and the spectrum of a graph changes when nodes and edges are added or removed. Numerical results highlight stability issues in the learning process on graphs. In this work, we aim to theoretically investigate how the topology and the spectrum of a graph changes when nodes and edges are added or removed. We propose the topological relevance function as a novel method to quantify the stability of graph-based neural networks when graph structures are perturbed. We also explore the relationship between this topological relevance function, Graph Edit Distance, and spectral similarity. Numerical results highlight stability issues in the learning process on graphs.

Deep learning has made significant progress in the fields of data science and natural science. Some studies have linked deep neural networks to dynamical systems, but the network structure is restricted to a residual network. It is known that residual networks can be regarded as a numerical discretization of dynamical systems. In this paper, we consider the traditional network structure and prove that vanilla feedforward networks can also be used for the numerical discretization of dynamical systems, where the width of the network is equal to the dimensions of the input and output. Our proof is based on the properties of the leaky-ReLU function and the numerical technique of the splitting method for solving differential equations. Our results could provide a new perspective for understanding the approximation properties of feedforward neural networks.