Ng Hon Keung Tony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 85-87). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Probability Analysis of Consecutive-k-out-of-n: F system with (k-l)-step Markov Dependence --- p.11 / Chapter 2.1 --- Model and Assumptions --- p.11 / Chapter 2.2 --- Find Out the Failure Risk of the System --- p.17 / Chapter 2.3 --- The Linear Consecutive-3-out-of-4: F Repairable system with 2-step Markov Dependence --- p.27 / Chapter 2.3.1 --- Failure risk of the system --- p.27 / Chapter 2.3.2 --- Priority repair rule --- p.32 / Chapter 2.4 --- The Circular Consecutive-3-out-of-4: F Repairable system with 2-step Markov Dependence --- p.41 / Chapter 2.4.1 --- Failure risk of the system --- p.41 / Chapter 2.4.2 --- Priority repair rule --- p.47 / Chapter Chapter 3 --- System Analysis for Linear Consecutive-3-out-of-4: F system with 2-step Markov Dependence by Laplace Transform Method --- p.57 / Chapter Chapter 4 --- Reliability Indices for Consecutive-3-out-of-4: F system with 2-step Markov Dependence by Numerical Method and Simulation Study --- p.69 / Chapter 4.1 --- Numerical Method --- p.69 / Chapter 4.1.1 --- Linear consecutive-3-out-of-4: F repairable system with 2-step Markov dependence --- p.70 / Chapter 4.1.2 --- Comparison between Laplace transform method and numerical method --- p.72 / Chapter 4.1.3 --- Circular consecutive-3-out-of-4: F repairable system with 2-step Markov dependence --- p.75 / Chapter 4.2 --- Numerical Results --- p.75 / Chapter 4.3 --- Simulation Study --- p.78 / Chapter 4.4 --- Comparison between Simulation Method and Numerical Method --- p.79 / FIGURES 1 to 7 --- p.82-84 / REFERENCES --- p.85-87

by Chi-Wai Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 112-117). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background and Motivations --- p.1 / Chapter 1.2 --- Problem Definition --- p.5 / Chapter 1.3 --- Contributions --- p.5 / Chapter 1.4 --- Thesis Organization --- p.7 / Chapter 2 --- Literature Review --- p.8 / Chapter 2.1 --- Electronic Commerce --- p.8 / Chapter 2.2 --- Agents for Electronic Commerce --- p.9 / Chapter 2.3 --- Online Auctions --- p.11 / Chapter 2.3.1 --- Business Models --- p.12 / Chapter 2.3.2 --- Auction Formats --- p.13 / Chapter 2.3.3 --- Time Duration of Auctions --- p.14 / Chapter 2.3.4 --- Minimum Bids and Reserve Prices --- p.15 / Chapter 2.3.5 --- Auction Properties and Bidder Behaviours --- p.15 / Chapter 2.3.6 --- "Comparison of English, Dutch and Double auction" --- p.16 / Chapter 2.4 --- Agents Developing Tools and Tool-kits --- p.17 / Chapter 2.5 --- Limitations of Agent Tool-kits --- p.18 / Chapter 2.6 --- Markov Processes for Stochastic Modeling --- p.20 / Chapter 2.6.1 --- Continuous Time Markov Chain --- p.21 / Chapter 2.6.2 --- Poisson Arrival Model --- p.22 / Chapter 2.6.3 --- Example: discrete time Markov chain with stationary probabilities --- p.22 / Chapter 3 --- Markov Chain Model --- p.25 / Chapter 3.1 --- Markov Chain for English Auction --- p.25 / Chapter 3.1.1 --- Variables --- p.27 / Chapter 3.1.2 --- Auction Assumptions --- p.27 / Chapter 3.1.3 --- Bidder Assumptions --- p.29 / Chapter 3.1.4 --- Propositions of the Markov Model --- p.31 / Chapter 3.1.5 --- Tractability --- p.35 / Chapter 3.2 --- Markov Chain for Dutch Auction --- p.38 / Chapter 3.2.1 --- Variables --- p.39 / Chapter 3.2.2 --- Model Assumptions --- p.39 / Chapter 3.2.3 --- Propositions of the Markov Model --- p.42 / Chapter 3.2.4 --- Tractability --- p.43 / Chapter 3.3 --- Progression of the Price Vector for English and Dutch Auction --- p.43 / Chapter 3.4 --- Markov Chain for Double auction --- p.45 / Chapter 3.4.1 --- Variables --- p.47 / Chapter 3.4.2 --- Model Assumptions --- p.47 / Chapter 3.4.3 --- Propositions of the Markov Model --- p.49 / Chapter 3.4.4 --- Tractability --- p.53 / Chapter 3.5 --- Progression of the Price Vector for Double Auction --- p.53 / Chapter 3.6 --- Summary --- p.54 / Chapter 4 --- System Design --- p.57 / Chapter 4.1 --- System Features --- p.58 / Chapter 4.2 --- System Architecture --- p.59 / Chapter 4.2.1 --- System Workflow --- p.60 / Chapter 4.2.2 --- Communication Layer --- p.61 / Chapter 4.2.3 --- Agent Logic Layer --- p.62 / Chapter 4.2.4 --- Database Abstraction Layer --- p.62 / Chapter 4.3 --- Roles of the Agents --- p.62 / Chapter 4.4 --- Implementation Details --- p.65 / Chapter 4.4.1 --- Choosing a Scripting Language --- p.65 / Chapter 4.4.2 --- Choosing a Database --- p.68 / Chapter 4.4.3 --- Server-Side Java with Jakarta-tomcat --- p.69 / Chapter 4.4.4 --- Agent API --- p.70 / Chapter 4.4.5 --- Class java.agent.Agent --- p.72 / Chapter 4.5 --- Summary --- p.73 / Chapter 5 --- Experimental Results --- p.75 / Chapter 5.1 --- Simulation Environment --- p.75 / Chapter 5.2 --- Experiment One: A small English auction --- p.76 / Chapter 5.3 --- Experiment Two: A large English auction --- p.80 / Chapter 5.4 --- Experiment Three: A small Dutch auction --- p.82 / Chapter 5.5 --- Experiment Four: A large Dutch auction --- p.83 / Chapter 5.6 --- Experiment Five: Partial knowledge on other BAs --- p.84 / Chapter 5.7 --- Experiment Six: Partial knowledge on closing time --- p.86 / Chapter 5.8 --- Experiment Seven: A small Double auction --- p.87 / Chapter 5.9 --- Comparisons and Discussions --- p.89 / Chapter 5.10 --- Summary --- p.90 / Chapter 6 --- Conclusion --- p.91 / Chapter A --- Markov Chain for English Auction --- p.93 / Chapter A.1 --- Graphs of F and F* Functions --- p.93 / Chapter A.2 --- Solution of a Small Example --- p.96 / Chapter A.2.1 --- Computation of Transition Probabilities --- p.97 / Chapter A.2.2 --- Progression of the Price Vector --- p.97 / Chapter B --- Markov Chain for Double Auction --- p.101 / Chapter B.1 --- Graphs of Fb(vbi) and Fs(vsi) Functions --- p.101 / Chapter B.2 --- Solution of a Small Example --- p.102 / Chapter B.2.1 --- Computation of Transition Probabilities --- p.102 / Chapter C --- Implementation Details --- p.105 / Chapter C.1 --- Tables Design in MySQL --- p.105 / Chapter C.2 --- Sample Apache Configuration File --- p.109 / Bibliography --- p.112

Huang, Liang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 109-116). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The use of networks to model the spread of epidemics through structured populations is widespread. However, epidemics on networks lead to intractable exact systems with the need to coarse grain and focus on some average quantities. Often, the underlying stochastic processes are Markovian and so are the resulting mean-field models constructed as systems of ordinary differential equations (ODEs). However, the lack of memory (or memorylessness) does not accurately describe real disease dynamics. For instance, many epidemiological studies have shown that the true distribution of the infectious period is rather centred around its mean, whereas the memoryless assumption imposes an exponential distribution on the infectious period. Assumptions such as these greatly affect the predicted course of an epidemic and can lead to inaccurate predictions about disease spread. Such limitations of existing approaches to modelling epidemics on networks motivated my efforts to develop non-Markovian models which would be better suited to capture essential realistic features of disease dynamics. In the first part of my thesis I developed a pairwise, multi-stage SIR (susceptible-infected-recovered) model. Each infectious node goes through some K 2 N infectious stages, which for K > 1 means that the infectious period is gamma-distributed. Analysis of the model provided analytic expressions for the epidemic threshold and the expected final epidemic size. Using available epidemiological data on the infectious periods of various diseases, I demonstrated the importance of considering the shape of the infectious period distribution. The second part of the thesis expanded the framework of