In this dissertation, we consider a complex biological system known as cortical microtubule (CMT) system, where stochastic dynamics of the components (i.e., the CMTs) are defined in both space and time. CMTs have an inherent spatial dimension of their own, as their length changes over time in addition to their location. As a result of their dynamics in a confined space, they run into and interact with each other according to simple stochastic rules. Over time, CMTs acquire an ordered structure that is achieved without any centralized control beginning with a completely disorganized system. It is also observed that this organization might be distorted, when parameters of dynamicity and interactions change due to genetic mutation or environmental conditions. The main question of interest is to explore the characteristics of this system and the drivers of its self-organization, which is not feasible relying solely on biological experiments. For this, we replicate the system dynamics and interactions using computer simulations. As the simulations successfully mimic the organization seen in plant cells, we conduct an extensive analysis to discover the effects of dynamics and interactions on system characteristics by experimenting with different input parameters. To compare simulation results, we characterize system properties and quantify organization level using metrics based on entropy, average length and number of CMTs in the system. Based on our findings and conjectures from simulations, we develop analytical models for more generalized conclusions and efficient computation of system metrics. As a fist step, we formulate a mean-field model, which we use to derive sufficient conditions for organization to occur in terms of input parameters. Next, considering the parameter ranges that satisfy these conditions, we develop predictive methodologies for estimation of expected average length and number of CMTs over time, using a fluid model, transient analysis, and approximation algorithms tailored to our problem. Overall, we build a comprehensive framework for analysis and control of microtubule organization in plant cells using a wide range of models and methodologies in conjunction. This research also has broader impacts related to the fields of bio-energy, healthcare, and nanotechnology; in addition to its methodological contribution to stochastic modeling of systems with high-level spatial and temporal complexity.

The increased concentration of greenhouse gases is associated with the global warming in the lower troposphere. For over twenty years, the space physics community has studied a hypothesis of global cooling in the thermosphere, attributable to greenhouse gases. While the global temperature increase in the lower troposphere has been relatively well established, the existence of global changes in the thermosphere is still under investigation. A central difficulty in reaching definite conclusions is the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Time series of data that cover several decades exist only in a few separated regions. The space physics community has struggled to combine the information contained in these data, and often contradictory conclusions have been reported based on the analyses relying on one or a few locations. To detect global changes in the ionosphere, we present a novel statistical methodology that uses all data, even those with incomplete temporal coverage. It is based on a new functional regression approach that can handle unevenly spaced, partially observed curves. While this research makes a solid contribution to the space physics community, our statistical methodology is very flexible and can be useful in other applied problems.

For many applications of location-based services, such as friend finding, buddy tracking,information sharing and cooperative caching in ad hoc networks, it is often important to be able to identify whether the positions of a given set of moving objects are within close proximity. To compute these kinds of proximity relations among large populations of moving objects, continuously available location position information of these objects must be correlated against each other to identify whether a given set of objects are in the specified proximity relation. In this dissertation, we state this problem, referring to it as the location constraint matching problem, both in the Euclidean space and the road network space. In the Euclidean space, we present an adaptive solution to this problem for various environments. We also study the position uncertainty associated with the constraint matching. For the road network space, where the object can only move along the edges of the road network, we propose an efficient algorithm based on graph partitioning, which dramatically restricts the search space and enhances performance. Our approaches reduce the constraint processing time by 80% for Euclidean space and by 90% for road network space respectively. The logical combination of individual constraints with conjunction, disjunction and negation results in more expressive constraint expressions than are possible based on single constraints. We model constraint expressions with Binary Decision Diagrams (BDD). Furthermore, we exploit the shared execution of constraint combinations based on the BDD modeling. All the algorithms for various aspects of the constraint processing are integrated in the research prototype L-ToPSS (Location-based Toronto Publish/Subscribe System). Through experimental study and the development of an analytical model, we show that the proposed solution scales to large numbers of constraints and large numbers of moving objects.

