{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T04:04:30Z","timestamp":1750737870317,"version":"3.41.0"},"publisher-location":"Singapore","reference-count":32,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819665846","type":"print"},{"value":"9789819665853","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-981-96-6585-3_15","type":"book-chapter","created":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T14:41:29Z","timestamp":1750689689000},"page":"211-225","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Leaky Wang kWTA"],"prefix":"10.1007","author":[{"given":"John","family":"Sum","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew Chi-Sing","family":"Leung","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janet C. C.","family":"Chang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,24]]},"reference":[{"key":"15_CR1","unstructured":"Majani, E., Erlanson, R., Abu-Mostafa, Y.S.: On the K-winners-take-all network. In: Touretzky, D.S. (ed.) Advances in Neural Information Processing Systems 1, pp. 634\u2013642. Morgan-Kaufmann (1988). http:\/\/papers.nips.cc\/paper\/157-on-the-k-winners-take-all-network.pdf"},{"issue":"1","key":"15_CR2","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1109\/72.737494","volume":"10","author":"JP Sum","year":"1999","unstructured":"Sum, J.P., Leung, C.-S., Tam, P.K., Young, G.H., Kan, W.-K., Chan, L.-W.: Analysis for a class of Winner-Take-All model. IEEE Trans. Neural Netw. 10(1), 64\u201371 (1999)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"4","key":"15_CR3","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1109\/72.857764","volume":"11","author":"BD Calvert","year":"2000","unstructured":"Calvert, B.D., Marinov, C.A.: Another k-Winners-Take-All analog neural network. IEEE Trans. Neural Netw. 11(4), 829\u2013838 (2000)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"4","key":"15_CR4","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1109\/TNN.2003.813833","volume":"14","author":"CA Marinov","year":"2003","unstructured":"Marinov, C.A., Calvert, B.D.: Performance analysis for a k-winners-take-all analog neural network: basic theory. IEEE Trans. Neural Netw. 14(4), 766\u2013780 (2003)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"2","key":"15_CR5","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1109\/TAC.2016.2578645","volume":"62","author":"S Li","year":"2017","unstructured":"Li, S., Zhou, M., Luo, X., You, Z.-H.: Distributed Winner-Take-All in dynamic networks. IEEE Trans. Autom. Control 62(2), 577\u2013589 (2017)","journal-title":"IEEE Trans. Autom. Control"},{"key":"15_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.108868","volume":"115","author":"Y Zhang","year":"2020","unstructured":"Zhang, Y., Li, S., Xu, B., Yang, Y.: Analysis and design of a distributed k-Winners-Take-All model. Automatica 115, 108868 (2020)","journal-title":"Automatica"},{"issue":"12","key":"15_CR7","doi-asserted-by":"publisher","first-page":"2022","DOI":"10.1109\/TNN.2008.2003287","volume":"19","author":"X Hu","year":"2008","unstructured":"Hu, X., Wang, J.: An improved dual neural network for solving a class of quadratic programming problems with its $$k$$-winners-take-all application. IEEE Trans. Neural Netw. 19(12), 2022\u20132031 (2008)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"9","key":"15_CR8","doi-asserted-by":"publisher","first-page":"1496","DOI":"10.1109\/TNN.2010.2052631","volume":"21","author":"J Wang","year":"2010","unstructured":"Wang, J.: Analysis and design of k-Winners-Take-All model with a single state variable and the Heaviside step activation function. IEEE Trans. Neural Netw. 21(9), 1496\u20131506 (2010)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"7","key":"15_CR9","doi-asserted-by":"publisher","first-page":"1140","DOI":"10.1109\/TNN.2010.2050781","volume":"21","author":"Q Liu","year":"2010","unstructured":"Liu, Q., Dang, C., Cao, J.: A novel recurrent neural network with one neuron and finite-time convergence for $$k$$-winners-take-all operation. IEEE Trans. Neural Netw. 21(7), 1140\u20131148 (2010)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"4","key":"15_CR10","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1109\/TNNLS.2012.2186315","volume":"23","author":"Y Xiao","year":"2012","unstructured":"Xiao, Y., Liu, Y., Leung, C.-S., Sum, J.P.-F., Ho, K.: Analysis on the convergence time of Dual Neural Network-based kWTA. IEEE Trans. Neural Netw. Learn. Syst. 23(4), 676\u2013682 (2012)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"5","key":"15_CR11","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1109\/3477.623239","volume":"27","author":"L Wang","year":"1997","unstructured":"Wang, L.: Noise injection into inputs in sparsely connected Hopfield and Winner-Take-All neural networks. IEEE Trans. Syst. Man Cybern. Part B 27(5), 868\u2013870 (1997)","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"issue":"3","key":"15_CR12","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1109\/TNN.2007.912320","volume":"19","author":"C-S Leung","year":"2008","unstructured":"Leung, C.-S., Sum, J.: A fault tolerant regularizer for RBF networks. IEEE Trans. Neural Netw. 19(3), 493\u2013507 (2008)","journal-title":"IEEE Trans. Neural Netw."},{"issue":"5","key":"15_CR13","first-page":"911","volume":"56","author":"J He","year":"2009","unstructured":"He, J., Zhan, S., Chen, D., Geiger, R.: Analyses of static and dynamic random offset voltages in dynamic comparators. IEEE Trans. Circuits Syst. I 56(5), 911\u2013919 (2009)","journal-title":"IEEE Trans. Circuits Syst. I"},{"key":"15_CR14","doi-asserted-by":"crossref","unstructured":"Hu, M., Li, H., Wu, Q., Rose, G., Chen, Y.: Memristor crossbar based hardware realization of BSB recall function. In: Proceedings of the 2012 International Joint Conference on Neural Networks (IJCNN 2012), pp. 1\u20137 (2012)","DOI":"10.1109\/IJCNN.2012.6252563"},{"issue":"3","key":"15_CR15","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1109\/81.915384","volume":"48","author":"A Orgenci","year":"2001","unstructured":"Orgenci, A., Dundar, G., Balkur, S.: Fault-tolerant training of neural networks in the presence of MOS transistor mismatches. IEEE Trans. Circuits Syst. II: Analog Digit. Sig. Process. 48(3), 272\u2013281 (2001)","journal-title":"IEEE Trans. Circuits Syst. II: Analog Digit. Sig. Process."},{"key":"15_CR16","unstructured":"Franco, S.: Design with Operational Amplifiers and Analog Integrated Circuits, 3rd\u00a0edn. McGraw-Hill, New York (2002)"},{"key":"15_CR17","unstructured":"Gray, P.R., Hurst, P., Meyer, R.G., Lewis, S.: Analysis and Design of Analog Integrated Circuits, 5th\u00a0edn. Wiley, New York (2010)"},{"key":"15_CR18","doi-asserted-by":"crossref","unstructured":"Wang, J., Guo, Z.: Parametric sensitivity and scalability of $$k$$-Winners-Take-All networks with a single state variable and infinity-gain activation functions. In: Zhang, L., Kwok, J., Lu, B.-L. (eds.) Proceedings of ISNN 2010 Part I. LNCS, vol. 6063, pp. 77 \u2013 85 (2010)","DOI":"10.1007\/978-3-642-13278-0_11"},{"key":"15_CR19","doi-asserted-by":"crossref","unstructured":"Sum, J.P.-F., Leung, C.-S., Ho, K.: Analysis on Wang\u2019s kWTA with stochastic output nodes. In: International Conference on Neural Information Processing, pp. 268\u2013275. Springer, Cham (2011)","DOI":"10.1007\/978-3-642-24965-5_29"},{"issue":"9","key":"15_CR20","doi-asserted-by":"publisher","first-page":"1472","DOI":"10.1109\/TNNLS.2013.2257182","volume":"24","author":"J Sum","year":"2013","unstructured":"Sum, J., Leung, C.-S., Ho, K.: Effect of input noise and output node stochastic on Wang\u2019s kWTA. IEEE Trans. Neural Netw. Learn. Syst. 24(9), 1472\u20131478 (2013)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"15_CR21","doi-asserted-by":"crossref","unstructured":"Feng, R., Leung, C.-S., Sum, J.: Analysis of the DNN-kWTA network model with drifts in the offset voltages of threshold logic units. In: International Conference on Neural Information Processing, pp. 270\u2013278. Springer, Cham (2016)","DOI":"10.1007\/978-3-319-46681-1_33"},{"issue":"9","key":"15_CR22","doi-asserted-by":"publisher","first-page":"4212","DOI":"10.1109\/TNNLS.2017.2759905","volume":"29","author":"J Sum","year":"2018","unstructured":"Sum, J., Leung, C.