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Semi-tensor Product of Matrices and Mathematics
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CHENG Daizhan
Complex Systems and Complexity Science. 2025, 22 (2): 7-17.
DOI: 10.13306/j.1672-3813.2025.02.003
After a brief review on the history of semi-tensor product (STP) of matrices, this survey paper introduces general definitions of STP and semi-tensor addition (STA), and the exploring researches on the mathematical essence of STP and STA, including three major branches: Modern Algebra, Geometry, and Analysis. The STP and STA, as cross-dimensional operators, enhance certain developments in classical mathematics, which is basically of fixed dimensions. As a survey paper, it mainly introduces fundamental concepts and basic results with few predictions. We hope to show such a fact that since the STP breaks the dimension barrier of matrix product, it will inevitably cause impact on the classical mathematics, which is of fixed dimensions.
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A Survey on Distributed Cooperative Localization for Multi-agent Systems
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YANG Guanghong, SHI Chongxiao
Complex Systems and Complexity Science. 2025, 22 (2): 18-30.
DOI: 10.13306/j.1672-3813.2025.02.004
Distributed cooperative localization is a key process in many cooperative tasks for multi-agent systems. Distributed cooperative localization aims to enable each agent to determine their own locations by using the available locations of anchors, the relative measurements to their neighbors, and the distributed network communication. This paper summarizes the advances in the distributed cooperative localization for multi-agent systems. First, according to the types of relative measurements, the distributed cooperative localization methods are classified into three types, i.e., distance-based, bearing-based, and mixed-measurement-based distributed cooperative localization methods. Then, by characterizing the constraint relationship between the measurement and the agents’ locations, the design schemes of the above distributed cooperative localization methods are elaborated in detail, and the advantages and disadvantages of the methods are compared. Moreover, this paper introduces the research status of reliable distributed cooperative localization methods for multi-agent systems with malicious measurements. Finally, the ongoing challenges in distributed cooperative localization are anticipated, and the potential directions for resolution are proposed.
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Standardizing Document Generation Based on Large Language Models
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LIU Zheze, ZHENG Nan, ZHANG Ning
Complex Systems and Complexity Science. 2025, 22 (2): 45-54.
DOI: 10.13306/j.1672-3813.2025.02.006
In order to promote the standardized development of various industries, corresponding standardizing documents need to be formulated in various fields, such as national standard and industry standard. These standardizing documents not only provide a unified operating standard for the industry, but also provide a clear guidance basis for relevant parties. The Central Committee of the CPC and the State Council clearly pointed out in the "the Outlines for the Development of National Standardization" that promoting the digitalization process of standard is an important measure to realize the modernization of the industry. Therefore, it is particularly important to carry out research on the automatic generation of standardizing documents. With the rapid development of artificial intelligence technology, especially the outstanding performance of large language models in text generation tasks, it is possible to use these advanced technologies to realize the automatic generation of standardizing documents. Based on this background, this paper proposes a two-stage scheme for generating standardizing documents. The scheme first generates the outline of the standardizing document through the large model, and then expands to generate the complete document content on this basis. By combining in-context learning and retrieval augmented generation techniques, this method can not only generate high-quality text, but also significantly improve the accuracy and professionalism of the generated content. In order to verify the feasibility of the scheme, we conducted a series of experiments on our self-built dataset, and the results show that the method can effectively generate documents that meet industry standards, and has good practicability and promotion potential.
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Research on Gait Investigation Technology Based on Multi-information Fusion
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FENG Lei,ZHAO Xingchun,ZHOU Yangjun
Complex Systems and Complexity Science. 2025, 22 (2): 73-81.
DOI: 10.13306/j.1672-3813.2025.02.009
Complex criminal cases today present systematic characteristics of multi-factor coupling and dynamic evolution, and their investigation process faces the challenge of nonlinear information integration. Criminal suspects use anti-detection methods such as changing clothes and shoes, facial obstruction, and posture camouflage, combined with complex environmental interference, which significantly reduces the practical effectiveness of single technical means such as face recognition and video structuring. In order to resolve this problem, this article focuses on the actual needs of suspect identification and tracking, breaks through the recognition bottleneck of a single modality, systematically integrates multi-information such as video structuring, face recognition, and gait recognition, and proposes a multi-information fusion video investigation system with gait recognition as the core, which realizes the dual characterization of suspect behavior patterns and identity characteristics, and provides a new technical path for improving identity recognition capabilities and the efficiency of solving complex cases.