non-Markovian dynamics to networks with heterogeneous degree distributions with non-negligible levels of clustering. These properties are ubiquitous in many real-world networks and make model development and analysis much more challenging. To this end, I have derived and analysed a compact pairwise model with the number of equations being independent of the range of node degrees, and investigated the effects of clustering on epidemic dynamics. My thesis culminated with the third part where I explored the relationships between several different modelling methodologies, and derived an original non-Markovian Edge-Based Compartmental Model (EBCM) which allows both transmission and recovery to be arbitrary independent stochastic processes. The major result is a rigorous mathematical proof that the message passing (MP) model and the EBCM are equivalent, and thus, the EBCM is statistically exact on the ensemble of configuration model networks. From this consideration I derived a generalised pairwise-like model which I then used to build a model hierarchy, and to show that, given corresponding parameters and initial conditions, these models are identical to MP model or EBCM. In the final part of my thesis I considered the important problem of coupling epidemic dynamics with changes in network structure in response to the perceived risk of the epidemic. This was framed as a susceptible-infected-susceptible (SIS) model on an adaptive network, where susceptible nodes can disconnect from infected neighbours and, after some fixed time delay, connect to a random susceptible node that they are not yet connected to. This model assumes that nodes have perfect information on the state of all other nodes. Robust oscillations were found in a significant region of the parameter space, including an enclosed region known as an 'endemic bubble'. The major contribution of this work was to show that oscillations can occur in a wide region of the parameter space, this is in stark contrast with most previous research where oscillations were limited to a very narrow region of the parameter space. Any mathematical model is a simplification of reality where assumptions must be made. The models presented here show the importance of interrogating these assumptions to ensure that they are as realistic as possible while still being amenable to analysis.

by Ma Ka Chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 50-52). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.7 / Chapter 2 --- Queueing Networks --- p.9 / Chapter 2.1 --- One-queue Networks --- p.9 / Chapter 2.2 --- Two-queue Free Networks --- p.12 / Chapter 2.3 --- Two-queue Overflow Networks --- p.13 / Chapter 2.4 --- Networks with Batch Arrivals --- p.14 / Chapter 3 --- ODE Solvers --- p.16 / Chapter 3.1 --- The Initial Value Methods --- p.16 / Chapter 3.1.1 --- The Linear System of Ordinary Differential Equations --- p.16 / Chapter 3.1.2 --- Euler's Method --- p.17 / Chapter 3.1.3 --- Runge-Kutta Methods --- p.17 / Chapter 3.1.4 --- The Stability of the IVMs --- p.19 / Chapter 3.1.5 --- Applications in Queueing Networks --- p.20 / Chapter 3.2 --- The Boundary Value Methods --- p.20 / Chapter 3.2.1 --- The Generalized Backward Differentiation For- mulae --- p.21 / Chapter 3.2.2 --- An example --- p.24 / Chapter 4 --- The Linear Equation Solver --- p.26 / Chapter 4.1 --- Iterative Methods --- p.26 / Chapter 4.1.1 --- The Jacobi method --- p.27 / Chapter 4.1.2 --- The Gauss-Seidel Method --- p.28 / Chapter 4.1.3 --- Other Iterative Methods --- p.29 / Chapter 4.1.4 --- Preconditioning --- p.29 / Chapter 4.2 --- The Multigrid Method --- p.30 / Chapter 4.2.1 --- Iterative Refinement --- p.30 / Chapter 4.2.2 --- Restriction and Prolongation --- p.30 / Chapter 4.2.3 --- The Geometric Multigrid Method --- p.33 / Chapter 4.2.4 --- The Algebraic Multigrid Method --- p.38 / Chapter 4.2.5 --- Higher Dimensional Cases --- p.38 / Chapter 4.2.6 --- Applications in Queueing Networks --- p.38 / Chapter 5 --- Numerical Experiments --- p.41 / Chapter 6 --- Concluding Remarks --- p.49 / Bibliography --- p.50

