统计模型在基因调控网络结构学习和被动传感器目标定位中的应用
|
摘要
基因调控网络的网络结构学习和被动传感器的目标定位问题是两个重要的应用统计研究课题。本文从实际的应用背景和基本的模型假设出发,对这两个课题中现有的统计学习方法进行了理论分析和适应性改进,取得了一些有意义的进展。
本文首先研究了利用网络的功能可靠性来优化网络结构学习的方法。现有的结构学习方法是在齐次布尔模型的框架下进行。在该模型中,网络节点的状态更新只在离散时间点进行,而且各个节点的更新是同步进行的。因此,结构学习的结果中会产生大量的”虚假网络结构”。它们与真实的网络结构在齐次模型下具有相同的功能,故难以区分。而功能可靠性是用来衡量调控网络在较真实的环境下(状态连续演化和随机因素干扰),完成特定生物学功能的能力。在齐次模型的基础上,本文引入了非齐次布尔模型来更加真实地模拟调控网络的状态演化过程。新的模型采用连续值变量来表示节点的浓度水平。浓度的变化过程服从一阶微分方程模型。并且,还考虑了节点之间传递调控作用的随机延迟。通过比较多个齐次模型中功能相同的网络结构在新的非齐次模型下的功能可靠性,发现真实的网络结构具有较高的功能可靠性,并且,其组成规律符合可设计性原则。所以,我们可以用功能可靠性要求来进一步提高网络结构学习的效率。
其次,本文研究了利用网络动力学稳定性来学习网络结构的方法。真实的调控网络具有很强的动力学稳定性。具体而言,在调控网络的相空间中,绝大多数的网络初始状态都能够演化到相同的稳定状态(称为吸引子),而且不同初态的演化路径也具有较高的重叠度。每个吸引子所吸引的初始状态定义为该吸引子的吸引域(或吸引盆),而它所吸引的初始状态的个数就是其吸引盆的大小。本章重点论证了网络拓扑结构与网络吸引子的吸引盆大小之间的关系,提出了理想传递链结构,并证明了理想传递链是保证网络具有全局吸引子的充分和必要条件(必要性是在网络中调控作用数量最少的约束下成立)。通过对真实生物网络的实例研究,也证明了在复杂的生物调控网络中,理想传递链上的作用边对网络的吸引盆大小的贡献明显大于其他的作用边。此外,理想传递链结构还可以帮助确定网络中另一种重要结构-负反馈环-的联接位置。通过比较发现,负反馈环在网络中的联接位置符合最大吸引盆原则,即在某个位置上加入负反馈环之后网络的吸引盆越大,那么,实际的网络中在该位置上越有可能出现负反馈环。这些结论不仅能够帮助改进和提高现有的网络结构学习方法,也能够为合成生物学中的设计工作提供指导意义。
最后,本文研究了被动传感器的目标定位问题。被动传感器具有能耗低和隐蔽性强等特点,在工业自动化和安防领域具有广阔的应用前景。利用被动传感器的探测信息来确定监视区域内目标的位置和运动状态是被动传感器应用的关键问题。本文提出基于工具变量方法的目标运动参数的线性估计。该方法具有显式表达,计算量低,而且具有良好的大样本性质(包括相合性和渐进正态性)。这些特点保证了该方法在实时跟踪系统中的良好表现。此外,该方法也具有很好的扩展性,能够推广到更加复杂的跟踪环境。
Structure learning of genetic regulatory networks and target tracking with pas-sive sensors are two important research topics of applied statistics. Based on thetheoretical analysis of basic assumptions and the adaptive improvement of exist-ing statistical methods, this thesis has made some adaptive improvements on theexisting methods and lead to some meaningful progresses.
Firstly, the property of functional reliability has been employed to improve theefciency of structure learning with functional process of regulatory networks. Mostexisting process-based learning algorithms have been developed under the assump-tions of Boolean model. The state of each node in a network is asynchronouslyupdated at discrete time instants. Therefore, the output of structure learning maycontain numerous forged structures which can also fulfill the given process of bio-logical function under Boolean model. It is difcult to tell the real structure fromthese forged ones. The property of functional reliability has been introduced tomeasure the ability of a structure to maintain its function under a more realisticsituation where the evolution process takes place at continuous time scale and with the presence of some random efects. Based on the classical Boolean model of net-work dynamics, an asynchronous Boolean model has been introduced to realisticallydescribe the evolution of the state of nodes in a network. For each node, a contin-uous variable is used to represent it concentration. The dynamics of each node’sconcentration follows an ordinary diferential equation. In addition, random timedelays are allowed in this model to model the transmission of regulatory signals.By comparing the functional reliability of all the network structures with equiva-lent function under the classical Boolean model, the real structures are shown tobe more functionally reliable. And the composition of the real structures also con-firms the generalized designability principle. Therefore, the property of functionalreliability is helpful to improve the efciency of structural learning.
Secondly, structure learning from networks’dynamical stability has been stud-ied. Real regulatory networks have shown significant dynamical stability. In otherwords, most of the initial states in a real network’s state space will evolve to thesame stable state (called attractor). All the initial states that attracted by an at-tractor are defined as its attraction domain (or attraction basin). The size of thisbasin (basin size) is the number of the initial states. The relationship between aregulatory network’s structure and the basin size of its attractors has been discussedin this section. It has been proposed the mode of ideal transmission chain (ITC).And the mode of ITC has been proven to be sufcient and necessary for a networkto attain huge basin size (The necessary condition is valid under the assumption ofminimum edges in a network). Based on the study of two biological examples, it hasbeen demonstrated that in real complex regulatory networks, the mode of ITC hasplayed an important role in determining the basin size (dynamical stability) of thesenetworks. Moreover, after identifying the ITC mode in real networks, the locationof double negative feedback loops (DNFLs) in real networks can also be specified.DNFL is a special mode in regulatory networks, and has shown special biologicalimplementation in previous researches. By making a comparison study of all possi-ble location of the DNFL in these real networks, it has been found that DNFLs in a biological network are arranged under the principle of maximum basin size. Theseresults not only help to improve the existing structure learning methods, but alsoprovide some useful guidance in designing robust networks in synthetic biology.
