The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale PEPA models suffers from this problem, which has limited wider applications of the PEPA language. This thesis focuses on developing PEPA, to overcome the state-space explosion problem, and make it suitable to validate and evaluate large scale computer and communications systems, in particular a content adaption framework proposed by the Mobile VCE. In this thesis, a new representation scheme for PEPA is proposed to numerically capture the structural and timing information in a model. Through this numerical representation, we have found that there is a Place/Transition structure underlying each PEPA model. Based on this structure and the theories developed for Petri nets, some important techniques for the structural analysis of PEPA have been given. These techniques do not suffer from the state-space explosion problem. They include a new method for deriving and storing the state space and an approach to finding invariants which can be used to reason qualitatively about systems. In particular, a novel deadlock-checking algorithm has been proposed to avoid the state-space explosion problem, which can not only efficiently carry out deadlock-checking for a particular system but can tell when and how a system structure lead to deadlocks. In order to avoid the state-space explosion problem encountered in the quantitative analysis of a large scale PEPA model, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying CTMC. This thesis presents an improved mapping from PEPA to ODEs based on the numerical representation scheme, which extends the class of PEPA models that can be subjected to fluid approximation. Furthermore, we have established the fundamental characteristics of the derived ODEs, such as the existence, uniqueness, boundedness and nonnegativeness of the solution. The convergence of the solution as time tends to infinity for several classes of PEPA models, has been proved under some mild conditions. For general PEPA models, the convergence is proved under a particular condition, which has been revealed to relate to some famous constants of Markov chains such as the spectral gap and the Log-Sobolev constant. This thesis has established the consistency between the fluid approximation and the underlying CTMCs for PEPA, i.e. the limit of the solution is consistent with the equilibrium probability distribution corresponding to a family of underlying density dependent CTMCs. These developments and investigations for PEPA have been applied to both qualitatively and quantitatively evaluate the large scale content adaptation system proposed by the Mobile VCE. These analyses provide an assessment of the current design and should guide the development of the system and contribute towards efficient working patterns and system optimisation.

Chen, Jian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 81-85). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Literature Review --- p.4 / Chapter 1.2.1 --- Vehicle Routing Problem with Stochastic Demands --- p.5 / Chapter 1.2.2 --- Vehicle Routing Problem with Stochastic Travel Times --- p.8 / Chapter 1.3 --- The Vehicle Routing Problem with Time Windows and Stochastic Travel Times --- p.10 / Chapter 2 --- Notations and Formulations --- p.12 / Chapter 2.1 --- Problem Definitions --- p.12 / Chapter 2.2 --- A Two-Index Stochastic Programming Model --- p.14 / Chapter 2.3 --- The Second Stage Problem --- p.17 / Chapter 3 --- The Scheduling Problem --- p.20 / Chapter 3.1 --- The Overtime Cost Problem --- p.22 / Chapter 3.2 --- The Waiting and Late Cost Problem --- p.27 / Chapter 3.3 --- The Algorithm --- p.37 / Chapter 4 --- The Integer L-Shaped Method --- p.40 / Chapter 4.1 --- Linearization of the Objective Function --- p.41 / Chapter 4.2 --- Handling the Constraints --- p.42 / Chapter 4.3 --- Branching --- p.44 / Chapter 4.4 --- The Algorithm --- p.44 / Chapter 5 --- Feasibility Cuts --- p.47 / Chapter 5.1 --- Connected Component Methods --- p.48 / Chapter 5.2 --- Shrinking Method --- p.49 / Chapter 6 --- Optimality Cuts --- p.52 / Chapter 6.1 --- Lower Bound I for the EOT Cost --- p.53 / Chapter 6.2 --- Lower Bounds II and III for the EOT Cost --- p.56 / Chapter 6.3 --- Lower Bound IV for the EWL Cost --- p.57 / Chapter 6.4 --- Lower Bound V for Partial Routes --- p.61 / Chapter 6.5 --- Adding Optimality Cuts --- p.66 / Chapter 7 --- Numerical Experiments --- p.70 / Chapter 7.1 --- Effectiveness in Separating the Rounded Capacity Inequalities --- p.71 / Chapter 7.2 --- Effectiveness of the Lower Bounds --- p.72 / Chapter 7.3 --- Performance of the L-shaped Method --- p.74 / Chapter 8 --- Conclusion and Future Research --- p.79 / Bibliography --- p.81 / Chapter A --- Generation of Test Instances --- p.86

