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Earth's core-mantle boundary marks the transition from the rocky mantle to the liquid outer core and exhibits the most extreme velocity jump in the Earth's radial seismic structure. In recent decades, seismological studies demonstrate that the seismic structure close to this boundary is far more complicated than a one-dimensional velocity model could describe. In particular, anomalous heterogeneities such as Large Low-Shear-Velocity Provinces (LLSVPs) and Ultra-Low Velocity Zones (ULVZs) have been reported in this region. We analyse seismic diffraction in different aspects including real data observations, numerical synthetics, asymptotic theory, and use it as a tool to resolve the fine-scale structure close to the core- mantle boundary. We present seismic observations of rare core-diffracted signals sensitive to the interior of the Hawaiian ULVZ at the highest frequency yet observed. This signal indicates a pronounced vertical structure on the scale of kilometres inside the ULVZ. We also explored a novel data set revealing a new ULVZ close to the area beneath Macdonald Island. These new observations reinforce the proposed correlation between the ULVZs and surface hotspots. Utilizing the latest computational advances in 3D synthetic waveform modelling, we also compare the waveforms of ULVZ models in different dimensions and demonstrate the consistency and nuance among the waveform in these modellings. We also discuss a new theoretical framework for modelling diffracted waves asymptotically, which extends surface wave ray theory to core-diffracted waves. To complement the discussion of the dynamics at the core-mantle boundary, we also analyse thermal boundary layer theory, where we validate the scaling of the core-mantle heat flux and the thermal boundary temperature under a strong temperature-dependent viscosity and compositional heterogeneity.

Epitaxial growth of semi-polar (11-22) AlGaN layers with different Al composition has been performed by using the metal organic chemical vapour deposition (MOCVD) technique. A two-step overgrowth technique has been developed to both improve the crystal quality and address the cracking issue simultaneously for the AlGaN growth. Comprehensive studies on the structural and optical properties of the AlGaN overgrowth layers have been performed. Semi-polar (11-22) AlGaN layers with various Al compositions have been obtained with two different approaches. The first one is the standard AlGaN growth on the planar (10-10) m-plane sapphire substrates with either AlN or GaN buffer layer. Semi-polar AlGaN multiple quantum wells (MQWs) with various QW thickness grown on this standard template show no clear blueshift in optical emission wavelength with increasing excitation power, indicating the absence of quantum-confined Stark effect (QCSE). However, this method results in inadequate crystal quality and serious wafer cracking in the epilayers. To address both issues, another approach - a two-step overgrowth technique - has been developed. With such overgrowth technique, we have achieved thick (> 2 μm) and crack-free semi-polar (11-22) AlGaN layers grown on the top of nearly but not yet fully-coalesced GaN overgrown on micro-rod arrayed templates. These overgrowth layers with the Al composition up to 55.3% exhibit the best crystal quality ever achieved compared to other reports. A comprehensive investigation on the reduction of defects including the basal-plane stacking faults (BSFs) and strain relaxation has been carried out on the AlGaN overgrowth layers. Detailed X-ray diffraction measurements in on-axis and off-axis planes for different AlGaN structures indicate significantly reduced dislocation density in the AlGaN overgrowth samples. The BSF density is also found to be greatly reduced with the overgrowth technique by performing both the (11-22) reciprocal space mapping (RSM) and the low temperature (LT) photoluminescence (PL) measurements. The in-plane and out-of-plane strain in the overgrown AlGaN layers have been calculated by adopting a triclinic unit cell model, exhibiting anisotropic strain along two primary in-plane directions and even compressive instead of tensile in-plane strain. The great strain relaxation has been attributed to the residual voids formed within the underlying GaN during the overgrowth process. It has been found that large lattice tilts between the AlGaN and the GaN are present, which also confirms dramatic strain relaxation along the in-plane direction. Furthermore, the optical properties of the AlGaN samples with Al composition ranging from 32.0% to 55.3% have been investigated systematically. Both the near-band-edge (NBE) and BSFs-related emission are studied by LT PL and room temperature cathodoluminescence (CL) measurements. The energy separation between the two emission peaks increases with increasing Al composition, which is mainly ascribed to the compositional discrepancy within BSF regions and enhanced QCSE also within the BSF regions. Temperature-dependent PL measurements have also been performed to study the exciton localization effect in both emission regions, showing the localization depth of the BSFs-related emission is larger than that of the NBE in each sample. More importantly, a detailed comparison study has been performed on these semi-polar AlGaN samples and their c-plane AlGaN counterparts with similar Al composition. All the semi-polar AlGaN samples show a clear reduction in exciton localization depth and PL linewidth compared with their c-plane counterparts. These results presented demonstrate that semi-polar (11-22) AlGaN may be more favourable to be employed towards deep UV laser diodes than c-plane AlGaN.

