This study constructs a bilevel network model based on heterogeneous financial data to explore the complex network characteristics and risk transmission mechanisms in the stock market. Using the trading data and textual sentiment data of Shanghai Stock Exchange (SSE) 50 constituent stocks over the past 5 years, a daily return network model and a textual sentiment analysis network model are constructed, which are then combined to form a bilevel network. The study finds that the bilevel network model can more comprehensively capture the multidimensional relationships and risk transmission behaviors in the market, revealing the close connection between sentiment factors and returns. By analyzing the interlayer coupling characteristics of the bilevel network, we found that information and risks are efficiently transmitted between different network layers. This method not only provides a new perspective for financial market analysis but also offers a valuable theoretical basis and practical tools for risk management and market regulation. The results show that the bilevel network model has significant implications for understanding and preventing financial risks.

Monitoring, governing, and guiding public opinion on social media during emergencies is challenging, often leading to mass panic, rumors, and public opinion crises. Understanding the scale evolution of information and subjects within the public opinion ecology of emergencies can aid in achieving macrocontrol. To address this, an information‐subject dual‐structure model was developed to illustrate the scale development trend. Fitting and prediction methods based on the model were proposed, and general rules were provided through simulation. For empirical research, data from three categories of six emergency events were downloaded from the GsData platform. The linear regression method was used to predict the trend of subjects and information, achieving an F 1 fit above 82% for the six datasets. Subsequently, a fine‐tuning matrix was established, increasing the F 1 values to over 98.30%, thereby confirming the model’s interpretability and universality.

In deep learning, the choice of activation function plays a vital role in enhancing model performance. We propose AHerfReLU, a novel activation function that combines the rectified linear unit (ReLU) function with the error function (erf), complemented by a regularization term 1/(1 + x 2 ), ensuring smooth gradients even for negative inputs. The function is zero centered, bounded below, and nonmonotonic, offering significant advantages over traditional activation functions like ReLU. We compare AHerfReLU with 10 adaptive activation functions and state‐of‐the‐art activation functions, including ReLU, Swish, and Mish. Experimental results show that replacing ReLU with AHerfReLU leads to 3.18% improvement in Top‐1 accuracy on the LeNet network for the CIFAR100 dataset, 0.63% improvement on CIFAR10%, and 1.3% improvement in mean average precision (mAP) on the SSD300 model in the Pascal VOC dataset. Our results demonstrate that AHerfReLU enhances model performance, offering improved accuracy, loss reduction, and convergence stability. The function outperforms existing activation functions, providing a promising alternative for deep learning tasks.

This work explores the challenges related to the 4‐part harmony problem, addressing both the computational complexity of the search space and the benefits of integrating human teaching/learning processes into evolutionary problem‐solving approaches. From a computational perspective, we analyze strategies to enhance algorithm efficiency, including parallelization, precomputation of fitness values, directed mutation, and adaptive directed mutation, which collectively reduce the time required to find solutions. Synthetic harmonic models are employed to validate these techniques. Complementing this, we investigate the role of human expertise, emphasizing the synergy between expert teaching and the learning processes of novice students. By examining how human teaching and learning paradigms can inspire innovative problem‐solving techniques, we draw on the concept of evolutionary machine teaching, which reduces the search space, applied here to a standard harmonic model. Our findings highlight the potential of integrating computational advancements with methodologies driven by human learning. Specifically, the search space produced by Sharpmony students accounts for less than 1% of the total space. Using this approach, we have achieved a fourfold speedup over previous results of the same quality. Moreover, longer runs of the new approach have provided solutions with an average fitness of less than 1 error, considering the complete set of 50 rules and exceptions.

