The main contribution of this thesis can be formulated in terms of a synchronization problem describing interactions between a system of harmonic oscillators (HO) and a given dynamical system, called HO synchronization. This thesis investigates the applications of HO synchronization in the area of controlling chaos. It proposes an innovative feedback stabilization technique, called HO feedback control, that utilizes an output of the synchronized system to stabilize periodic orbits of dynamical systems. A particularly attractive application of this stabilization technique is found in controlling chaotic systems, where the aim is to stabilize unstable periodic orbits embedded in the chaotic attractors. This thesis utilizes the same concept of synchronization to develop a novel method of detecting unstable periodic motions in chaotic time series, called HO time series analysis. To do so, the proposed method does not require any information about the underlying dynamics beyond a recorded time history. Therefore, it is appealing in experimental situations. The information obtained from the HO time series analysis can be used in various methods of controlling chaos, including the HO feedback control. In a different, but related application, this thesis proposes a novel transformation of a time delay system to a system of ordinary differential equations featuring the same concept of synchronization, called HO transformation. This transformation yields an efficient finite dimensional approximation to the original time delay system. It is practically important as it allows implementation of classical theories and conventional tools, developed for finite dimensional systems, to analyze time delay systems. This thesis utilizes the HO transformation to reveal the relation between the delayed feedback control and the HO feedback control. / February 2017

Synchronization of data across an integrated system of heterogeneous databases is a difficult but important task, especially in the context of integrating health care information throughout a region, state, or nation. This thesis describes the design and implementation of a data replication and synchronization tool, called the Sync Engine, which allows users to define custom data-sharing patterns and transformations for an integrated system of heterogeneous person-centric databases. This thesis also discusses the relationship between the Sync Engine's contributions and several relevant issues in the area of data integration and replication. The Sync Engine's design and implementation was validated by adapting it to CHARM, a real world integrated system currently in use at the Utah Department of Health.

The next generation (4G) wireless systems are expected to provide universal personal and multimedia communications with seamless connection and very high rate transmissions and without regard to the users’ mobility and location. OFDM technique is recognized as one of the leading candidates to provide the wireless signalling for 4G systems. The major challenges in downlink multiuser OFDM based 4G systems include the wireless channel, the synchronization and radio resource management. Thus algorithms are required to achieve accurate timing and frequency offset estimation and the efficient utilization of radio resources such as subcarrier, bit and power allocation. The objectives of the thesis are of two fields. Firstly, we presented the frequency offset estimation algorithms for OFDM systems. Building our work upon the classic single user OFDM architecture, we proposed two FFT-based frequency offset estimation algorithms with low computational complexity. The computer simulation results and comparisons show that the proposed algorithms provide smaller error variance than previous well-known algorithm. Secondly, we presented the resource allocation algorithms for OFDM systems. Building our work upon the downlink multiuser OFDM architecture, we aimed to minimize the total transmit power by exploiting the system diversity through the management of subcarrier allocation, adaptive modulation and power allocation. Particularly, we focused on the dynamic resource allocation algorithms for multiuser OFDM system and multiuser MIMO-OFDM system. For the multiuser OFDM system, we proposed a lowiv complexity channel gain difference based subcarrier allocation algorithm. For the multiuser MIMO-OFDM system, we proposed a unit-power based subcarrier allocation algorithm. These proposed algorithms are all combined with the optimal bit allocation algorithm to achieve the minimal total transmit power. The numerical results and comparisons with various conventional nonadaptive and adaptive algorithmic approaches are provided to show that the proposed resource allocation algorithms improve the system efficiencies and performance given that the Quality of Service (QoS) for each user is guaranteed. The simulation work of this project is based on hand written codes in the platform of the MATLAB R2007b.