{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T03:37:48Z","timestamp":1772941068628,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,4,8]],"date-time":"2012-04-08T00:00:00Z","timestamp":1333843200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2013,2]]},"DOI":"10.1007\/s00180-012-0324-2","type":"journal-article","created":{"date-parts":[[2012,4,8]],"date-time":"2012-04-08T06:52:41Z","timestamp":1333867961000},"page":"19-36","source":"Crossref","is-referenced-by-count":47,"title":["Attractors in Boolean networks: a tutorial"],"prefix":"10.1007","volume":"28","author":[{"given":"Martin","family":"Hopfensitz","sequence":"first","affiliation":[]},{"given":"Christoph","family":"M\u00fcssel","sequence":"additional","affiliation":[]},{"given":"Markus","family":"Maucher","sequence":"additional","affiliation":[]},{"given":"Hans A.","family":"Kestler","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,4,8]]},"reference":[{"issue":"1","key":"324_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-5193(03)00035-3","volume":"223","author":"R Albert","year":"2003","unstructured":"Albert R, Othmer H (2003) The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J Theor Biol 223(1): 1\u201318","journal-title":"J Theor Biol"},{"issue":"1","key":"324_CR2","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0167-2789(03)00174-X","volume":"185","author":"M Aldana","year":"2003","unstructured":"Aldana M (2003) Boolean dynamics of networks with scale-free topology. Physica D: Nonlinear Phenomena 185(1): 45\u201366","journal-title":"Physica D: Nonlinear Phenomena"},{"issue":"5747","key":"324_CR3","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1126\/science.1119959","volume":"310","author":"S Bornholdt","year":"2005","unstructured":"Bornholdt S (2005) Systems biology. Less is more in modeling large genetic networks. Science 310(5747): 449\u2013451","journal-title":"Science"},{"issue":"Suppl. 1","key":"324_CR4","doi-asserted-by":"crossref","first-page":"S85","DOI":"10.1098\/rsif.2008.0132.focus","volume":"5","author":"S Bornholdt","year":"2008","unstructured":"Bornholdt S (2008) Boolean network models of cellular regulation: prospects and limitations. J R Soc Interface 5(Suppl. 1): S85\u2013S94","journal-title":"J R Soc Interface"},{"issue":"3","key":"324_CR5","doi-asserted-by":"crossref","first-page":"e1000702","DOI":"10.1371\/journal.pcbi.1000702","volume":"6","author":"L Calzone","year":"2010","unstructured":"Calzone L, Tournier L, Fourquet S, Thieffry D, Zhivotovsky B, Barillot E, Zinovyev A (2010) Mathematical modelling of cell-fate decision in response to death receptor engagement. PLoS Comput Biol 6(3): e1000702","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"324_CR6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1089\/10665270252833208","volume":"9","author":"H Jong de","year":"2002","unstructured":"de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9(1): 67\u2013103","journal-title":"J Comput Biol"},{"key":"324_CR7","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1186\/1471-2105-7-249","volume":"7","author":"N Dojer","year":"2006","unstructured":"Dojer N, Gambin A, Mizera A, Wilczy\u0144ski B, Tiuryn J (2006) Applying dynamic Bayesian networks to perturbed gene expression data. BMC Bioinform 7: 249","journal-title":"BMC Bioinform"},{"issue":"14","key":"324_CR8","doi-asserted-by":"crossref","first-page":"e124","DOI":"10.1093\/bioinformatics\/btl210","volume":"22","author":"A Faur\u00e9","year":"2006","unstructured":"Faur\u00e9 A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14): e124\u2013e131","journal-title":"Bioinformatics"},{"key":"324_CR9","doi-asserted-by":"crossref","unstructured":"Garg A, Banerjee D, De Micheli G (2008) Implicit methods for probabilistic modeling of gene regulatory networks. In: Proceedings of the 30th annual international IEEE EMBS conference, pp 4621\u20134627","DOI":"10.1109\/IEMBS.2008.4650243"},{"issue":"17","key":"324_CR10","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1093\/bioinformatics\/btn336","volume":"24","author":"A Garg","year":"2008","unstructured":"Garg