{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T08:06:59Z","timestamp":1768982819357,"version":"3.49.0"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T00:00:00Z","timestamp":1672012800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T00:00:00Z","timestamp":1672012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272109"],"award-info":[{"award-number":["62272109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Zeroing neural networks (ZNN) have shown their state-of-the-art performance on dynamic problems. However, ZNNs are vulnerable to perturbations, which causes reliability concerns in these models owing to the potentially severe consequences. Although it has been reported that some models possess enhanced robustness but cost worse convergence speed. In order to address these problems, a robust neural dynamic with an adaptive coefficient (RNDAC) model is proposed, aided by the novel adaptive activation function and robust evolution formula to boost convergence speed and preserve robustness accuracy. In order to validate and analyze the performance of the RNDAC model, it is applied to solve the dynamic matrix square root (DMSR) problem. Related experiment results show that the RNDAC model reliably solves the DMSR question perturbed by various noises. Using the RNDAC model, we are able to reduce the residual error from 10<jats:inline-formula><jats:alternatives><jats:tex-math>$$^1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow\/>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to 10<jats:inline-formula><jats:alternatives><jats:tex-math>$$^{-4}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow\/>\n                    <mml:mrow>\n                      <mml:mo>-<\/mml:mo>\n                      <mml:mn>4<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with noise perturbed and reached a satisfying and competitive convergence speed, which converges within 3\u00a0s.<\/jats:p>","DOI":"10.1007\/s40747-022-00954-9","type":"journal-article","created":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T14:06:42Z","timestamp":1672063602000},"page":"4213-4226","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Robust neural dynamics with adaptive coefficient applied to solve the dynamic matrix square root"],"prefix":"10.1007","volume":"9","author":[{"given":"Chengze","family":"Jiang","sequence":"first","affiliation":[]},{"given":"Chaomin","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Xiuchun","family":"Xiao","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6055-9648","authenticated-orcid":false,"given":"Cong","family":"Lin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,26]]},"reference":[{"issue":"2","key":"954_CR1","first-page":"1557","volume":"15","author":"S Yu","year":"2021","unstructured":"Yu S, Fan X, Chau T, Trinh H, Nahavandi S (2021) Square-root sigma-point filtering approach to state estimation for wind turbine generators in interconnected energy systems. IEEE Sens J 15(2):1557\u20131566","journal-title":"IEEE Sens J"},{"key":"954_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.116272","volume":"92","author":"Z Sun","year":"2022","unstructured":"Sun Z, Wang G, Jin L, Cheng C, Zhang B, Yu J (2022) Noise-suppressing zeroing neural network for online solving time-varying matrix square roots problems: a control-theoretic approach. Expert Syst Appl 92:116272","journal-title":"Expert Syst Appl"},{"key":"954_CR3","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1109\/TASLP.2020.2966891","volume":"28","author":"T Dietzen","year":"2020","unstructured":"Dietzen T, Doclo S, Moonen M, Waterschoot T (2020) Square root-based multi-source early PSD estimation and recursive RETF update in reverberant environments by means of the orthogonal procrustes problem. IEEE\/ACM Trans Audio Speech Lang Process 28:755\u2013769","journal-title":"IEEE\/ACM Trans Audio Speech Lang Process"},{"issue":"1","key":"954_CR4","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1109\/TIE.2020.2967671","volume":"68","author":"C Shen","year":"2021","unstructured":"Shen C, Zhang Y, Guo X, Chen X, Cao H, Tang J, Li J, Liu J (2021) Seamless GPS\/inertial navigation system based on self-learning square-root cubature Kalman filter. IEEE Trans Ind Electron 68(1):499\u2013508","journal-title":"IEEE Trans Ind Electron"},{"key":"954_CR5","doi-asserted-by":"publisher","first-page":"1568","DOI":"10.1016\/j.asoc.2020.106674","volume":"96","author":"H Huang","year":"2020","unstructured":"Huang H, Fu D, Zhang J, Xiao X, Wang G, Liao S (2020) Modified newton integration neural algorithm for solving the multi-linear M-tensor equation. Appl Soft Comput 96:1568\u20134946","journal-title":"Appl Soft Comput"},{"issue":"2","key":"954_CR6","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1007\/s11075-020-00979-6","volume":"87","author":"H