Skin constitutes a barrier between our body and outside environment providing the first line defence against microbial infection. Epithelial repair and skin wound healing starts with inflammation to clear up invading pathogens and debris followed by cell proliferation and tissue remodelling. The immune response is vital for protecting the body from infection and diseases, however, it remains controversial whether the immune cells contribute to wound closure and tissue repair, or cause scarring and pathology. In this thesis, I investigate the role of Notch signalling in epithelial tissue repair. I demonstrate Notch1 signalling activation in epidermal keratinocytes following acute skin injury recruits innate lymphoid cells (i.e. ILC3s) to the site of injury in a TNF-α/CCL20-dependent mechanism and controls macrophage/monocyte recruitment via ILC3-dependent CCL3. Notch1 also induces epidermal production of IL23 which facilitates ILC3s to produce IL22 for re-epithelialization and skin repair.

One of the problems with current practice in software development is that often customer requirements are not well captured, understood and analysed, and there is no clear traceable path from customer requirements to software specifications. This often leads to a mismatch between what the customer needs and what the software developer understands the customer needs. In addition to capturing, understanding and analysing requirements, requirements engineering (RE) aims to provide methods to allow software development practitioners to derive software specifications from requirements. Although work exists towards this aim, the systematic derivation of specifications from requirements is still an open problem. This thesis provides practical techniques to implement the idea of problem progression as the basis for transforming requirements into specifications. The techniques allow us to progress a software problem towards identifying its solution by carefully investigating the problem context and re-expressing the requirement statement until a specification is reached. We develop two classes of progression techniques, one formal, based on Hoare's Communicating Sequential Processes (CSP), and one semi-formal, based on a notion of causality between events. The case studies in this thesis provide some validation for the techniques we have developed.

The global ocean plays a major role in moderating atmospheric temperature rise, thereby buffering climate change. Amongst the various oceanic regions undergoing warming, the Southern Ocean is a primary heat sink in the climate system. Subantarctic Mode Water (SAMW) and Antarctic Intermediate Water (AAIW) are the dominant water masses in the upper Southern Ocean, and play a fundamental role in ocean ventilation and the uptake of heat and carbon into the ocean interior. This thesis focuses on understanding the geographic and seasonal variability in the formation of SAMW and AAIW, as well as the role of SAMW, AAIW, and other mode and intermediate waters in recent global ocean warming, using observationally based hydrography and estimates of mixing strength. Firstly, the mechanisms controlling the volumetric change of SAMW within the mixed layer and in the ocean interior are investigated separately. We find that the seasonal variability of SAMW volume in the mixed layer is governed by formation due to air-sea buoyancy fluxes (45%, lasting from July to August) and entrainment (35%), while the interior SAMW formation is controlled by subduction during August-October. The annual mean subduction estimate shows strong regional variability with hotspots of large SAMW subduction, consistent with the distribution and export pathways of SAMW over the central and eastern parts of the south Indian and Pacific Oceans. Secondly, a volume budget analysis is performed to identify the mechanisms governing the spatial and seasonal variability of AAIW. Firstly, Ekman pumping upwells the dense variety of AAIW into the mixed layer south of the Polar Front, which can be advected northward by Ekman transport into the subduction regions of lighter variety AAIW and SAMW. The subduction of light AAIW occurs mainly by lateral advection in the southeast Pacific and Drake Passage as well as eddy-induced flow between the Subantarctic and Polar Fronts. Secondly, the diapycnal transport from subducted SAMW into the AAIW layer is predominantly by mesoscale mixing near the Subantarctic Front and vertical mixing in the South Pacific, while AAIW is further replenished by transformation from Upper Circumpolar Deep Water by vertical mixing. Lastly, part of AAIW is exported out of the Southern Ocean. Our results suggest that the distribution of AAIW is set by its formation due to subduction and mixing, and its circulation eastward along the Antarctic Circumpolar Current (ACC) and northward into the subtropical gyres. Finally, the ocean absorbs >90% of anthropogenic heat in the Earth system. However, it remains unclear how this heat uptake is distributed across water masses. Here we show that ocean heat accumulation during 2010–2020 has more than doubled relative to 1990–2000. Of the total ocean heat uptake, 94% is found in global mode and intermediate water layers that have subsequently warmed and increased in volume. After factoring out volumetric changes, warming of mode and intermediate waters explains ~40% of net global ocean warming, despite occupying just ~16% of the total ocean volume. These water masses in the subtropical Pacific and Atlantic Oceans, as well as in the Southern Ocean, are responsible for a large fraction of total heat uptake, with important implications for ongoing ocean warming, sea-level rise, and climate impacts.

