{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T15:39:54Z","timestamp":1778081994947,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":13,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540404088","type":"print"},{"value":"9783540449898","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/3-540-44989-2_117","type":"book-chapter","created":{"date-parts":[[2010,11,19]],"date-time":"2010-11-19T22:10:02Z","timestamp":1290204602000},"page":"985-992","source":"Crossref","is-referenced-by-count":56,"title":["On Activation Functions for Complex-Valued Neural Networks \u2014 Existence of Energy Functions \u2014"],"prefix":"10.1007","author":[{"given":"Yasuaki","family":"Kuroe","sequence":"first","affiliation":[]},{"given":"Mitsuo","family":"Yoshid","sequence":"additional","affiliation":[]},{"given":"Takehiro","family":"Mori","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2003,6,18]]},"reference":[{"key":"117_CR1","doi-asserted-by":"publisher","first-page":"3088","DOI":"10.1073\/pnas.81.10.3088","volume":"81","author":"J. J. Hopfield","year":"1984","unstructured":"J. J. Hopfield, \u201cNeurons with graded response have collective computational properties like those of two-state neurons\u201d, Proc. Natl. Acad. of Sci. U.S.A., Vol.81, pp. 3088\u20133092, 1984.","journal-title":"Proc. Natl. Acad. of Sci. U.S.A."},{"key":"117_CR2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","volume":"81","author":"J. J. Hopfield","year":"1985","unstructured":"J. J. Hopfield and D. W. Tank, \u201c\u201cNeural\u201d Computation of Decisions in Optimization Problems\u201d, Biol. Cybern., Vol. 81, pp. 141\u2013152, 1985.","journal-title":"Biol. Cybern."},{"key":"117_CR3","unstructured":"Y. Kuroe, N. Hashimoto and T. Mori, \u201cOn Energy Function for Complex-valued Neural Networks and Its Application\u201d, CD-ROM Proc. of 9th International Conference on Neural Information Processing (ICONIP\u201902) Nov., 2002."},{"key":"117_CR4","doi-asserted-by":"publisher","first-page":"2101","DOI":"10.1109\/78.134446","volume":"39","author":"H. Leung","year":"1991","unstructured":"H. Leung and S. Haykin, \u201cThe Complex Backpropagation Algorithm\u201d, IEEE Transactions on Signal Processing, Vol.39, pp. 2101\u20132104, 1991.","journal-title":"IEEE Transactions on Signal Processing"},{"key":"117_CR5","first-page":"881","volume":"II","author":"D. L. Birx","year":"1992","unstructured":"D. L. Birx, S. J. Pipenberg, \u201cChaotic Oscillators and Complex Mapping Feed Forward Networks (CMFFNS) for Signal Detection in Noisy Environments\u201d, Proc. IEEE IJCNN\u201992, Vol. II, pp. 881\u2013888, 1992.","journal-title":"Proc. IEEE IJCNN\u201992"},{"key":"117_CR6","first-page":"584","volume-title":"Neural Information Processing Systems","author":"A.J. Noest","year":"1988","unstructured":"A.J. Noest, \u201cPhaser Neural Network,\u201d Neural Information Processing Systems, pp. 584\u2013591, D.Z. Anderson,ed., AIP, New York, 1988."},{"issue":"6","key":"117_CR7","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1209\/0295-5075\/6\/5\/016","volume":"6","author":"A. J. Noest","year":"1988","unstructured":"A. J. Noest, \u201cAssociative Memory in Sparse Phasor Neural Networks\u201d, Europhysics Letters, Vol. 6,No. 6, pp. 469\u2013474, 1988.","journal-title":"Europhysics Letters"},{"issue":"5","key":"117_CR8","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1109\/82.142037","volume":"39","author":"G. M. Georgiou","year":"1992","unstructured":"G. M. Georgiou and C. Koutsougeras, \u201cComplex Domain Backpropagation\u201d, IEEE Transactions on Circuits and Systems-II, Vol. 39,No. 5, pp. 330\u2013334, 1992.","journal-title":"IEEE Transactions on Circuits and Systems-II"},{"key":"117_CR9","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1109\/78.127967","volume":"40","author":"N. Benvenuto","year":"1992","unstructured":"N. Benvenuto and F. Piazza, \u201cOn the Complex Backpropagation Algorithm\u201d IEEE Transactions on Signal Processing, Vol.40, pp. 967\u2013969, 1992.","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"3","key":"117_CR10","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1109\/82.279210","volume":"41","author":"G. Kechriotis","year":"1994","unstructured":"G. Kechriotis and E. S. Manolakos, \u201cTraining Fully Recurrent Neural Networks with Complex Weights\u201d, IEEE Transactions on Circuits and Systems-II, Vol.41,No.3, pp. 235\u2013238, 1994.","journal-title":"IEEE Transactions on Circuits and Systems-II"},{"key":"117_CR11","first-page":"3165","volume":"VI","author":"M. Kinouchi","year":"1995","unstructured":"M. Kinouchi and M. Hagiwara, \u201cLearning Temporal Sequences by Complex Neurons with Local Feedback\u201d, Proc. IEEE ICNN\u2019 95, Vol. VI, pp. 3165\u20133169, 1995.","journal-title":"Proc. IEEE ICNN\u2019 95"},{"issue":"2","key":"117_CR12","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/1069-0115(94)90014-0","volume":"2","author":"A. Hirose","year":"1994","unstructured":"A. Hirose, \u201cApplications of Complex-Valued Neural Networks to Coherent Optical Computing Using Phase-Sensitive Detection Scheme\u201d, Information Sciences-Applications, Vol. 2,No. 2, pp. 103\u2013117, 1994.","journal-title":"Information Sciences-Applications"},{"issue":"6","key":"117_CR13","first-page":"750","volume":"J83-A","author":"N. Hashimoto","year":"2000","unstructured":"N. Hashimoto, Y. Kuroe and T. Mori, \u201cTheoretical Study of Qualitative Behaviors of Self-Correlation Type Associative Memory on Complex-valued Neural Networks,\u201d Trans. of IEICE, Vol.J83-A,No.6, pp.750\u2013760, June 2000 (in Japanese).","journal-title":"Trans. of IEICE"}],"container-title":["Lecture Notes in Computer Science","Artificial Neural Networks and Neural Information Processing \u2014 ICANN\/ICONIP 2003"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-44989-2_117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,4]],"date-time":"2023-06-04T07:24:01Z","timestamp":1685863441000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-44989-2_117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540404088","9783540449898"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/3-540-44989-2_117","relation":{},"ISSN":["0302-9743"],"issn-type":[{"value":"0302-9743","type":"print"}],"subject":[],"published":{"date-parts":[[2003]]}}}