Lastly, the second part of this thesis has been devoted to studying the prob-lem of target tracking with bearings-only measurements. Passive sensors, such assonar, passive radar and vision camera, have been widely used in the field of in-dustry automation and security. The problem of target tracking with bearings onlymeasurements has been a hot point of research in the application of passive sensors.Based on instrumental variable method, a linear estimation of target motion param-eters has been proposed. This estimation is of closed form, and is easy to calculate.The asymptotical properties of this new method have also been studied (includingits consistence and asymptotical normality). All these desired characteristics of thismethod ensure its better performance in real-time tracking systems. In addition,this method can be easily modified to adapt to other complex tracking situations.
本文首先研究了利用网络的功能可靠性来优化网络结构学习的方法。现有的结构学习方法是在齐次布尔模型的框架下进行。在该模型中,网络节点的状态更新只在离散时间点进行,而且各个节点的更新是同步进行的。因此,结构学习的结果中会产生大量的”虚假网络结构”。它们与真实的网络结构在齐次模型下具有相同的功能,故难以区分。而功能可靠性是用来衡量调控网络在较真实的环境下(状态连续演化和随机因素干扰),完成特定生物学功能的能力。在齐次模型的基础上,本文引入了非齐次布尔模型来更加真实地模拟调控网络的状态演化过程。新的模型采用连续值变量来表示节点的浓度水平。浓度的变化过程服从一阶微分方程模型。并且,还考虑了节点之间传递调控作用的随机延迟。通过比较多个齐次模型中功能相同的网络结构在新的非齐次模型下的功能可靠性,发现真实的网络结构具有较高的功能可靠性,并且,其组成规律符合可设计性原则。所以,我们可以用功能可靠性要求来进一步提高网络结构学习的效率。
其次,本文研究了利用网络动力学稳定性来学习网络结构的方法。真实的调控网络具有很强的动力学稳定性。具体而言,在调控网络的相空间中,绝大多数的网络初始状态都能够演化到相同的稳定状态(称为吸引子),而且不同初态的演化路径也具有较高的重叠度。每个吸引子所吸引的初始状态定义为该吸引子的吸引域(或吸引盆),而它所吸引的初始状态的个数就是其吸引盆的大小。本章重点论证了网络拓扑结构与网络吸引子的吸引盆大小之间的关系,提出了理想传递链结构,并证明了理想传递链是保证网络具有全局吸引子的充分和必要条件(必要性是在网络中调控作用数量最少的约束下成立)。通过对真实生物网络的实例研究,也证明了在复杂的生物调控网络中,理想传递链上的作用边对网络的吸引盆大小的贡献明显大于其他的作用边。此外,理想传递链结构还可以帮助确定网络中另一种重要结构-负反馈环-的联接位置。通过比较发现,负反馈环在网络中的联接位置符合最大吸引盆原则,即在某个位置上加入负反馈环之后网络的吸引盆越大,那么,实际的网络中在该位置上越有可能出现负反馈环。这些结论不仅能够帮助改进和提高现有的网络结构学习方法,也能够为合成生物学中的设计工作提供指导意义。
最后,本文研究了被动传感器的目标定位问题。被动传感器具有能耗低和隐蔽性强等特点,在工业自动化和安防领域具有广阔的应用前景。利用被动传感器的探测信息来确定监视区域内目标的位置和运动状态是被动传感器应用的关键问题。本文提出基于工具变量方法的目标运动参数的线性估计。该方法具有显式表达,计算量低,而且具有良好的大样本性质(包括相合性和渐进正态性)。这些特点保证了该方法在实时跟踪系统中的良好表现。此外,该方法也具有很好的扩展性,能够推广到更加复杂的跟踪环境。
Structure learning of genetic regulatory networks and target tracking with pas-sive sensors are two important research topics of applied statistics. Based on thetheoretical analysis of basic assumptions and the adaptive improvement of exist-ing statistical methods, this thesis has made some adaptive improvements on theexisting methods and lead to some meaningful progresses.
Firstly, the property of functional reliability has been employed to improve theefciency of structure learning with functional process of regulatory networks. Mostexisting process-based learning algorithms have been developed under the assump-tions of Boolean model. The state of each node in a network is asynchronouslyupdated at discrete time instants. Therefore, the output of structure learning maycontain numerous forged structures which can also fulfill the given process of bio-logical function under Boolean model. It is difcult to tell the real structure fromthese forged ones. The property of functional reliability has been introduced tomeasure the ability of a structure to maintain its function under a more realisticsituation where the evolution process takes place at continuous time scale and with the presence of some random efects. Based on the classical Boolean model of net-work dynamics, an asynchronous Boolean model has been introduced to realisticallydescribe the evolution of the state of nodes in a network. For each node, a contin-uous variable is used to represent it concentration. The dynamics of each node’sconcentration follows an ordinary diferential equation. In addition, random timedelays are allowed in this model to model the transmission of regulatory signals.By comparing the functional reliability of all the network structures with equiva-lent function under the classical Boolean model, the real structures are shown tobe more functionally reliable. And the composition of the real structures also con-firms the generalized designability principle. Therefore, the property of functionalreliability is helpful to improve the efciency of structural learning.
Secondly, structure learning from networks’dynamical stability has been stud-ied. Real regulatory networks have shown significant dynamical stability. In otherwords, most of the initial states in a real network’s state space will evolve to thesame stable state (called attractor). All the initial states that attracted by an at-tractor are defined as its attraction domain (or attraction basin). The size of thisbasin (basin size) is the number of the initial states. The relationship between aregulatory network’s structure and the basin size of its attractors has been discussedin this section. It has been proposed the mode of ideal transmission chain (ITC).And the mode of ITC has been proven to be sufcient and necessary for a networkto attain huge basin size (The necessary condition is valid under the assumption ofminimum edges in a network). Based on the study of two biological examples, it hasbeen demonstrated that in real complex regulatory networks, the mode of ITC hasplayed an important role in determining the basin size (dynamical stability) of thesenetworks. Moreover, after identifying the ITC mode in real networks, the locationof double negative feedback loops (DNFLs) in real networks can also be specified.DNFL is a special mode in regulatory networks, and has shown special biologicalimplementation in previous researches. By making a comparison study of all possi-ble location of the DNFL in these real networks, it has been found that DNFLs in a biological network are arranged under the principle of maximum basin size. Theseresults not only help to improve the existing structure learning methods, but alsoprovide some useful guidance in designing robust networks in synthetic biology.
