Application Of Statistical Models In Structure Learning Of Genetic Regulatory Networks And Target Tracking With Passive Sensors

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.