The primary objective of this research paper is to conduct a bibliometric analysis of the prevailing research landscape pertaining to agent‐based modeling (ABM). This analysis encompasses an examination of key contributors, affiliated academic institutions, influential publications, and prominent journals within the domain. To achieve this, a dataset consisting of 11,477 scholarly papers retrieved from the ISI Web of Science database has been curated, using keywords specifically related to ABM, spanning the period from 1996 to 2024. Employing n ‐gram analysis techniques on titles, keywords, abstracts, and keyword‐plus fields has unearthed a multitude of domains wherein ABM has been applied with notable success. Our findings, as delineated in this paper, underscore a sustained and robust growth in scholarly interest in the realm of ABM during the specified temporal span, characterized by an impressive annual growth rate of 25.29%. Furthermore, our study contributes to the identification and analysis of salient keywords and emerging trends, thereby elucidating key research trajectories within this domain. The identification of collaborative networks among authors, their respective academic affiliations, and the geographical distribution across various countries and territories offers valuable insights into the global proliferation of ABM as a research methodology. The findings offer valuable insights into the widespread applications of ABM across various domains, including climate change, social networks, supply chain dynamics, public health studies, financial market analysis, and population dynamics. The results of the study can help in guiding future research and practical applications of ABM in these and other multifaceted areas.

The present paper employs topological data analysis methods to reveal ‘holes’ (stable persistent homologies) in the semantic spaces of words, bigrams, and trigrams of the English and Russian languages, and to ascertain their boundaries. Furthermore, the paper selects those holes that belong to the large‐scale (coarse‐grained) structure of the language that are not just local inhomogeneities of the sample—it appears that there are around a dozen of them for each of the languages (English and Russian). These boundaries delineate ‘blind spots’ of the respective language—the regions of the semantic spaces that do not contain words/bigrams/trigrams of the language—that is, regions of concepts that the language cannot see through its lens. The secondary goal of the paper is to solve the bot‐detection problem in its strong statement, that is, one trains the classifiers on one set of bots and tests on the another set of bots. To this end, we estimate the average distances from words, bigrams, and trigrams of a text to the boundaries of the nearest ‘hole’, for texts both written by humans and generated by bots, and construct classifiers. The classifiers show comparatively good results: the average accuracy amounts to 0.8.

In the context of rapid development of social networks, users gather together through social network platforms (SNPs) to form social circles, which become the main carriers for users to disseminate public opinion information and emotions, and it is easy to form the phenomenon of network public opinion polarization in social circles. To prevent the polarization of network public opinions in social circles, the application of blockchain technology to SNPs can provide a credible database for the traceability of public opinions and avoid the spread of false information in social circles. Based on blockchain traceability, this paper establishes a three‐party evolutionary game model consisting of government, SNPs, and social circle managers (SCMs). Through model solving and numerical simulation, the influencing factors of each party’s strategy are analyzed. The findings suggest: (1) Although the rising cost of building blockchain platforms may undermine the government’s incentive to regulate, the government will still prioritise support for their construction if they can significantly enhance social welfare. (2) The government could boost SNPs’ willingness to adopt blockchain technology through subsidy measures, but increased privacy risks could undermine this willingness. (3) Blockchain technology realizes the traceability of public opinion and improves the rational guidance tendency of SCMs. Therefore, in order to promote and strengthen the collaborative governance of network public opinion in social circles, SNPs should enhance the use of blockchain technology, while the government should give full play to its regulatory and supervisory roles. This study introduces blockchain technology for public opinion traceability; explores a collaborative network public opinion governance system based on strict regulation by the government, introduction of blockchain technology by SNPs, and rational guidance by SCMs; expands the related research on network public opinion governance; and provides a new idea for the study of network public opinion governance of social circles based on blockchain traceability.

Nonlinear science represents a foundational frontier in scientific inquiry that explores the shared characteristics inherent in nonlinear phenomena. This study focused on the perturbed Boussinesq (PB) equation incorporating dual perturbation terms. Soliton solutions were deduced by leveraging the traveling wave hypothesis. Furthermore, by employing the generalized Jacobi elliptic expansion function (JEEF) method and the improved tan (Λ/2) method, diverse nonlinear wave solutions, including kink, dark, periodic, bright, singular, periodic waves, bell‐shaped solitons, solitary waves, shock waves, and kink‐shaped soliton solutions, were acquired. The establishment of constraint relations is detailed to delineate the criteria for the existence of these wave solutions. Notably, these solutions are innovative and present novel contributions that have not yet been documented in the literature. In addition, 2D and 3D graphics were constructed to visually elucidate the physical behavior inherent to these newly acquired exact solutions.