【作者】 张云俊；

【导师】 耿直；

【作者基本信息】 北京大学 ， 数理统计， 2012， 博士

【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。更多还原

【Abstract】 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.更多还原