{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T16:20:18Z","timestamp":1772554818412,"version":"3.50.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"26","license":[{"start":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T00:00:00Z","timestamp":1716768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T00:00:00Z","timestamp":1716768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"National Key Research and Development Program of China under Grant","award":["2022YFC3103101"],"award-info":[{"award-number":["2022YFC3103101"]}]},{"name":"Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory under Contract","award":["GML2021GD0809"],"award-info":[{"award-number":["GML2021GD0809"]}]},{"name":"National Natural Science Foundation of China under Contract","award":["42206187"],"award-info":[{"award-number":["42206187"]}]},{"name":"Key projects of the Guangdong Education Department under Grant","award":["2023ZDZX4009"],"award-info":[{"award-number":["2023ZDZX4009"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s00521-024-09762-3","type":"journal-article","created":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T05:01:45Z","timestamp":1716786105000},"page":"16395-16409","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A zeroing feedback gradient-based neural dynamics model for solving dynamic quadratic programming problems with linear equation constraints in finite time"],"prefix":"10.1007","volume":"36","author":[{"given":"Shangfeng","family":"Du","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0426-4356","authenticated-orcid":false,"given":"Dongyang","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Long","family":"Jin","sequence":"additional","affiliation":[]},{"given":"Yang","family":"Si","sequence":"additional","affiliation":[]},{"given":"Yongze","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,27]]},"reference":[{"issue":"3","key":"9762_CR1","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1109\/MSP.2010.936020","volume":"27","author":"J Mattingley","year":"2010","unstructured":"Mattingley J, Boyd S (2010) Real-Time convex optimization in signal processing. IEEE Signal Process Mag 27(3):50\u201361","journal-title":"IEEE Signal Process Mag"},{"issue":"10","key":"9762_CR2","doi-asserted-by":"publisher","first-page":"6864","DOI":"10.1109\/TII.2020.3047959","volume":"17","author":"C Jiang","year":"2021","unstructured":"Jiang C, Xiao X, Liu D, Huang H, Xiao H, Lu H (2021) Nonconvex and bound constraint zeroing neural network for solving time-varying complex-valued quadratic programming problem. IEEE Trans Ind Informat 17(10):6864\u20136874","journal-title":"IEEE Trans Ind Informat"},{"issue":"7","key":"9762_CR3","doi-asserted-by":"publisher","first-page":"2937","DOI":"10.1109\/TAC.2018.2872201","volume":"64","author":"D Liao-McPherson","year":"2019","unstructured":"Liao-McPherson D, Huang M, Kolmanovsky I (2019) A regularized and smoothed fischer-burmeister method for quadratic programming with applications to model predictive control. IEEE Trans Autom Control 64(7):2937\u20132944","journal-title":"IEEE Trans Autom Control"},{"key":"9762_CR4","doi-asserted-by":"publisher","first-page":"4535","DOI":"10.1007\/s10462-022-10284-4","volume":"56","author":"G Wang","year":"2023","unstructured":"Wang G, Hao Z, Huang H, Zhang B (2023) A proportional-integral iterative algorithm for time-variant equality-constrained quadratic programming problem with applications. Artif Intell Rev 56:4535\u20134556","journal-title":"Artif Intell Rev"},{"issue":"4303017","key":"9762_CR5","first-page":"1","volume":"60","author":"D Fu","year":"2022","unstructured":"Fu D, Huang H, Xiao X, Xia L, Jin L (2022) A generalized complex-valued constrained energy minimization scheme for the arctic sea ice extraction aided with neural algorithm. IEEE Trans Geosci Remote Sens 60(4303017):1\u201317","journal-title":"IEEE Trans Geosci Remote Sens"},{"issue":"22","key":"9762_CR6","doi-asserted-by":"publisher","first-page":"4276","DOI":"10.1364\/AO.50.004276","volume":"50","author":"J