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Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 159-165) Also available in print.

Understanding cell motion facilitates the understanding of many biological processes such as wound healing and cancer growth. Constructing mathematical models that replicate amoeboid cell motion can help us understand and make predictions about real-world cell movement. We review a force-based model of cell motion that considers a cell as a nucleus and several adhesion sites connected to the nucleus by springs. In this model, the cell moves as the adhesion sites attach to and detach from a substrate. This model is then reformulated as a random process that tracks the attachment characteristic (attached or detached) of each adhesion site, the location of each adhesion site, and the centroid of the attached sites. It is shown that this random process is a continuous-time jump-type Markov process and that the sub-process that counts the number of attached adhesion sites is also a Markov process with an attracting invariant distribution. Under certain hypotheses, we derive a formula for the velocity of the expected location of the centroid.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

For life insurance and annuity products whose payoffs depend on the future mortality rates, there is a risk that realized mortality rates will be different from the anticipated rates accounted for in their pricing and reserving calculations. This is termed as mortality risk. Since mortality risk is difficult to diversify and has significant financial impacts on insurance policies and pension plans, it is now a well-accepted fact that stochastic approaches shall be adopted to model the mortality risk and to evaluate the mortality-linked securities. The objective of this thesis is to propose the use of a time-changed Markov process to describe stochastic mortality dynamics for pricing and risk management purposes. Analytical and empirical properties of this dynamics have been investigated using a matrix-analytic methodology. Applications of the proposed model in the evaluation of fair values for mortality linked securities have also been explored. To be more specific, we consider a finite-state Markov process with one absorbing state. This Markov process is related to an underlying aging mechanism and the survival time is viewed as the time until absorption. The resulting distribution for the survival time is a so-called phase-type distribution. This approach is different from the traditional curve fitting mortality models in the sense that the survival probabilities are now linked with an underlying Markov aging process. Markov mathematical and phase-type distribution theories therefore provide us a flexible and tractable framework to model the mortality dynamics. And the time-changed Markov process allows us to incorporate the uncertainties embedded in the future mortality evolution. The proposed model has been applied to price the EIB/BNP Longevity Bonds and other mortality derivatives under the independent assumption of interest rate and mortality rate. A calibrating method for the model is suggested so that it can utilize both the market price information involving the relevant mortality risk and the latest mortality projection. The proposed model has also been fitted to various type of population mortality data for empirical study. The fitting results show that our model can interpret the stylized mortality patterns very well.

Master of Science / Department of Electrical and Computer Engineering / Karen Garrett / Bala Natarajan / Caterina Scoglio / In this thesis, we propose a statistical model to predict disease dispersal in dynamic networks. We model the process of disease spreading using discrete time Markov chain. In this case, the vector of probability of infection is the state vector and every element of the state vector is a continuous variable between zero and one. In discrete time Markov chains, state probability vectors in each time step depends on state probability vector in the previous time step and one step transition probability matrix. The transition probability matrix can be time variant or time invariant. If this matrix’s elements are functions of elements of vector state probability in previous step, the corresponding Markov chain is non linear dynamical system. However, if those elements are independent of vector state probability, the corresponding Markov chain is a linear dynamical system. We especially focus on the dispersal of soybean rust. In our problem, we have a network of US counties and we aim at predicting that which counties are more likely to get infected by soybean rust during a year based on observations of soybean rust up to that time as well as corresponding observations to previous years. Other data such as soybean and kudzu densities in each county, daily wind data, and distance between counties helps us to build the model. The rapid growth in the number of Internet users in recent years has led malware generators to exploit this potential to attack computer users around the word. Internet users are frequent targets of malicious software every day. The ability of malware to exploit the infrastructures of networks for propagation determines how detrimental they can be to the network’s security. Malicious software can make large outbreaks if they are able to exploit the structure of the Internet and interactions between users to propagate. Epidemics typically start with some initial infected nodes. Infected nodes can cause their healthy neighbors to become infected with some probability. With time and in some cases with external intervention, infected nodes can be cured and go back to a healthy state. The study of epidemic dispersals on networks aims at explaining how epidemics evolve and spread in networks. One of the most interesting questions regarding an epidemic spread in a network is whether the epidemic dies out or results in a massive outbreak. Epidemic threshold is a parameter that addresses this question by considering both the network topology and epidemic strength.