Lastly, the second part of this thesis has been devoted to studying the prob-lem of target tracking with bearings-only measurements. Passive sensors, such assonar, passive radar and vision camera, have been widely used in the field of in-dustry automation and security. The problem of target tracking with bearings onlymeasurements has been a hot point of research in the application of passive sensors.Based on instrumental variable method, a linear estimation of target motion param-eters has been proposed. This estimation is of closed form, and is easy to calculate.The asymptotical properties of this new method have also been studied (includingits consistence and asymptotical normality). All these desired characteristics of thismethod ensure its better performance in real-time tracking systems. In addition,this method can be easily modified to adapt to other complex tracking situations.
引文
[1] G. Wang, C. Du, H. Chen, R. Simha, Y. Rong, Y. Xiao, C. Zeng. Process-basednetwork decomposition reveals backbone motif structure[J]. Proceedings of theNational Academy of Sciences. 2010, 107(23):10478
[2] F. Li, T. Long, Y. Lu, Q. Ouyang, C. Tang. The yeast cell-cycle network isrobustly designed[J]. Proceedings of the National Academy of Sciences. 2004,101(14):4781
[3] Y.J. Zhang, G.Z. Xu. Bearings-only target motion analysis via instrumen-tal variable estimation[J]. Signal Processing, IEEE Transactions on. 2010,58(11):5523–5533
[4] N. Geard, K. Willadsen. Dynamical approaches to modeling developmentalgene regulatory networks[J]. Birth Defects Research Part C: Embryo Today:Reviews. 2009, 87(2):131–142
[5] W.J.R. Longabaugh, E.H. Davidson, H. Bolouri. Visualization, documenta-tion, analysis, and communication of large-scale gene regulatory networks[J].Biochimica et Biophysica Acta (BBA)-Gene Regulatory Mechanisms. 2009,1789(4):363–374
[6] W. Xiong, J.E. Ferrell. A positive-feedback-based bistable m memory mod-ulen that governs a cell fate decision[J]. Nature. 2003, 426(6965):460–465
[7] R.J. Johnston Jr, S. Chang, J.F. Etchberger, C.O. Ortiz, O. Hobert. Fromthe Cover: MicroRNAs acting in a double-negative feedback loop to control aneuronal cell fate decision[J]. Science’s STKE. 2005, 102(35):12449
[8] R. Thomas, et al. Laws for the dynamics of regulatory networks[J]. Interna-tional Journal of Developmental Biology. 1998, 42:479–485
[9] J.J. Tyson, K. Chen, B. Novak, et al. Network dynamics and cell physiology[J].Nature Reviews Molecular Cell Biology. 2001, 2(12):908–916
[10] E.E. Schadt, P.Y. Lum. Thematic review series: systems biology approachesto metabolic and cardiovascular disorders. Reverse engineering gene networksto identify key drivers of complex disease phenotypes[J]. Journal of LipidResearch. 2006, 47(12):2601–2613
[11] T. Schlitt, A. Brazma. Current approaches to gene regulatory network mod-elling[J]. BMC Bioinformatics. 2007, 8(Suppl 6):S9
[12] R. Albert. Scale-free networks in cell biology[J]. Journal of Cell Science. 2005,118(21):4947–4957
[13] G. Karlebach, R. Shamir. Modelling and analysis of gene regulatory net-works[J]. Nature Reviews Molecular Cell Biology. 2008, 9(10):770–780
[14] L. Glass, S.A. Kaufman. The logical analysis of continuous, non-linear bio-chemical control networks[J]. Journal of Theoretical Biology. 1973, 39(1):103–129
[15] R. Thomas. Boolean formalization of genetic control circuits[J]. Journal ofTheoretical Biology. 1973, 42(3):563–585
[16] E.H. Davidson, J.P. Rast, P. Oliveri, A. Ransick, C. Calestani, C.H. Yuh, T.Minokawa, G. Amore, V. Hinman, C. Arenas-Mena, et al. A genomic regulatorynetwork for development[J]. Science’s STKE. 2002, 295(5560):1669
[17] J. Smith, C. Theodoris, E.H. Davidson. A gene regulatory network subcir-cuit drives a dynamic pattern of gene expression[J]. Science’s STKE. 2007,318(5851):794
[18] S.A. Kaufman. The origins of order: Self organization and selection in evolu-tion[M]. Oxford University Press, USA, 1993
[19] S.A. Kaufman, C. Peterson, B. Samuelsson, C. Troein. Random booleannetwork models and the yeast transcriptional network[J]. Proceedings ofthe National Academy of Sciences of the United States of America. 2003,100(25):14796
[20] H. La¨hdesma¨ki, I. Shmulevich, O. Yli-Harja. On learning gene regulatorynetworks under the Boolean network model[J]. Machine Learning. 2003,52(1):147–167
[21] T. Akutsu, S. Miyano, S. Kuhara, et al. Identification of genetic networks from asmall number of gene expression patterns under the Boolean network model[C].Pacific Symposium on Biocomputing. World Scientific Maui, Hawaii, 1999, vol.4, 17–28
[22] I. Shmulevich, E.R. Dougherty, S. Kim, W. Zhang. Probabilistic boolean net-works: a rule-based uncertainty model for gene regulatory networks[J]. Bioin-formatics. 2002, 18(2):261–274
[23] I. Shmulevich, I. Gluhovsky, R.F. Hashimoto, E.R. Dougherty, W. Zhang.Steady-state analysis of genetic regulatory networks modelled by probabilisticBoolean networks[J]. Comparative and Functional Genomics. 2003, 4(6):601–608
[24] W.R. Gilks, S. Richardson, D.J. Spiegelhalter. Markov chain monte carlo inpractice[M]. Chapman & Hall/CRC, 1996
[25] I. Gat-Viks, A. Tanay, R. Shamir. Modeling and analysis of heterogeneousregulation in biological networks[J]. Journal of Computational Biology. 2004,11(6):1034–1049
[26] I. Gat-Viks, A. Tanay, D. Raijman, R. Shamir. A probabilistic methodology forintegrating knowledge and experiments on biological networks[J]. Journal ofComputational Biology. 2006, 13(2):165–181
