The core of financial institutions’ big data lies in risk control, making network security threat identification essential for enhancing data processing and service levels. This study applies the principles of network information transmission security prevention, combining frequency domain analysis and distributed processing to extract threat characteristics. A financial network security threat identification model is developed using BiGRU and Transformer models, and a SQLIA defense system is constructed by integrating multi-variant execution and SQL injection attack prevention. Additionally, an intelligent network security defense strategy is formulated based on finite rationality theory. Simulation results show an F1 composite score of 90.78% for threat identification, and the STRIPS-BR defense strategy reduces relative risk by 74.81% during peak times compared to other strategies. Supported by big data, this system ensures secure data transmission and enhances the network service capabilities of financial institutions.

Fine chemical processes are integral to modern industries such as automotive, environmental protection, aviation, and new energy. However, these processes involve highly toxic substances and complex chemical interactions, making them vulnerable to uncontrollable circumstances and posing significant risks to human safety and the environment. This work proposes an enhanced GA-LVW algorithm for reliability assessment of fine chemical processes, focusing on essential operating units. The method utilizes global-local structure analysis to extract features from operating unit variables, reducing data noise, simplifying the construction of fuzzy rules, and improving model resilience. The extracted features are integrated into a fuzzy inference system. The proposed approach is validated using the Tennessee Eastman (TE) process model and the R-22 production process in a fluoride facility. Results demonstrate that the enhanced GA-LVW algorithm significantly improves the system’s efficiency and maintainability compared to conventional fuzzy inference systems.

Over the past two decades, with the support of the Party and the state, universities have established educational principles integrating curriculum reform, teaching beliefs, and political theories. Despite significant progress in ideological and political theory research, challenges remain that hinder sustainable development. This paper leverages a computerized algorithmic model of complex information networks to explore the intersection of scientific and humanistic approaches in education. By combining these methods, the study provides an optimized knowledge and political model for university education and analyzes its credibility. Empirical results indicate that the proposed model achieves a 91% accuracy rate. The improved model enhances the intellectual and political vitality of university theoretical courses, strengthens educational principles, and ensures the quality of university education.

A positive integer \(k\) is called a magic constant if there is a graph \(G\) along with a bijective function \(f\) from \(V(G)\) to the first \(|V(G)|\) natural numbers such that the weight of the vertex \(w(v) = \sum_{uv \in E} f(u) = k\) for all \(v \in V\). It is known that all odd positive integers greater than or equal to \(3\) and the integer powers of \(2\), \(2^{t}\), \(t \geq 6\), are magic constants. In this paper, we characterize all positive integers that are magic constants and generate all distance magic graphs, up to isomorphism, of order up to \(10\).

The Radenković and Gutman conjecture establishes a relationship between the Laplacian eigenvalues of any tree \(T_n\), the star graph \(S_n\), and the path graph \(P_n\), i.e., \({LE}(P_n) \leq {LE}(T_n) \leq {LE}(S_n).\) In this paper, we prove this conjecture for a class of trees with \(n\) vertices and having diameter \(16\) to \(30\).

To address large prediction errors in traditional risk assessment methods, the X-means clustering algorithm is utilized to segment financial product customers, combined with correlation strength analysis to understand customer behaviors and needs. Using the Hoteling model, a two-step pricing strategy is proposed, revealing that data product prices are inversely proportional to depreciation rate, timeliness, and customization degree, and deriving the platform’s optimal pricing strategy. A financial risk indicator system is developed using principal component analysis for systematic risk assessment. In call option pricing prediction, the model converges at Epoch=40, achieving a normalized predicted price of 0.154 (true value: 0.153). For put options, the model converges at Epoch=100, with a predicted normalized price of 0.146 (true value: 0.145). The results demonstrate the model’s accuracy in pricing prediction, providing effective support for real-time market risk monitoring and timely risk prevention.

This study develops a stereoscopic vision system using a two-camera calibration method and BP neural networks combined with genetic algorithms to measure precision component dimensions. Images are processed using edge detection and Hough transform algorithms, and a machine vision-based inspection model is constructed. Bearing components are used as the research object to detect dimensions, edges, geometric parameters, and loose components under six angles. Maximum measurement deviation is 0.04 mm, and edge detection results are clear and concise. Geometric parameter deviations remain within [-5%, 5%], achieving high recognition accuracy. The detection model’s classification accuracy is 97.49%, with verification accuracy at 98.01%. Comprehensive false detection and leakage rates are 1.03% and 0.46%, respectively. The model demonstrates superior detection performance across various angles for bearing components.

We study a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar to the burning number, in this problem, information spreads in rounds and a new source can appear in each round. For a graph \(G\), we are interested in \(b_2(G)\), the minimum number of rounds until the information has spread to all vertices of graph \(G\). We are also interested in finding \(t_2(G)\), the minimum number of sources necessary so that the information spreads to all vertices of \(G\) in \(b_2(G)\) rounds. In addition to general results, we find \(b_2(G)\) and \(t_2(G)\) for the classes of spiders and wheels and show that their behavior differs with respect to these two parameters. We also provide examples and prove upper bounds for these parameters for Cartesian products of graphs.

This study explores how employee satisfaction moderates the relationship between corporate performance and innovative behavior using deep learning models: Autoencoder and restricted Boltzmann machines (RBM). The Autoencoder extracts key features for better analysis, while the RBM-based model analyzes the relationships among employee satisfaction, corporate performance, and innovative behavior. Results show a positive correlation between employee satisfaction and innovative behavior (0.460) and between innovative behavior and corporate performance (0.348). Regression analysis reveals that employee satisfaction indirectly impacts corporate performance through innovative behavior (impact: 0.10, t = 5.25). Differences in satisfaction, innovative behavior, and performance were observed across employee attributes. This study highlights the role of employee satisfaction in enhancing corporate performance and innovation, offering insights for human resource strategies.

An hourglass \(\Gamma_0\) is the graph with degree sequence \(\{4,2,2,2,2\}\). In this paper, for integers \(j\geq i\geq 1\), the bull \(B_{i,j}\) is the graph obtained by attaching endvertices of two disjoint paths of lengths \(i,j\) to two vertices of a triangle. We show that every 3-connected \(\{K_{1,3},\Gamma_0,X\}\)-free graph, where \(X\in \{ B_{2,12},\,B_{4,10},\,B_{6,8}\}\), is Hamilton-connected. Moreover, we give an example to show the sharpness of our result, and complete the characterization of forbidden induced bulls implying Hamilton-connectedness of a 3-connected {claw, hourglass, bull}-free graph.