Minet","year":"2011","unstructured":"Minet J, Taboury J, Goudail F, P\u00e8alat M, Roux N, Lonnoy J, Ferrec Y (2011) Influence of band selection and target estimation error on the performance of the matched filter in hyperspectral imaging. Appl Opt 50(22):4276\u20134285","journal-title":"Appl Opt"},{"key":"9762_CR7","doi-asserted-by":"crossref","unstructured":"Manolakis D, Lockwood R, Cooley T, Jacobson J (2009) Hyperspectral detection algorithms: use covariances or subspaces? Proc. SPIE 7457, Imaging Spectrometry XIV, Aug","DOI":"10.1117\/12.828397"},{"key":"9762_CR8","doi-asserted-by":"crossref","unstructured":"Si Y, Wang D, Chou Y, Fu D (2023) Non-convex activated zeroing neural network model for solving time-varying nonlinear minimization problems with finite-time convergence, Knowl.-Based Syst., vol. 274, Aug","DOI":"10.1016\/j.knosys.2023.110633"},{"key":"9762_CR9","doi-asserted-by":"crossref","unstructured":"Ya\u01e7mur N, Alag\u00f6z BB (2019) Comparision of solutions of numerical gradient descent method and continous time gradient descent dynamics and lyapunov stability. In: Proceedings on 2019 27th signal processing and communications applications conference (SIU), pp. 1\u20134","DOI":"10.1109\/SIU.2019.8806396"},{"issue":"3","key":"9762_CR10","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1137\/0803022","volume":"3","author":"W Li","year":"1993","unstructured":"Li W, Swetits J (1993) A Newton method for convex regression, data smoothing, and quadratic programming with bounded constraints. SIAM J Optim 3(3):466\u2013488","journal-title":"SIAM J Optim"},{"issue":"4","key":"9762_CR11","doi-asserted-by":"publisher","first-page":"2156","DOI":"10.1109\/TNNLS.2021.3106044","volume":"34","author":"M Liu","year":"2023","unstructured":"Liu M, Chen L, Du X, Jin L, Shang M (2023) Activated gradients for deep neural networks. IEEE Trans Neural Netw Learn Syst 34(4):2156\u20132168","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"1","key":"9762_CR12","first-page":"48","volume":"26","author":"V Plevris","year":"2010","unstructured":"Plevris V, Papadrakakis M (2010) A hybrid particle swarm?gradient algorithm for global structural optimization. Comput-Aided Civ Infrastruct Eng 26(1):48\u201368","journal-title":"Comput-Aided Civ Infrastruct Eng"},{"key":"9762_CR13","doi-asserted-by":"publisher","first-page":"4535","DOI":"10.1007\/s10462-022-10284-4","volume":"56","author":"G Wang","year":"2023","unstructured":"Wang G, Hao Z, Huang H, Zhang B (2023) A proportional-integral iterative algorithm for time-variant equality-constrained quadratic programming problem with applications. Artif Intell Rev 56:4535\u20134556","journal-title":"Artif Intell Rev"},{"key":"9762_CR14","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1007\/s11075-013-9718-7","volume":"65","author":"N Andrei","year":"2014","unstructured":"Andrei N (2014) An accelerated subspace minimization three-term conjugate gradient algorithm for unconstrained optimization. Numer. Algor. 65:859\u2013874","journal-title":"Numer. Algor."},{"key":"9762_CR15","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1007\/s11075-013-9757-0","volume":"66","author":"F Wang","year":"2014","unstructured":"Wang F, Jian J, Wang C (2014) A model-hybrid approach for unconstrained optimization problems. Numer Algor 66:741\u2013759","journal-title":"Numer Algor"},{"key":"9762_CR16","unstructured":"Mathews JH, Fink KD (2004) Numerical Methods using MATLAB., Englewood Cliffs, NJ, USA: Prentice-Hall"},{"issue":"5","key":"9762_CR17","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1109\/TNN.2002.1031938","volume":"13","author":"Y Zhang","year":"2002","unstructured":"Zhang Y, Jiang D, Wang J (2002) A recurrent neural network for solving sylvester equation with time-varying coefficients. IEEE Trans Neural Netw 13(5):1053\u20131063","journal-title":"IEEE Trans Neural Netw"},{"key":"9762_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2020.125093","volume":"375","author":"B Sun","year":"2020","unstructured":"Sun B, Cao