[{"keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Computer Vision and Pattern Recognition","Software"],"file":[{"success":1,"date_updated":"2024-01-08T10:09:14Z","file_id":"14740","file_name":"2023_IEEEToP_Ali.pdf","checksum":"465c28ef0b151b4b1fb47977ed5581ab","access_level":"open_access","relation":"main_file","date_created":"2024-01-08T10:09:14Z","content_type":"application/pdf","creator":"dernst","file_size":2370988}],"date_published":"2023-12-01T00:00:00Z","page":"14069-14080","publication_identifier":{"eissn":["1939-3539"],"issn":["0162-8828"]},"article_processing_charge":"Yes (in subscription journal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","date_updated":"2024-01-08T10:11:46Z","type":"journal_article","day":"01","department":[{"_id":"HeEd"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"doi":"10.1109/tpami.2023.3308391","acknowledgement":"The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028. The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la Universidad de Sevilla para la recualificacion del sistema universitario español, 2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON developers, for their work and their support. We are also grateful to Streamlit for providing extra resources to deploy the web app\r\nonline on Streamlit community cloud. We thank the anonymous referees for their helpful suggestions.","volume":45,"issue":"12","file_date_updated":"2024-01-08T10:09:14Z","article_type":"original","publisher":"IEEE","intvolume":"        45","month":"12","date_created":"2024-01-08T09:59:46Z","status":"public","citation":{"ieee":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023.","ama":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 2023;45(12):14069-14080. doi:<a href=\"https://doi.org/10.1109/tpami.2023.3308391\">10.1109/tpami.2023.3308391</a>","short":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023) 14069–14080.","chicago":"Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/tpami.2023.3308391\">https://doi.org/10.1109/tpami.2023.3308391</a>.","ista":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. 2023. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.","mla":"Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:<a href=\"https://doi.org/10.1109/tpami.2023.3308391\">10.1109/tpami.2023.3308391</a>.","apa":"Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., &#38; Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE. <a href=\"https://doi.org/10.1109/tpami.2023.3308391\">https://doi.org/10.1109/tpami.2023.3308391</a>"},"quality_controlled":"1","author":[{"first_name":"Dashti","last_name":"Ali","full_name":"Ali, Dashti"},{"full_name":"Asaad, Aras","first_name":"Aras","last_name":"Asaad"},{"full_name":"Jimenez, Maria-Jose","first_name":"Maria-Jose","last_name":"Jimenez"},{"first_name":"Vidit","last_name":"Nanda","full_name":"Nanda, Vidit"},{"full_name":"Paluzo-Hidalgo, Eduardo","last_name":"Paluzo-Hidalgo","first_name":"Eduardo"},{"orcid":"0000-0003-2449-1433","full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","last_name":"Soriano Trigueros","first_name":"Manuel"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2023","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","title":"A survey of vectorization methods in topological data analysis","_id":"14739","oa":1,"ddc":["000"],"abstract":[{"text":"Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.","lang":"eng"}],"publication_status":"published"},{"article_type":"original","publisher":"IOP Publishing","file_date_updated":"2023-01-23T10:42:04Z","issue":"4","volume":3,"article_number":"040501","status":"public","date_created":"2023-01-12T12:02:21Z","month":"11","isi":1,"intvolume":"         3","year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"first_name":"Carl","last_name":"Poelking","full_name":"Poelking, Carl"},{"first_name":"Felix A","last_name":"Faber","full_name":"Faber, Felix A"},{"last_name":"Cheng","first_name":"Bingqing","id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","orcid":"0000-0002-3584-9632","full_name":"Cheng, Bingqing"}],"quality_controlled":"1","citation":{"mla":"Poelking, Carl, et al. “BenchML: An Extensible Pipelining Framework for Benchmarking Representations of Materials and Molecules at Scale.” <i>Machine Learning: Science and Technology</i>, vol. 3, no. 4, 040501, IOP Publishing, 2022, doi:<a href=\"https://doi.org/10.1088/2632-2153/ac4d11\">10.1088/2632-2153/ac4d11</a>.","apa":"Poelking, C., Faber, F. A., &#38; Cheng, B. (2022). BenchML: An extensible pipelining framework for