[27] F.R. Kschischang, B.J. Frey, H.A. Loeliger. Factor graphs and the sum-productalgorithm[J]. Information Theory, IEEE Transactions on. 2001, 47(2):498–519
[28] D.J.C. MacKay. Introduction to monte carlo methods[J]. Nato Asi Series DBehavioural and Social Sciences. 1998, 89:175–204
[29] I. Gat-Viks, R. Shamir. Refinement and expansion of signaling pathways: theosmotic response network in yeast[J]. Genome research. 2007, 17(3):358–367
[30] A. Carl. Petri. kommunikation mit automaten[R]. Tech. rep., Technical Report2 (Schriften des IIM), Institutfur Instrumentelle Mathematik, Bonn, Germany,1962
[31] I. Koch, M. Schuler, M. Heiner. STEPP-Search tool for exploration of Petri netpaths: a new tool for Petri net-based path analysis in biochemical networks[J].In Silico Biology. 2005, 5(2):129–138
[32] V.N. Reddy, M.N. Liebman, M.L. Mavrovouniotis. Qualitative analysis ofbiochemical reaction systems[J]. Computers in Biology and Medicine. 1996,26(1):9–24
[33] L.J. Steggles, R. Banks, O. Shaw, A. Wipat. Qualitatively modelling andanalysing genetic regulatory networks: a Petri net approach[J]. Bioinformatics.2007, 23(3):336–343
[34] M.K. Yeung, J. Tegn′er, J.J. Collins. Reverse engineering gene networks us-ing singular value decomposition and robust regression[J]. Proceedings of theNational Academy of Sciences. 2002, 99(9):6163
[35] D.C. Weaver, C.T. Workman, G.D. Stormo, et al. Modeling regulatory net-works with weight matrices[C]. Pacific Symposium on Biocomputing. 1999, vol.4, 112–123
[36] M. Bansal, G. Della Gatta, D. Di Bernardo. Inference of gene regulatory net-works and compound mode of action from time course gene expression pro-files[J]. Bioinformatics. 2006, 22(7):815–822
[37] M.S. Dasika, A. Gupta, C.D. Maranas, JD Varner. A mixed integer linearprogramming (MILP) framework for inferring time delay in gene regulatorynetworks[C]. Pac Symp Biocomput. 2004, vol. 9, 474–485
[38] I. Nachman, A. Regev, N. Friedman. Inferring quantitative models of regulatorynetworks from expression data[J]. Bioinformatics. 2004, 20(suppl 1):i248–i256
[39] S.Y. Kim, S. Imoto, S. Miyano. Inferring gene networks from time series mi-croarray data using dynamic Bayesian networks[J]. Briefings in Bioinformatics.2003, 4(3):228–235
[40] A. Tanay, R. Shamir. Modeling transcription programs: inferring binding siteactivity and dose-response model optimization[C]. Proceedings of the SeventhAnnual International Conference on Research in Computational Molecular Bi-ology. ACM, 2003, 301–310
[41] Y. Pan, T. Durfee, J. Bockhorst, M. Craven. Connecting quantita-tive regulatory-network models to the genome[J]. Bioinformatics. 2007,23(13):i367–i376
[42] J. Holtzendorf, D. Hung, P. Brende, A. Reisenauer, P.H. Viollier, H.H.McAdams, L. Shapiro. Oscillating global regulators control the genetic circuitdriving a bacterial cell cycle[J]. Science’s STKE. 2004, 304(5673):983
[43] K.C. Chen, L. Calzone, A. Csikasz-Nagy, F.R. Cross, B. Novak, J.J. Tyson.Integrative analysis of cell cycle control in budding yeast[J]. Molecular Biologyof the Cell. 2004, 15(8):3841–3862
[44] S. Li, P. Brazhnik, B. Sobral, J.J. Tyson. A quantitative study of the divisioncycle of Caulobacter crescentus stalked cells[J]. PLoS Computational Biology.2008, 4(1):e9
[45] J.C.W. Locke, M.M. Southern, L. Kozma-Bogna′r, V. Hibberd, P.E. Brown,M.S. Turner, A.J. Millar. Extension of a genetic network model by iterativeexperimentation and mathematical analysis[J]. Molecular Systems Biology.2005, 1(1)
[46] E. Klipp, B. Nordlander, R. Kru¨ger, P. Gennemark, S. Hohmann. Integrativemodel of the response of yeast to osmotic shock[J]. Nature Biotechnology. 2005,23(8):975–982
[47] M.W. Covert, B. . Palsson. Transcriptional regulation in constraints-basedmetabolic models of Escherichia coli[J]. Journal of Biological Chemistry. 2002,277(31):28058–28064
[48] T. Shlomi, Y. Eisenberg, R. Sharan, E. Ruppin. A genome-scale computationalstudy of the interplay between transcriptional regulation and metabolism[J].Molecular Systems Biology. 2007, 3(1)
[49] E.P. Gianchandani, J.A. Papin, N.D. Price, A.R. Joyce, B.O. Palsson. Matrixformalism to describe functional states of transcriptional regulatory systems[J].PLoS Computational Biology. 2006, 2(8):e101
[50] K. Bae, C. Lee, P.E. Hardin, I. Edery. dCLOCK is present in limiting amountsand likely mediates daily interactions between the dCLOCK–CYC transcrip-tion factor and the PER–TIM complex[J]. The Journal of Neuroscience. 2000,20(5):1746–1753
[51] P. Guptasarma. Does replication-induced transcription regulate synthesis ofthe myriad low copy number proteins of Escherichia coli?[J]. Bioessays. 1995,17(11):987–997
[52] A. Bailone, A. Levine, R. Devoret. Inactivation of prophageλrepressor i inVivo /i [J]. Journal of Molecular Biology. 1979, 131(3):553–572
[53] M.A. Shea, G.K. Ackers. The O sub R /sub control system of bacteriophagelambda: A physical-chemical model for gene regulation[J]. Journal of MolecularBiology. 1985, 181(2):211–230
[54] H.H. McAdams, A. Arkin. Stochastic mechanisms in gene expression[J]. Pro-ceedings of the National Academy of Sciences. 1997, 94(3):814
[55] M.A. Gibson, J. Bruck. Efcient exact stochastic simulation of chemical sys-tems with many species and many channels[J]. The Journal of Physical Chem-istry A. 2000, 104(9):1876–1889
