This study conducts a comprehensive bibliometric analysis to map the landscape and research trends of artificial intelligence (AI) applications within higher education. Utilizing data from the Scopus database, encompassing 4,696 datasets from 1939 to 2024, we employed VOSviewer for visualizing and analyzing co‑authorship networks, citation patterns, and keyword occurrences. The analysis identifies primary research areas, influential authors, and emerging topics, offering valuable insights into the dynamic field of AI in higher education. Key findings include the identification of significant research themes such as AI applications in education, student engagement, and the development of learning systems. Influential contributors were highlighted for their substantial impact on the research landscape. The study also revealed strong collaborative networks, particularly involving key figures, underscoring the importance of co‑authorship in advancing AI research. Strong collaborative networks refer to the co‑authorship and international partnerships that connect these contributors, producing high‑impact research through shared expertise, resources, and cross‑regional knowledge exchange. The findings validate the hypotheses that significant research areas and influential contributors can be identified, and that collaborative networks and emerging technologies play crucial roles in the field’s advancement. Influential contributors are the authors, institutions, or countries whose publications and citation impacts significantly shape the research landscape of AI in higher education, setting key directions for scholarship and practice. This study provides a roadmap for future research, emphasizing the importance of strategic collaborations and innovative technologies in shaping the future of AI in higher education.

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Living systems maintain structural and functional stability while adapting to environmental changes, a capability independent of specific system‑environment states. Existing frameworks, such as self‑organization theory and free energy principles, cannot measure system‑environment interaction at the causal level. In this article, we propose a new causal indicator, Flexibility, to measure a system’s ability to respond to its environment. We construct this indicator based on information theory and interventional operations from causal inference, which implies the indicator depends only on the dynamical causal mechanism. We show this indicator satisfies the axiom system of the partial information decomposition (PID) framework and decomposes into two components, Expansiveness and Introversion, which correspond to different strategic tendencies for environmental adaptation. This decomposition reveals that Flexibility depends on the entanglement between system‑environment variables and noise magnitude. Through experiments on cellular automata (CA), random Boolean networks, and real gene regulatory networks (GRNs), we validate that the indicator identifies the most complex and computationally capable CA (Langton’s parameter at 0.5), while demonstrating that feedback loops carrying important biological functions in GRNs exhibit the highest flexibility. We also find that flexibility peaks at a moderate level of dynamical noise. Furthermore, we combine this framework with machine learning techniques to demonstrate its applicability when the underlying dynamics are unknown.

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