For many applications of location-based services, such as friend finding, buddy tracking,information sharing and cooperative caching in ad hoc networks, it is often important to be able to identify whether the positions of a given set of moving objects are within close proximity. To compute these kinds of proximity relations among large populations of moving objects, continuously available location position information of these objects must be correlated against each other to identify whether a given set of objects are in the specified proximity relation. In this dissertation, we state this problem, referring to it as the location constraint matching problem, both in the Euclidean space and the road network space. In the Euclidean space, we present an adaptive solution to this problem for various environments. We also study the position uncertainty associated with the constraint matching. For the road network space, where the object can only move along the edges of the road network, we propose an efficient algorithm based on graph partitioning, which dramatically restricts the search space and enhances performance. Our approaches reduce the constraint processing time by 80% for Euclidean space and by 90% for road network space respectively. The logical combination of individual constraints with conjunction, disjunction and negation results in more expressive constraint expressions than are possible based on single constraints. We model constraint expressions with Binary Decision Diagrams (BDD). Furthermore, we exploit the shared execution of constraint combinations based on the BDD modeling. All the algorithms for various aspects of the constraint processing are integrated in the research prototype L-ToPSS (Location-based Toronto Publish/Subscribe System). Through experimental study and the development of an analytical model, we show that the proposed solution scales to large numbers of constraints and large numbers of moving objects.

This thesis contains two components of research: studies of supercontinuum pulses generated in the novel microstructure fiber, and research on spatio-temporal coupling in ultrafast laser beams. One of the most exciting developments in optics in recent years has been the invention of the microstructure optical fiber. By controlling the structural parameters of these novel fibers in design and manufacturing, their dispersion profile can be freely tailored, opening up a huge application base. One particularly interesting effect in the microstructure fiber is the generation of ultrabroadband supercontinuum with only nJ-level Ti:sapphire oscillator pulse pump. This supercontinuum is arguably the most complicated ultrafast pulse ever generated, with its huge time-bandwidth product (> 1000 from a 16-cm-long fiber). Although many applications have been demonstrated or envisioned with this continuum, its generation is a very complicated process that is poorly understood, and the characteristics of the continuum pulses are not clearly known. In this work, we make a full-intensity-and-phase measurement of the continuum pulses using cross-correlation frequency-resolved optical gating (XFROG). The results reveal surprising unstable fine spectral structure in the continuum pulses, which is confirmed by single-shot measurements. Our study on the coherence of the continuum, on the other hand, shows that the spectral phase of the supercontinuum is fairly stable. Numerical simulations are carried out whose results are in good agreement with experiments. The second component of this thesis is the study of spatio-temporal coupling in ultrafast beams. We propose two definitions of spatial chirp, point out their respective physical meanings, and derive their relationship. On the common perception of the equivalence between pulse-front tilt and angular dispersion, we show that the equivalence only holds for plane waves. We establish a generalized theory of ultrafast laser beams with first-order spatio-temporal couplings, and discover a new pulse-front tilt effect associated with the combination of spatial chirp and temporal chirp. For the measurement of spatio-temporal distortions, the effects of such distortions in the input beam to a GRENOUILLE trace are carefully studied. An algorithm is proposed and tested to retrieve information about the distortions from the GRENOUILLE trace.

The thesis develops two characterizations of spatio-temporal complex patterns. While these are developed for the patterns of fluid flow in experiments on Rayleigh-Benard Convection(RBC), they are adaptable to a wide range of spatially extended systems. The characterizations may be especially useful in cases where one does not have good models describing the dynamics, making numerical and analytic studies difficult. In Spiral Defect Chaos(SDC), a weakly turbulent regime of RBC, the convective rolls exhibit complex spatial and temporal dynamics. We study the dynamics of SDC through local defect formations between convective rolls as well as the topological rearrangements of these rolls at a global scale. A laser based thermal actuation system is developed to reproducibly impose initial states for the fluid flow and construct ensembles of trajectories in the neighborhood of defect nucleation. This is used to extract the modes and their growth rates, characterizing the linear manifold corresponding to defect nucleation. The linear manifold corresponding to instabilities resulting in defect formation is key to building efficient schemes to control the dynamics exhibited. We also develop the use of computational homology as a tool to study spatially extended dynamical systems. A quantitative measure of the topological features of patterns is shown to provide insights into the underlying dynamics not easily uncovered otherwise. In the case of RBC, the homology of the patterns is seen to indicate asymmetries between hot and cold regions of the flow, stochastic evolution at a global scale as well as bifurcations occurring well into the turbulent regime of the flow.