A hydrological model is an indispensable tool in Earth system science and engineering operations to understand, predict, and manage water resources on Earth. The Coupled Routing and Excess Storage (CREST) model, released in 2011, is one such to simulate distributed hydrologic states and fluxes at variable scales. Over the last decade, CREST model has been actively under development and applied by different sectors to tackle water-related problems worldwide. This dissertation is dedicated to expanding the capacity of CREST model from three main fronts: (1) hydrologic data, (2) model development, and (3) applications. To start, the decadal development and applications of CREST model family were reviewed to lay the foundation for my contribution (Chapter 1). First, uncertainties in hydrologic input data were evaluated comprehensively for three state-of-the-science precipitation datasets derived from in-situ instruments, ground weather radar, and satellites during extreme events (Chapter 2); then a 120-year CONUS-wide flood database was compiled into a unified format as a validation source for models and hydroclimatic research (Chapter 3). From the model development front, a Hydrologic&Hydraulic (H&H) framework was developed to empower flood inundation mapping capacity for CREST (Chapter 4); furthermore, the re-infiltration, an important yet often ignored hydrologic process during the flooding period, was incorporated to improve the more realistic rainfall-runoff modeling representation (Chapter 5). To further improve the model efficiency, a vector-based CREST model was developed that can achieve 10x speedup for a continental-scale simulation, as well as improved model accuracy (Chapter 6). Finally on the model application, the high-resolution CREST model was applied in quantifying future US floods in a warmer climate: flood flashiness is becoming 7.9% higher for the continent (Chapter 7); and extreme rainfall and floods are becoming more frequent, widespread, and less seasonal (Chapter 8). The final Chapter 9 summarizes the contributions to the CREST model family development, outlooks, and general remarks for advancing our understanding of hydrologic science and engineering.

Abnormalities of cardiac rhythms are correlated with significant morbidity. For example, atrial fibrillation, affecting at least 2.3 million people in the United States, is associated with an increased risk of both stroke and mortality; supra-ventricular tachycardia, detected in approximately 90,000 cases annually in the United States, ventricular arrhythmias cause 75% to 80% of the cases of sudden cardiac death; bradyarrhythmias may cause syncope, fatigue from chronotropic incompetence, or sudden death from asystole or ventricular tachycardia. Due to the time-sensitive nature of cardiac events, it is of utmost importance to ensure that medical intervention is provided in a timely manner, which could benefit greatly from a cardiac arrhythmia monitoring system that can detect and preferably also predict abnormal cardiac events. In recent years, with the development of medical monitoring devices, vast amounts of physiological signal data have been collected and become available for analysis. However, the extraction of the relevant information from physiological signals is hindered by the complexity within signal morphology, which leads to vague definitions and ambiguous guidelines, causing difficulties even for medical expert. To address the variability-related issues, most traditional methods depend heavily on pre-processing to identify specific morphology types and extract the related features. Despite many successes, one of the drawbacks of these methods is that they require signal data of high quality and tend to be less effective in the presence of noise. Although not an issue in almost noiseless situations, such pre-processing--based methods have become insufficient with the advent of portable arrhythmia monitoring devices in recent years capable of collecting physiological signals in real time, albeit with more noise. Therefore, to enable automated clinical decision, it is desirable to introduce new methods that require minimal pre-processing prior to analysis and are robust to noise. This thesis aims to develop a cardiac arrhythmia monitoring and prediction system applicable to portable arrhythmia monitoring devices. The analysis is based on a novel algorithm which does not rely on the detailed morphological information contained within each heartbeat, thus minimizing the impact of noise. Instead, the method works by analyzing the similarity and variability within strings of consecutive heartbeats, relying only on the broad morphology type of each heartbeat and utilizing the computer's ability to store and process a large number of heartbeats beyond humanly possible. The novel algorithm is based on deterministic probabilistic finite-state automata which have found great success in the field of natural language processing by studying the relationships among different words in a sentence rather than the detailed structure of the individual words. The proposed algorithm has been employed in experiments on both detection and prediction of various cardiac arrhythmia types and has achieved an AUC in the range of 0.70 to 0.95 for detection and prediction of different types of cardiac arrhythmias and cardiac events with data collected from publicly available databases, hospital bedside database and data collected from portable devices. Comparing with other well-established methods, the proposed algorithm has achieved equal or better classification results. In addition, the performance of the proposed algorithm is almost identical with or without any pre-processing on the data. The work in the thesis could be deployed as a cardiac arrhythmia monitoring and severe event prediction system which could alert patients and clinicians of an impending event, thereby enabling timely medical interventions.