benchmarking representations of materials and molecules at scale. <i>Machine Learning: Science and Technology</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/2632-2153/ac4d11\">https://doi.org/10.1088/2632-2153/ac4d11</a>","chicago":"Poelking, Carl, Felix A Faber, and Bingqing Cheng. “BenchML: An Extensible Pipelining Framework for Benchmarking Representations of Materials and Molecules at Scale.” <i>Machine Learning: Science and Technology</i>. IOP Publishing, 2022. <a href=\"https://doi.org/10.1088/2632-2153/ac4d11\">https://doi.org/10.1088/2632-2153/ac4d11</a>.","short":"C. Poelking, F.A. Faber, B. Cheng, Machine Learning: Science and Technology 3 (2022).","ista":"Poelking C, Faber FA, Cheng B. 2022. BenchML: An extensible pipelining framework for benchmarking representations of materials and molecules at scale. Machine Learning: Science and Technology. 3(4), 040501.","ama":"Poelking C, Faber FA, Cheng B. BenchML: An extensible pipelining framework for benchmarking representations of materials and molecules at scale. <i>Machine Learning: Science and Technology</i>. 2022;3(4). doi:<a href=\"https://doi.org/10.1088/2632-2153/ac4d11\">10.1088/2632-2153/ac4d11</a>","ieee":"C. Poelking, F. A. Faber, and B. Cheng, “BenchML: An extensible pipelining framework for benchmarking representations of materials and molecules at scale,” <i>Machine Learning: Science and Technology</i>, vol. 3, no. 4. IOP Publishing, 2022."},"publication_status":"published","abstract":[{"lang":"eng","text":"We introduce a machine-learning (ML) framework for high-throughput benchmarking of diverse representations of chemical systems against datasets of materials and molecules. The guiding principle underlying the benchmarking approach is to evaluate raw descriptor performance by limiting model complexity to simple regression schemes while enforcing best ML practices, allowing for unbiased hyperparameter optimization, and assessing learning progress through learning curves along series of synchronized train-test splits. The resulting models are intended as baselines that can inform future method development, in addition to indicating how easily a given dataset can be learnt. Through a comparative analysis of the training outcome across a diverse set of physicochemical, topological and geometric representations, we glean insight into the relative merits of these representations as well as their interrelatedness."}],"related_material":{"link":[{"relation":"software","url":"https://github.com/capoe/benchml"}]},"ddc":["000"],"oa":1,"_id":"12128","title":"BenchML: An extensible pipelining framework for benchmarking representations of materials and molecules at scale","publication":"Machine Learning: Science and Technology","date_published":"2022-11-17T00:00:00Z","external_id":{"isi":["000886534000001"]},"file":[{"checksum":"8930d4ad6ed9b47358c6f1a68666adb6","file_name":"2022_MachLearning_Poelking.pdf","access_level":"open_access","success":1,"date_updated":"2023-01-23T10:42:04Z","file_id":"12343","file_size":13814559,"creator":"dernst","content_type":"application/pdf","relation":"main_file","date_created":"2023-01-23T10:42:04Z"}],"keyword":["Artificial Intelligence","Human-Computer Interaction","Software"],"publication_identifier":{"issn":["2632-2153"]},"scopus_import":"1","day":"17","date_updated":"2023-08-04T08:49:53Z","type":"journal_article","oa_version":"Published Version","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"C P acknowledges funding from Astex through the Sustaining Innovation Program under the Milner Consortium. B C acknowledges resources provided by the Cambridge Tier-2 system operated by the University of Cambridge Research Computing Service funded by EPSRC Tier-2 capital Grant EP/P020259/1. F A F acknowledges funding from the Swiss National Science Foundation (Grant No. P2BSP2_191736). ","doi":"10.1088/2632-2153/ac4d11","language":[{"iso":"eng"}],"department":[{"_id":"BiCh"}],"has_accepted_license":"1"},{"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"25","oa_version":"Published Version","date_updated":"2023-02-13T09:15:13Z","type":"journal_article","department":[{"_id":"BjHo"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"doi":"10.1088/2632-072x/ac99cd","acknowledgement":"We acknowledge support from the Volkswagen Foundation under Grant No. 99720 and the German Federal Ministry for Education and Research (BMBF) under Grant No. 16ICR01. This research was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2068—390729961—Cluster of Excellence Physics of Life of TU