Thesis (M.S.)--Ohio State University, 1964. / Includes bibliographical references. Available online via OhioLINK's ETD Center

published_or_final_version / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Applied Geosciences / Master / Master of Science

published_or_final_version / Mathematics / Master / Master of Philosophy

Efficient and comprehensive forecasting of information is of great importance to traffic management. Three types of forecasting methods based on irregularly spaced data—for situations when traffic detectors cannot be installed to generate regularly spaced data on all roads—are studied in this thesis, namely, the single segment forecasting method, multi-segment forecasting method and model-based forecasting method. The proposed models were tested using Global Positioning System (GPS) data from 400 Hong Kong taxis collected within a 2-kilometer section on Princess Margaret Road and Hong Chong Road, approaching the Cross Harbour Tunnel. The speed limit for the road is 70 km/h. It has flyovers and ramps, with a small number of merges and diverges. There is no signalized intersection along this road section. A total of 14 weeks of data were collected, in which the first 12 weeks of data were used to calibrate the models and the last two weeks of data were used for validation. The single-segment forecasting method for irregularly spaced data uses a neural network to aggregate the predicted speeds from the naive method, simple exponential smoothing method and Holt’s method, with explicit consideration of acceleration information. The proposed method shows a great improvement in accuracy compared with using the individual forecasting method separately. The acceleration information, which is viewed as an indicator of the phase-transition effect, is considered to be the main contribution to the improvement. The multi-segment forecasting method aggregates not only the information from the current forecasting segment, but also from adjacent segments. It adopts the same sub-methods as the single-segment forecasting method. The forecasting results from adjacent segments help to describe the phase-transition effect, so that the forecasting results from the multi-segment forecasting method are more accurate than those that are obtained from the single segment forecasting method. For one-second forecasting length, the correlation coefficient between the forecasts from the multi-segment forecasting method and observations is 0.9435, which implies a good consistency between the forecasts and observations. While the first two methods are based on pure data fitting techniques, the third method is based on traffic models and is called the model-based forecasting method. Although the accuracy of the one-second forecasting length of the model-based method lies between those of the single-segment and multi-segment forecasting methods, its accuracy outperforms the other two for longer forecasting steps, which offers a higher potential for practical applications. / published_or_final_version / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Discrete representation of a surface, especially the triangle mesh, is ubiquitous in numerical simulation and computer graphics. Compared with isotropic triangle meshes, anisotropic triangle meshes provide more accurate results in numerical simulation by capturing anisotropic features more faithfully. Furthermore, emerging applications in computer graphics and geometric modeling require reliable differential geometry information estimated on these anisotropic meshes. The first part of this thesis proposes a special type of anisotropic meshes, called shape-preserving meshes, provides guaranteed convergence of discrete differential operators on these meshes and devises an algorithm for generating shape-preserving meshes on free-form surfaces based on the mesh optimization framework with centroidal Voronoi tessellation (CVT). To improve the numerical stability in simulation, we discuss how to reduce the number of obtuse triangles in the mesh. The second part of the thesis discusses the non-uniqueness of anisotropic meshes to represent the same anisotropy defined on a domain, shows that of all anisotropic meshes, there exists one instance minimizing the number of obtuse triangles, and proposes a variational approach to suppressing obtuse triangles in anisotropic meshes by introducing a Minkowski metric in the CVT framework. On a complex shape, its topological information is also highly useful to guide the mesh generation. To extract topology properties, the Morse-Smale complex (MSC) is a classical tool and widely used in computer graphics. However, on a manifold with boundary, its MSC is not well defined. The final part of this thesis generalizes the MSC to manifolds with boundaries. Based on this generalized MSC (GMSC), an operator to merge n GMSCs of manifolds partitioning a large manifold is proposed. The merging operator is used in a divide-and-conquer approach on a massive data set, providing the potential to employ the computational power in a parallel manner. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Systems biology is a comprehensive quantitative analysis of the manner in which all the components of a biological system interact functionally along with time. Mathematical modeling and computational methods are indispensable in such kind of studies, especially for interpreting and predicting the complex interactions among all the components so as to obtain some desirable system properties. System dynamics, system robustness and control method are three crucial properties in systems biology. In this thesis, the above properties are studied in four different biological systems. The outbreak and spread of infectious diseases have been questioned and studied for years. The spread mechanism and prediction about the disease could enable scientists to evaluate isolation plans to have significant effects on a particular epidemic. A differential equation model is proposed to study the dynamics of HIV spread in a network of prisons. In prisons, screening and quarantining are both efficient control manners. An optimization model is proposed to study optimal strategies for the control of HIV spread in a prison system. A primordium (plural: primordia) is an organ or tissue in its earliest recognizable stage of development. Primordial development in plants is critical to the proper positioning and development of plant organs. An optimization model and two control mechanisms are proposed to study the dynamics and robustness of primordial systems. Probabilistic Boolean Networks (PBNs) are mathematical models for studying the switching behavior in genetic regulatory networks. An algorithm is proposed to identify singleton and small attractors in PBNs which correspond to cell types and cell states. The captured problem is NP-hard in general. Our algorithm is theoretically and computationally demonstrated to be much more efficient than the naive algorithm that examines all the possible states. The goal of studying the long-term behavior of a genetic regulatory network is to study the control strategies such that the system can obtain desired properties. A control method is proposed to study multiple external interventions meanwhile minimizing the control cost. Robustness is a paramount property for living organisms. The impact degree is a measure of robustness of a metabolic system against the deletion of single or multiple reaction(s). An algorithm is proposed to study the impact degree in Escherichia coli metabolic system. Moreover, approximation method based on Branching process is proposed for estimating the impact degree of metabolic networks. The effectiveness of our method is assured by testing with real-world Escherichia coli, Bacillus subtilis, Saccharomyces cerevisiae and Homo Sapiens metabolic systems. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Rousing applications of robot teams abound over the past three decades, but ferocious demands for viable systems to coordinate teams of mobile robots in dynamic environments still linger on. To meet this challenge, this project proposes a performance optimisation system for mobile robots to make the team performance more reliable and efficient in dynamic environments. A wide range of applications will benefit from the system, such as logistics, military, and disaster rescue. The performance optimisation system comprises three main modules: (1) a task allocation module to assign tasks to robots, (2) a motion planning module to navigate robots, and (3) a graphical simulation module to visualise robot operations and to validate the methodologies of performance optimisation. The task allocation module features a closed-loop bid adjustment mechanism for auctioning tasks to capable robots. Unlike most traditional open-looped methods, each of the robots evaluates its own performance after completing a task as feedback correction to improve its future bid prices of similar tasks. Moreover, a series of adjustments are weighed and averaged to damp out drastic deviations due to operational uncertainties. As such, the accuracy of bid prices is improved, and tasks are more likely allocated to suitable robots that are expected to perform better by offering more reliable bids. The motion planning module is bio-inspired intelligent, characterised by detection of imminent neighbours and design flexibility of virtual forces to enhance the responsiveness of robot motions. Firstly, while similar methods unnecessarily entail each robot to consider all the neighbours, the detection of imminent neighbours instead enables each robot to mimic creatures to identify and only consider imminent neighbours which pose collision dangers. Hence, redundant computations are reduced and undesirable robot movements eliminated. Secondly, to imitate the responsive motion behaviours of creatures, a virtual force method is adopted. It composes virtual attractive forces that drive the robots towards their targets and, simultaneously, exerts virtual repulsive forces to steer the robots away from one another. To enhance the design flexibility of the virtual forces, a twosection function and, more significantly, a spline-based method are proposed. The shapes of force curves can be flexibly designed and adjusted to generate smooth forces with desirable magnitudes. Accordingly, robot motions are streamlined and likelihood of robot collisions reduced. The graphical simulation module simulates and visualises robot team operations, and validates the proposed methodologies. It effectively emulates the operational scenarios and enables engineers to tackle downstream problems earlier in the design cycle. Furthermore, time and costs of robotic system development in the simulation module are considerably cut, compared with a physical counterpart. The performance optimisation system is indeed viable in improving the operational safety and efficiency of robot teams in dynamic environments. It has substantially pushed the frontiers of this field, and may be adapted as an intelligent control software system for practical operations of physical robot teams to benefit various applications. / HKU 3 Minute Thesis Award, 1st Runner-up (2012) / published_or_final_version / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