Continuing the discussion of interpreting J. S. Bach's lute music on the guitar, this dissertation seeks to demonstrate that Schenkerian analysis can assist the modern classical guitarist to better understand Bach's music. In particular, the Schenkerian approach provides an important methodology for studying Bach's music in depth, and then guiding performance practice on the guitar. Although there are many books and articles about transcribing, interpreting and performing Bach's music on the guitar, they do not apply Schenkerian analysis to guitar performance. This research will fill in the lacuna in this field, while promoting music scholarship and enhancing the performance practice of classical guitarists.

One of the major progress of modern condensed matter physics is the discovery of topological phases beyond Landau's paradigm--phases that are characterized by topology besides symmetries. In this thesis, we address topological phases of free fermionic systems by considering their topological classification and real-space invariants. Although the theory for topological classification is fairly complete in momentum space, essentially based on the topological classification of fiber bundles, the theory in real space is more difficult. In this thesis, we discuss a formula for the Z2 invariant of topological insulators. As a real-space formula, it is valid with or without translational invariance. Moreover, our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. It is the local nature of this invariant that guarantees the existence of gapless mode on the boundary. Based on almost commute matrices, we provide a method to approximate this invariant with local information. The validity of the formula and the approximation method is rigorously proved. The topological classification problem can be extended to non-Hermitian systems, an effective theory for systems with loss and gain. In this thesis, we propose a novel framework towards the topological classification of non-Hermitian band structures. Different from previous K-theoretical approaches, this approach is homotopical, which enables us to find more topological invariants. We find that the whole classification set is decomposed into several sectors, based on the braiding of energy levels. Each sector can be further classified based on the topology of eigenstates (wave functions). Due to the interplay between energy level braiding and eigenstates topology, we find some torsion invariants, which only appear in the non-Hermitian world. We further prove that these new topological invariants are unstable, in the sense that adding more bands will trivialize these invariants.

Hydrodynamic modeling of flow and salinity transport through shallow coastal marshes often suffers from errors introduced through inadequate representation of the underlying bathymetry. Although high-resolution topographic data has become available through lidar, it generally requires upscaling to a coarser resolution to maintain practical computational costs for large coastal marshes. The effects of simulating at coarse resolution, along methods to improve such simulations, are illustrated in this study by comparing model results with field data for the Nueces River delta in Texas (USA). It is shown that with simple upscaling techniques surface connectivity of the model domain is altered, where existing flow paths are smoothed and new paths are created. Narrow channels are widened to the grid scale, leading to discrepancies in modeled flux and salinity. Subgrid topography models have been used to reproduce effects of high-resolution topographic features on computationally-efficient coarse grids, but four major issues are associated with existing subgrid models: (i) surface connectivity is not always maintained, (ii) salinity transport is rarely modeled, (iii) effects of large topographic features in the cell interior are often neglected, and (iv) sensitivity of subgrid model to mesh design is strong. This research presents a new high-performance subgrid model to address these issues associated with grid-coarsening. In this new model, The high-resolution topographic data is parametrized into the model equations to scale grid cell storage and flow rate across cell faces. A block-checking procedure is designed to maintain surface connectivity during coarsening. The existence of interior features generates additional reaction forces and enhances longitudinal dispersion, which are modeled by reducing grid cell volumes and face areas. A mesh-shifting method is used to alleviate sensitivity of model performance to mesh design. The new subgrid model is tested on both synthetic domains and real Nueces Delta bathymetry. Compare to simple upscaling, using the proposed subgrid method better approximates fine-grid simulation results for surface elevation, inundation area, in-channel flow rate and salinity with negligible additional computational cost. Model-data agreements for salinity is also improved. This new model can be applied to large domains where coarse-grid model performance significantly deteriorates due to interrupted surface connectivity. Compare to existing approaches that model all interior topographic features as drag effects, the new subgrid model builds stronger physical connections between the geometry of the features and their effects on the flow fields. The use of the mesh-shifting method restrains numerical diffusion caused by misalignment between channel and grids, making model results less sensitive to mesh design.

