Digitized by Kansas Correctional Industries

Digitized by Kansas Correctional Industries

Biological tissue is distinguished from materials described historically by continuum mechanical theory by its ability to grow and remodel adaptively, driven by a wide range of processes across multiple spatial and temporal scales. In this thesis we derive new mathematical descriptions that capture details from across various scales and their effect on the resulting overall behaviour. Motivated by tissue engineering, we consider tissue growth on a porous scaffold. Using the multiscale homogenisation method of O'Dea \emph{et al.}, [Mathematical Medicine and Biology, 32(3):345--366, 2014] and Penta \emph{et al.}, [The Quarterly Journal of Mechanics and Applied Mathematics, 67(1):69--91, 2014] we derive a macroscale description from one posed on the microscale. Through use of a multiphase mixture model for the tissue we extend the ideas in the above to incorporate interstitial growth and cell motility. Macroscale models are obtained via two simplifications which facilitate the homogenisation: first, by taking the limit of large interphase drag and second, by linearisation about a uniform steady state. These models consist of Darcy flow and differential equations for the cell volume fraction within the scaffold and concentration of nutrient, required for growth. Effective parameters are obtained via solution of a cell problems, hence providing explicit dependence on the microscale geometry and dynamics. Closure of the model is provided by an expression for the tissue-interstitium boundary velocity, obtained from numerical investigation of the underlying multiphase description, and solutions for a sample geometry are given. The same multiscale homogenisation technique is then employed in a different context: drug uptake by cancer cells and spheroids. Beginning with a description of drug uptake and binding for a single spheroid, two different macroscale models are derived based on different scaling assumptions. These are fitted to experimental data to provide insight into uptake behaviour, with a view to revealing underlying dynamics.

Various physical phenomena have found use as resources in quantum information processing tasks, and the study of their properties is necessary to provide optimal methods to harness their power. The thesis presents a series of results aiming to characterise the quantitative and operational aspects of general quantum resources, and in particular to establish methods applicable to a variety of resources and emphasise the similarities in their characterisation. Our approach relies on the underlying convex structure of quantum resource theories, employing techniques from convex analysis and optimisation to gain a better understanding of both the fundamental properties of quantum resources as well as our ability to manipulate them efficiently in information processing protocols such as resource distillation. The first part of the thesis introduces a unified framework for resource quantification, establishing general properties of arbitrary convex quantum resource theories and providing insight into the common structure of many physically relevant resources. The second part of the thesis deals with the convex optimisation problems involved in the operational characterisation of two representative quantum resources, quantum entanglement and quantum coherence, where we in particular establish a detailed description of their distillation under several classes of operations, and introduce methods for the interconversion between the two resources. In the final part, we employ geometric methods to characterise the quantification of entanglement measures based on polynomial invariants and apply the results to investigate the monogamy properties of multipartite entanglement.

Chan Sze-ki. / Thesis submitted in: December 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 73-76). / Abstracts in English and Chinese. / ABSTRACT (English Version) --- p.iii / ABSTRACT (Chinese Version) --- p.iv / ACKNOWLEDGEMENTS --- p.v / TABLE OF CONTENTS --- p.vi / LIST OF TABLES --- p.viii / LIST OF FIGURES --- p.xi / Chapter CHAPTER 1 --- INTRODUCTION / Chapter 1.1. --- Structure of Deoxyribonucleic acid (DNA) / Chapter 1.1.1. --- Configuration and Conformation of Deoxyribonucleic acid (DNA) --- p.1 / Chapter 1.1.2. --- Torsion Angle --- p.2 / Chapter 1.1.3. --- Base Pairing --- p.5 / Chapter 1.2. --- DNA Damage --- p.6 / Chapter 1.3. --- The Objective of this Project --- p.11 / Chapter CHAPTER 2 --- theory and Computational Details / Chapter 2.1. --- Computational Theory / Chapter 2.1.1. --- Density Functional Theory (DFT) --- p.12 / Chapter 2.1.2. --- Closed-shell and Open-shell Determinantal Wavefunctions --- p.13 / Chapter 2.1.3. --- Calculation Method --- p.13 / Chapter 2.1.4. --- Basis Set Details --- p.14 / Chapter 2.2. --- Ionization Potential and Electron Affinity --- p.15 / Chapter 2.3. --- Charge Distribution --- p.16 / Chapter 2.4. --- Molecular Orbital --- p.16 / Chapter 2.5. --- Computation Details in this Project / Chapter 2.5.1. --- Calculation Method --- p.17 / Chapter 2.5.2. --- Studied Model --- p.17 / Chapter CHPATER 3 --- Results and Discussion / Chapter 3.1. --- Neutral State / Chapter 3.1.1. --- Bond Length --- p.19 / Chapter 3.1.2. --- Torsion Angle of DNA backbone --- p.19 / Chapter 3.1.3. --- Sugar Ring Puckering Mode --- p.25 / Chapter 3.1.4. --- Natural Population Analysis (NAP) --- p.28 / Chapter 3.1.5. --- Molecular Orbitals --- p.31 / Chapter 3.2. --- Cationic State / Chapter 3.2.1. --- Ionization Potential --- p.33 / Chapter 3.2.2. --- Bond Length --- p.34 / Chapter 3.2.3. --- Backbone Torsion Angles --- p.38 / Chapter 3.2.4. --- Puckering Mode of Sugar Ring --- p.40 / Chapter 3.2.5. --- Charge Distribution --- p.43 / Chapter 3.2.6. --- Molecular Orbitals --- p.43 / Chapter 3.2.7. --- Summary --- p.47 / Chapter 3.3. --- Anionic State / Chapter 3.3.1. --- Ionization Potential --- p.51 / Chapter 3.3.2. --- Bond Lengths --- p.52 / Chapter 3.3.3. --- Torsion Angles of Backbone --- p.54 / Chapter 3.3.4. --- Sugar Ring Puckering Mode --- p.54 / Chapter 3.3.5. --- Charge Distribution --- p.58 / Chapter 3.3.6. --- Molecular Orbital --- p.63 / Chapter 3.3.7. --- Summary --- p.66 / Chapter CHAPTER 4 --- CONCLUSION AND FUTURE WORK / Chapter 4.1. --- Conclusion --- p.68 / Chapter 4.2. --- Future Work --- p.71 / REFERENCE --- p.73