A, Di Cara A, Xenarios I, Mendoza L, De Micheli G (2008) Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics 24(17): 1917\u20131925","journal-title":"Bioinformatics"},{"issue":"1","key":"324_CR11","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0022-5193(73)90208-7","volume":"39","author":"L Glass","year":"1973","unstructured":"Glass L, Kauffman SA (1973) The logical analysis of continuous, non-linear biochemical networks. J Theor Biol 39(1): 103\u2013129","journal-title":"J Theor Biol"},{"key":"324_CR12","doi-asserted-by":"crossref","DOI":"10.5962\/bhl.title.6268","volume-title":"Temporal organization in cells: a dynamic theory of cellular control processes","author":"B Goodwin","year":"1963","unstructured":"Goodwin B (1963) Temporal organization in cells: a dynamic theory of cellular control processes. Academic Press, London"},{"issue":"2","key":"324_CR13","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s00180-010-0201-9","volume":"26","author":"M Grzegorczyk","year":"2010","unstructured":"Grzegorczyk M, Husmeier D, Rahnenf\u00fchrer J (2010) Modelling non-stationary dynamic gene regulatory processes with the BGM model. Comput Stat 26(2): 199\u2013218","journal-title":"Comput Stat"},{"key":"324_CR14","unstructured":"Harvey I, Bossomaier T (1997) Time out of joint: attractors in asynchronous random Boolean networks. In: Proceedings of the forth European conference on artificial life, pp 67\u201375"},{"issue":"6","key":"324_CR15","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s001099900023","volume":"77","author":"S Huang","year":"1999","unstructured":"Huang S (1999) Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery. J Mol Med 77(6): 469\u2013480","journal-title":"J Mol Med"},{"issue":"3","key":"324_CR16","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","volume":"22","author":"SA Kauffman","year":"1969","unstructured":"Kauffman SA (1969) Metabolic stability and epigensis in randomly constructed genetic nets. J Theor Biol 22(3): 437\u2013467","journal-title":"J Theor Biol"},{"key":"324_CR17","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195079517.001.0001","volume-title":"The origins of order: self-organization and selection in evolution","author":"SA Kauffman","year":"1993","unstructured":"Kauffman SA (1993) The origins of order: self-organization and selection in evolution. Oxford University Press, Oxford"},{"issue":"49","key":"324_CR18","doi-asserted-by":"crossref","first-page":"17,102","DOI":"10.1073\/pnas.0407783101","volume":"101","author":"S Kauffman","year":"2004","unstructured":"Kauffman S, Peterson C, Samuelsson B, Troein C (2004) Genetic networks with canalyzing Boolean rules are always stable. PNAS 101(49): 17,102\u201317,107","journal-title":"PNAS"},{"issue":"1\u20132","key":"324_CR19","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1023\/A:1023905711304","volume":"52","author":"H L\u00e4hdesm\u00e4ki","year":"2003","unstructured":"L\u00e4hdesm\u00e4ki H, Shmulevich I, Yli-Harja O (2003) On learning gene regulatory networks under the Boolean network model. Mach Learn 52(1\u20132): 147\u2013167","journal-title":"Mach Learn"},{"key":"324_CR20","doi-asserted-by":"crossref","first-page":"4781","DOI":"10.1073\/pnas.0305937101","volume":"101","author":"F Li","year":"2004","unstructured":"Li F, Long T, Ouyang Q, Tang C (2004) The yeast cell-cycle network is robustly designed. PNAS 101: 4781\u20134786","journal-title":"PNAS"},{"key":"324_CR21","first-page":"18","volume":"3","author":"S Liang","year":"1998","unstructured":"Liang S, Fuhrman S, Somogyi R (1998) REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. Pac Symp Biocomput 3: 18\u201329","journal-title":"Pac Symp Biocomput"},{"issue":"2\u20133","key":"324_CR22","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1002\/rsa.3240060212","volume":"6","author":"J Lynch","year":"1995","unstructured":"Lynch J (1995) On the threshold of chaos in random Boolean cellular automata. Random Struct Algorithms 6(2\u20133): 239\u2013260","journal-title":"Random Struct