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Reception of one or more signals, overlapping in frequency and time with the desired signal, is commonly called cochannel interference. Joint detection is the optimal minimum probability of error decision rule for cochannel interference. This dissertation investigates the optimum approach and a number of suboptimum approaches to joint detection when a priori information based in fields, or sets of transmitted symbols, is available. In the general case the solution presents itself as a time-varying estimation problem that may be efficiently solved with a modified Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm. The low-entropy properties of a particular signal of interest, the Automatic Identifi- cation System (AIS), are presented. Prediction methods are developed for this signal to be used as a priori information for a joint field-based maximum a posteriori (MAP) detector. Advanced joint detection techniques to mitigate cochannel interference are found to have superior bit error rate (BER) performance than can be obtained compared to traditional methods.

In this thesis we develop an approach to nonequilibrium quantum-statistical mechanics which is based on the consideration of the thermodynamic entropy as being a quantum observable with an associated hermitian operator and with its own equation of motion, from which the rate of entropy production can be studied. The relationship of this quantum observable---the expectation value of which is proved to obey the laws of thermodynamics and is thus called the thermodynamic entropy---with heat dissipation in quantum many-body systems is investigated in detail. After showing how the classical theory of nonequilibrium thermodynamics is obtained from our entropy-production formalism in the limit of very weakly coupled subsystems of a larger isolated quantum system, the solution of the equation of motion for the thermodynamic entropy operator is formally obtained and applied to the case of electrons interacting with phonons and being driven by an external electric field, arriving at an explicit expression for the Joule heat without any a priori consideration of the rate of change of the energy of the system. Finally, the formalism is applied to solve a puzzle introduced with the most basic model for atom-light interactions: the Jaynes-Cummings model. Without using the correct thermodynamic arguments implied by our entropy-production theory, this model leads to the conclusion that a stream of two-level atoms sent to a cavity filled with monochromatic photons---in the so called one-atom maser configuration---thermalize, under off-resonant conditions, to a temperature different from that of the photons, casting doubts on the validity of the principle of conservation of energy.

Lo Ying Hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 80-81). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Background --- p.4 / Chapter Chapter 3 --- Commutative Partition Pair Analysis --- p.9 / Chapter Chapter 4 --- Entropy Inequalities for Partition Pair --- p.19 / Chapter Chapter 5 --- Entropy Characterization of Commutative Partition Pair --- p.32 / Chapter Chapter 6 --- Ordered Commutative Partitions --- p.43 / Chapter Chapter 7 --- Running Intersection Property for Partitions --- p.45 / Chapter Chapter 8 --- Entropy Characterization of Ordered Commutative Partitions --- p.53 / Chapter Chapter 9 --- Significance and Application --- p.72 / Chapter Chapter 10 --- Future Plan --- p.78 / Chapter Chapter 11 --- Conclusion --- p.79 / Bibliography --- p.80

令N = {1, ..., n}. 一組n個隨機變量{Xi : i ∈ N} 的熵函數h是一個2n維的向量，該向量的每個分量h(A) = H(XA);A ⊂ N, 即該組隨機變量的子集的(聯合)熵且空集的熵按傳統看做為0。所有n個隨機變量的熵函數組成的區 域稱為n階熵函數區域，記作Γ* n。熵函數區域Γ* n及其閉包Γ* n的表徵是信息論中著名的開放問題。 / 在本文中，我們研究劃分對稱熵函數。令p = {N₁... ,Nt}為N的 一個t-劃分 。一個熵函數h稱為p-對稱的，若h滿足:對於N的所有子集A，B，對於p的每一 個分塊，只要A和該分塊的交集的基數與B和該分塊交集的基數相等，那麼h(A) = h(B)。所有p-對稱熵函數的集合稱作p-對稱熵函數區域。我們證明p-對稱熵函數區域的 閉包可以由香農型信息不等式完全表徵當且僅當p為1-劃分或者有一個分塊為單元 素集合的2-劃分。 / 劃分對稱熵函數的表徵能應用於那些結構中含有對稱的信息論問題及其相關問題。 / Let N = {1, ..., n}. The entropy function h of a set of n discrete randomvariables {Xi : i ∈ N} is a 2n-dimensional vector whose entries are h(A)H(XA),ACN, the (joint) entropies of the subsets of the set of n randomvariables with H(X) = 0 by convention. The set of all entropy functions for n discrete random variables, denoted by Γ* n , is called the entropy function region for n. Characterization of Γ* n and its closure Γ* n are well-known open problems in information theory. They are important not only because they play key roles in information theory problems but also they are related to other subjects in mathematics and physics. / In this thesis, we consider partition-symmetrical entropy functions. Let p ={N₁... ,Nt} be a t-partition of N. An entropy function h is called p-symmetricalif for all A,B ⊂ N, h(A) = h(B) whenever / The characterization of the partition-symmetrical entropy functions can beuseful for solving some information theory and related problems where symmetryexists in the structure of the problems. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Qi. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 70-73). / Abstracts also in Chinese.

