{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T19:32:23Z","timestamp":1783020743785,"version":"3.54.6"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T00:00:00Z","timestamp":1747699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62476080"],"award-info":[{"award-number":["62476080"]}]},{"name":"National Natural Science Foundation of China","award":["U2443231"],"award-info":[{"award-number":["U2443231"]}]},{"name":"National Natural Science Foundation of China","award":["Y723008"],"award-info":[{"award-number":["Y723008"]}]},{"name":"Yellow River Water Science Research Joint Fund, Key Technologies and Methods for Intelligent Dam Construction Facing Digital Twins","award":["62476080"],"award-info":[{"award-number":["62476080"]}]},{"name":"Yellow River Water Science Research Joint Fund, Key Technologies and Methods for Intelligent Dam Construction Facing Digital Twins","award":["U2443231"],"award-info":[{"award-number":["U2443231"]}]},{"name":"Yellow River Water Science Research Joint Fund, Key Technologies and Methods for Intelligent Dam Construction Facing Digital Twins","award":["Y723008"],"award-info":[{"award-number":["Y723008"]}]},{"name":"Basic Research Business Expenses Project of Nanjing Institute of Water Resources","award":["62476080"],"award-info":[{"award-number":["62476080"]}]},{"name":"Basic Research Business Expenses Project of Nanjing Institute of Water Resources","award":["U2443231"],"award-info":[{"award-number":["U2443231"]}]},{"name":"Basic Research Business Expenses Project of Nanjing Institute of Water Resources","award":["Y723008"],"award-info":[{"award-number":["Y723008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet\u2019s tree symmetry and FrameNet\u2019s frame symmetry fail to formalize dynamic adjustments through quantitative metrics, leading to path dependency and delayed responses. This study addresses this gap by introducing a novel symmetry-entropy-constrained matrix fusion algorithm, which integrates algebraic direct sum operations and Hadamard product with entropy-driven adaptive weighting. The original contribution lies in the symmetry entropy metric, which quantifies structural deviations during fusion to systematically balance semantic stability and adaptability. This work formalizes ontology evolution as a symmetry-driven optimization process. Experimental results demonstrate that shared concepts between ontologies (s = 3) reduce structural asymmetry by 25% compared to ontologies (s = 1), while case studies validate the algorithm\u2019s ability to reconcile discrepancies between theoretical models and practical challenges in evacuation efficiency and crowd dynamics. This advancement promotes the evolution of traditional emergency management systems towards an adaptive intelligent form.<\/jats:p>","DOI":"10.3390\/sym17050792","type":"journal-article","created":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T06:54:28Z","timestamp":1747724068000},"page":"792","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Symmetry-Entropy-Constrained Matrix Fusion for Dynamic Dam-Break Emergency Planning"],"prefix":"10.3390","volume":"17","author":[{"given":"Shuai","family":"Liu","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Xihua University, Chengdu 610039, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dewei","family":"Yang","sequence":"additional","affiliation":[{"name":"Nanjing Hydraulic Research Institute, Nanjing 210029, China"},{"name":"Dam Safety Management Center of the Ministry of Water Resources, Nanjing 210029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Hu","sequence":"additional","affiliation":[{"name":"Zhejiang Institute of Hydraulics & Estuary (Zhejiang Institute of Marine Planning and Design), Hangzhou 310020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junping","family":"Wang","sequence":"additional","affiliation":[{"name":"Hangzhou Water Resources & Hydropower Survey Designing Institute, Hangzhou 835000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,20]]},"reference":[{"key":"ref_1","unstructured":"Ministry of Water Resources of the People\u2019s Republic of China (2023). 2023 National Statistical Bulletin on Water Conservancy Development, China Water & Power Press."},{"key":"ref_2","first-page":"1581","article-title":"Dam safety and risk management in China and its strategic consideration","volume":"30","author":"Li","year":"2008","journal-title":"Chin. 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