As entropy is also an important quantity in physics, we relate our results to physical processes by demonstrating that the discontinuity of entropy can occur in a Markov chain. We also discuss the possible implications of this phenomenon in thermodynamics and cosmology. / For two probability distributions with finite alphabets, some bounds on the difference of their entropies as a function of their alphabet sizes and variational distance are obtained. These bounds, which are tighter than some existing results, show that entropy estimation by finite alphabet approximation may not work as we expected. On the other hand, we show that there always exists a finite alphabet approximation that works for entropy estimation provided that the alphabet used is sufficiently large. Some necessary and sufficient conditions under which the entropy of a sequence of probability distributions converges are given in terms of four new information divergence measures, where the square root of two of them are metrics. / In information theory, weak typicality and strong typicality are essential tools for proving coding theorems. Strong typicality, which is more powerful than weak typicality, can be applied to finite alphabet only, while weak typicality can be applied to both finite and countably infinite alphabets. We introduce a unified typicality for finite or countably infinite alphabet which is stronger than both weak typicality and strong typicality. With this unified typicality, the asymptotic equipartition property and the structural properties of strong typicality are preserved. / The Shannon information measures are well known to be continuous functions of the probability distribution for finite alphabet. In this thesis, however, we show that these measures are discontinuous with respect to almost all commonly used "distance" measures when the alphabet is countably infinite. Such "distance" measures include the Kullback-Leibler divergence and the variational distance. Specifically, we show that all the Shannon information measures are in fact discontinuous at all probability distributions. / Ho Siu Wai. / "August 2006." / Adviser: Wai Ho Raymond Yeung. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1824. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 121-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

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Thesis (Ph. D.)--University of Chicago, Dept. of Economics, March 2000. / Includes bibliographical references. Also available on the Internet.

Repetitive control (RC) was proven to enable high performance for systems that are subject to periodically repeating signals by enhancing an existing feedback control system so that it produces zero tracking error to a periodic command, or zero tracking error in the presence of a periodic disturbance of known period. Periodic signals are very common in many applications like robotics, disk drive systems, power converters, photolithography, jitter or vibration elimination in spacecraft and many more. Due to the growth in micro-processor and micro-controller technologies, most of the controllers are implemented in digital domain. Digital RC is typically designed by assuming a known constant period of command/disturbance signal, which then leads to the selection of a fixed sampling period that keeps it synchronized with the command/disturbance signal. However, in practice, the period for these signals might not be accurately known or might vary with time. In order to overcome this problem, higher order RC (HORC) was proposed as one method to make RC less sensitive to period error or period fluctuations. This dissertation investigates HORC, specifically second and third order RC designs (SORC and TORC), to identify the limitations, gaps, and design tradeoffs that a control system designer faces. New designs and methods are developed to address such gaps including stability, designer tradeoffs, robustness and other related performance characteristics. This dissertation has three major parts: SORC designs and stability, SORC design tradeoffs, and TORC designs and stability.

This research attempts to answer the question of how to measure the performance of management tools. This study integrates qualitative and quantitative research by developing a set of definitions and a set of indicators for information-oriented performance measurement and by validating the indicators with a statistical analysis. Criteria for measuring organizational system performance are borrowed from Sink (1985) and operationalized for measuring information-oriented performance. The operational measures are applied to a set of information documents. The documents are evaluated by four different groups of subjects. The evaluations are compared to the calculations from the operational measures to address the validity of the measures. The evaluations support the productivity, input quality, and output quality measures. The evaluations don't support the efficiency and effectiveness measures. Further refinement of the validation procedures is suggested before further refinement of the performance measures. This research makes two general contributions: a foundation for further development of performance measures for management tools and recommendations for future research. / Master of Science

The characterization, analysis and filtering of a slowly time-varying (STV) deterministic signal are considered. A STV signal is characterized as a sophisticated signal whose windowed sections are elementary signals. Mixed time-frequency representations (MTFRs) such as the Wigner distribution (WD), the Pseudo-Wigner distribution (PWD), the Short-time Fourier transform (STFT) and the optimally smoothed Wigner distribution (OSWD) used in analyzing STV signals are analyzed and compared. The OSWD is shown to perform satisfactorily even if the signals are amplitude modulated. The OSWD is shown to yield the exact instantaneous frequency for STV signals having quadratic phase: and to have a minimal and meaningful Bandwidth (BW) that does not depend on the slope of the instantaneous frequency curve in the time-frequency plane, unlike the BW of the spectrogram. We also present some contributions to the ongoing debate addressing the issue of choosing the MTFR that is best suited to the analysis of STV signals. Using analytical and experimental results, the performances of the different MTFRs are compared, and the conditions under which a given MTFR performs better are considered. The filtering of a signal from a noise-corrupted measurement, and the decomposition of a STV signal into its components in the presence of noise, are considered. These two related problems have been solved through masking the MTFRs of the measured signal. This approach has been successfully used in the case of the WD, PWD and the STFT. We propose extending the use of this approach to the OSWD. An equivalent time-domain implementation based on linear shift-variant (LSV) filters is derived and fully analyzed. It is based on the concept of local nonstationarity cancellation. The proposed filter is shown to have a superior performance when compared to the filter based on masking the STFT. The sensitivity of the filter is studied. The filter ability to suppress white noise and to decompose a STV signal into its components is analyzed and illustrated. / Master of Science