Huang","year":"2020","unstructured":"Huang H, Fu D, Wang G, Jin L, Liao S, Wang H (2020) Modified newton integration algorithm with noise suppression for online dynamic nonlinear optimization. Numer Algorithms 87(2):575\u2013599","journal-title":"Numer Algorithms"},{"key":"954_CR7","doi-asserted-by":"publisher","first-page":"7203","DOI":"10.1016\/j.jfranklin.2021.07.006","volume":"358","author":"Z Sun","year":"2021","unstructured":"Sun Z, Shi T, Jin L, Zhang B, Pang Z, Yu J (2021) Discrete-time zeroing neural network of O($$\\tau $$4) pattern for online time-varying nonlinear optimization: application to manipulator motion generation. J Franklin Inst Appl Math Comput 358:7203\u20137220","journal-title":"J Franklin Inst Appl Math Comput"},{"issue":"5","key":"954_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.109883","volume":"257","author":"X Xu","year":"2022","unstructured":"Xu X, Liu S, Zhang N, Xiao G, Wu S (2022) Channel exchange and adversarial learning guided cross-modal person re-identification. Knowl Based Syst 257(5):109883","journal-title":"Knowl Based Syst"},{"key":"954_CR9","first-page":"1","volume":"71","author":"H Xing","year":"2022","unstructured":"Xing H, Xiao Z, Qu R, Zhu Z, Zhao B (2022) An efficient federated distillation learning system for multitask time series classification. IEEE Trans Instrum Meas 71:1\u201312","journal-title":"IEEE Trans Instrum Meas"},{"key":"954_CR10","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.ins.2020.03.043","volume":"524","author":"X Xiao","year":"2020","unstructured":"Xiao X, Jiang C, Lu H, Jin L, Liu D, Huang H, Pan Y (2020) A parallel computing method based on zeroing neural networks for time-varying complex-valued matrix Moore\u2013Penrose inversion. Inf Sci 524:216\u2013228","journal-title":"Inf Sci"},{"issue":"9","key":"954_CR11","doi-asserted-by":"publisher","first-page":"2603","DOI":"10.1109\/TFUZZ.2020.3005272","volume":"29","author":"L Jia","year":"2021","unstructured":"Jia L, Xiao L, Dai J, Cao Y (2021) A novel fuzzy-power zeroing neural network model for time-variant matrix Moore\u2013Penrose inversion with guaranteed performance. IEEE Trans Fuzzy Syst 29(9):2603\u20132611","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"6","key":"954_CR12","doi-asserted-by":"publisher","first-page":"2663","DOI":"10.1109\/TNNLS.2020.3007509","volume":"32","author":"Y Zhang","year":"2021","unstructured":"Zhang Y, Ling Y, Yang M, Yang S, Zhang Z (2021) Inverse-free discrete ZNN models solving for future matrix pseudoinverse via combination of extrapolation and ZeaD formulas. IEEE Trans Neural Netw Learn Syst 32(6):2663\u20132675","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"8","key":"954_CR13","doi-asserted-by":"publisher","first-page":"3415","DOI":"10.1109\/TNNLS.2021.3052896","volume":"33","author":"VN Katsikis","year":"2022","unstructured":"Katsikis VN, Mourtas SD, Stanimirovic PS, Zhang Y (2022) Solving complex-valued time-varying linear matrix equations via QR decomposition with applications to robotic motion tracking and on angle-of-arrival localization. IEEE Trans Neural Netw Learn Syst 33(8):3415\u20133424","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"5","key":"954_CR14","doi-asserted-by":"publisher","first-page":"3539","DOI":"10.1109\/TCYB.2020.3009110","volume":"52","author":"B Qiu","year":"2022","unstructured":"Qiu B, Guo J, Li X, Zhang Z, Zhang Y (2022) Discrete-time advanced zeroing neurodynamic algorithm applied to future equality-constrained nonlinear optimization with various noises. IEEE Trans Cybern 52(5):3539\u20133552","journal-title":"IEEE Trans Cybern"},{"issue":"10","key":"954_CR15","doi-asserted-by":"publisher","first-page":"9844","DOI":"10.1109\/TIE.2020.3029478","volume":"68","author":"L Jin","year":"2021","unstructured":"Jin L, Liu Y, Lu H, Zhang Z (2021) Saturation allows neural dynamics to be applied to linear equations and perturbed time-dependent systems of robotics. IEEE Trans Ind Electron 68(10):9844\u20139854","journal-title":"IEEE Trans Ind Electron"},{"issue":"9","key":"954_CR16","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":"954_CR17","doi-asserted-by":"crossref","unstructured":"Qi Y, Jin L, Luo X, Shi Y, Liu M (2022) Robust k-WTA network generation, analysis, and applications to multiagent coordination. IEEE Trans Cybern 52(8): 8515\u20138527","DOI":"10.1109\/TCYB.2021.3079457"},{"issue":"7","key":"954_CR18","doi-asserted-by":"publisher","first-page":"4627","DOI":"10.1109\/TII.2019.2944517","volume":"16","author":"D Guo","year":"2020","unstructured":"Guo D, Li S, Stanimirovic P (2020) Analysis and application of modified ZNN design with robustness against harmonic noise. IEEE Trans Ind Inform 16(7):4627\u20134638","journal-title":"IEEE Trans Ind Inform"},{"key":"954_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2021.104306","volume":"103","author":"K Liu","year":"2021","unstructured":"Liu K, Liu Y, Zhang Y, Wei L, Sun Z, Jin L (2021) Five-step discrete-time noise-tolerant zeroing neural network model for time-varying matrix inversion: application to manipulator motion generation. Eng Appl Artif Intell 103:104306","journal-title":"Eng Appl Artif Intell"},{"key":"954_CR20","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s10514-021-09988-3","volume":"45","author":"Z Sun","year":"2021","unstructured":"Sun Z, Li F, Duan X, Jin L, Lian Y, Liu S, Liu K (2021) A novel adaptive iterative learning control approach and human-in-the-loop control pattern for lower limb rehabilitation robot in disturbances environment. Auton Robot 45:595\u2013610","journal-title":"Auton Robot"},{"key":"954_CR21","unstructured":"Jiang C, Jin L, Xiao X (2021) Residual-based adaptive coefficient and noise-immunity ZNN for perturbed time-dependent quadratic minimization. arXiv preprint arXiv:2112.01773"},{"issue":"10","key":"954_CR22","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 Inform 17(10):6864\u20136874","journal-title":"IEEE Trans Ind Inform"},{"issue":"2","key":"954_CR23","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"},{"issue":"11","key":"954_CR24","doi-asserted-by":"publisher","first-page":"6978","DOI":"10.1109\/TIE.2016.2590379","volume":"63","author":"L Jin","year":"2016","unstructured":"Jin L, Zhang Y, Li S, Zhang Y (2016) Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans Ind Electron 63(11):6978\u20136988","journal-title":"IEEE Trans Ind Electron"},{"issue":"9","key":"954_CR25","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"},{"issue":"8","key":"954_CR26","doi-asserted-by":"publisher","first-page":"4729","DOI":"10.1109\/TSMC.2019.2944152","volume":"51","author":"L Xiao","year":"2021","unstructured":"Xiao L, Dai J, Jin L, Li W, Li S, Hou J (2021) A noise-enduring and finite-time zeroing neural network for equality-constrained time-varying nonlinear optimization. IEEE Trans Syst Man Cybern Syst 51(8):4729\u20134740","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"11","key":"954_CR27","doi-asserted-by":"publisher","first-page":"4362","DOI":"10.1109\/TSMC.2018.2853598","volume":"50","author":"W Li","year":"2020","unstructured":"Li W (2020) Design and analysis of a novel finite-time convergent and noise-tolerant recurrent neural network for time-variant matrix inversion. IEEE Trans Syst Man Cybern Syst 50(11):4362\u20134376","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"5","key":"954_CR28","first-page":"4977","volume":"69","author":"Y Kong","year":"2022","unstructured":"Kong Y, Jiang Y, Li X, Lei J (2022) A time-specified zeroing neural network for quadratic programming with its redundant manipulator application. IEEE Trans Power Electron 69(5):4977\u20134987","journal-title":"IEEE Trans Power Electron"},{"issue":"3","key":"954_CR29","doi-asserted-by":"publisher","first-page":"1562","DOI":"10.1109\/TII.2021.3090063","volume":"18","author":"L Xiao","year":"2022","unstructured":"Xiao L, Liu S, Wang X, He Y, Jia L, Xu Y (2022) Zeroing neural networks for dynamic quaternion matrix inversion. IEEE Trans Ind Inform 18(3):1562\u20131571","journal-title":"IEEE Trans Ind Inform"},{"key":"954_CR30","doi-asserted-by":"publisher","unstructured":"Song Z, Lu Z, Wu J, Xiao X, Wang G Improved ZND model for solving dynamic linear complex matrix equation and its application. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-022-07581-y (in press)","DOI":"10.1007\/s00521-022-07581-y"},{"issue":"10","key":"954_CR31","doi-asserted-by":"publisher","first-page":"6139","DOI":"10.1109\/TSMC.2021.3138550","volume":"52","author":"L Wei","year":"2022","unstructured":"Wei L, Jin L, Luo X (2022) Noise-suppressing neural dynamics for time-dependent constrained nonlinear optimization with applications. IEEE Trans Syst Man Cybern Syst 52(10):6139\u20136150","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"954_CR32","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.neucom.2020.02.011","volume":"394","author":"X Xiao","year":"2020","unstructured":"Xiao X, Fu D, Wang G, Liao S, Qi Y, Huang H, Jin L (2020) Two neural dynamics approaches for computing system of time-varying nonlinear equations. Neurocomputing 394:84\u201394","journal-title":"Neurocomputing"},{"issue":"2","key":"954_CR33","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1109\/TCSI.2020.3036847","volume":"68","author":"W Qi","year":"2021","unstructured":"Qi W, Zong G, Zheng W (2021) Adaptive event-triggered SMC for stochastic switching systems with Semi-Markov process and application to boost converter circuit model. IEEE Trans Circuits Syst I Regul Pap 68(2):786\u2013796","journal-title":"IEEE Trans Circuits