Fine particulate matter (PM2.5) affects the environment in a variety of ways, including of human health, visibility impairment, acid deposition, and climate change. As of March, 2006, 47 counties are designated as non-attainment areas in terms of PM2.5 in the southeastern United States. State agencies with PM2.5 non-attainment counties must develop plans that demonstrate how they will achieve attainment status. State agencies also have to address emission sources of visibility impairment and develop strategies to improve visibility. It is essential to understand PM2.5 composition and sources in order to develop effective control strategies to reduce PM2.5. In this thesis, actual prescribed burning emissions were characterized for better estimation of their impacts on air quality. Chemical mass balance (CMB) modeling, a receptor-oriented source apportionment technique, was applied to understand regional characteristics of PM2.5 source impacts in the Southeast. Uncertainty issues in the CMB source apportionment results due to both poor spatial representativeness and measurement errors was addressed for better understanding and estimation of the uncertainties. Possible future research is recommended based on the findings in this thesis.

Along with rapid development of information technology, all kinds of algorithms have been presented, to achieve significant progress in image tracking. Most methods tend to identify features of moving objects, and filter out background components which do not meet these features. This thesis uses a spatio-temporal planar-resonant filter to accomplish moving object tracking tasks. Under the condition without prior knowledge about features of moving objects, choosing appropriate filter¡¦s parameters is able to enhance the object with a certain moving speed and reduce intensity of objects with different velocities. Nevertheless, this filter cannot solve the problem background filtering. Therefore, a homomorphic filtering with fast optical flow estimation is implemented to identify and separate the background and moving components in dynamic images. This thesis also considers different 3-D bandwidth parameters. To develop a systematic approach to design filter¡¦s parameters for actual implementations.

Based on the acquisition trajectory, PROPELLER MRI repeatedly sampled the center k-space in every blade, which was used to provide most of the energy of an image. The purpose of view sharing PROPELLER is to improve the spatio-temporal resolution of dynamic imaging by reducing the acquisition time of single frame to that of single blade. With the center k-space provided by only one blade, which is called the target blade, the high spatial-frequency components were appropriately contributed by a set of neighboring blades with different rotation angles, leading to the high spatial resolution after reconstruction. In this study, a flow phantom experiment with the injection of T1-shortening Gd-DTPA solution was performed to exam the feasibility and accuracy of view-sharing PROPELLER. Furthermore, cardiac imaging of healthy volunteer obtained by the proposed technique was also done with ECG gating to test the image quality without any injection of contrast agent. The in-vivo experiment was done with and without breath holding. In addition to slight aliasing artifact due to insufficient FOV, no other artifact was observed.

In this dissertation, we explore the properties of correlation structure for spatio-temporal point processes and a quantitative spatial process. Spatio-temporal point processes are often assumed to be separable; we propose a formal approach for testing whether a particular data set is indeed separable. Because of the resampling methodology, the approach requires minimal conditions on the underlying spatio-temporal process to perform the hypothesis test, and thus is appropriate for a wide class of models. Africanized Honey Bees (AHBs, Apis mellifera scutellata) abscond more frequently and defend more quickly than colonies of European origin. That they also utilize smaller cavities for building colonies expands their range of suitable hive locations to common objects in urban environments. The aim of the AHB study is to create a model of this quantitative spatial process to predict where AHBs were more likely to build a colony, and to explore what variables might be related to the occurrences of colonies. We constructed two generalized linear models to predict the habitation of water meter boxes, based on surrounding landscape classifications, whether there were colonies in surrounding areas, and other variables. The presence of colonies in the area was a strong predictor of whether AHBs occupied a water meter box, suggesting that AHBs tend to form aggregations, and that the removal of a colony from a water meter box may make other nearby boxes less attractive to the bees.