近年来，随着机会约束规划被广泛应用以及凸分析和概率论的新进展，如何有效的处理机会约束成为一个炙手可热的研究方向。其中，一个成功的解决方法就是考虑其安全可解近似，也就是说将机会约束转化成一组方便处理的确定性约束，并且保持原机会约束在新的约束下成立。目前这样的方法主要应用于带有独立分布的数据扰动的机会约束规划，或者已知扰动的协方差矩阵的情况。同时，带有相关数据扰动的机会约束下的锥不等式广泛应用于供应链管理、金融、控制以及信号处理等学科，而现有的优化理论却极少涵盖。 / 在这篇论文中我们主要研究机会约束下的线性矩阵不等式，并假设扰动分布不必相互独立，其仅有的相关性信息只由一系列子扰动的独立关系结构提供。通过推导矩阵值随机变量的大偏差上界，我们得出这一类条件约束的安全可解近似。我们随后考虑了基于条件风险价值度量的机会约束规划问题, 以及带多项式扰动的机会约束优化问题。另外，通过构造相应的鲁棒对等式的不确定集合，我们把机会约束规划转换成鲁棒优化问题。由于这种近似可以表示为一组线性矩阵不等式，因而可以使用现成的优化软件方便地求解。最后，我们把该安全可解近似方法运用到一个控制理论问题，以及一个带风险价值约束的投资组合优化问题中。 / The wide applicability of chanceconstrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so-called safe tractable approximations of chance-constrained programs, where a chance constraint is replaced by a deterministic and efficiently computable inner approximation. Currently, such an approach applies mainly to chance-constrained linear inequalities, in which the data perturbations are either independent or define a known covariance matrix. However, its applicability to the case of chanceconstrained conic inequalities with dependent perturbations--which arises in supply chain management, finance, control and signal processing applications--remains largely unexplored. / In this thesis, we consider the problem of processing chance-constrained affinely perturbed linear matrix inequalities, in which the perturbations are not necessarily independent, and the only information available about the dependence structure is a list of independence relations. Using large deviation bounds for matrix-valued random variables, we develop safe tractable approximations of those chance constraints. Extensions to the Matrix CVaR (Conditional Value-at-Risk) risk measure and general polynomials perturbations are also provided separately. Further more, we show that the chanceconstrained linear matrix inequalities optimization problem can be converted to a robust optimization problem by constructing the uncertainty set of the corresponding robust counterpart. A nice feature of our approximations is that they can be expressed as systems of linear matrix inequalities, thus allowing them to be solved easily and efficiently by off-the-shelf optimization solvers. We also provide a numerical illustration of our constructions through a problem in control theory and a portfolio VaR (Value-at-Risk) optimization problem. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Kuncheng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 94-101). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.vi / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivations and Philosophy --- p.1 / Chapter 1.2 --- Background --- p.2 / Chapter 1.3 --- Literature Review --- p.4 / Chapter 1.4 --- Contribution --- p.7 / Chapter 2 --- Preliminaries --- p.10 / Chapter 2.1 --- Probabilistic Inequalities --- p.10 / Chapter 2.2 --- Exact Proper Fractional Covers --- p.12 / Chapter 2.2.1 --- Exact Proper Fractional Cover of Quadratic Perturbations --- p.15 / Chapter 3 --- Large Deviations of Sums of Dependent Random Matrices --- p.18 / Chapter 3.1 --- The Matrix Exponential Function and Its Properties --- p.18 / Chapter 3.2 --- Main Theorem --- p.19 / Chapter 4 --- From Large Deviations to ChanceConstrained LMIs --- p.26 / Chapter 4.1 --- General Results --- p.26 / Chapter 4.2 --- Application to ChanceConstrained Quadratically Perturbed Linear Matrix Inequalities --- p.30 / Chapter 4.3 --- Bounding the Matrix Moment Generating Functions --- p.31 / Chapter 4.4 --- Iterative Improvement of the Proposed Approximations --- p.42 / Chapter 5 --- Computational Studies --- p.49 / Chapter 5.1 --- Application to