Y, Guo Z, Yan Z, Wen S (2020) Synchronization of discrete-time recurrent neural networks with time-varying delays via quantized sliding mode control. Appl Math Comput 375:125093","journal-title":"Appl Math Comput"},{"issue":"4","key":"9762_CR19","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1049\/cit2.12019","volume":"6","author":"X Zhang","year":"2021","unstructured":"Zhang X, Chen L, Li S, Stanimirovi\u0107 P, Zhang J, Jin L (2021) Design and analysis of recurrent neural network models with non-linear activation functions for solving time-varying quadratic programming problems. CAAI Trans Intell Technol 6(4):394\u2013404","journal-title":"CAAI Trans Intell Technol"},{"key":"9762_CR20","doi-asserted-by":"publisher","first-page":"118012","DOI":"10.1109\/ACCESS.2022.3220800","volume":"10","author":"C Jia","year":"2022","unstructured":"Jia C, Kong D, Du L (2022) Recursive terminal Sliding-Mode control method for nonlinear system based on double hidden layer fuzzy emotional recurrent neural network. IEEE Access 10:118012\u2013118023","journal-title":"IEEE Access"},{"issue":"3","key":"9762_CR21","doi-asserted-by":"publisher","first-page":"1423","DOI":"10.1109\/TMECH.2017.2683561","volume":"22","author":"Z Zhang","year":"2017","unstructured":"Zhang Z, Zheng L, Yu J, Li Y, Yu Z (2017) Three recurrent neural networks and three numerical methods for solving a repetitive motion planning scheme of redundant robot manipulators. IEEE \/ ASME Trans Mechatr 22(3):1423\u20131434","journal-title":"IEEE \/ ASME Trans Mechatr"},{"key":"9762_CR22","doi-asserted-by":"publisher","first-page":"1161","DOI":"10.1016\/S0005-1098(01)00092-9","volume":"37","author":"Y Zhang","year":"2001","unstructured":"Zhang Y, Wang J (2001) Recurrent neural networks for nonlinear output regulation. Automatica 37:1161\u20131173","journal-title":"Automatica"},{"issue":"9","key":"9762_CR23","doi-asserted-by":"publisher","first-page":"4385","DOI":"10.1109\/TNNLS.2017.2764529","volume":"29","author":"D Chen","year":"2018","unstructured":"Chen D, Zhang Y (2018) Robust zeroing neural-dynamics and its time-varying disturbances suppression model applied to mobile robot manipulators. IEEE Trans Neural Netw Learn Syst 29(9):4385\u20134397","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"9762_CR24","doi-asserted-by":"publisher","first-page":"112674","DOI":"10.1016\/j.chaos.2022.112674","volume":"164","author":"G Wang","year":"2022","unstructured":"Wang G, Li Q, Liu S, Xiao H, Zhang B (2022) New zeroing neural network with finite-time convergence for dynamic complex-value linear equation and its applications. Chaos Soliton Fractal 164:112674","journal-title":"Chaos Soliton Fractal"},{"issue":"4","key":"9762_CR25","doi-asserted-by":"publisher","first-page":"1776","DOI":"10.1109\/TNNLS.2020.2991088","volume":"32","author":"D Chen","year":"2021","unstructured":"Chen D, Li S, Wu Q (2021) A novel supertwisting zeroing neural network with application to mobile robot manipulators. IEEE Trans Neural Netw Learn Syst 32(4):1776\u20131787","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"9762_CR26","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2023.3290187","author":"Y Shi","year":"2023","unstructured":"Shi Y, Sheng W, Li S, Li B, Sun X (2023) Neurodynamics for equality-constrained time-variant nonlinear optimization using discretization. IEEE Trans Ind Inf. https:\/\/doi.org\/10.1109\/TII.2023.3290187","journal-title":"IEEE Trans Ind Inf"},{"issue":"6","key":"9762_CR27","doi-asserted-by":"publisher","first-page":"7414","DOI":"10.1109\/TII.2022.3210255","volume":"19","author":"Y Shi","year":"2023","unstructured":"Shi Y, Wang J, Li S, Li B, Sun X (2023) Tracking control of cable-driven planar robot based on discrete-time recurrent neural network with immediate discretization method. IEEE Trans Ind Inf 19(6):7414\u20137423","journal-title":"IEEE Trans Ind Inf"},{"issue":"6","key":"9762_CR28","doi-asserted-by":"publisher","first-page":"2781","DOI":"10.1109\/TNNLS.2021.3108050","volume":"34","author":"Y