This paper analyzes a proposed release controlmethodology, WIPLOAD Control (WIPLCtrl), using a transfer line case modeled by Markov process modeling methodology. The performance of WIPLCtrl is compared with that of CONWIP under 13 system configurations in terms of throughput, average inventory level, as well as average cycle time. As a supplement to the analytical model, a simulation model of the transfer line is used to observe the performance of the release control methodologies on the standard deviation of cycle time. From the analysis, we identify the system configurations in which the advantages of WIPLCtrl could be observed. / Singapore-MIT Alliance (SMA)

For life insurance and annuity products whose payoffs depend on the future mortality rates, there is a risk that realized mortality rates will be different from the anticipated rates accounted for in their pricing and reserving calculations. This is termed as mortality risk. Since mortality risk is difficult to diversify and has significant financial impacts on insurance policies and pension plans, it is now a well-accepted fact that stochastic approaches shall be adopted to model the mortality risk and to evaluate the mortality-linked securities. The objective of this thesis is to propose the use of a time-changed Markov process to describe stochastic mortality dynamics for pricing and risk management purposes. Analytical and empirical properties of this dynamics have been investigated using a matrix-analytic methodology. Applications of the proposed model in the evaluation of fair values for mortality linked securities have also been explored. To be more specific, we consider a finite-state Markov process with one absorbing state. This Markov process is related to an underlying aging mechanism and the survival time is viewed as the time until absorption. The resulting distribution for the survival time is a so-called phase-type distribution. This approach is different from the traditional curve fitting mortality models in the sense that the survival probabilities are now linked with an underlying Markov aging process. Markov mathematical and phase-type distribution theories therefore provide us a flexible and tractable framework to model the mortality dynamics. And the time-changed Markov process allows us to incorporate the uncertainties embedded in the future mortality evolution. The proposed model has been applied to price the EIB/BNP Longevity Bonds and other mortality derivatives under the independent assumption of interest rate and mortality rate. A calibrating method for the model is suggested so that it can utilize both the market price information involving the relevant mortality risk and the latest mortality projection. The proposed model has also been fitted to various type of population mortality data for empirical study. The fitting results show that our model can interpret the stylized mortality patterns very well.

Today the web has become a major conduit for information. As the World Wide Web?s popularity continues to increase, information security on the web has become an increasing concern. Web information security is related to availability, confidentiality, and data integrity. According to the reports from http://www.securityfocus.com in May 2006, operating systems account for 9% vulnerability, web-based software systems account for 61% vulnerability, and other applications account for 30% vulnerability. In this dissertation, I present a security analysis model using the Markov Process Model. Risk analysis is conducted using fuzzy logic method and information entropy theory. In a web-based application system, security risk is most related to the current states in software systems and hardware systems, and independent of web application system states in the past. Therefore, the web-based applications can be approximately modeled by the Markov Process Model. The web-based applications can be conceptually expressed in the discrete states of (web_client_good; web_server_good, web_server_vulnerable, web_server_attacked, web_server_security_failed; database_server_good, database_server_vulnerable, database_server_attacked, database_server_security_failed) as state space in the Markov Chain. The vulnerable behavior and system response in the web-based applications are analyzed in this dissertation. The analyses focus on functional availability-related aspects: the probability of reaching a particular security failed state and the mean time to the security failure of a system. Vulnerability risk index is classified in three levels as an indicator of the level of security (low level, high level, and failed level). An illustrative application example is provided. As the second objective of this dissertation, I propose a security improvement model for the web-based applications using the GeoIP services in the formal methods. In the security improvement model, web access is authenticated in role-based access control using user logins, remote IP addresses, and physical locations as subject credentials to combine with the requested objects and privilege modes. Access control algorithms are developed for subjects, objects, and access privileges. A secure implementation architecture is presented. In summary, the dissertation has developed security analysis and improvement model for the web-based application. Future work will address Markov Process Model validation when security data collection becomes easy. Security improvement model will be evaluated in performance aspect.

The first half of this thesis deals with the line of thought that leads to the development of discrete games of chance as models in statistical physics, with an emphasis on analysis of Parrondo’s games. The second half of the thesis is concerned with applying discrete games of chance to the modelling of other phenomena in the discipline of electrical engineering. The important features being the element of switching that is implicit in discrete games of chance and the element of uncertainty, introduced by the random aspect of discrete games of chance. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1474722 / Thesis (Ph.D.) - University of Adelaide, School of Electrical and Electronic Engineering, 2009