-S., Ho, K.: On Wang kWTA with input noise, output node stochastic and recurrent state noise. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4212\u20134222 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"9","key":"15_CR23","doi-asserted-by":"publisher","first-page":"2188","DOI":"10.1109\/TNNLS.2014.2358851","volume":"26","author":"R Feng","year":"2015","unstructured":"Feng, R., Leung, C.-S., Sum, J., Xiao, Y.: Properties and performance of imperfect Dual Neural Network-based WTA networks. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 2188\u20132193 (2015)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"4","key":"15_CR24","doi-asserted-by":"publisher","first-page":"1082","DOI":"10.1109\/TNNLS.2016.2645602","volume":"29","author":"R Feng","year":"2018","unstructured":"Feng, R., Leung, C.-S., Sum, J.P.-F.: Robustness analysis on dual neural network-based kWTA with input noise. IEEE Trans. Neural Netw. Learn. Syst. 29(4), 1082\u20131094 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"15_CR25","unstructured":"Filippov, A.F.: Differential equations with discontinuous righthand side. Mat. Sb. (N.S.) 51(93)(1), 99\u2013128 (1960). (in Russian)"},{"key":"15_CR26","doi-asserted-by":"crossref","unstructured":"Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht (1988)","DOI":"10.1007\/978-94-015-7793-9"},{"issue":"1","key":"15_CR27","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1109\/TCS.1987.1086038","volume":"34","author":"B Paden","year":"1987","unstructured":"Paden, B., Sastry, S.: A calculus for computing Filippov\u2019s differential inclusion with application to the variable structure control of robot manipulators. IEEE Trans. Circuits Syst. 34(1), 73\u201382 (1987)","journal-title":"IEEE Trans. Circuits Syst."},{"issue":"3","key":"15_CR28","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1109\/MCS.2008.919306","volume":"28","author":"J Cort\u00e9s","year":"2008","unstructured":"Cort\u00e9s, J.: Discontinuous dynamical systems: a tutorial on solutions, nonsmooth analysis and stability. IEEE Control Syst. Mag. 28(3), 36\u201373 (2008)","journal-title":"IEEE Control Syst. Mag."},{"key":"15_CR29","unstructured":"Haley, D.C.: Estimation of the dosage mortality relationship when the dose is subject to error. Technical report, STANFORD UNIV CA APPLIED MATHEMATICS AND STATISTICS LABS (1952)"},{"key":"15_CR30","doi-asserted-by":"crossref","unstructured":"Lu, W., Leung, C.-S., Sum, J.: Influence of imperfections on the operational correctness of DNN-kWTA model. IEEE Trans. Neural Netw. Learn. Syst. (2023, inpress)","DOI":"10.1109\/TNNLS.2023.3281523"},{"key":"15_CR31","doi-asserted-by":"crossref","unstructured":"Sum, G., Sum, J., Chi-Sing\u00a0Leung, A., Chang, J.C.C.: A distributed kwta for decentralized auctions. In: Luo, B., Cheng, L., Wu, Z.-G., Li, H., Li, C. (eds.) Neural Information Processing, pp. 136\u2013147. Springer, Singapore (2024)","DOI":"10.1007\/978-981-99-8132-8_11"},{"key":"15_CR32","unstructured":"Krishna, V.: Auction Theory. Academic Press, Cambridge (2009)"}],"container-title":["Lecture Notes in Computer Science","Neural Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-96-6585-3_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T14:41:34Z","timestamp":1750689694000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-96-6585-3_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9789819665846","9789819665853"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-981-96-6585-3_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"24 June 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICONIP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Neural Information Processing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Auckland","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"New Zealand","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iconip2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/iconip2024.org","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}