{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:29:39Z","timestamp":1787502579526,"version":"build-2736575974"},"reference-count":68,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Molecular property prediction, as one of the important tasks in cheminformatics, is attracting more and more attention. The structure of a molecule is closely related to its properties, and a symmetrical molecular structure may differ significantly from an asymmetrical structure in terms of properties, such as the melting point, boiling point, water solubility, and so on. However, a single molecular representation does not provide a better overall representation of the molecule. And, it is also a challenge to better use graph neural networks to aggregate the information of neighboring nodes in the molecular graph. So, in this paper, we constructed a novel graph neural network with additive attention (termed Add-GNN) for molecular property prediction, which fuses the molecular graph and molecular descriptors to jointly represent molecular features in order to make the molecular representations more comprehensive. Then, in the message-passing stage, we designed an additive attention mechanism that can effectively fuse the features of neighboring nodes and the features of edges to better capture the intrinsic information of molecules. In addition, we applied L2-norm to calculate the importance of each atom to the predicted results and visualized it, providing interpretability to the model. We validated the proposed model on public datasets and showed that the model outperforms graph-based baseline methods and some graph neural network variants, proving that our proposed method is feasible and competitive.<\/jats:p>","DOI":"10.3390\/sym17060873","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T10:10:16Z","timestamp":1749031816000},"page":"873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Add-GNN: A Dual-Representation Fusion Molecular Property Prediction Based on Graph Neural Networks with Additive Attention"],"prefix":"10.3390","volume":"17","author":[{"given":"Ronghe","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4586-3737","authenticated-orcid":false,"given":"Yong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5534-1705","authenticated-orcid":false,"given":"Kai","family":"He","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Science, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1186\/s13321-023-00698-9","article-title":"ABT-MPNN: An atom-bond transformer-based message-passing neural network for molecular property prediction","volume":"15","author":"Liu","year":"2023","journal-title":"J. Cheminform."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1016\/j.cell.2020.01.021","article-title":"A deep learning approach to antibiotic discovery","volume":"180","author":"Stokes","year":"2020","journal-title":"Cell"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.drudis.2018.11.014","article-title":"Artificial intelligence in drug development: Present status and future prospects","volume":"24","author":"Mak","year":"2019","journal-title":"Drug Discov. Today"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2692","DOI":"10.1039\/b407105k","article-title":"Effect of molecular symmetry on melting temperature and solubility","volume":"2","author":"Pinal","year":"2004","journal-title":"Org. Biomol. Chem."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Cai, H., Zhang, H., Zhao, D., Wu, J., and Wang, L. (2022). FP-GNN: A versatile deep learning architecture for enhanced molecular property prediction. Briefings Bioinform., 23.","DOI":"10.1093\/bib\/bbac408"},{"key":"ref_6","first-page":"100022","article-title":"Learning functional group chemistry from molecular images leads to accurate prediction of activity cliffs","volume":"1","author":"Iqbal","year":"2021","journal-title":"Artif. Intell. Life Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"117755","DOI":"10.1016\/j.molliq.2021.117755","article-title":"Understanding functional group effect on corrosion inhibition efficiency of selected organic compounds","volume":"344","author":"Assad","year":"2021","journal-title":"J. Mol. Liq."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1021\/ja01062a035","article-title":"p-\u03c3-\u03c0 Analysis. A Method for the Correlation of Biological Activity and Chemical Structure","volume":"86","author":"Hansch","year":"1964","journal-title":"J. Am. Chem. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4977","DOI":"10.1021\/jm4004285","article-title":"QSAR modeling: Where have you been? Where are you going to?","volume":"57","author":"Cherkasov","year":"2014","journal-title":"J. Med. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3525","DOI":"10.1039\/D0CS00098A","article-title":"QSAR without borders","volume":"49","author":"Muratov","year":"2020","journal-title":"Chem. Soc. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"21292","DOI":"10.1039\/D0RA02701D","article-title":"A joint optimization QSAR model of fathead minnow acute toxicity based on a radial basis function neural network and its consensus modeling","volume":"10","author":"Wang","year":"2020","journal-title":"RSC Adv."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wu, Z., Jiang, D., Hsieh, C.Y., Chen, G., Liao, B., Cao, D., and Hou, T. (2021). Hyperbolic relational graph convolution networks plus: A simple but highly efficient QSAR-modeling method. Briefings Bioinform., 22.","DOI":"10.1093\/bib\/bbab112"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, B., Lin, M., Chen, T., and Wang, L. (2023). FG-BERT: A generalized and self-supervised functional group-based molecular representation learning framework for properties prediction. Briefings Bioinform., 24.","DOI":"10.1093\/bib\/bbad398"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Guo, G., Wang, H., Bell, D., Bi, Y., and Greer, K. (2003, January 3\u20137). KNN model-based approach in classification. Proceedings of the On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE: OTM Confederated International Conferences, CoopIS, DOA, and ODBASE 2003, Catania, Sicily, Italy.","DOI":"10.1007\/978-3-540-39964-3_62"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103373","DOI":"10.1016\/j.drudis.2022.103373","article-title":"Deep learning methods for molecular representation and property prediction","volume":"27","author":"Li","year":"2022","journal-title":"Drug Discov. Today"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1021\/acs.accounts.0c00699","article-title":"Applications of deep learning in molecule generation and molecular property prediction","volume":"54","author":"Walters","year":"2020","journal-title":"Accounts Chem. Res."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wu, C.K., Zhang, X.C., Yang, Z.J., Lu, A.P., Hou, T.J., and Cao, D.S. (2021). Learning to SMILES: BAN-based strategies to improve latent representation learning from molecules. Briefings Bioinform., 22.","DOI":"10.1093\/bib\/bbab327"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15246","DOI":"10.1007\/s10489-022-04280-y","article-title":"TranGRU: Focusing on both the local and global information of molecules for molecular property prediction","volume":"53","author":"Jiang","year":"2023","journal-title":"Appl. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1186\/s40537-021-00444-8","article-title":"Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions","volume":"8","author":"Alzubaidi","year":"2021","journal-title":"J. Big Data"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Dhruv, P., and Naskar, S. (2020). Image classification using convolutional neural network (CNN) and recurrent neural network (RNN): A review. Machine Learning and Information Processing: Proceedings of ICMLIP 2019, Springer.","DOI":"10.1007\/978-981-15-1884-3_34"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"132306","DOI":"10.1016\/j.physd.2019.132306","article-title":"Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network","volume":"404","author":"Sherstinsky","year":"2020","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1093\/bib\/bbz125","article-title":"A novel molecular representation with BiGRU neural networks for learning atom","volume":"21","author":"Lin","year":"2020","journal-title":"Briefings Bioinform."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"18601","DOI":"10.1109\/ACCESS.2020.2968535","article-title":"Molecular property prediction based on a multichannel substructure graph","volume":"8","author":"Wang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8778","DOI":"10.1021\/acs.jmedchem.9b01129","article-title":"Practical high-quality electrostatic potential surfaces for drug discovery using a graph-convolutional deep neural network","volume":"63","author":"Rathi","year":"2019","journal-title":"J. Med. Chem."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13321-019-0407-y","article-title":"Building attention and edge message passing neural networks for bioactivity and physical\u2013chemical property prediction","volume":"12","author":"Withnall","year":"2020","journal-title":"J. Cheminform."},{"key":"ref_28","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_29","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y. (2017). Graph attention networks. arXiv."},{"key":"ref_30","unstructured":"Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., and Dahl, G.E. (2017, January 6\u201311). Neural message passing for quantum chemistry. Proceedings of the International Conference on Machine Learning, Sydney, Australia."},{"key":"ref_31","unstructured":"Xu, K., Hu, W., Leskovec, J., and Jegelka, S. (2018). How powerful are graph neural networks?. arXiv."},{"key":"ref_32","unstructured":"Hamilton, W., Ying, Z., and Leskovec, J. (2017). Inductive representation learning on large graphs. Adv. Neural Inf. Process. Syst., 30."