In this paper, we introduce the concept of the Over-inversion number, which counts the overlined permutations of length \(n\) with \(k\) inversions, allowing the first elements associated with the inversions to be independently overlined or not. We explore its properties and combinatorial interpretations through lattice paths, overpartitions, and tilings, and provide a combinatorial proof demonstrating that these numbers form a log-concave and unimodal sequence.

This paper aims at resolving the issue that the conventional literature study can’t deal with the large amount of data, the author proposes a research method for theme clustering and text mining of Chinese modern and contemporary literary texts in the network era. The author studied how to effectively improve the thematic clustering performance of literary texts based on keyword clustering ensemble method. Comparing two clustering ensemble methods (K-means based data ensemble and incremental clustering based algorithm ensemble) and four keyword extraction methods (TF-ISF CSI, ECC, TextRank), the effects of various keywords on the results of thematic clustering were analysed. Experiments indicate that the clustering algorithm can greatly increase the topic clustering efficiency, and it is more stable when the key words are less. The author’s research provides new technological means for text mining and thematic clustering in contemporary Chinese literature, which helps to promote the development of digital humanities research.

The undifferentiated recommendations in current library management systems fail to meet the diverse and personalized needs of users, and the vast amounts of user data accumulated over the years remain largely untapped. This paper integrates personalized recommendation requirements in self-service libraries with K-means clustering to design a labeling system and set user profile weights. Building on traditional reinforcement learning, we propose an Actor–Critic based recommendation algorithm that models the library recommendation task as a Markov decision process to automatically learn an optimal strategy by maximizing expected long-term rewards. The DDPG algorithm is employed to train the parameters of this framework, achieving improved personalized performance. Comparative experiments on datasets (ML-100k, Yahoo! Music, ML-1M, and Jester) demonstrate that our model outperforms traditional methods and DeepFM, with scores of 0.7708, 0.1918, 0.7155, and 0.3936, respectively. This study provides innovative insights for accurate recommendations and enhanced user experience in libraries.

The application of virtual reality (VR) technology in teaching is increasingly widespread. This study leverages VR to create cross-cultural teaching contexts and develop speech recognition models for language learning. An ecological model of language learning based on VR is constructed, and a cross-cultural contextual VR system is implemented and introduced into language education. Testing reveals that the system achieves a speech recognition efficiency of 99.7% and a correctness rate of 99.5%. Moreover, a comparison of pre- and post-test data between experimental and control groups shows that the experimental group significantly outperformed the control group in English proficiency (p < 0.05). Overall, the cross-cultural contextual VR system demonstrates a significant positive impact on language learning outcomes.

New media advertising boosts platform revenue, and intelligent content optimization enhances its effectiveness. This paper applies a multi-task deep learning neural network to optimize advertisement content, leveraging attention mechanisms and loss functions to improve performance. Blockchain technology is integrated to create a personalized and accurate recommendation system. Experimental results show that the proposed model effectively optimizes ad content, meeting functional and performance requirements. Most users’ ad browsing duration exceeds 50 seconds, outperforming traditional recommendation systems. The proposed system offers strong targeting, fast results, and cost efficiency, significantly enhancing user engagement with ad content.

With the frequent occurrence of global climate change and extreme weather events, meteorological forecasting technology has gradually become an auxiliary technology for production activities. In order to improve the quality of meteorological analysis results, a technology utilizing cloud radar data as the core is proposed. The vertical distribution of water vapor and liquid water in the atmosphere is detected by a ground-based microwave radiometer. The median filtering method is used to further smooth the classified and preliminarily removed reflectance factor data, and computer information processing technology is used for data analysis. The experimental results of Taiyuan ground based remote sensing high altitude detection experiment showed that in the data availability test, the research method had a data availability rate of 97.3% when the height was 2km in humidity data. When conducting accuracy analysis of the results, the root mean square error of the relative humidity profile was only 22.0% when the height increased to 12km. This indicates that the research method can conduct high-quality meteorological analysis and provide assistance for meteorological forecasting.

A \((d, 1)\)-total labelling of a graph \(G\) is an assignment of integers \(\{0,1,\cdots,l\}\) to the vertices and edges of the graph such that adjacent vertices receive distinct integers, adjacent edges receive distinct integers, and the integer received by a vertex differs at least \(d\) from those received by its incident edges. The minimum number \(l\) required for such an assignment is called the \((d, 1)\)-total number of the graph \(G\). This paper contributes to \((d,1)\)-total labelling of two infinite families of snarks, the Goldberg family and the Loupekhine family. We completely determine the \((d,1)\)-total numbers of these two families of snarks for all \(d\geq2\).

A prism fuzzy number is the integration of triangular and trapezoidal fuzzy numbers. In this artifact, the balancing point and the grading value of the prism fuzzy number is defined. By using prism fuzzy number, we were able to infer the Trapezoidal and Triangular fuzzy numbers. A comparative study with the current model is done to corroborate our findings. An enhanced grading technique for evaluating the prism fuzzy numbers is defined. Finally, the application of prism fuzzy numbers to assess student’s interest in higher studies and employment is illustrated using the MATLAB simulation. A statistical analysis is demonstrated using the Python programme with real-life data.

Achieving accurate prediction of financial market fluctuations is beneficial for investors to make decisions, while machine learning algorithms can utilize a large amount of data for training and learning, which has good effect on predicting financial market fluctuations. The article first analyzes the financial dataset, and then constructs a feature selection model by combining Boruta and SHAP to screen the financial data features. Based on the LSTM model, a new Dropout layer and fully connected layer are designed to construct the AMP-LSTM model to realize the prediction of financial market fluctuations. The Boruta SHAP algorithm has a RMSPE of 0.242, which is good for screening. The prediction performance of the AMP-LSTM model is significantly better than that of the traditional LSTM (p<0.01), and the predicted values are closer to the actual values. The method in this paper performs better than MLP, RNN and other methods in general in terms of error performance when predicting indicators such as WTI, Brent, LGO, etc., and is able to realize the prediction of financial market volatility in the digital economy environment.

Aiming to address shortcomings in existing time series prediction models, this paper proposes an LSTM model enhanced by fused multi-scale convolutional attention (MCA-LSTM). We design the experimental parameters, construct a stock price dataset, and model the improved LSTM using individual stock closing prices, with prediction accuracy evaluated via RMSE, MAPE, and MAD. To assess the arbitrage and generalization performance of the MCA-LSTM portfolio model, we compare the application of the MCA-LSTM-BL model. Furthermore, within the framework of a mean semi-absolute deviation (MSAD) portfolio optimization model, we develop a new portfolio optimization approach based on return forecasting (MCA-LSTM+MSAD). The asset values and return predictions of various portfolio models are analyzed under transaction cost considerations, and the proposed MCA-LSTM+MSAD model achieves an excess return of 56.98%, consistently maintaining the highest portfolio value throughout the trading period. Overall, our findings indicate that the MCA-LSTM+MSAD model is a promising tool for portfolio optimization and warrants further development for real investment applications.