[56] D.T. Gillespie. Stochastic simulation of chemical kinetics[J]. Annu Rev PhysChem. 2007, 58:35–55
[57] S.A. Kaufman. Metabolic stability and epigenesis in randomly constructedgenetic nets[J]. Journal of Theoretical Biology. 1969, 22(3):437–467
[58] M.I. Davidich, S. Bornholdt. Boolean network model predicts cell cycle se-quence of fission yeast[J]. PLoS One. 2008, 3(2):e1672
[59] Y. Wu, X. Zhang, J. Yu, Q. Ouyang. Identification of a topological character-istic responsible for the biological robustness of regulatory networks[J]. PLoSComputational Biology. 2009, 5(7):e1000442
[60] M. Chaves, R. Albert, E.D. Sontag. Robustness and fragility of Boolean mod-els for genetic regulatory networks[J]. Journal of Theoretical Biology. 2005,235(3):431–449
[61] K. Klemm, S. Bornholdt. Topology of biological networks and reliability ofinformation processing[J]. Proceedings of the National Academy of Sciences.2005, 102(51):18414
[62] S. Braunewell, S. Bornholdt. Superstability of the yeast cell-cycle dynamics:ensuring causality in the presence of biochemical stochasticity[J]. Journal ofTheoretical Biology. 2007, 245(4):638–643
[63] Y.D. Nochomovitz, H. Li. Highly designable phenotypes and mutational bufersemerge from a systematic mapping between network topology and dynamic out-put[J]. Proceedings of the National Academy of Sciences. 2006, 103(11):4180
[64] G. Von Dassow, E. Meir, E.M. Munro, G.M. Odell. The segment polaritynetwork is a robust developmental module[J]. Nature. 2000, 406(6792):188–192
[65] W. Ma, L. Lai, Q. Ouyang, C. Tang. Robustness and modular design of theDrosophila segment polarity network[J]. Molecular Systems Biology. 2006,2(1)
[66] M. Aldana, P. Cluzel. A natural class of robust networks[J]. Proceedings of theNational Academy of Sciences. 2003, 100(15):8710
[67] M.R. Domingo-Sananes, B. Nov′ak. Diferent efects of redundant feedbackloops on a bistable switch[J]. Chaos. 2010, 20(4):5120
[68] J.E. Ferrell Jr. Feedback regulation of opposing enzymes generates robust,all-or-none bistable responses[J]. Current Biology. 2008, 18(6):R244–R245
[69] B. Nov′ak, J.J. Tyson. Design principles of biochemical oscillators[J]. NatureReviews Molecular Cell Biology. 2008, 9(12):981–991
[70] B. Nov′ak, J.J. Tyson, B. Gyorfy, A. Csikasz-Nagy. Irreversible cell-cycle transi-tions are due to systems-level feedback[J]. Nature Cell Biology. 2007, 9(7):724–728
[71] A.G. Lingren, K.F. Gong. Position and velocity estimation via bearing obser-vations[J]. Aerospace and Electronic Systems, IEEE Transactions on. 1978,(4):564–577
[72] K. Dogancay. Bias compensation for the bearings-only pseudolinear target trackestimator[J]. Signal Processing, IEEE Transactions on. 2006, 54(1):59–68
[73] D.T. Pham. Some quick and efcient methods for bearing-only target motionanalysis[J]. Signal Processing, IEEE Transactions on. 1993, 41(9):2737–2751
[74] S.C. Nardone, M.L. Graham. A closed-form solution to bearings-only targetmotion analysis[J]. Oceanic Engineering, IEEE Journal of. 1997, 22(1):168–178
[75] T. Kirubarajan, Y. Bar-Shalom. Low observable target motion analysis usingamplitude information[J]. Aerospace and Electronic Systems, IEEE Transac-tions on. 1996, 32(4):1367–1384
[76] B. Ristic, S. Arulampalam, N. Gordon. Beyond the Kalman filter: Particlefilters for tracking applications[M]. Artech House Publishers, 2004
[77] X. Lin, T. Kirubarajan, Y. Bar-Shalom, S. Maskell. Comparison of EKF, pseu-domeasurement and particle filters for a bearing-only target tracking prob-lem[C]. Proc. SPIE on Signal and Data Processing of Small Targets. Citeseer,2002, vol. 4728
[78] S.C. Nardone, A. Lindgren, K. Gong. Fundamental properties and performanceof conventional bearings-only target motion analysis[J]. Automatic Control,IEEE Transactions on. 1984, 29(9):775–787
[79] K. Dog an cay. On the bias of linear least squares algorithms for passive targetlocalization[J]. Signal Processing. 2004, 84(3):475–486
[80] R.J. Bowden, D.A. Turkington. Instrumental variables[M], vol. 8. CambridgeUniv Pr, 1990
[81] A.G. Lindgren, K.F. Gong. Properties of a nonlinear estimator for determiningposition and velocity from angle-of-arrival measurements[C]. Asilomar Confer-ence on Circuits, Systems and Computers, 14 th, Pacific Grove, CA. 1981,394–401
[82] J.P. Le Cadre, C. Jaetfret. On the convergence of iterative methods forbearings-only tracking[J]. Aerospace and Electronic Systems, IEEE Trans-actions on. 1999, 35(3):801–818
[83] Y.T. Chan, S.W. Rudnicki. Bearings-only and Doppler-bearing tracking usinginstrumental variables[J]. Aerospace and Electronic Systems, IEEE Transac-tions on. 1992, 28(4):1076–1083
[84] K. Dog anc ay. Passive emitter localization using weighted instrumental vari-ables[J]. Signal Processing. 2004, 84(3):487–497
[85] K.C. Ho, Y.T. Chan. An asymptotically unbiased estimator for bearings-onlyand Doppler-bearing target motion analysis[J]. Signal Processing, IEEE Trans-actions on. 2006, 54(3):809–822
[86] S. Koteswara Rao. Comments ono Discrete-time observability and estimabilityanalysis for bearings-only target motion analysisp [J]. Aerospace and ElectronicSystems, IEEE Transactions on. 1998, 34(4):1361–1367
[87] J.P. Le Cadre, C. Jaufret. Discrete-time observability and estimability analysisfor bearings-only target motion analysis[J]. Aerospace and Electronic Systems,IEEE Transactions on. 1997, 33(1):178–201