Although carbon monoxide is well known as a poisonous gas causing several adverse effects including fatality, CO has also been found to play a significant role in anti-inflammation, anti-apoptosis, wound healing, and vasorelaxation in mammals through various mechanisms. However, gaseous CO has a very low solubility in water (~1.8 mM) and hemoglobin's high affinity for CO serves as a buffer against beneficial effects at the cellular level. Photochemical CO release from appropriate precursors (mostly metal carbonyls) can give spatial and temporal control. Those precursors, known as photoCORMs (photo-induced carbon monoxide releasing moieties), should have biocompatibility, aerobic and thermal stability in dark and decent solubility in biosystem for in vivo CO delivery. Some of photoCORMs meet the above requirements but require Uv light which has low penetration into biological system and causes detrimental effects on cells during irradiation. Although employment of UCNP (upconverting nanoparticles) is accessible, multiphoton upconversion efficiency is still a limiting factor. Developing long wavelength visible light or near infrared light activated photoCORMs remains a challenge in this area.In this work, a new strategy has been proposed for the delivery of carbon monoxide to physiological targets: rhenium-manganese dinuclear metal carbonyl complexes were synthesized, of which metal-metal (M-M) bond is the most labile bond, and the homolytic cleavage of this bond occur through the photo-excitation of a σMMb to σMM* transition. With conjugated diimine ligands (L), σMMb to πL* charge transfer appears at even lower energy. The homolytic cleavage of the M-M bond generates the mononuclear metal radicals. Although the radicals themselves are unlikely to be particularly reactive toward CO release, they have proved to be reactive with dioxygen to form metal oxides, at the same time to form species that are much more labile toward CO release. In this context, we are studying photochemistry of these dinuclear carbonyl complexes and explored using the hydrophobic versions of these dinuclear complexes with biocompatible polymer PLGA (poly(lactic-co-glycolic acid)) matrices as their drug delivery systems in the form of nano/micro carriers.

This dissertation verifies Professor Han, Xianguang as the most significant Chinese horn player and teacher in the twentieth century. He was the first Chinese horn player to win in an international horn competition and the first president of the China Horn Association. He was the premier performer of the only known Chinese horn concerto: Fantasy-Concerto , composed by Professor Shi Yongkang in 1962. Professor Han also served as a judge for many international horn solo and chamber music competitions, and was president of the first (2012), second (2013), and third (2014) CCOM (Central College of Music) International Horn Festivals in Beijing. This dissertation explores Professor Han’s professional and pedagogical contributions to the horn world. These contributions will, in turn, provide an overview of the evolution of the horn and horn playing in China. The horn, historically and musically an instrument of Western Europe, was transported to Asia by many horn players and teachers, with Professor Han the most significant figure in its evolution in China. During Professor Han’s 60-year teaching career, he developed a special pedagogical system. A number of his outstanding horn students, including two sons, eventually became principal hornists in orchestras throughout China, with a few hired by European orchestras, and some have won international competitions. A secondary purpose of this dissertation is to offer historical and pedagogical information to young horn players, especially those of Asian descent, to give them a more thorough musical and aesthetical understanding of their instrument in the Asian history and culture. As part of his DMA Lecture Recital on September 6, 2015, the author presented the US premiere of Fantasy-Concerto in its piano reduction.