Dresden.","keyword":["Artificial Intelligence","Computer Networks and Communications","Computer Science Applications","Information Systems"],"file":[{"date_created":"2023-01-24T07:24:37Z","relation":"main_file","file_size":1006106,"content_type":"application/pdf","creator":"dernst","date_updated":"2023-01-24T07:24:37Z","file_id":"12350","success":1,"access_level":"open_access","checksum":"35c5c5cb0eb17ea1b5184755daab9fc9","file_name":"2022_JourPhysics_Boerner.pdf"}],"date_published":"2022-10-25T00:00:00Z","scopus_import":"1","publication_identifier":{"issn":["2632-072X"]},"quality_controlled":"1","author":[{"full_name":"Börner, Georg","first_name":"Georg","last_name":"Börner"},{"first_name":"Malte","last_name":"Schröder","full_name":"Schröder, Malte"},{"last_name":"Scarselli","first_name":"Davide","id":"40315C30-F248-11E8-B48F-1D18A9856A87","full_name":"Scarselli, Davide","orcid":"0000-0001-5227-4271"},{"orcid":"0000-0003-0423-5010","full_name":"Budanur, Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","first_name":"Nazmi B","last_name":"Budanur"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754","full_name":"Hof, Björn","last_name":"Hof","first_name":"Björn"},{"full_name":"Timme, Marc","first_name":"Marc","last_name":"Timme"}],"citation":{"chicago":"Börner, Georg, Malte Schröder, Davide Scarselli, Nazmi B Budanur, Björn Hof, and Marc Timme. “Explosive Transitions in Epidemic Dynamics.” <i>Journal of Physics: Complexity</i>. IOP Publishing, 2022. <a href=\"https://doi.org/10.1088/2632-072x/ac99cd\">https://doi.org/10.1088/2632-072x/ac99cd</a>.","short":"G. Börner, M. Schröder, D. Scarselli, N.B. Budanur, B. Hof, M. Timme, Journal of Physics: Complexity 3 (2022).","ista":"Börner G, Schröder M, Scarselli D, Budanur NB, Hof B, Timme M. 2022. Explosive transitions in epidemic dynamics. Journal of Physics: Complexity. 3(4), 04LT02.","ama":"Börner G, Schröder M, Scarselli D, Budanur NB, Hof B, Timme M. Explosive transitions in epidemic dynamics. <i>Journal of Physics: Complexity</i>. 2022;3(4). doi:<a href=\"https://doi.org/10.1088/2632-072x/ac99cd\">10.1088/2632-072x/ac99cd</a>","ieee":"G. Börner, M. Schröder, D. Scarselli, N. B. Budanur, B. Hof, and M. Timme, “Explosive transitions in epidemic dynamics,” <i>Journal of Physics: Complexity</i>, vol. 3, no. 4. IOP Publishing, 2022.","apa":"Börner, G., Schröder, M., Scarselli, D., Budanur, N. B., Hof, B., &#38; Timme, M. (2022). Explosive transitions in epidemic dynamics. <i>Journal of Physics: Complexity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/2632-072x/ac99cd\">https://doi.org/10.1088/2632-072x/ac99cd</a>","mla":"Börner, Georg, et al. “Explosive Transitions in Epidemic Dynamics.” <i>Journal of Physics: Complexity</i>, vol. 3, no. 4, 04LT02, IOP Publishing, 2022, doi:<a href=\"https://doi.org/10.1088/2632-072x/ac99cd\">10.1088/2632-072x/ac99cd</a>."},"year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"_id":"12134","oa":1,"ddc":["530"],"publication":"Journal of Physics: Complexity","title":"Explosive transitions in epidemic dynamics","abstract":[{"lang":"eng","text":"Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third-order explosive phase transition in complex systems."}],"publication_status":"published","volume":3,"issue":"4","publisher":"IOP Publishing","article_type":"original","file_date_updated":"2023-01-24T07:24:37Z","intvolume":"         3","article_number":"04LT02","status":"public","month":"10","date_created":"2023-01-12T12:03:43Z"},{"page":"992-1003","file":[{"date_created":"2023-01-24T09:49:44Z","relation":"main_file","file_size":3259553,"content_type":"application/pdf","creator":"dernst","file_id":"12355","date_updated":"2023-01-24T09:49:44Z","success":1,"access_level":"open_access","checksum":"b4789122ce04bfb4ac042390f59aaa8b","file_name":"2022_NatureMachineIntelligence_Hasani.pdf"}],"external_id":{"arxiv":["2106.13898"],"isi":["000884215600003"]},"keyword":["Artificial Intelligence","Computer Networks and Communications","Computer Vision and Pattern Recognition","Human-Computer Interaction","Software"],"date_published":"2022-11-15T00:00:00Z","scopus_import":"1","publication_identifier":{"issn":["2522-5839"]},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","day":"15","oa_version":"Published Version","type":"journal_article","date_updated":"2023-08-04T09:00:10Z","has_accepted_license":"1","department":[{"_id":"ToHe"}],"language":[{"iso":"eng"}],"doi":"10.1038/s42256-022-00556-7","acknowledgement":"This research was supported in part by the AI2050 program at Schmidt Futures (grant G-22-63172), the Boeing Company, and the United States Air Force Research Laboratory and the United States Air Force Artificial Intelligence Accelerator and was accomplished under cooperative agreement number FA8750-19-2-1000. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the United States Air Force or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes, notwithstanding any copyright notation herein. This work was further supported by The Boeing Company and Office of Naval Research grant N00014-18-1-2830. M.T. is supported by the Poul Due Jensen Foundation, grant 883901. M.L. was supported in part by the Austrian Science Fund under grant Z211-N23 (Wittgenstein Award). A.A. was supported by the National Science Foundation Graduate Research Fellowship Program. We thank T.-H. Wang, P. Kao, M. Chahine, W. Xiao, X. Li, L. Yin and Y. Ben for useful suggestions and for testing of CfC models to confirm the results across other domains.","volume":4,"issue":"11","article_type":"original","publisher":"Springer Nature","file_date_updated":"2023-01-24T09:49:44Z","isi":1,"intvolume":"         4","status":"public","month":"11","date_created":"2023-01-12T12:07:21Z","quality_controlled":"1","author":[{"full_name":"Hasani, Ramin","last_name":"Hasani","first_name":"Ramin"},{"last_name":"Lechner","first_name":"Mathias","full_name":"Lechner, Mathias","id":"3DC22916-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Amini","first_name":"Alexander","full_name":"Amini, Alexander"},{"full_name":"Liebenwein, Lucas","last_name":"Liebenwein","first_name":"Lucas"},{"first_name":"Aaron","last_name":"Ray","full_name":"Ray, Aaron"},{"full_name":"Tschaikowski, Max","last_name":"Tschaikowski","first_name":"Max"},{"full_name":"Teschl, Gerald","last_name":"Teschl","first_name":"Gerald"},{"full_name":"Rus, Daniela","last_name":"Rus","first_name":"Daniela"}],"citation":{"ieee":"R. Hasani <i>et al.</i>, “Closed-form continuous-time neural networks,” <i>Nature Machine Intelligence</i>, vol. 4, no. 11. Springer Nature, pp. 992–1003, 2022.","ama":"Hasani R, Lechner M, Amini A, et al. Closed-form continuous-time neural networks. <i>Nature Machine Intelligence</i>. 2022;4(11):992-1003. doi:<a href=\"https://doi.org/10.1038/s42256-022-00556-7\">10.1038/s42256-022-00556-7</a>","ista":"Hasani R, Lechner M, Amini A, Liebenwein L, Ray A, Tschaikowski M, Teschl G, Rus D. 2022. Closed-form continuous-time neural networks. Nature Machine Intelligence. 4(11), 992–1003.","short":"R. Hasani, M. Lechner, A. Amini, L. Liebenwein, A. Ray, M. Tschaikowski, G. Teschl, D. Rus, Nature Machine Intelligence 4 (2022) 992–1003.","chicago":"Hasani, Ramin, Mathias Lechner, Alexander Amini, Lucas Liebenwein, Aaron Ray, Max Tschaikowski, Gerald Teschl, and Daniela Rus. “Closed-Form Continuous-Time Neural Networks.” <i>Nature Machine Intelligence</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1038/s42256-022-00556-7\">https://doi.org/10.1038/s42256-022-00556-7</a>.","mla":"Hasani, Ramin, et al. “Closed-Form Continuous-Time Neural Networks.” <i>Nature Machine Intelligence</i>, vol. 4, no. 11, Springer Nature, 2022, pp. 992–1003, doi:<a href=\"https://doi.org/10.1038/s42256-022-00556-7\">10.1038/s42256-022-00556-7</a>.","apa":"Hasani, R., Lechner, M., Amini, A., Liebenwein, L., Ray, A., Tschaikowski, M., … Rus, D. (2022). Closed-form continuous-time neural networks. <i>Nature Machine Intelligence</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s42256-022-00556-7\">https://doi.org/10.1038/s42256-022-00556-7</a>"},"year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"_id":"12147","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1038/s42256-022-00597-y"}]},"oa":1,"ddc":["000"],"title":"Closed-form continuous-time neural networks","publication":"Nature Machine Intelligence","abstract":[{"text":"Continuous-time neural networks are a class of machine learning systems that can tackle representation learning on spatiotemporal decision-making tasks. These models are typically represented by continuous differential equations. However, their expressive power when they are deployed on computers is bottlenecked by numerical differential equation solvers. This limitation has notably slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show that it is possible to closely approximate the interaction between neurons and synapses—the building blocks of natural and artificial neural networks—constructed by liquid time-constant networks efficiently in closed form. To this end, we compute a tightly bounded approximation of the solution of an