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A Comparative Study of China and the United States’ Digital Economy Policies Based on Cross-lingual Model
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ZOU Yuheng, LU Dongyuan, SANG Dong
Complex Systems and Complexity Science. 2025, 22 (2): 82-89.
DOI: 10.13306/j.1672-3813.2025.02.010
In the context of escalating Sino-American strategic competition, a comparative study of Chinese and the USA digital economy policies bears significant strategic value. Traditional methods of policy comparison are limited by cost, can’t solve this problem well. This paper focuses on the contrast between digital economy policies in China and the USA, proposing a resolution framework based on a cross-language model. The framework initially classifies Sino-American digital economic policies by fine-tuning language models and calculating multilingual similarity, thereby achieving automated comparative analysis of the policy environments. Experiments demonstrate that the proposed method can accurately and efficiently identify and extract policy text features, outperforming baseline methods in accuracy across multiple classification dimensions. Finally, by comparing over 16,000 Sino-American digital economic policy texts, this paper reveals key differences in policy tool usage and the focus of digital economic industry development between the two countries, providing a comprehensive and objective portrayal of the disparities in digital economy policy environments. Concurrently, it also brings a fresh perspective to policy comparison research.
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On State Estimation for Hypergraphs with Two Types of Coupling
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ZHOU Xuanxin, WU Yayong, JIANG Guoping
Complex Systems and Complexity Science. 2025, 22 (2): 90-96.
DOI: 10.13306/j.1672-3813.2025.02.011
This paper investigates the node state estimation of hypergraphs. First, the network model of hypergraphs with pairwise and triplet interactions is built. Second, considering the presence and absence of diffusive coupling, the observer networks are established, and the error dynamical networks are constructed for the two types of hypergraph network models, respectively. Then, using the Lyapunov stability theory, the asymptotic stability of the two types of error dynamical networks is proved and sufficient conditions for state estimation are derived. Finally, the accuracy and effectiveness of the proposed method are verified by numerical simulations. The results indicate the applicability of our method in accurately estimating states within the diffusively coupled and non-diffusively coupled hypergraphs, thereby advancing our capabilities in estimating and controlling higher-order complex networks.
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Gender Recognition of Social Network Users Based on Heterogeneous Motif Features
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XIANG Yuping, XU Xiaoke
Complex Systems and Complexity Science. 2025, 22 (2): 105-112.
DOI: 10.13306/j.1672-3813.2025.02.013
User gender is one of the core aspects of user profiling, and existing methods for accurately identifying user gender mainly rely on user public attributes, with less consideration given to network structure information. This study integrates gender information based on motif theory, subdivides homogeneous motifs into heterogeneous motifs, and proposes a gender recognition method based on heterogeneous motif features, extracting more detailed local information to distinguish users of different genders. Compared to the current popular network embedding methods, the method proposed in this article has improved the Accuracy index by 2.8% to 14.2%, and the AUC index by 2.7% to 15.8%, with stable performance on different proportion training sets. The heteromorphic method can be applied to the identity detection of social users, which helps to conduct in-depth research on the structural characteristics of social networks.
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Data-driven Modeling on Incentive Residents′ Behavior in Garbage Classification
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ZHAN Xiuxiu, CHEN Wei, MAO Jiangqun, CHEN Xiang, SHEN Shuying, LIU Chuang, ZHANG Zike
Complex Systems and Complexity Science. 2025, 22 (2): 151-158.
DOI: 10.13306/j.1672-3813.2025.02.019
To explore the driving effect of incentive mechanisms on residents′ enthusiasm for participating in garbage classification, this article is based on empirical data analysis of garbage classification in multiple communities. Using the RFM model, it quantifies residents′ enthusiasm for participating in garbage classification and categorizes user value. Based on this, a multi-agent simulation model of user value transformation is established around subjective norms, classification knowledge, and classification attitudes. The results show that residents′ enthusiasm for garbage disposal is influenced by subjective norms; there is a positive correlation between classification knowledge, classification attitudes, and residents′ enthusiasm for garbage disposal.
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