Algorithms"},{"issue":"10","key":"324_CR23","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1093\/bioinformatics\/btq124","volume":"26","author":"C M\u00fcssel","year":"2010","unstructured":"M\u00fcssel C, Hopfensitz M, Kestler HA (2010) BoolNet\u2014an R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics 26(10): 1378\u20131380","journal-title":"Bioinformatics"},{"issue":"7197","key":"324_CR24","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1038\/nature06955","volume":"453","author":"DA Orlando","year":"2008","unstructured":"Orlando DA, Lin CY, Bernard A, Wang JY, Socolar JES, Iversen ES, Hartemink AJ, Haase SB (2008) Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 453(7197): 944\u2013947","journal-title":"Nature"},{"issue":"1","key":"324_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1752-0509-3-1","volume":"3","author":"O Sahin","year":"2009","unstructured":"Sahin O, Fr\u00f6hlich H, L\u00f6bke C, Korf U, Burmester S, Majety M, Mattern J, Schupp I, Chaouiya C, Thieffry D, Poustka A, Wiemann S, Beissbarth T, Arlt D (2009) Modeling ERBB receptor-regulated G1\/S transition to find novel targets for de novo trastuzumab resistance. BMC Syst Biol 3(1): 1","journal-title":"BMC Syst Biol"},{"issue":"9","key":"324_CR26","doi-asserted-by":"crossref","first-page":"098701","DOI":"10.1103\/PhysRevLett.90.098701","volume":"90","author":"B Samuelsson","year":"2003","unstructured":"Samuelsson B, Troein C (2003) Superpolynomial growth in the number of attractors in Kauffman networks. Phys Rev Lett 90(9): 098701","journal-title":"Phys Rev Lett"},{"issue":"2","key":"324_CR27","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1093\/bioinformatics\/18.2.261","volume":"18","author":"I Shmulevich","year":"2002","unstructured":"Shmulevich I, Dougherty ER, Kim S, Zhang W (2002) Probabilistic Boolean networks: a rule-based uncertainty model for gene-regulatory networks. Bioinformatics 18(2): 261\u2013274","journal-title":"Bioinformatics"},{"issue":"6","key":"324_CR28","doi-asserted-by":"crossref","first-page":"068","DOI":"10.1103\/PhysRevLett.90.068702","volume":"90","author":"JE Socolar","year":"2003","unstructured":"Socolar JE, Kauffman SA (2003) Scaling in ordered and critical random Boolean networks. Phys Rev Lett 90(6): 068\u2013702","journal-title":"Phys Rev Lett"},{"issue":"1","key":"324_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-5193(05)80350-9","volume":"153","author":"R Thomas","year":"1991","unstructured":"Thomas R (1991) Regulatory networks seen as asynchronous automata: a logical description. J Theor Biol 153(1): 1\u201323","journal-title":"J Theor Biol"},{"issue":"21","key":"324_CR30","doi-asserted-by":"crossref","first-page":"4043","DOI":"10.1016\/j.febslet.2007.07.043","volume":"581","author":"C Wawra","year":"2007","unstructured":"Wawra C, K\u00fchl M, Kestler HA (2007) Extended analyses of the Wnt\/\u03b2-catenin pathway: Robustness and oscillatory behaviour. FEBS Lett 581(21): 4043\u20134048","journal-title":"FEBS Lett"},{"issue":"10","key":"324_CR31","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1093\/bioinformatics\/btm093","volume":"23","author":"Y Xiao","year":"2007","unstructured":"Xiao Y, Dougherty ER (2007) The impact of function perturbations in Boolean networks. Bioinformatics 23(10): 1265\u20131273","journal-title":"Bioinformatics"},{"key":"324_CR32","unstructured":"Zhou D, M\u00fcssel C, Lausser L, Hopfensitz M, K\u00fchl M, Kestler HA (2009) Boolean networks for modeling and analysis of gene regulation. Ulmer Informatik-Bericht 2009\u20132010, Ulm University"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-012-0324-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00180-012-0324-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-012-0324-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T23:24:17Z","timestamp":1713828257000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00180-012-0324-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,8]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["324"],"URL":"https:\/\/doi.org\/10.1007\/s00180-012-0324-2","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,8]]}}}