{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:04:07Z","timestamp":1760241847809,"version":"build-2065373602"},"reference-count":73,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,1]],"date-time":"2018-09-01T00:00:00Z","timestamp":1535760000000},"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>Modelling the multimedia data such as text, images, or videos usually involves the analysis, prediction, or reconstruction of them. The recurrent neural network (RNN) is a powerful machine learning approach to modelling these data in a recursive way. As a variant, the long short-term memory (LSTM) extends the RNN with the ability to remember information for longer. Whilst one can increase the capacity of LSTM by widening or adding layers, additional parameters and runtime are usually required, which could make learning harder. We therefore propose a Tensor LSTM where the hidden states are tensorised as multidimensional arrays (tensors) and updated through a cross-layer convolution. As parameters are spatially shared within the tensor, we can efficiently widen the model without extra parameters by increasing the tensorised size; as deep computations of each time step are absorbed by temporal computations of the time series, we can implicitly deepen the model with little extra runtime by delaying the output. We show by experiments that our model is well-suited for various multimedia data modelling tasks, including text generation, text calculation, image classification, and video prediction.<\/jats:p>","DOI":"10.3390\/sym10090370","type":"journal-article","created":{"date-parts":[[2018,9,3]],"date-time":"2018-09-03T10:50:51Z","timestamp":1535971851000},"page":"370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multimedia Data Modelling Using Multidimensional Recurrent Neural Networks"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1658-0399","authenticated-orcid":false,"given":"Zhen","family":"He","sequence":"first","affiliation":[{"name":"College of Intelligence Science, National University of Defense Technology, Changsha 410073, China"},{"name":"Department of Computer Science, University College London, London WC1E 6BT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaobing","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6959-4343","authenticated-orcid":false,"given":"Liang","family":"Xiao","sequence":"additional","affiliation":[{"name":"Unmanned Systems Research Center, National Innovation Institute of Defense Technology, Beijing 100071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daxue","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Intelligence Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hangen","family":"He","sequence":"additional","affiliation":[{"name":"College of Intelligence Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Socher, R., Perelygin, A., Wu, J., Chuang, J., Manning, C.D., Ng, A., and Potts, C. (2013, January 18\u201321). Recursive deep models for semantic compositionality over a sentiment treebank. Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing, Seattle, WA, USA.","DOI":"10.18653\/v1\/D13-1170"},{"key":"ref_2","unstructured":"Santos, C.D., and Zadrozny, B. (2014, January 21\u201326). Learning character-level representations for part-of-speech tagging. Proceedings of the 31st International Conference on International Conference on Machine Learning, Beijing, China."},{"key":"ref_3","unstructured":"Bahdanau, D., Cho, K., and Bengio, Y. (2015, January 7\u20139). Neural machine translation by jointly learning to align and translate. Proceedings of the International Conference on Learning Representations 2015, San Diego, CA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Iyyer, M., Boyd-Graber, J., Claudino, L., Socher, R., and Daum\u00e9, H. (2014, January 25\u201329). A neural network for factoid question answering over paragraphs. Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), Doha, Qatar.","DOI":"10.3115\/v1\/D14-1070"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Byeon, W., Breuel, T.M., Raue, F., and Liwicki, M. (2015, January 7\u201312). Scene labeling with lstm recurrent neural networks. Proceedings of the 28th IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298977"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kumar, A.C., Bhandarkar, S.M., and Prasad, M. (2018, January 18\u201322). Depthnet: A recurrent neural network architecture for monocular depth prediction. Proceedings of the 2018 Conference on Computer Vision and Pattern Recognition (CVPR), Salt Lake City, UT, USA.","DOI":"10.1109\/CVPRW.2018.00066"},{"key":"ref_7","unstructured":"Van den Oord, A., Kalchbrenner, N., and Kavukcuoglu, K. (2016, January 19\u201324). Pixel Recurrent Neural Networks. Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA."},{"key":"ref_8","unstructured":"Huang, Y., Wang, W., and Wang, L. (2015, January 7\u201312). Bidirectional recurrent convolutional networks for multi-frame super-resolution. Proceedings of the Twenty-ninth Conference on Neural Information Processing Systems, Montreal, QC, Canada."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Milan, A., Rezatofighi, S.H., Dick, A.R., Reid, I.D., and Schindler, K. (2017, January 4\u20139). Online Multi-Target Tracking Using Recurrent Neural Networks. Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA.","DOI":"10.1609\/aaai.v31i1.11194"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Tokmakov, P., Alahari, K., and Schmid, C. (2017, January 22\u201329). Learning Video Object Segmentation with Visual Memory. Proceedings of the International Conference on Computer Vision, Venice, Italy.","DOI":"10.1109\/ICCV.2017.480"},{"key":"ref_11","unstructured":"Ranzato, M., Szlam, A., Bruna, J., Mathieu, M., Collobert, R., and Chopra, S. (arXiv, 2014). Video (language) modeling: A baseline for generative models of natural videos, arXiv."},{"key":"ref_12","unstructured":"Villegas, R., Yang, J., Hong, S., Lin, X., and Lee, H. (2017, January 24\u201326). Decomposing motion and content for natural video sequence prediction. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1207\/s15516709cog1402_1","article-title":"Finding structure in time","volume":"14","author":"Elman","year":"1990","journal-title":"Cognit. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/72.279181","article-title":"Learning long-term dependencies with gradient descent is difficult","volume":"5","author":"Bengio","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1162\/089976600300015015","article-title":"Learning to forget: Continual prediction with LSTM","volume":"12","author":"Gers","year":"2000","journal-title":"Neural Comput."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Bengio, Y. (2009). Learning deep architectures for AI. Foundations and Trends\u00ae in Machine Learning, University of California, Berkeley.","DOI":"10.1561\/9781601982957"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Graves, A., Mohamed, A.R., and Hinton, G. (2013, January 26\u201330). Speech recognition with deep recurrent neural networks. Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638947"},{"key":"ref_20","unstructured":"He, Z., Gao, S., Xiao, L., Liu, D., He, H., and Barber, D. (2017, January 4\u20139). Wider and Deeper, Cheaper and Faster: Tensorized LSTMs for Sequence Learning. Proceedings of the Thirty-first Conference on Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Taylor, G.W., and Hinton, G.E. (2009, January 14\u201318). Factored conditional restricted Boltzmann machines for modeling motion style. Proceedings of the 26th Annual International Conference on Machine Learning, Montreal, QC, Canada.","DOI":"10.1145\/1553374.1553505"},{"key":"ref_22","unstructured":"Sutskever, I., Martens, J., and Hinton, G.E. (July, January 28). Generating text with recurrent neural networks. Proceedings of the 28th International Conference on Machine Learning, Bellevue, WA, USA."},{"key":"ref_23","unstructured":"Denil, M., Shakibi, B., Dinh, L., de Freitas, N., and Ranzato, M.A. (2013, January 5\u201310). Predicting parameters in deep learning. Proceedings of the Twenty-seventh Conference on Neural Information Processing Systems, Stateline, NV, USA."},{"key":"ref_24","unstructured":"Irsoy, O., and Cardie, C. (2015, January 7\u20139). Modeling compositionality with multiplicative recurrent neural networks. Proceedings of the International Conference on Learning Representations 2015, San Diego, CA, USA."},{"key":"ref_25","unstructured":"Novikov, A., Podoprikhin, D., Osokin, A., and Vetrov, D.P. (2015, January 7\u201312). Tensorizing neural networks. Proceedings of the Twenty-ninth Conference on Neural Information Processing Systems, Montreal, QC, Canada."},{"key":"ref_26","unstructured":"Wu, Y., Zhang, S., Zhang, Y., Bengio, Y., and Salakhutdinov, R. (2016, January 5\u201310). On Multiplicative Integration with Recurrent Neural Networks. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_27","unstructured":"Bertinetto, L., Henriques, J.F., Valmadre, J., Torr, P., and Vedaldi, A. (2016, January 5\u201310). Learning feed-forward one-shot learners. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_28","unstructured":"Garipov, T., Podoprikhin, D., Novikov, A., and Vetrov, D. (2016, January 5\u201310). Ultimate tensorization: Compressing convolutional and FC layers alike. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_29","unstructured":"Krause, B., Lu, L., Murray, I., and Renals, S. (2017, January 24\u201326). Multiplicative LSTM for sequence modelling. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1162\/neco.1989.1.4.541","article-title":"Backpropagation applied to handwritten zip code recognition","volume":"1","author":"LeCun","year":"1989","journal-title":"Neural Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"LeCun","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_32","unstructured":"Appleyard, J., Kocisky, T., and Blunsom, P. (arXiv, 2016). Optimizing Performance of Recurrent Neural Networks on GPUs, arXiv."},{"key":"ref_33","unstructured":"Chung, J., Gulcehre, C., Cho, K., and Bengio, Y. (2015, January 6\u201311). Gated Feedback Recurrent Neural Networks. Proceedings of the 32nd International Conference on Machine Learning, Lille, France."},{"key":"ref_34","first-page":"3313","article-title":"Cells in multidimensional recurrent neural networks","volume":"17","author":"Leifert","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1162\/neco.1992.4.1.131","article-title":"Learning to control fast-weight memories: An alternative to dynamic recurrent networks","volume":"4","author":"Schmidhuber","year":"1992","journal-title":"Neural Comput."},{"key":"ref_36","unstructured":"De Brabandere, B., Jia, X., Tuytelaars, T., and Van Gool, L. (2016, January 5\u201310). Dynamic filter networks. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_37","unstructured":"Ha, D., Dai, A., and Le, Q.V. (2017, January 24\u201326). HyperNetworks. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."},{"key":"ref_38","unstructured":"Ba, J.L., Kiros, J.R., and Hinton, G.E. (arXiv, 2016). Layer Normalization, arXiv."},{"key":"ref_39","unstructured":"Xingjian, S., Chen, Z., Wang, H., Yeung, D.Y., Wong, W.K., and Woo, W.C. (2015, January 7\u201312). Convolutional LSTM network: A machine learning approach for precipitation nowcasting. Proceedings of the Twenty-ninth Conference on Neural Information Processing Systems, Montreal, QC, Canada."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Romera-Paredes, B., and Torr, P.H.S. (2016, January 11\u201314). Recurrent instance segmentation. Proceedings of the 14th European Conference on Computer Vision, Amsterdam, The Netherlands.","DOI":"10.1007\/978-3-319-46466-4_19"},{"key":"ref_41","unstructured":"Patraucean, V., Handa, A., and Cipolla, R. (2016, January 2\u20134). Spatio-temporal video autoencoder with differentiable memory. Proceedings of the International Conference on Learning Representations, San Juan, Puerto Rico."},{"key":"ref_42","unstructured":"Wu, L., Shen, C., and Hengel, A.V.D. (arXiv, 2016). Deep Recurrent Convolutional Networks for Video-based Person Re-identification: An End-to-End Approach, arXiv."},{"key":"ref_43","unstructured":"Stollenga, M.F., Byeon, W., Liwicki, M., and Schmidhuber, J. (2015, January 7\u201312). Parallel multi-dimensional LSTM, with application to fast biomedical volumetric image segmentation. Proceedings of the Twenty-ninth Conference on Neural Information Processing Systems, Montreal, QC, Canada."},{"key":"ref_44","unstructured":"Chen, J., Yang, L., Zhang, Y., Alber, M., and Chen, D.Z. (2016, January 5\u201310). Combining Fully Convolutional and Recurrent Neural Networks for 3D Biomedical Image Segmentation. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_45","unstructured":"Graves, A. (arXiv, 2013). Generating sequences with recurrent neural networks, arXiv."},{"key":"ref_46","unstructured":"Kalchbrenner, N., Danihelka, I., and Graves, A. (2016, January 2\u20134). Grid long short-term memory. Proceedings of the International Conference on Learning Representations (ICLR), San Juan, Puerto Rico."},{"key":"ref_47","unstructured":"Zilly, J.G., Srivastava, R.K., Koutn\u00edk, J., and Schmidhuber, J. (2017, January 6\u201311). Recurrent Highway Networks. Proceedings of the 34th International Conference on Machine Learning (ICML 2017), Sydney, Australia."},{"key":"ref_48","unstructured":"Bradbury, J., Merity, S., Xiong, C., and Socher, R. (2017, January 24\u201326). Quasi-recurrent neural networks. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."},{"key":"ref_49","unstructured":"Graves, A. (arXiv, 2016). Adaptive Computation Time for Recurrent Neural Networks, arXiv."},{"key":"ref_50","unstructured":"Mujika, A., Meier, F., and Steger, A. (2017, January 4\u20139). Fast-Slow Recurrent Neural Networks. Proceedings of the Thirty-first Conference on Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_51","unstructured":"Diamos, G., Sengupta, S., Catanzaro, B., Chrzanowski, M., Coates, A., Elsen, E., Engel, J., Hannun, A., and Satheesh, S. (2016, January 19\u201324). Persistent RNNs: Stashing Recurrent Weights On-Chip. Proceedings of the 33rd International Conference on Machine Learning (ICML 2016), New York, NY, USA."},{"key":"ref_52","unstructured":"Kaiser, \u0141., and Sutskever, I. (2016, January 2\u20134). Neural gpus learn algorithms. Proceedings of the International Conference on Learning Representations (ICLR), San Juan, Puerto Rico."},{"key":"ref_53","unstructured":"Kaiser, \u0141., and Bengio, S. (2016, January 5\u201310). Can Active Memory Replace Attention?. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_54","unstructured":"Van den Oord, A., Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., Kalchbrenner, N., Senior, A., and Kavukcuoglu, K. (arXiv, 2016). Wavenet: A generative model for raw audio, arXiv."},{"key":"ref_55","unstructured":"Lei, T., and Zhang, Y. (arXiv, 2017). Training RNNs as Fast as CNNs, arXiv."},{"key":"ref_56","unstructured":"Chang, S., Zhang, Y., Han, W., Yu, M., Guo, X., Tan, W., Cui, X., Witbrock, M., Hasegawa-Johnson, M., and Huang, T. (2017, January 4\u20139). Dilated Recurrent Neural Networks. Proceedings of the Thirty-first Conference on Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_57","unstructured":"Kingma, D., and Ba, J. (2015, January 7\u20139). Adam: A method for stochastic optimization. Proceedings of the International Conference on Learning Representations 2015, San Diego, CA, USA."},{"key":"ref_58","unstructured":"Jozefowicz, R., Zaremba, W., and Sutskever, I. (2015, January 6\u201311). An Empirical Exploration of Recurrent Network Architectures. Proceedings of the 32nd International Conference on Machine Learning (ICML 2015), Lille, France."},{"key":"ref_59","unstructured":"Collobert, R., Kavukcuoglu, K., and Farabet, C. (2011, January 12\u201317). Torch7: A matlab-like environment for machine learning. Proceedings of the Twenty-fifth Conference on Neural Information Processing Systems, Sierra Nevada, Spain."},{"key":"ref_60","unstructured":"Hutter, M. (2018, July 13). The Human Knowledge Compression Contest. Available online: http:\/\/prize.hutter1.net."},{"key":"ref_61","unstructured":"Chung, J., Ahn, S., and Bengio, Y. (2017, January 24\u201326). Hierarchical multiscale recurrent neural networks. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."},{"key":"ref_62","unstructured":"Le, Q.V., Jaitly, N., and Hinton, G.E. (arXiv, 2015). A simple way to initialize recurrent networks of rectified linear units, arXiv."},{"key":"ref_63","unstructured":"Arjovsky, M., Shah, A., and Bengio, Y. (2016, January 19\u201324). Unitary Evolution Recurrent Neural Networks. Proceedings of the 33rd International Conference on Machine Learning (ICML 2016), New York, NY, USA."},{"key":"ref_64","unstructured":"Wisdom, S., Powers, T., Hershey, J., Le Roux, J., and Atlas, L. (2016, January 5\u201310). Full-capacity unitary recurrent neural networks. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_65","unstructured":"Zhang, S., Wu, Y., Che, T., Lin, Z., Memisevic, R., Salakhutdinov, R.R., and Bengio, Y. (2016, January 5\u201310). Architectural Complexity Measures of Recurrent Neural Networks. Proceedings of the Thirtieth Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_66","unstructured":"Cooijmans, T., Ballas, N., Laurent, C., and Courville, A. (2017, January 24\u201326). Recurrent Batch Normalization. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Schuldt, C., Laptev, I., and Caputo, B. (2004, January 23\u201326). Recognizing human actions: A local SVM approach. Proceedings of the 17th International Conference on Pattern Recognition, Cambridge, UK.","DOI":"10.1109\/ICPR.2004.1334462"},{"key":"ref_68","unstructured":"Soomro, K., Zamir, A.R., and Shah, M. (arXiv, 2012). UCF101: A dataset of 101 human actions classes from videos in the wild, arXiv."},{"key":"ref_69","unstructured":"Mathieu, M., Couprie, C., and LeCun, Y. (2016, January 2\u20134). Deep multi-scale video prediction beyond mean square error. Proceedings of the International Conference on Learning Representations (ICLR), San Juan, Puerto Rico."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Karpathy, A., Toderici, G., Shetty, S., Leung, T., Sukthankar, R., and Fei-Fei, L. (2014, January 23\u201328). Large-scale video classification with convolutional neural networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.223"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_72","unstructured":"Srivastava, N., Mansimov, E., and Salakhudinov, R. (2015, January 6\u201311). Unsupervised learning of video representations using lstms. Proceedings of the 32nd International Conference on Machine Learning (ICML 2015), Lille, France."},{"key":"ref_73","unstructured":"Lotter, W., Kreiman, G., and Cox, D. (2017, January 24\u201326). Deep predictive coding networks for video prediction and unsupervised learning. Proceedings of the 5th International Conference on Learning Representations, Toulon, France."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/9\/370\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:22:32Z","timestamp":1760196152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/9\/370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,1]]},"references-count":73,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["sym10090370"],"URL":"https:\/\/doi.org\/10.3390\/sym10090370","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,9,1]]}}}