乘積型劃分模型最近被擴展為容許個體有協變量的隨機聚類模型，然而協變量受限與對個體性質的描述。隨著科技發展，於越來越多生物醫學或社會研究的聚類問題中，我們需要考慮聚類對象間兩兩關連的額外資料，如基因間的調節關係或人際關係中的社交網絡。為此我們提出一個基於模型的方法，綜合乘積型劃分模型的一種改型與隱馬可夫隨機場對有網絡和協變量信息的對象做聚類。統計推論以貝葉斯方法進行。模型計算以馬可夫鏈蒙地卡羅運算法則進行。為了使馬可夫鏈能更好地混和，使用循序分配合併分裂取樣器進行群體移動以減少困於區域性頂點的機會。 / 為了測試本文提出的新方法的聚類性能，我們在兩個合成數據集上進行了模擬實驗。該實驗涵括多種類型的應變量，協變量網絡結構。結果顯示該方法在大部分實驗條件下都具有高正確聚類率。我們還將此返法應用於兩個真實數據集。第一個真實數據集利用學術期刊間相互引用的信息幫助對學術期刊的分門別類。第二個真實數據集合併酵母中基因的表達、轉錄因子結合位點和基因間的調控網絡信息，已對基因做詳細的功能分類。這兩個基於真實數據的實驗都給出諸多有意義的結果。 / The product partition model was recently extended for the covariate-dependent random partition of subjects, where the covariates are limited to properties of individual subjects. For many clustering problems in biomedical or social studies, we often have extra clustering information from the pairwise association among subjects, such as the regulatory relationship between genes or the social network among people. Here we propose a model-based method for clustering with network information by combining a modified product partition model with hidden Markov random field. The Bayesian approach is used for statistical inference. Markov Chain Monte Carlo algorithms are used to compute the model. In order to improve the mixing of the chain, the Sequentially-Allocated Merge-Split Sampler is adapted to perform group moves as an eort to lower the chance of trapping in local modes. / The new method is tested on two synthesized data sets to evaluate its performance on different types of response variables, covariates and networks. The correct clustering rate is satisfactory under a wide range of conditions. We also applied this new method on two real data sets. The first real data set is the journal data, where the cross citation information among journals is used to groups journals to different categories. The second real data set involves the gene expression, motif binding and gene network of yeast, where the goal is to find detail gene functional groups. Both experiments yielded interesting results. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Fung, Ling Hiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Technical Background --- p.7 / Chapter 2.1 --- Variable notation --- p.8 / Chapter 2.2 --- Two exemplary models for the response variable --- p.10 / Chapter 2.3 --- PPMx --- p.12 / Chapter 2.3.1 --- PPM - definition and its equivalence to DPM --- p.12 / Chapter 2.3.2 --- PPMx - extension with covariates --- p.15 / Chapter 2.3.3 --- Posterior inference --- p.18 / Chapter 2.4 --- HMRF --- p.19 / Chapter 2.4.1 --- Definition --- p.19 / Chapter 2.4.2 --- Constrained Dirichlet Process Mixture --- p.21 / Chapter 3 --- Model-based Clustering with Network Covariates --- p.27 / Chapter 3.1 --- Design of the model --- p.27 / Chapter 3.2 --- The Bayesian MCNC model --- p.30 / Chapter 3.3 --- MCMC computing --- p.31 / Chapter 3.4 --- Performance evaluation criteria --- p.37 / Chapter 4 --- Simulation study --- p.39 / Chapter 4.1 --- Network --- p.39 / Chapter 4.2 --- Covariates --- p.41 / Chapter 4.3 --- The Phase model (M1) --- p.42 / Chapter 4.4 --- The Normal model (M2) --- p.52 / Chapter 4.5 --- Comparing correct clustering percentage and correct co-occurrence percentage --- p.62 / Chapter 5 --- Real data --- p.68 / Chapter 5.1 --- Journal cross-citation data --- p.68 / Chapter 5.2 --- Gene Network of yeast data --- p.76 / Chapter 6 --- Conclusions --- p.89 / Chapter A --- p.91 / Chapter A.1 --- Covariates --- p.91 / Chapter A.1.1 --- Continuous covariates --- p.91 / Chapter A.1.2 --- Categorical covariates --- p.94 / Chapter A.1.3 --- Count covariates --- p.96 / Chapter A.2 --- Phase model --- p.98 / Chapter A.2.1 --- Prior specification --- p.99 / Chapter A.2.2 --- Data generation --- p.99 / Chapter A.2.3 --- Posterior estimation --- p.100 / Chapter A.3 --- Normal model --- p.111 / Chapter A.3.1 --- Prior specification --- p.111 / Chapter A.3.2 --- Data generation --- p.112 / Chapter A.3.3 --- Posterior estimation --- p.112 / Chapter A.4 --- Journal dataset --- p.115

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