The synergy of human arm and wearable robot systems studies the compatibility of a wearable robot system and its operators. Ideally, the motion of a wearable robot system should be dynamically transparent to a healthy operator, sensitively responsible to the voluntary and involuntary motions of its operator. When used for robot-assisted stroke rehabilitation and/or power augmentation, a wearable robot system is expected to provide assist to the operator's motor skills and correct the abnormal movements resulted from motor disabilities. Inspired by the control strategies of human motor system, the robot systems can be more dexterous in manipulations and more adaptable to various tasks and uncertain environments.The study on synergy of human arm and wearable robot systems intends to find out the motor control strategies that dominate human arm movements, in order to apply to the control of robotic systems, such as the upper limb exoskeletons and the surgical robot systems. This research experimentally investigated the arm movements in various tasks, to enhance the understanding of human motor control and to benefit the control robotic systems. With the data collected from point-to-point reaching movements, it proposed a redundancy resolution methodology based on multi-criterion performance optimization, which provides real-time predictions of arm postures with improved accuracy. Based on the comparison between reaching and reach-to-grasp movements, it further studied arm postures affected by grasping orientations and pointed out the control strategy that dominates the macro- and micro- structure coordination. From both healthy subjects and stroke patients, experimental data of unimanual and bimanual movements are recorded for identical tasks. The statistical analysis shows that motor function of the paretic arm can be improved when moving symmetrically with the non-paretic arm, which reveals the beneficial effects of the inter-arm coupling on stroke rehabilitation.The dissertation contributed to answer the following three research questions:* How to predict the natural arm postures of reaching movement?The kinematic redundancy of the human arm enables the elbow position to rotate about the axis going through the shoulder and wrist, which results in infinite possible arm postures when the arm reaches to a target in a 3-dimensional workspace. To infer the control strategy the human motor system uses to resolve redundancy in reaching movements, this research compares five redundancy resolution criteria and evaluates their arm posture prediction performance using data on healthy human motion. Two synthesized criteria are developed to provide better real-time arm posture prediction than the five individual criteria. Of these two, the criterion synthesized using an exponential method predicts the arm posture more accurately than that using a least squares approach, and therefore is preferable for inferring the contributions of the individual criteria to motor control during reaching movements. As a methodology contribution, this paper proposes a framework to compare and evaluate redundancy resolution criteria for arm motion control. A cluster analysis which associates criterion contributions with regions of the workspace provides a guideline for designing a real-time motion control system applicable to upper-limb exoskeletons for stroke rehabilitation.* How do the arm joints coordinate in reach-to-grasp movement?Reach-to-grasp movements are widely observed in activities of daily living, particularly in tool manipulations. In order to reduce the complexity in redundancy resolution and facilitate upper-limb exoskeleton control in reach-to-grasp tasks, we studied joint coordination in the human arm during such movements. Experimental data were collected on reach-to-grasp movements in a 3-dimensional (3D) workspace for cylinder targets of different positions and grasping orientations. For comparison, reaching movements toward the same targets are also recorded. In the kinematic analysis, the redundant degree of freedom in human arm is represented by the swivel angle. The four grasping-relevant degrees of freedom (GR-DOFs), including the swivel angle and the three wrist joints, behave differently in reach-to-grasp movements comparing to how they behave in reaching movements. The ratio of active motion range (R-AMR) is proposed for quantitatively comparison the task-relevance of the GR-DOFs. Analysis on the R-AMR values shows that the task-relevant GR-DOFs are more actively used, while the task-irrelevant joints are left uncontrolled and maintain their neutral positions. Among the task-relevant GR-DOFs, the smaller joints (micro-structure) are more actively used than the larger joints (macro-structure). The coordination of the task-relevant GR-DOFs is shown to be synergistic. Analysis of the acceleration/deceleration at the GR-DOFs indicates different levels of voluntary control in three phases of the movements. The study of the characteristics of the joint coordination in reach-to-grasp movements provides guidelines for simplifying the control of the upper limb exoskeleton.* Can the bilateral training benefit the post-stroke stroke recovery?Bilateral training has been used for post-stroke rehabilitation of patients with paretic upper arms. This training method exploits the inter-arm coupling in bimanual movements which tends to synchronize the paretic arm with the non-paretic arm for motor function recovery. Different levels of motor function recovery have been reported in clinical studies, yet the efficacy of bilateral training is still not clear. As a result, this paper collected data on bimanual symmetric reaching movements in a 3-dimensional (3D) workspace from ten healthy subjects and eight chronic stroke patients, to investigate the effects of inter-arm coupling. In reaching experiments, identical tasks are also performed unimanually and recorded. Mapping variables are proposed to measure arm behavior changes and to quantify the similarity of the movements of the two arms. Among the four proposed mapping variables, mapping linearity and mapping complexity were found to reflect both the motion complexity and the task-relevance of a joint, while the other two variables captured changes in motion range and relative velocity. Statistical analysis shows that inter-arm coupling increases inter-arm symmetry more at task-relevant joints than at task-irrelevant joints. To achieve symmetric bimanual movement, the dominant arm of healthy subjects and the non-paretic arm of stroke patients deviate more from their unilateral behavior than the non-dominant/paretic arms. For stroke patients, the effect of inter-arm coupling on arm function depends on the task-relevance of a joint. During bimanual movement, joint behavior at task-irrelevant joints is different from behavior during unimanual movement, which implies that bimanual rehabilitation may help break abnormal movement patterns for these joints. For task-relevant joints, the average arm posture of the paretic arm is significantly higher in bimanual movement, which indicates the possible efficacy of bilateral rehabilitation.