Control Problems --- p.49 / Chapter 5.2 --- Application to Value-at-Risk Portfolio Optimization --- p.57 / Chapter 6 --- ChanceConstrained LMIs with CVaR Risk Measure --- p.64 / Chapter 6.1 --- Matrix CVaR Risk Measure --- p.65 / Chapter 6.2 --- Some Useful Inequalities --- p.68 / Chapter 6.3 --- From Matrix CVaR to ChanceConstrained LMIs --- p.69 / Chapter 6.3.1 --- Bound π¹(A₀, · · · ,A[subscript m]) --- p.70 / Chapter 6.3.2 --- Bound π²(A₀, · · · ,A[subscript m]) --- p.71 / Chapter 6.3.3 --- Bound π³(A₀, · · · ,A[subscript m]) --- p.72 / Chapter 6.3.4 --- Convex Approximation of π[superscript i](A0, · · · ,Am) --- p.73 / Chapter 7 --- Extension to Polynomials Perturbations --- p.75 / Chapter 7.1 --- Decoupling Theory --- p.75 / Chapter 7.2 --- Safe Tractable Approximation by SecondOrder Cone Programming --- p.77 / Chapter 8 --- Construct Uncertainty Set for Chance Constraints --- p.81 / Chapter 8.1 --- Problem Statement --- p.82 / Chapter 8.2 --- Fractional Cover for Quartic Perturbations --- p.83 / Chapter 8.3 --- Probabilistic Guarantees --- p.85 / Chapter 8.3.1 --- Probabilistic Bound Based on Large Deviations --- p.85 / Chapter 8.4 --- The Value of Ω for Bounds --- p.88 / Chapter 8.5 --- Computational Study --- p.89 / Chapter 8.5.1 --- Independent Standard Normal Perturbations --- p.89 / Chapter 8.5.2 --- Independent Bounded Quadratic Perturbations --- p.91 / Chapter 9 --- Conclusion --- p.93 / Bibliography --- p.94

Typescript (photocopy). / Digitized by Kansas Correctional Industries

The genetic profiles of evidentiary samples found at crime scenes are generated in order to determine the likelihood that a person contributed to DNA to the sample. One of the most challenging aspects of forensic deoxyribonucleic acid (DNA) analysis is that samples collected from crime scenes often contain only trace amounts of DNA; these samples are often referred to as low template DNA (LTDNA). Due to the low initial concentration of genetic material in LTDNA samples, substantive environmental insults will likely result in compromised DNA profiles that exhibit lower allele peak heights than expected, or in some cases, complete allele drop-out. The research detailed in this study investigates the impact various sources of compromise have on relative fluorescent unit (RFU) signal obtained from LTDNA samples. The potential for stochastic allele loss during a silica extraction of DNA prior to downstream processing is first considered using a dynamic systems model simulating the probability for allelic loss at each step in the procedure. Next, the impacts of damaging or degrading the DNA on the electropherogram signal are explored. Trends in RFU signal of LTDNA samples subjected to sonication by a sonic dismembrator probe, ultraviolet (UV) irradiation, and enzymatic digestion by two different enzymes are assessed, with the aim of creating a reference for typical behaviors in RFU signal data in compromised LTDNA. The distributions of electropherogram profile data from compromised LTDNA are then compared against one another in order to determine if the compromising methods explored in the study act on the samples in similar ways. The RFU signal data from the compromised LTDNA are then evaluated alongside the provided degradation index (DI) value resulting from quantification using the Quantifiler® Trio quantification kit (Thermo Fisher Scientific, Oyster Point, CA). The DI value acts as an early assessment of the quality of DNA samples and can be used to optimize downstream processing. Its ability to accurately predict behavior in compromised LTDNA samples is assessed through comparison of the DI value to the decrease in RFU signal as the samples are subjected to higher levels of simulated environmental insults.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: p. 252-256. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Lawrence Charles Vallot. / M.S.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Vita. / Bibliography: leaves 111-114. / by Marjorie G. Hahn. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Henry Rolan Shomber. / M.S.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Vita. / Bibliography: leaves 147-157. / Ph.D.