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3370","DOI":"10.1021\/acs.jcim.9b00237","article-title":"Analyzing learned molecular representations for property prediction","volume":"59","author":"Yang","year":"2019","journal-title":"J. Chem. Inf. Model."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"120005","DOI":"10.1016\/j.eswa.2023.120005","article-title":"Few-shot learning with transformers via graph embeddings for molecular property prediction","volume":"225","author":"Torres","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1007\/s10822-016-9938-8","article-title":"Molecular graph convolutions: Moving beyond fingerprints","volume":"30","author":"Kearnes","year":"2016","journal-title":"J. Comput.-Aided Mol. Des."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1021\/acs.jcim.1c01263","article-title":"Interpretation of structure\u2013activity relationships in real-world drug design data sets using explainable artificial intelligence","volume":"62","author":"Harren","year":"2022","journal-title":"J. Chem. Inf. Model."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Mauri, A. (2020). alvaDesc: A tool to calculate and analyze molecular descriptors and fingerprints. Ecotoxicological QSARs, Humana.","DOI":"10.1007\/978-1-0716-0150-1_32"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Consonni, V., and Todeschini, R. (2010). Molecular descriptors. Recent Advances in QSAR Studies: Methods and Applications, Springer.","DOI":"10.1007\/978-1-4020-9783-6_3"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1016\/j.drudis.2016.06.013","article-title":"Descriptors and their selection methods in QSAR analysis: Paradigm for drug design","volume":"21","author":"Danishuddin","year":"2016","journal-title":"Drug Discov. Today"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1186\/s13321-018-0258-y","article-title":"Mordred: A molecular descriptor calculator","volume":"10","author":"Moriwaki","year":"2018","journal-title":"J. Cheminform."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1002\/jcc.21707","article-title":"PaDEL-descriptor: An open source software to calculate molecular descriptors and fingerprints","volume":"32","author":"Yap","year":"2011","journal-title":"J. Comput. Chem."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8373","DOI":"10.1039\/D0CP00305K","article-title":"Are 2D fingerprints still valuable for drug discovery?","volume":"22","author":"Gao","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1021\/ci100050t","article-title":"Extended-connectivity fingerprints","volume":"50","author":"Rogers","year":"2010","journal-title":"J. Chem. Inf. Model."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.apm.2024.04.057","article-title":"Multi-strategy enhanced snake optimizer for quantitative structure-activity relationship modeling","volume":"132","author":"Wang","year":"2024","journal-title":"Appl. Math. Model."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"128567","DOI":"10.1016\/j.chemosphere.2020.128567","article-title":"Development of classification models for predicting inhibition of mitochondrial fusion and fission using machine learning methods","volume":"273","author":"Tang","year":"2021","journal-title":"Chemosphere"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1021\/acs.chemrestox.0c00343","article-title":"Prediction of the blood\u2013brain barrier (BBB) permeability of chemicals based on machine-learning and ensemble methods","volume":"34","author":"Liu","year":"2021","journal-title":"Chem. Res. Toxicol."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Choi, K.E., Balupuri, A., and Kang, N.S. (2020). The study on the hERG blocker prediction using chemical fingerprint analysis. Molecules, 25.","DOI":"10.3390\/molecules25112615"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1021\/ci00062a008","article-title":"SMILES. 2. Algorithm for generation of unique SMILES notation","volume":"29","author":"Weininger","year":"1989","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Zhang, X., Wang, S., Zhu, F., Xu, Z., Wang, Y., and Huang, J. (September, January 29). Seq3seq fingerprint: Towards end-to-end semi-supervised deep drug discovery. Proceedings of the 2018 ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics, Washington, DC, USA.","DOI":"10.1145\/3233547.3233548"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1692","DOI":"10.1039\/C8SC04175J","article-title":"Learning continuous and data-driven molecular descriptors by translating equivalent chemical representations","volume":"10","author":"Winter","year":"2019","journal-title":"Chem. Sci."