[88] K. Wong, E. Polak. Identification of linear discrete time systems using theinstrumental variable method[J]. Automatic Control, IEEE Transactions on.1967, 12(6):707–718
[89] Y. Bar-Shalom, X.R. Li, T. Kirubarajan, J. Wiley. Estimation with applicationsto tracking and navigation[M]. Wiley Online Library, 2001
[90] T. Amemiya. Regression analysis when the dependent variable is truncatednormal[J]. Econometrica: Journal of the Econometric Society. 1973:997–1016
[91] R.J. Serfling. Approximation theorems of mathematical statistics[J]. New York.1980, 34
[2] F. Li, T. Long, Y. Lu, Q. Ouyang, C. Tang. The yeast cell-cycle network isrobustly designed[J]. Proceedings of the National Academy of Sciences. 2004,101(14):4781
[3] Y.J. Zhang, G.Z. Xu. Bearings-only target motion analysis via instrumen-tal variable estimation[J]. Signal Processing, IEEE Transactions on. 2010,58(11):5523–5533
[4] N. Geard, K. Willadsen. Dynamical approaches to modeling developmentalgene regulatory networks[J]. Birth Defects Research Part C: Embryo Today:Reviews. 2009, 87(2):131–142
[5] W.J.R. Longabaugh, E.H. Davidson, H. Bolouri. Visualization, documenta-tion, analysis, and communication of large-scale gene regulatory networks[J].Biochimica et Biophysica Acta (BBA)-Gene Regulatory Mechanisms. 2009,1789(4):363–374
[6] W. Xiong, J.E. Ferrell. A positive-feedback-based bistable m memory mod-ulen that governs a cell fate decision[J]. Nature. 2003, 426(6965):460–465
[7] R.J. Johnston Jr, S. Chang, J.F. Etchberger, C.O. Ortiz, O. Hobert. Fromthe Cover: MicroRNAs acting in a double-negative feedback loop to control aneuronal cell fate decision[J]. Science’s STKE. 2005, 102(35):12449
[8] R. Thomas, et al. Laws for the dynamics of regulatory networks[J]. Interna-tional Journal of Developmental Biology. 1998, 42:479–485
[9] J.J. Tyson, K. Chen, B. Novak, et al. Network dynamics and cell physiology[J].Nature Reviews Molecular Cell Biology. 2001, 2(12):908–916
[10] E.E. Schadt, P.Y. Lum. Thematic review series: systems biology approachesto metabolic and cardiovascular disorders. Reverse engineering gene networksto identify key drivers of complex disease phenotypes[J]. Journal of LipidResearch. 2006, 47(12):2601–2613
[11] T. Schlitt, A. Brazma. Current approaches to gene regulatory network mod-elling[J]. BMC Bioinformatics. 2007, 8(Suppl 6):S9
[12] R. Albert. Scale-free networks in cell biology[J]. Journal of Cell Science. 2005,118(21):4947–4957
[13] G. Karlebach, R. Shamir. Modelling and analysis of gene regulatory net-works[J]. Nature Reviews Molecular Cell Biology. 2008, 9(10):770–780
[14] L. Glass, S.A. Kaufman. The logical analysis of continuous, non-linear bio-chemical control networks[J]. Journal of Theoretical Biology. 1973, 39(1):103–129
[15] R. Thomas. Boolean formalization of genetic control circuits[J]. Journal ofTheoretical Biology. 1973, 42(3):563–585
[16] E.H. Davidson, J.P. Rast, P. Oliveri, A. Ransick, C. Calestani, C.H. Yuh, T.Minokawa, G. Amore, V. Hinman, C. Arenas-Mena, et al. A genomic regulatorynetwork for development[J]. Science’s STKE. 2002, 295(5560):1669
[17] J. Smith, C. Theodoris, E.H. Davidson. A gene regulatory network subcir-cuit drives a dynamic pattern of gene expression[J]. Science’s STKE. 2007,318(5851):794
[18] S.A. Kaufman. The origins of order: Self organization and selection in evolu-tion[M]. Oxford University Press, USA, 1993
[19] S.A. Kaufman, C. Peterson, B. Samuelsson, C. Troein. Random booleannetwork models and the yeast transcriptional network[J]. Proceedings ofthe National Academy of Sciences of the United States of America. 2003,100(25):14796
[20] H. La¨hdesma¨ki, I. Shmulevich, O. Yli-Harja. On learning gene regulatorynetworks under the Boolean network model[J]. Machine Learning. 2003,52(1):147–167
[21] T. Akutsu, S. Miyano, S. Kuhara, et al. Identification of genetic networks from asmall number of gene expression patterns under the Boolean network model[C].Pacific Symposium on Biocomputing. World Scientific Maui, Hawaii, 1999, vol.4, 17–28
[22] I. Shmulevich, E.R. Dougherty, S. Kim, W. Zhang. Probabilistic boolean net-works: a rule-based uncertainty model for gene regulatory networks[J]. Bioin-formatics. 2002, 18(2):261–274
[23] I. Shmulevich, I. Gluhovsky, R.F. Hashimoto, E.R. Dougherty, W. Zhang.Steady-state analysis of genetic regulatory networks modelled by probabilisticBoolean networks[J]. Comparative and Functional Genomics. 2003, 4(6):601–608
[24] W.R. Gilks, S. Richardson, D.J. Spiegelhalter. Markov chain monte carlo inpractice[M]. Chapman & Hall/CRC, 1996
[25] I. Gat-Viks, A. Tanay, R. Shamir. Modeling and analysis of heterogeneousregulation in biological networks[J]. Journal of Computational Biology. 2004,11(6):1034–1049
[26] I. Gat-Viks, A. Tanay, D. Raijman, R. Shamir. A probabilistic methodology forintegrating knowledge and experiments on biological networks[J]. Journal ofComputational Biology. 2006, 13(2):165–181
[27] F.R. Kschischang, B.J. Frey, H.A. Loeliger. Factor graphs and the sum-productalgorithm[J]. Information Theory, IEEE Transactions on. 2001, 47(2):498–519
[28] D.J.C. MacKay. Introduction to monte carlo methods[J]. Nato Asi Series DBehavioural and Social Sciences. 1998, 89:175–204
[29] I. Gat-Viks, R. Shamir. Refinement and expansion of signaling pathways: theosmotic response network in yeast[J]. Genome research. 2007, 17(3):358–367