Shi","year":"2023","unstructured":"Shi Y, Zhao W, Li S, Li B, Sun X (2023) Novel discrete-time recurrent neural network for robot manipulator: a direct discretization technical route. IEEE Trans Neural Netw Learn Syst 34(6):2781\u20132790","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"2","key":"9762_CR29","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1109\/TNNLS.2020.3028136","volume":"33","author":"Y Shi","year":"2022","unstructured":"Shi Y, Jin L, Li S, Li J, Qiang J, Gerontitis DK (2022) Novel discrete-time recurrent neural networks handling discrete-form time-variant multi-augmented Sylvester matrix problems and manipulator application. IEEE Trans. Neural Netw. Learn. Syst. 33(2):587\u2013599","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"2","key":"9762_CR30","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1109\/TNNLS.2015.2435014","volume":"27","author":"B Liao","year":"2016","unstructured":"Liao B, Zhang Y, Jin L (2016) Taylor $$O(h^{3})$$ discretization of ZNN models for dynamic equality-constrained quadratic programming with application to manipulators. IEEE Trans Neural Netw Learn Syst 27(2):225\u2013237","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"9","key":"9762_CR31","doi-asserted-by":"publisher","first-page":"5913","DOI":"10.1109\/TSMC.2021.3129855","volume":"52","author":"S Liao","year":"2022","unstructured":"Liao S, Liu J, Qi Y, Huang H, Zheng R, Xiao X (2022) An adaptive gradient neural network to solve dynamic linear matrix equations. IEEE Trans, Syst, Man, Cybern, Syst 52(9):5913\u20135924","journal-title":"IEEE Trans, Syst, Man, Cybern, Syst"},{"key":"9762_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neucom.2019.10.080","volume":"379","author":"S Liao","year":"2020","unstructured":"Liao S, Liu J, Xiao X, Fu D, Wang G, Jin L (2020) Modified gradient neural networks for solving the time-varying sylvester equation with adaptive coefficients and elimination of matrix inversion. Neurocomputing 379:1\u201311","journal-title":"Neurocomputing"},{"key":"9762_CR33","doi-asserted-by":"crossref","unstructured":"Wang G, Hao Z, Li H, Zhang B (2023) An activated variable parameter gradient-based neural network for time-variant constrained quadratic programming and its applications. CAAI Trans Intell Technol, pp. 1\u201310, Feb","DOI":"10.1049\/cit2.12192"},{"key":"9762_CR34","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1007\/s00521-021-06465-x","volume":"34","author":"W Li","year":"2022","unstructured":"Li W, Han L, Xiao X et al (2022) A gradient-based neural network accelerated for vision-based control of an RCM-constrained surgical endoscope robot. Neural Comput Appl 34:1329\u20131343","journal-title":"Neural Comput Appl"},{"issue":"2","key":"9762_CR35","first-page":"973","volume":"10","author":"Y Liufu","year":"2022","unstructured":"Liufu Y, Jin L, Xu J, Xiao X, Fu D (2022) Reformative noise-immune neural network for equality-constrained optimization applied to image target detection. IEEE Trans Emerg Top Comput 10(2):973\u2013984","journal-title":"IEEE Trans Emerg Top Comput"},{"key":"9762_CR36","doi-asserted-by":"crossref","unstructured":"Liu B, Fu D, Qi Y, Huang H, Jin L (2021) Noise-tolerant gradient-oriented neurodynamic model for solving the sylvester equation. Appl Soft Comput J, vol. 109","DOI":"10.1016\/j.asoc.2021.107514"},{"key":"9762_CR37","doi-asserted-by":"publisher","first-page":"840","DOI":"10.1016\/j.asoc.2017.09.016","volume":"62","author":"L Jin","year":"2018","unstructured":"Jin L, Li S, Wang H, Zhang Z (2018) Nonconvex projection activated zeroing neurodynamic models for time-varying matrix pseudoinversion with accelerated finite-time convergence. Appl Soft Comput J 62:840\u2013850","journal-title":"Appl Soft Comput J"},{"key":"9762_CR38","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1016\/j.neucom.2017.06.030","volume":"267","author":"L Jin","year":"2017","unstructured":"Jin L, Li S, Liao B, Zhang Z (2017) Zeroing neural networks: a survey. Neurocomputing 