The analysis of broadened x-ray diffraction profiles provides a useful insight into the structural properties of materials, including crystallite size and inhomogenous strain. In this work a general method for analysing broadened x-ray diffraction profiles is developed. The proposed method consists of a two-fold maximum entropy (MaxEnt) approach. Conventional deconvolution/inversion methods presently in common use are analysed and shown not to preserve the positivity of the specimen profile; these methods usually result in ill-conditioning of the solution profile. It is shown that the MaxEnt method preserves the positivity of the specimen profile and the underlying size and strain distributions, while determining the maximally noncommital solution. Moreover, the MaxEnt method incorporates any available a priori information and quantifies the uncertainties of the specimen profile and the size and strain distributions. Numerical simulations are used to demonstrate that the MaxEnt method can be applied at two levels: firstly, to determine the specimen profile, and secondly to calculate the size or strain distribution, as well as their average values. The simulations include both sizeand strain-broadened specimen profiles. The experimental conditions under which the data is recorded are also simulated by introducing instrumental broadening, a background level and statistical noise to produce the observed profile. The integrity of the MaxEnt results is checked by comparing them with the traditional results and examining problems such as deconvolving in the presence of noisy data, using non-ideal instrument profiles, and the effects of truncation and background estimation in the observed profile. The MaxEnt analysis is also applied to alumina x-ray diffraction data. It is found that the problems of determining the specimen profile, column-length and strain distributions can be solved using the MaxEnt method, with superior results compared with traditional methods. Finally, the issues of defining the a priori information in each problem and correctly characterising the instrument profile are shown to be critically important in profile analysis.

Although entanglement is a well studied property in the context of quantum systems, the ability to measure it in Monte Carlo methods is relatively new. Through measures of the Renyi entanglement entropy and mutual information one is able to examine and characterize criticality, pinpoint phase transitions, and probe universality. We describe the most basic algorithms for calculating these quantities in straightforward Monte Carlo methods and state of the art techniques used in high performance computing. This description emphasizes the core principal of these measurements and allows one to both build an intuition for these quantities and how they are useful in numerical studies. Using the Renyi entanglement entropy we demonstrate the ability to detect thermal phase transitions in the Ising model and XY model without use of an order parameter. The scaling near the critical point also shows signatures identifying the universality class of the model. Improved methods are explored using extended ensemble techniques that can increase calculation efficiency, and show good agreement with the standard approach. We explore the "ratio trick" at finite temperature and use it to explore the quantum critical fan of the one dimensional transverse field Ising model, showing agreement with finite temperature and finite size scaling from field theory. This same technique is used at zero temperature to explore the geometric dependence of the entanglement entropy and examine the universal scaling functions in the two dimensional transverse field Ising model. All of this shows the multitude of ways in which the study of the Renyi entanglement entropy can be efficiently and practically used in conventional and exotic condensed matter systems, and should serve as a reference for those wishing to use it as a tool.

A thesis dedicated to getting things done.

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Although entanglement is a well studied property in the context of quantum systems, the ability to measure it in Monte Carlo methods is relatively new. Through measures of the Renyi entanglement entropy and mutual information one is able to examine and characterize criticality, pinpoint phase transitions, and probe universality. We describe the most basic algorithms for calculating these quantities in straightforward Monte Carlo methods and state of the art techniques used in high performance computing. This description emphasizes the core principal of these measurements and allows one to both build an intuition for these quantities and how they are useful in numerical studies. Using the Renyi entanglement entropy we demonstrate the ability to detect thermal phase transitions in the Ising model and XY model without use of an order parameter. The scaling near the critical point also shows signatures identifying the universality class of the model. Improved methods are explored using extended ensemble techniques that can increase calculation efficiency, and show good agreement with the standard approach. We explore the "ratio trick" at finite temperature and use it to explore the quantum critical fan of the one dimensional transverse field Ising model, showing agreement with finite temperature and finite size scaling from field theory. This same technique is used at zero temperature to explore the geometric dependence of the entanglement entropy and examine the universal scaling functions in the two dimensional transverse field Ising model. All of this shows the multitude of ways in which the study of the Renyi entanglement entropy can be efficiently and practically used in conventional and exotic condensed matter systems, and should serve as a reference for those wishing to use it as a tool.