設T為一於二維環面T²上，特徵值為整數的線性自同態，而D為一T²的Markov分割。那麼每一個D上定義的符號空間有限型子轉移則對應一個T²的T -不變緊子集K。判斷K的 Hausdor和Minkowski維數何時相等是一有趣問題。Kenyon and Peres [15]說明了此問題與(K, T )的測度熵及拓撲熵關係密切。這篇論文將進一步說明兩種維數的相等與符號動力系統及矩陣乘積的漸近性態的密切關係。此外我們描述一種算法以判斷兩個譜半徑為1的本原矩陣的任意乘積的譜半徑何時維持1，以及此算法對於研究sofic自仿集K的應用。 / Let T be a linear endomorphism on the 2-torus T² with integer eigenvalues, and D be a natural Markov partition (c.f. Bowen [4]) of T² . Then a subshift of nite type over D corresponds to a T-invariant compact subset K of T². An interesting problem is to determine when the Hausdorff and Minkowski dimensions of K conincide. Kenyon and Peres [15] showed that this is closely related to the measure-theoretic and topological entropies of (K, T). In this thesis, we further show that the coincidence of dimensions has a deep connection to symbolic dynamics and the asymptotic behaviour of matrix products. Moreover, we develop an algorithm to determine when the spectral radii of arbitrary products of two primitive matrices, with spectral radius 1, are preserved, and apply this algorithm to some sofic self-affine sets considered above. / Detailed summary in vernacular field only. / Lo, Chiu Hong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 55-56). / Abstracts also in Chinese. / Chapter 1 --- Introduction and Main Results --- p.6 / Chapter 2 --- Preliminaries --- p.12 / Chapter 2.1 --- Basic symbolic dynamics --- p.12 / Chapter 2.2 --- The symbolic representations --- p.13 / Chapter 2.3 --- An adapted covering of the invariant set KT (A) --- p.17 / Chapter 2.4 --- Some basic lemmas and theorems --- p.18 / Chapter 3 --- Proofs of Proposition 1.2 and Theorem 1.3 --- p.22 / Chapter 3.1 --- Proof of Proposition 1.2 --- p.22 / Chapter 3.2 --- Proof of Theorem 1.3 --- p.24 / Chapter 4 --- Projection of measure of maximal entropy for sub-shifts of finite type --- p.26 / Chapter 4.1 --- Projection of the Parry measure via a general factor map --- p.26 / Chapter 4.2 --- Proof of Theorem 1.4 --- p.36 / Chapter 5 --- Spectral radii of products of primitive matrices --- p.38 / Chapter 5.1 --- The algorithm --- p.40 / Chapter 5.2 --- Some applications and examples --- p.51 / Bibliography --- p.55

Chang, Kwong Wa = 一般量子系統非馬可夫領域的主方程 / 張光華. / "October 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 89-92). / Abstracts in English and Chinese. / Chang, Kwong Wa = Yi ban liang zi xi tong fei Makefu ling yu de zhu fang cheng / Zhang Guanghua. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Born-Markov Master Equations --- p.4 / Chapter 2.1 --- Master Equations from von Neumann equation --- p.4 / Chapter 2.2 --- Born Approximation --- p.6 / Chapter 2.3 --- Markov Approximation --- p.8 / Chapter 2.4 --- Born-Markov Approximation --- p.10 / Chapter 2.5 --- Lindblad Equation --- p.12 / Chapter 2.6 --- The Limitations of the Born-Markov Approximation --- p.16 / Chapter 2.7 --- Beyond Born and Markov Approximations --- p.20 / Chapter 2.7.1 --- General projection operator approach --- p.20 / Chapter 2.7.2 --- Time-local form of the master equation --- p.21 / Chapter 3 --- TCL non-Markovian Master Equation for Linear Systems --- p.24 / Chapter 3.1 --- Model --- p.24 / Chapter 3.2 --- The General Structure of the TCL non-Markovian Master Equation for Initially Factorizable States --- p.27 / Chapter 3.3 --- Determination of Unknown Coefficients --- p.32 / Chapter 3.4 --- Weak-Coupling Approximation --- p.46 / Chapter 3.5 --- Steady State Solutions --- p.51 / Chapter 4 --- An Application: Coherence Protection by Parity Kicks --- p.54 / Chapter 4.1 --- Review on Parity Kicks --- p.54 / Chapter 4.2 --- Parity Kicks oil Damped Harmonic Oscillators --- p.58 / Chapter 4.3 --- Numerical Results for Soft Pulses --- p.61 / Chapter 5 --- Other Initial States --- p.67 / Chapter 5.1 --- Factorizable States --- p.67 / Chapter 5.2 --- Non-Factorizable States --- p.73 / Chapter 6 --- Non-Markovianity --- p.75 / Chapter 6.1 --- The Concept of non-Markovianity --- p.75 / Chapter 6.2 --- A Recent Measure --- p.76 / Chapter 6.3 --- A Prospective Measure --- p.79 / Chapter 7 --- Conclusion --- p.87 / Bibliography --- p.89 / Chapter A --- Evolution of Factorizable Coherent State for Linear Damped Harmonic Oscillator with RWA --- p.93 / Chapter B --- "Derivation of G, L and F" --- p.95 / Chapter C --- Comparison of Equations of Motion for Master Equation Coefficients --- p.98