Syst I Regul Pap"},{"issue":"10","key":"954_CR34","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.1002\/acs.3304","volume":"35","author":"W Su","year":"2021","unstructured":"Su W, Niu B, Wang H, Qi W (2021) Adaptive neural network asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints. Int J Adapt Control Signal Process 35(10):2007\u20132024","journal-title":"Int J Adapt Control Signal Process"},{"issue":"13","key":"954_CR35","doi-asserted-by":"publisher","first-page":"2813","DOI":"10.1080\/00207721.2021.1909775","volume":"52","author":"X Wang","year":"2021","unstructured":"Wang X, Jiang K, Zhang G, Niu B (2021) Adaptive output-feedback neural tracking control for uncertain switched MIMO nonlinear systems with time delays. Int J Syst Sci 52(13):2813\u20132830","journal-title":"Int J Syst Sci"},{"issue":"10","key":"954_CR36","doi-asserted-by":"publisher","first-page":"6359","DOI":"10.1109\/TII.2020.2964817","volume":"16","author":"L Jin","year":"2020","unstructured":"Jin L, Yan J, Du X, Xiao X, Fu D (2020) RNN for solving time-variant generalized Sylvester equation with applications to robots and acoustic source localization. IEEE Trans Ind Inform 16(10):6359\u20136369","journal-title":"IEEE Trans Ind Inform"},{"issue":"5","key":"954_CR37","doi-asserted-by":"publisher","first-page":"1833","DOI":"10.1109\/TSMC.2018.2789337","volume":"50","author":"D Zhang","year":"2020","unstructured":"Zhang D, Lee TC, Sun XM, Wu Y (2020) Practical regulation of nonholonomic systems using virtual trajectories and Lasalle invariance principle. IEEE Trans Syst Man Cybern Syst 50(5):1833\u20131839","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"2","key":"954_CR38","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1109\/TAC.2019.2910948","volume":"65","author":"Y Qin","year":"2020","unstructured":"Qin Y, Cao M, Anderson B (2020) Lyapunov criterion for stochastic systems and its applications in distributed computation. IEEE Trans Autom Control 65(2):546\u2013560","journal-title":"IEEE Trans Autom Control"},{"key":"954_CR39","doi-asserted-by":"crossref","unstructured":"Rosenvasser YN, Polyakov EY, Lampe B (1999) Application of Laplace transformation for digital redesign of continuous control systems. lIEEE Trans Autom Control 44(4):883\u2013886","DOI":"10.1109\/9.754840"},{"issue":"12","key":"954_CR40","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1109\/9.40780","volume":"34","author":"A Packard","year":"1989","unstructured":"Packard A, Helwig M (1989) Relating the gap and graph metrics via the triangle inequality. IEEE Trans Autom Control 34(12):1296\u20131297","journal-title":"IEEE Trans Autom Control"},{"issue":"11","key":"954_CR41","doi-asserted-by":"publisher","first-page":"4393","DOI":"10.1016\/j.eswa.2013.01.045","volume":"40","author":"Y Zhang","year":"2013","unstructured":"Zhang Y, Li W, Guo D, Ke Z (2013) Different Zhang functions leading to different ZNN models illustrated via time-varying matrix square roots finding. Expert Syst Appl 40(11):4393\u20134403","journal-title":"Expert Syst Appl"},{"key":"954_CR42","doi-asserted-by":"crossref","unstructured":"Sun Z, Shi T, Wei L, Sun LY, Liu K, Jin L (2020) Noise-suppressing zeroing neural network for online solving time-varying nonlinear optimization problem: a control-based approach. Neural Comput Appl 32:11505\u201311520","DOI":"10.1007\/s00521-019-04639-2"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-022-00954-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-022-00954-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-022-00954-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T13:23:51Z","timestamp":1690464231000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-022-00954-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,26]]},"references-count":42,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["954"],"URL":"https:\/\/doi.org\/10.1007\/s40747-022-00954-9","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,26]]},"assertion":[{"value":"23 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 December 2022","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 wish to draw the attention of the Editor to the following facts which may be considered as potential conflicts of interest and to significant financial contributions to this work. 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 and that the second author prepared the revision information letter and addressed most of the comments. 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 approve of proof. We confirm that we have provided a current email address which is accessible by the Corresponding Author and which has been configured to accept email from the Complex and Intelligent Systems Editorial Office.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}