[30] A. Carl. Petri. kommunikation mit automaten[R]. Tech. rep., Technical Report2 (Schriften des IIM), Institutfur Instrumentelle Mathematik, Bonn, Germany,1962
[31] I. Koch, M. Schuler, M. Heiner. STEPP-Search tool for exploration of Petri netpaths: a new tool for Petri net-based path analysis in biochemical networks[J].In Silico Biology. 2005, 5(2):129–138
[32] V.N. Reddy, M.N. Liebman, M.L. Mavrovouniotis. Qualitative analysis ofbiochemical reaction systems[J]. Computers in Biology and Medicine. 1996,26(1):9–24
[33] L.J. Steggles, R. Banks, O. Shaw, A. Wipat. Qualitatively modelling andanalysing genetic regulatory networks: a Petri net approach[J]. Bioinformatics.2007, 23(3):336–343
[34] M.K. Yeung, J. Tegn′er, J.J. Collins. Reverse engineering gene networks us-ing singular value decomposition and robust regression[J]. Proceedings of theNational Academy of Sciences. 2002, 99(9):6163
[35] D.C. Weaver, C.T. Workman, G.D. Stormo, et al. Modeling regulatory net-works with weight matrices[C]. Pacific Symposium on Biocomputing. 1999, vol.4, 112–123
[36] M. Bansal, G. Della Gatta, D. Di Bernardo. Inference of gene regulatory net-works and compound mode of action from time course gene expression pro-files[J]. Bioinformatics. 2006, 22(7):815–822
[37] M.S. Dasika, A. Gupta, C.D. Maranas, JD Varner. A mixed integer linearprogramming (MILP) framework for inferring time delay in gene regulatorynetworks[C]. Pac Symp Biocomput. 2004, vol. 9, 474–485
[38] I. Nachman, A. Regev, N. Friedman. Inferring quantitative models of regulatorynetworks from expression data[J]. Bioinformatics. 2004, 20(suppl 1):i248–i256
[39] S.Y. Kim, S. Imoto, S. Miyano. Inferring gene networks from time series mi-croarray data using dynamic Bayesian networks[J]. Briefings in Bioinformatics.2003, 4(3):228–235
[40] A. Tanay, R. Shamir. Modeling transcription programs: inferring binding siteactivity and dose-response model optimization[C]. Proceedings of the SeventhAnnual International Conference on Research in Computational Molecular Bi-ology. ACM, 2003, 301–310
[41] Y. Pan, T. Durfee, J. Bockhorst, M. Craven. Connecting quantita-tive regulatory-network models to the genome[J]. Bioinformatics. 2007,23(13):i367–i376
[42] J. Holtzendorf, D. Hung, P. Brende, A. Reisenauer, P.H. Viollier, H.H.McAdams, L. Shapiro. Oscillating global regulators control the genetic circuitdriving a bacterial cell cycle[J]. Science’s STKE. 2004, 304(5673):983
[43] K.C. Chen, L. Calzone, A. Csikasz-Nagy, F.R. Cross, B. Novak, J.J. Tyson.Integrative analysis of cell cycle control in budding yeast[J]. Molecular Biologyof the Cell. 2004, 15(8):3841–3862
[44] S. Li, P. Brazhnik, B. Sobral, J.J. Tyson. A quantitative study of the divisioncycle of Caulobacter crescentus stalked cells[J]. PLoS Computational Biology.2008, 4(1):e9
[45] J.C.W. Locke, M.M. Southern, L. Kozma-Bogna′r, V. Hibberd, P.E. Brown,M.S. Turner, A.J. Millar. Extension of a genetic network model by iterativeexperimentation and mathematical analysis[J]. Molecular Systems Biology.2005, 1(1)
[46] E. Klipp, B. Nordlander, R. Kru¨ger, P. Gennemark, S. Hohmann. Integrativemodel of the response of yeast to osmotic shock[J]. Nature Biotechnology. 2005,23(8):975–982
[47] M.W. Covert, B. . Palsson. Transcriptional regulation in constraints-basedmetabolic models of Escherichia coli[J]. Journal of Biological Chemistry. 2002,277(31):28058–28064
[48] T. Shlomi, Y. Eisenberg, R. Sharan, E. Ruppin. A genome-scale computationalstudy of the interplay between transcriptional regulation and metabolism[J].Molecular Systems Biology. 2007, 3(1)
[49] E.P. Gianchandani, J.A. Papin, N.D. Price, A.R. Joyce, B.O. Palsson. Matrixformalism to describe functional states of transcriptional regulatory systems[J].PLoS Computational Biology. 2006, 2(8):e101
[50] K. Bae, C. Lee, P.E. Hardin, I. Edery. dCLOCK is present in limiting amountsand likely mediates daily interactions between the dCLOCK–CYC transcrip-tion factor and the PER–TIM complex[J]. The Journal of Neuroscience. 2000,20(5):1746–1753
[51] P. Guptasarma. Does replication-induced transcription regulate synthesis ofthe myriad low copy number proteins of Escherichia coli?[J]. Bioessays. 1995,17(11):987–997
[52] A. Bailone, A. Levine, R. Devoret. Inactivation of prophageλrepressor i inVivo /i [J]. Journal of Molecular Biology. 1979, 131(3):553–572
[53] M.A. Shea, G.K. Ackers. The O sub R /sub control system of bacteriophagelambda: A physical-chemical model for gene regulation[J]. Journal of MolecularBiology. 1985, 181(2):211–230
[54] H.H. McAdams, A. Arkin. Stochastic mechanisms in gene expression[J]. Pro-ceedings of the National Academy of Sciences. 1997, 94(3):814
[55] M.A. Gibson, J. Bruck. Efcient exact stochastic simulation of chemical sys-tems with many species and many channels[J]. The Journal of Physical Chem-istry A. 2000, 104(9):1876–1889
[56] D.T. Gillespie. Stochastic simulation of chemical kinetics[J]. Annu Rev PhysChem. 2007, 58:35–55
[57] S.A. Kaufman. Metabolic stability and epigenesis in randomly constructedgenetic nets[J]. Journal of Theoretical Biology. 1969, 22(3):437–467
[58] M.I. Davidich, S. Bornholdt. Boolean network model predicts cell cycle se-quence of fission yeast[J]. PLoS One. 2008, 3(2):e1672
[59] Y. Wu, X. Zhang, J. Yu, Q. Ouyang. Identification of a topological character-istic responsible for the biological robustness of regulatory networks[J]. PLoSComputational Biology. 2009, 5(7):e1000442