The purpose of this PhD thesis is to study mesoscopic and macroscopic fluctuations in Interacting Particle Systems. The thesis is split into two main parts. In the first part, we consider a system of Ising spins interacting via Kac potential evolving with Glauber dynamics and study the macroscopic motion of an one-dimensional interface under forced displacement as the result of large scale fluctuations. In the second part, we consider a diffusive system modelled by a Simple Symmetric Exclusion Process (SSEP) which is driven out of equilibrium by the action of current reservoirs at the boundary and study the non-equilibrium fluctuations around the hydrodynamic limit for the SSEP with current reservoirs. We give a brief summary of the first part. In recent years, there has been significant effort to derive deterministic models describing two-phase materials and their dynamical properties. In this context, we investigate the law that governs the power needed to force a motion of a one dimensional macroscopic interface between two different phases of a given ferromagnetic sample with a prescribed speed V at low temperature. We show that given the mesoscopic deterministic non-local evolution equation for the magnetisation (a non local version of the Allen-Cahn equation), we consider a stochastic Ising spin system with Glauber dynamics and Kac interaction (the underlying microscopic stochastic process) whose mesoscopic scaling limit (intermediate scale between microscale and macroscale) is the given PDE, and we calculate the corresponding large deviations functional which would provide the action functional. We obtain that by deriving upper and lower bounds of the large deviation cost functional. Concepts from statistical mechanics such as contours, free energy, local equilibrium allow a better understanding of the structure of the cost functional. Then we characterise the limiting behaviour of the action functional under a parabolic rescaling, by proving that for small values of the ratio between the distance and the time, the interface moves with a constant speed, while for larger values the occurrence of nucleations is the preferred way to make the transition. This led to a production of two published papers [12] and [14] with my supervisor D. Tsagkarogiannis and N. Dirr. In the second part we study the non-equilibrium fluctuations of a system modelled by SSEP with current reservoirs around its hydrodynamic limit. In particular, we prove that, in the limit, the appropriately scaled fluctuation field is given by a Generalised Ornstein- Uhlenbeck process. For the characterisation of the limiting fluctuation field we implement the Holley-Stroock theory. This is not straightforward due to the boundary terms coming from the nature of the model. Hence, by following a martingale approach (martingale decomposition) and the derivation of the equation of the variance for this model combined with “good” enough correlation estimates (the so-called v-estimates), we reduce the problem to a form whose Holley-Stroock result in [45] is now applicable. This is work in progress jointly with my supervisor and P. Gonçalves, [13].

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

by J. Keilson, M. Zachmann. / Bibliography: p. 28. / "August 1981." / U.S.A.F. OSR Grant Number AFOSR-79-0043 U. S. Air Force Geophysics Laboratory Grant Number F19628-80-C-0003 National Science Foundation Grant Number NSF/ECS 79-19880