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Xu, Z., Wang, S., Zhu, F., and Huang, J. (2017, January 20\u201323). Seq2seq fingerprint: An unsupervised deep molecular embedding for drug discovery. Proceedings of the 8th ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics, Boston, MA, USA.","DOI":"10.1145\/3107411.3107424"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Wang, S., Guo, Y., Wang, Y., Sun, H., and Huang, J. (2019, January 7\u201310). Smiles-bert: Large scale unsupervised pre-training for molecular property prediction. Proceedings of the 10th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics, Niagara Falls, NY, USA.","DOI":"10.1145\/3307339.3342186"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Hou, Y., Wang, S., Bai, B., Chan, H.S., and Yuan, S. (2022). Accurate physical property predictions via deep learning. Molecules, 27.","DOI":"10.3390\/molecules27051668"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"8749","DOI":"10.1021\/acs.jmedchem.9b00959","article-title":"Pushing the boundaries of molecular representation for drug discovery with the graph attention mechanism","volume":"63","author":"Xiong","year":"2019","journal-title":"J. Med. Chem."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1021\/acs.jcim.2c01099","article-title":"HiGNN: A hierarchical informative graph neural network for molecular property prediction equipped with feature-wise attention","volume":"63","author":"Zhu","year":"2022","journal-title":"J. Chem. Inf. Model."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"121016","DOI":"10.1016\/j.eswa.2023.121016","article-title":"EMPPNet: Enhancing Molecular Property Prediction via Cross-modal Information Flow and Hierarchical Attention","volume":"234","author":"Zheng","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.knosys.2018.03.022","article-title":"Graph embedding techniques, applications, and performance: A survey","volume":"151","author":"Goyal","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_58","unstructured":"Fey, M., and Lenssen, J.E. (2019). Fast graph representation learning with PyTorch Geometric. arXiv."},{"key":"ref_59","first-page":"5281","article-title":"RDKit: A software suite for cheminformatics, computational chemistry, and predictive modeling","volume":"8","author":"Landrum","year":"2013","journal-title":"Greg Landrum"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1039\/C7SC02664A","article-title":"MoleculeNet: A benchmark for molecular machine learning","volume":"9","author":"Wu","year":"2018","journal-title":"Chem. Sci."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Wu, Z., Jiang, D., Wang, J., Zhang, X., Du, H., Pan, L., Hsieh, C.Y., Cao, D., and Hou, T. (2022). Knowledge-based BERT: A method to extract molecular features like computational chemists. Briefings Bioinform., 23.","DOI":"10.1093\/bib\/bbac131"},{"key":"ref_62","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019). Pytorch: An imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst., 32."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"014008","DOI":"10.1088\/1749-4699\/8\/1\/014008","article-title":"Hyperopt: A python library for model selection and hyperparameter optimization","volume":"8","author":"Bergstra","year":"2015","journal-title":"Comput. Sci. Discov."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Guo, Z., Zhang, C., Yu, W., Herr, J., Wiest, O., Jiang, M., and Chawla, N.V. (2021, January 19\u201323). Few-shot graph learning for molecular property prediction. Proceedings of the Web Conference 2021, Ljubljana, Slovenia.","DOI":"10.1145\/3442381.3450112"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Li, P., Li, Y., Hsieh, C.Y., Zhang, S., Liu, X., Liu, H., Song, S., and Yao, X. (2021). TrimNet: Learning molecular representation from triplet messages for biomedicine. Briefings Bioinform., 22.","DOI":"10.1093\/bib\/bbaa266"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.neucom.2022.05.010","article-title":"A new approach for evaluating node importance in complex networks via deep learning methods","volume":"497","author":"Zhang","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.1021\/ja00084a067","article-title":"Amide-amide and amide-water hydrogen bonds: Implications for protein folding and stability","volume":"116","author":"Eberhardt","year":"1994","journal-title":"J. Am. Chem. Soc."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/j.snb.2017.05.120","article-title":"A novel hydrophilic conjugated polymer containing hydroxyl groups: Syntheses and sensing performance for NACs in aqueous solution","volume":"251","author":"Ma","year":"2017","journal-title":"Sens. Actuators B Chem."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/873\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:46:16Z","timestamp":1760031976000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/873"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,4]]},"references-count":68,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sym17060873"],"URL":"https:\/\/doi.org\/10.3390\/sym17060873","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,4]]}}}