Computer graphics applications call for various mesh generation techniques to visualize objects, store shape data, perform numerical analyses, etc. Mesh generation is also a fundamental research topic in many other engineering areas related to physical models described by partial differential equations. The reason that meshed surfaces are preferred over spline surfaces in many engineering applications is its flexibility in handling complex objects, while sharp features and boundaries can be represented without trimming, which is highly desired in numerical simulations. In this thesis, we study two methods for generating meshes with sharp features. Sharp features, such as creases and corners, are very common in mechanical objects. Hence effectively handling sharp features is of great importance to this kind of objects. The first method is to generate triangular subdivision surfaces with sharp features. Although there have been various methods to fit subdivision surfaces to different types of shape data, e.g., dense meshes and point clouds, none of these methods can handle sharp features effectively. We present a new exact evaluation scheme for all types of sharp features in Loop subdivision, and integrate the new evaluation scheme into the optimization framework to fit Loop subdivision surfaces to dense meshes. The second method is to generate quadrilateral meshes with varying element sizes which observe the user requirement. This method is inspired by the idea of spectral quadrangulation, but existing spectral quadrangulation methods are limited to closed surfaces due to its lack of proper boundary treatment. We present a new set of boundary conditions, and introduce the Quasi-Eigenfunction to assist the mesh generation process. The proposed boundary treatment is further applied to sharp features to handle mechanical objects. The quasi-eigenfunction based quadrangulation framework is also extended to 3D volumetric domain to generate hexahedral meshes. Experimental results and comparisons with existing methods are presented in each chapter to demonstrate the effectiveness of the proposed methods. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy