{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:52:28Z","timestamp":1740099148049,"version":"3.37.3"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319999562"},{"type":"electronic","value":"9783319999579"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-99957-9_11","type":"book-chapter","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T04:26:31Z","timestamp":1534825591000},"page":"170-180","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Revealing Bistability in Neurological Disorder Models By Solving Parametric Polynomial Systems Geometrically"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7412-7667","authenticated-orcid":false,"given":"Changbo","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenyuan","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,8,22]]},"reference":[{"key":"11_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87708-2","volume-title":"Mathematical Foundations of Neuroscience","author":"G Bard Ermentrout","year":"2010","unstructured":"Bard Ermentrout, G., Terman, D.H.: Mathematical Foundations of Neuroscience. Springer, Heidelberg (2010). \nhttps:\/\/doi.org\/10.1007\/978-0-387-87708-2"},{"key":"11_CR2","series-title":"Springer Series in Computational Neuroscience","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-1424-7","volume-title":"20 Years of Computational Neuroscience","year":"2013","unstructured":"Bower, J.M. (ed.): 20 Years of Computational Neuroscience. Springer Series in Computational Neuroscience, vol. 9. Springer, Heidelberg (2013). \nhttps:\/\/doi.org\/10.1007\/978-1-4614-1424-7"},{"key":"11_CR3","doi-asserted-by":"crossref","unstructured":"Bradford, R.J., et al.: A case study on the parametric occurrence of multiple steady states. In: ISSAC 2017, pp. 45\u201352 (2017)","DOI":"10.1145\/3087604.3087622"},{"key":"11_CR4","doi-asserted-by":"crossref","unstructured":"Chen, C., Wu, W.: A numerical method for analyzing the stability of bi-parametric biological systems. In: SYNASC 2016, pp. 91\u201398 (2016)","DOI":"10.1109\/SYNASC.2016.026"},{"key":"11_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1007\/978-3-319-45641-6_11","volume-title":"Computer Algebra in Scientific Computing","author":"C Chen","year":"2016","unstructured":"Chen, C., Wu, W.: A numerical method for computing border curves of bi-parametric real polynomial systems and applications. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2016. LNCS, vol. 9890, pp. 156\u2013171. Springer, Cham (2016). \nhttps:\/\/doi.org\/10.1007\/978-3-319-45641-6_11"},{"issue":"5","key":"11_CR6","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.jsc.2015.11.008","volume":"7","author":"C Chen","year":"2016","unstructured":"Chen, C., Moreno Maza, M.: Quantifier elimination by cylindrical algebraic decomposition based on regular chains. J. Symb. Comput. 7(5), 74\u201393 (2016)","journal-title":"J. Symb. Comput."},{"key":"11_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/978-3-642-23568-9_9","volume-title":"Computer Algebra in Scientific Computing","author":"C Chen","year":"2011","unstructured":"Chen, C., Maza, M.M.: Semi-algebraic description of the equilibria of dynamical systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2011. LNCS, vol. 6885, pp. 101\u2013125. Springer, Heidelberg (2011). \nhttps:\/\/doi.org\/10.1007\/978-3-642-23568-9_9"},{"key":"11_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1007\/3-540-07407-4_17","volume-title":"Automata Theory and Formal Languages, 2nd GI Conference","author":"GE Collins","year":"1975","unstructured":"Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134\u2013183. Springer, Heidelberg (1975). \nhttps:\/\/doi.org\/10.1007\/3-540-07407-4_17"},{"key":"11_CR9","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.jtbi.2013.04.015","volume":"331","author":"J Caluw\u00e9 De","year":"2013","unstructured":"De Caluw\u00e9, J., Dupont, G.: The progression towards Alzheimer\u2019s disease described as a bistable switch arising from the positive loop between amyloids and $${C}a^{2+}$$Ca2+. J. Theor. Biol. 331, 12\u201318 (2013)","journal-title":"J. Theor. Biol."},{"key":"11_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-59731-7","volume-title":"Modeling Life: The Mathematics of Biological Systems","author":"A Garfinkel","year":"2017","unstructured":"Garfinkel, A., Shevtsov, J., Guo, Y.: Modeling Life: The Mathematics of Biological Systems. Springer, Heidelberg (2017). \nhttps:\/\/doi.org\/10.1007\/978-3-319-59731-7"},{"key":"11_CR11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107447615","volume-title":"Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition","author":"W Gerstner","year":"2014","unstructured":"Gerstner, W., Kistler, W.M., Naud, R., Paninski, L.: Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press, Cambridge (2014)"},{"key":"11_CR12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719543","volume-title":"Numerical Methods for Bifurcations of Dynamical Equilibria","author":"W Govaerts","year":"2000","unstructured":"Govaerts, W.: Numerical Methods for Bifurcations of Dynamical Equilibria. Society for Industrial and Applied Mathematics, Philadelphia (2000)"},{"issue":"2","key":"11_CR13","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/j.neuron.2017.06.011","volume":"95","author":"D Hassabis","year":"2017","unstructured":"Hassabis, D., Kumaran, D., Summerfield, C., Botvinick, M.: Neuroscience-inspired artificial intelligence. Neuron 95(2), 245\u2013258 (2017)","journal-title":"Neuron"},{"issue":"1","key":"11_CR14","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s10440-012-9782-3","volume":"125","author":"JD Hauenstein","year":"2012","unstructured":"Hauenstein, J.D.: Numerically computing real points on algebraic sets. Acta Applicandae Mathematicae 125(1), 105\u2013119 (2012)","journal-title":"Acta Applicandae Mathematicae"},{"key":"11_CR15","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.jsc.2014.09.039","volume":"70","author":"H Hong","year":"2015","unstructured":"Hong, H., Tang, X., Xia, B.: Special algorithm for stability analysis of multistable biological regulatory systems. J. Symb. Comput. 