integral appearing in liquid time-constant dynamics that has had no known closed-form solution so far. This closed-form solution impacts the design of continuous-time and continuous-depth neural models. For instance, since time appears explicitly in closed form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared with differential equation-based counterparts. More importantly, in contrast to ordinary differential equation-based continuous networks, closed-form networks can scale remarkably well compared with other deep learning instances. Lastly, as these models are derived from liquid networks, they show good performance in time-series modelling compared with advanced recurrent neural network models.","lang":"eng"}],"publication_status":"published","project":[{"grant_number":"Z211","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"25F42A32-B435-11E9-9278-68D0E5697425"}]},{"date_published":"2021-06-01T00:00:00Z","external_id":{"isi":["000625002100001"]},"file":[{"access_level":"open_access","checksum":"22b4253a2e5da843622a2df713784b4c","file_name":"2021_NetworksSpatialEconomics_Shehu.pdf","date_updated":"2021-08-11T12:44:16Z","file_id":"9884","success":1,"creator":"kschuh","content_type":"application/pdf","file_size":834964,"date_created":"2021-08-11T12:44:16Z","relation":"main_file"}],"keyword":["Computer Networks and Communications","Software","Artificial Intelligence"],"page":"291-323","publication_identifier":{"issn":["1566-113X"],"eissn":["1572-9427"]},"scopus_import":"1","type":"journal_article","date_updated":"2023-09-05T15:32:32Z","oa_version":"Published Version","day":"01","article_processing_charge":"Yes (via OA deal)","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","acknowledgement":"The authors sincerely thank the Editor-in-Chief and anonymous referees for their careful reading, constructive comments and fruitful suggestions that help improve the manuscript. The research of the first author is supported by the National Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral Fellowship; Grant Number: 120784). The first author also acknowledges the financial support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Postdoctoral Fellowship. The second author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). Open Access funding provided by Institute of Science and Technology (IST Austria).","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/s11067-021-09517-w","department":[{"_id":"VlKo"}],"has_accepted_license":"1","file_date_updated":"2021-08-11T12:44:16Z","publisher":"Springer Nature","article_type":"original","issue":"2","volume":21,"date_created":"2021-03-10T12:18:47Z","month":"06","status":"public","intvolume":"        21","isi":1,"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2021","citation":{"ieee":"C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity,” <i>Networks and Spatial Economics</i>, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021.","ama":"Izuchukwu C, Shehu Y. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. <i>Networks and Spatial Economics</i>. 2021;21(2):291-323. doi:<a href=\"https://doi.org/10.1007/s11067-021-09517-w\">10.1007/s11067-021-09517-w</a>","short":"C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323.","chicago":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” <i>Networks and Spatial Economics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11067-021-09517-w\">https://doi.org/10.1007/s11067-021-09517-w</a>.","ista":"Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. 21(2), 291–323.","mla":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” <i>Networks and Spatial Economics</i>, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323, doi:<a href=\"https://doi.org/10.1007/s11067-021-09517-w\">10.1007/s11067-021-09517-w</a>.","apa":"Izuchukwu, C., &#38; Shehu, Y. (2021). New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. <i>Networks and Spatial Economics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11067-021-09517-w\">https://doi.org/10.1007/s11067-021-09517-w</a>"},"quality_controlled":"1","author":[{"last_name":"Izuchukwu","first_name":"Chinedu","full_name":"Izuchukwu, Chinedu"},{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","last_name":"Shehu"}],"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","abstract":[{"lang":"eng","text":"In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps."}],"publication":"Networks and Spatial Economics","title":"New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity","oa":1,"ddc":["510"],"_id":"9234"}]