267:597\u2013604","journal-title":"Neurocomputing"},{"issue":"8","key":"9762_CR39","doi-asserted-by":"publisher","first-page":"1940","DOI":"10.1109\/TAC.2009.2023779","volume":"54","author":"Y Zhang","year":"2009","unstructured":"Zhang Y, Chen K, Tan H-Z (2009) Performance analysis of gradient neural network exploited for online Time-Varying matrix inversion. IEEE Trans Autom Control 54(8):1940\u20131945","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"9762_CR40","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1109\/TAC.2022.3144135","volume":"68","author":"L Jin","year":"2023","unstructured":"Jin L, Wei L, Li S (2023) Gradient-based differential neural-solution to time-dependent nonlinear optimization. IEEE Trans Autom Control 68(1):620\u2013627","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"9762_CR41","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.apnum.2018.08.011","volume":"135","author":"E Jarlebring","year":"2019","unstructured":"Jarlebring E, Poloni F (2019) Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning. Appl Numer Math 135(1):173\u2013185","journal-title":"Appl Numer Math"},{"key":"9762_CR42","unstructured":"Hunger R (2005) Floating point operations in matrix-vector calculus[M]. Munich, Germany: Munich University of Technology, Inst. for Circuit Theory and Signal Processing"},{"key":"9762_CR43","doi-asserted-by":"publisher","first-page":"5114","DOI":"10.1109\/TSMC.2021.3115555","volume":"52","author":"Q Zuo","year":"2021","unstructured":"Zuo Q, Li K, Xiao L, Wang Y, Li K (2021) On generalized zeroing neural network under discrete and distributed time delays and its application to dynamic Lyapunov equation. IEEE Trans Syst, Man, Cybern, Syst 52:5114\u20135126","journal-title":"IEEE Trans Syst, Man, Cybern, Syst"},{"key":"9762_CR44","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.neucom.2022.05.067","volume":"500","author":"L Xiao","year":"2022","unstructured":"Xiao L, Song W, Jia L, Li X (2022) ZNN for time-variant nonlinear inequality systems: A finite-time solution. Neurocomputing 500:319\u2013328","journal-title":"Neurocomputing"},{"key":"9762_CR45","doi-asserted-by":"crossref","unstructured":"Zhang Y, Li Z, Guo D, Chen K, Chen P (2013) Superior robustness of using power-sigmoid activation functions in Z-type models for time-varying problems solving. ICMLC., pp. 759\u2013764","DOI":"10.1109\/ICMLC.2013.6890387"},{"issue":"8","key":"9762_CR46","doi-asserted-by":"publisher","first-page":"5114","DOI":"10.1109\/TSMC.2021.3115555","volume":"52","author":"Q Zuo","year":"2022","unstructured":"Zuo Q, Li K, Xiao L, Wang Y, Li K (2022) On generalized zeroing neural network under discrete and distributed time delays and its application to dynamic Lyapunov Equation. IEEE Trans Syst, Man, Cybernet: Syst 52(8):5114\u20135126. https:\/\/doi.org\/10.1109\/TSMC.2021.3115555","journal-title":"IEEE Trans Syst, Man, Cybernet: Syst"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-024-09762-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-024-09762-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-024-09762-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T18:12:28Z","timestamp":1724436748000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-024-09762-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,27]]},"references-count":46,"journal-issue":{"issue":"26","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["9762"],"URL":"https:\/\/doi.org\/10.1007\/s00521-024-09762-3","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,27]]},"assertion":[{"value":"27 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the other of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). He is responsible for communicating with the other authors about progress, submissions of revision, and final approval of proof. We confirm that we have provided a current email address, which is accessible by the corresponding author, which has been configured to accept email from the Neural Computing and Applications Editorial Office.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}