70, 112\u2013135 (2015)","journal-title":"J. Symb. Comput."},{"key":"11_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2421-9","volume-title":"Elements of Applied Bifurcation Theory","author":"YA Kuznetsov","year":"1995","unstructured":"Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, Heidelberg (1995). \nhttps:\/\/doi.org\/10.1007\/978-1-4757-2421-9"},{"issue":"6","key":"11_CR17","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1016\/j.jsc.2007.01.007","volume":"42","author":"D Lazard","year":"2007","unstructured":"Lazard, D., Rouillier, F.: Solving parametric polynomial systems. J. Symb. Comput. 42(6), 636\u2013667 (2007)","journal-title":"J. Symb. Comput."},{"key":"11_CR18","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1017\/S0962492900002749","volume":"6","author":"TY Li","year":"1997","unstructured":"Li, T.Y.: Numerical solution of multivariate polynomial systems by homotopy continuation methods. Acta Numerica 6, 399\u2013436 (1997)","journal-title":"Acta Numerica"},{"issue":"3","key":"11_CR19","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s11786-007-0039-x","volume":"1","author":"W Niu","year":"2008","unstructured":"Niu, W., Wang, D.: Algebraic approaches to stability analysis of biological systems. Math. Comput. Sci. 1(3), 507\u2013539 (2008)","journal-title":"Math. Comput. Sci."},{"issue":"1","key":"11_CR20","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1186\/1752-0509-4-181","volume":"4","author":"H Ogasawara","year":"2010","unstructured":"Ogasawara, H., Kawato, M.: The protein kinase M$$\\zeta $$\u03b6 network as a bistable switch to store neuronal memory. BMC Syst. Biol. 4(1), 181 (2010)","journal-title":"BMC Syst. Biol."},{"key":"11_CR21","series-title":"Springer Series in Bio-\/Neuroinformatics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-49959-8","volume-title":"Computational Neurology and Psychiatry","year":"2017","unstructured":"\u00c9rdi, P., Bhattacharya, B.S., Cochran, A.L. (eds.): Computational Neurology and Psychiatry. SSB, vol. 6. Springer, Cham (2017). \nhttps:\/\/doi.org\/10.1007\/978-3-319-49959-8"},{"issue":"4","key":"11_CR22","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1006\/jcom.2000.0563","volume":"16","author":"F Rouillier","year":"2000","unstructured":"Rouillier, F., Roy, M.F., Safey El Din, M.: Finding at least one point in each connected component of a real algebraic set defined by a single equation. J. Complex. 16(4), 716\u2013750 (2000)","journal-title":"J. Complex."},{"issue":"1","key":"11_CR23","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1186\/1756-6606-5-31","volume":"5","author":"TC Sacktor","year":"2012","unstructured":"Sacktor, T.C.: Memory maintenance by PKM$$\\zeta $$\u03b6 \u2013 an evolutionary perspective. Mol. Brain 5(1), 31 (2012)","journal-title":"Mol. Brain"},{"key":"11_CR24","volume-title":"Biological Modeling and Simulation","author":"R Schwartz","year":"2008","unstructured":"Schwartz, R.: Biological Modeling and Simulation. The MIT Press, Cambridge (2008)"},{"key":"11_CR25","doi-asserted-by":"publisher","DOI":"10.1142\/5763","volume-title":"The Numerical Solution of Systems of Polynomials Arising in Engineering and Science","author":"A Sommese","year":"2005","unstructured":"Sommese, A., Wampler, C.: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific Press, Singapore (2005)"},{"key":"11_CR26","doi-asserted-by":"crossref","unstructured":"Wang, D.M., Xia, B.: Stability analysis of biological systems with real solution classification. In: Kauers, M. (ed.) ISSAC 2005, pp. 354\u2013361 (2005)","DOI":"10.1145\/1073884.1073933"},{"key":"11_CR27","first-page":"339","volume":"2013","author":"W Wu","year":"2013","unstructured":"Wu, W., Reid, G.: Finding points on real solution components and applications to differential polynomial systems. ISSAC 2013, 339\u2013346 (2013)","journal-title":"ISSAC"},{"key":"11_CR28","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.tcs.2017.03.035","volume":"681","author":"W Wu","year":"2017","unstructured":"Wu, W., Reid, G., Feng, Y.: Computing real witness points of positive dimensional polynomial systems. Theor. Comput. Sci. 681, 217\u2013231 (2017)","journal-title":"Theor. Comput. Sci."},{"key":"11_CR29","unstructured":"Yang, L., Xia, B.: Real solution classifications of a class of parametric semi-algebraic systems. In: A3L 2005, pp. 281\u2013289 (2005)"}],"container-title":["Lecture Notes in Computer Science","Artificial Intelligence and Symbolic Computation"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-99957-9_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T04:34:17Z","timestamp":1534826057000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-99957-9_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319999562","9783319999579"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-99957-9_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2018]]}}}