[60] M. Chaves, R. Albert, E.D. Sontag. Robustness and fragility of Boolean mod-els for genetic regulatory networks[J]. Journal of Theoretical Biology. 2005,235(3):431–449
[61] K. Klemm, S. Bornholdt. Topology of biological networks and reliability ofinformation processing[J]. Proceedings of the National Academy of Sciences.2005, 102(51):18414
[62] S. Braunewell, S. Bornholdt. Superstability of the yeast cell-cycle dynamics:ensuring causality in the presence of biochemical stochasticity[J]. Journal ofTheoretical Biology. 2007, 245(4):638–643
[63] Y.D. Nochomovitz, H. Li. Highly designable phenotypes and mutational bufersemerge from a systematic mapping between network topology and dynamic out-put[J]. Proceedings of the National Academy of Sciences. 2006, 103(11):4180
[64] G. Von Dassow, E. Meir, E.M. Munro, G.M. Odell. The segment polaritynetwork is a robust developmental module[J]. Nature. 2000, 406(6792):188–192
[65] W. Ma, L. Lai, Q. Ouyang, C. Tang. Robustness and modular design of theDrosophila segment polarity network[J]. Molecular Systems Biology. 2006,2(1)
[66] M. Aldana, P. Cluzel. A natural class of robust networks[J]. Proceedings of theNational Academy of Sciences. 2003, 100(15):8710
[67] M.R. Domingo-Sananes, B. Nov′ak. Diferent efects of redundant feedbackloops on a bistable switch[J]. Chaos. 2010, 20(4):5120
[68] J.E. Ferrell Jr. Feedback regulation of opposing enzymes generates robust,all-or-none bistable responses[J]. Current Biology. 2008, 18(6):R244–R245
[69] B. Nov′ak, J.J. Tyson. Design principles of biochemical oscillators[J]. NatureReviews Molecular Cell Biology. 2008, 9(12):981–991
[70] B. Nov′ak, J.J. Tyson, B. Gyorfy, A. Csikasz-Nagy. Irreversible cell-cycle transi-tions are due to systems-level feedback[J]. Nature Cell Biology. 2007, 9(7):724–728
[71] A.G. Lingren, K.F. Gong. Position and velocity estimation via bearing obser-vations[J]. Aerospace and Electronic Systems, IEEE Transactions on. 1978,(4):564–577
[72] K. Dogancay. Bias compensation for the bearings-only pseudolinear target trackestimator[J]. Signal Processing, IEEE Transactions on. 2006, 54(1):59–68
[73] D.T. Pham. Some quick and efcient methods for bearing-only target motionanalysis[J]. Signal Processing, IEEE Transactions on. 1993, 41(9):2737–2751
[74] S.C. Nardone, M.L. Graham. A closed-form solution to bearings-only targetmotion analysis[J]. Oceanic Engineering, IEEE Journal of. 1997, 22(1):168–178
[75] T. Kirubarajan, Y. Bar-Shalom. Low observable target motion analysis usingamplitude information[J]. Aerospace and Electronic Systems, IEEE Transac-tions on. 1996, 32(4):1367–1384
[76] B. Ristic, S. Arulampalam, N. Gordon. Beyond the Kalman filter: Particlefilters for tracking applications[M]. Artech House Publishers, 2004
[77] X. Lin, T. Kirubarajan, Y. Bar-Shalom, S. Maskell. Comparison of EKF, pseu-domeasurement and particle filters for a bearing-only target tracking prob-lem[C]. Proc. SPIE on Signal and Data Processing of Small Targets. Citeseer,2002, vol. 4728
[78] S.C. Nardone, A. Lindgren, K. Gong. Fundamental properties and performanceof conventional bearings-only target motion analysis[J]. Automatic Control,IEEE Transactions on. 1984, 29(9):775–787
[79] K. Dog an cay. On the bias of linear least squares algorithms for passive targetlocalization[J]. Signal Processing. 2004, 84(3):475–486
[80] R.J. Bowden, D.A. Turkington. Instrumental variables[M], vol. 8. CambridgeUniv Pr, 1990
[81] A.G. Lindgren, K.F. Gong. Properties of a nonlinear estimator for determiningposition and velocity from angle-of-arrival measurements[C]. Asilomar Confer-ence on Circuits, Systems and Computers, 14 th, Pacific Grove, CA. 1981,394–401
[82] J.P. Le Cadre, C. Jaetfret. On the convergence of iterative methods forbearings-only tracking[J]. Aerospace and Electronic Systems, IEEE Trans-actions on. 1999, 35(3):801–818
[83] Y.T. Chan, S.W. Rudnicki. Bearings-only and Doppler-bearing tracking usinginstrumental variables[J]. Aerospace and Electronic Systems, IEEE Transac-tions on. 1992, 28(4):1076–1083
[84] K. Dog anc ay. Passive emitter localization using weighted instrumental vari-ables[J]. Signal Processing. 2004, 84(3):487–497
[85] K.C. Ho, Y.T. Chan. An asymptotically unbiased estimator for bearings-onlyand Doppler-bearing target motion analysis[J]. Signal Processing, IEEE Trans-actions on. 2006, 54(3):809–822
[86] S. Koteswara Rao. Comments ono Discrete-time observability and estimabilityanalysis for bearings-only target motion analysisp [J]. Aerospace and ElectronicSystems, IEEE Transactions on. 1998, 34(4):1361–1367
[87] J.P. Le Cadre, C. Jaufret. Discrete-time observability and estimability analysisfor bearings-only target motion analysis[J]. Aerospace and Electronic Systems,IEEE Transactions on. 1997, 33(1):178–201
[88] K. Wong, E. Polak. Identification of linear discrete time systems using theinstrumental variable method[J]. Automatic Control, IEEE Transactions on.1967, 12(6):707–718
[89] Y. Bar-Shalom, X.R. Li, T. Kirubarajan, J. Wiley. Estimation with applicationsto tracking and navigation[M]. Wiley Online Library, 2001
[90] T. Amemiya. Regression analysis when the dependent variable is truncatednormal[J]. Econometrica: Journal of the Econometric Society. 1973:997–1016
[91] R.J. Serfling. Approximation theorems of mathematical statistics[J]. New York.1980, 34