When a ferromagnet/antiferromagnet (FM/AF) bilayer is cooled below the Neel temperature TN& lt;/sub> of the AF in a magnetic field, exchange bias (EB) phenomenon arises. Although EB was discovered nearly 50 years ago, a general understanding is still lacking regarding the competing interactions and length scales involved and how they give rise to a rich variety of magnetization reversal behavior. In this thesis, I will address these questions by studying the cooling field dependence, asymmetric magnetization reversal, and spontaneous reversal in epitaxial FeF₂ / polycrystalline FM bilayers. Two types of transitions from negative to positive EB with increasing cooling fields were found: for in-plane twinned FeF₂, a continuous transition was found, while coexistence of EB of both signs was observed for untwinned FeF₂. This is attributed to the relevance between the AF "domain" size and the FM domain wall width and confirmed by micromagnetic simulation. Nanostructuring the FM significantly decreases the onset cooling field for positive EB with decreasing dot sizes when the FM dot size is comparable with the AF "domain" size (̃500nm). The high quality epitaxial exchange bias system also constitutes a model system for studying magnetization reversal asymmetry. By vector magnetometry and simulation, we found that the FM reverses through parallel domain walls, which results in highly asymmetric hysteresis loops. Also, the FM near the FM/AF interface exhibits a more asymmetric reversal than that farther away from the interface. These results unambiguously show the existence of a FM parallel domain wall and its importance in asymmetric magnetization reversal. Moreover, we found another surprising phenomenon that when positively exchange biased, the FM can spontaneously reverse its magnetization in a constant field when cooled below TN due to the strong interfacial coupling. When heating up in the same field, the FM magnetization reverses at T& lt;sub>N, giving rise to a tunable thermal hysteresis. Discovery of this phenomenon suggests a revised energy competition mechanism for positive EB, which includes parallel FM and AF domain wall energy. By studying these different but strongly related magnetization reversal behaviors, we demonstrated the central role of competing length scales and interactions in heterostructured magnetic systems

The resource allocation problem usually involves optimization on uniform resources. This thesis solves the problem of finding matchings between several resources and activities which are optimal for a given linear objective function and are stable with regard to preferences of the resources and activities. The concept of a stable matching comes from the stable marriage problem. Given an equal number of men and women, and, for each person, a strictly ordered preference list containing all the members of the opposite sex, a stable marriage is a one-to-one matching of men and women in which there is no man and woman who prefer each other to their partners. Although this stable marriage problem with its strictly ordered preference lists (no ties or indifference) has been studied for three decades in computer science, there are few applications. When arbitrary indifference is allowed, the stable marriage problem has more applications but fails to have some valuable properties such as Pareto Efficiency and majority assignment. We suggest using group preference lists to allow limited indifference in applications. That is, each person belongs to a group that has a preference list for all groups of the opposite sex. We show that with this approach, stability guarantees Pareto Efficiency. We have constructed a correct definition of majority assignment for our case, and show that stability also guarantees majority assignment. For our approach, there is also a polynomial-size representation of all the stable matchings for a given problem. Thus polynomial-time complexity algorithms are possible for optimization over all such matchings. We give algorithms to find the maximal elements in the solution lattice, to find the polynomial-size representation of the solution lattice using rotations, and to find the partial order on the set of rotations. The first two algorithms generalize those of Gale-Shapley and Gusfield. The third one is new. All three algorithms run in O(Np) time, where N is the total number of men or women, p is the number of groups in the other sex. We also develop the lattice structure theory supporting the algorithms.