The following thesis proposes solutions to problems in two main areas of focus, computer vision and machine learning. Chapter 2 utilizes traditional computer vision methods implemented in a novel manner to successfully identify overlays contained in broadcast footage. The remaining chapters explore machine learning algorithms and apply them in various manners to big data, multi-channel image data, and ECG data. L1 and L2 principal component analysis (PCA) algorithms are implemented and tested against each other in Python, providing a metric for future implementations. Selected algorithms from this set are then applied in conjunction with other methods to solve three distinct problems. The first problem is that of big data error detection, where PCA is effectively paired with statistical signal processing methods to create a weighted controlled algorithm. Problem 2 is an implementation of image fusion built to detect and remove noise from multispectral satellite imagery, that performs at a high level. The final problem examines ECG medical data classification. PCA is integrated into a neural network solution that achieves a small performance degradation while requiring less then 20% of the full data size.

This thesis targets at providing an algebraic method to indicate network behaviors. Furthermore, for a signed-average consensus problem of the system behaviors, event-triggering signed-average algorithms are designed to reduce the communication overheads. In Chapter 1, the background is introduced, and the problem is formulated. In Chapter 2, notations and basics of graph theory are presented. It is known that the terminal value of the system state is determined by the initial state, left eigenvector and right eigenvector associated with zero eigenvalue of the Laplacian matrix. Since there is no mathematical expression of right eigenvector, in Chapter 3, mathematical expression of right eigenvector is given. In Chapter 4, algebraic trait for structurally balanced property of a node is proposed. In Chapter 5, a method for characterization of collective behaviors under directed signed networks is developed. In Chapter 6, dynamic event-triggering signed-average algorithms are proposed and proved for the purpose of relieving the communication burden between agents. Chapter 7 summarizes the thesis and gives future directions.

This thesis presents a series of neural network classifiers for object detection in both optical and infrared images. The focus of this work is on efficient and accurate solutions. The thesis discusses the evolution of the highly efficient and tiny network Binary Classification Vision Transformer (BC-ViT) and how through thoughtful modifications and improvements, the BC-ViT can be utilized for tasks of increasing complexity. Chapter 2 discusses the creation of BC-ViT and its initial use case for underwater image classification of optical images. The BC-ViT is able to complete its task with an accuracy of 99.29\% while being comprised of a mere 15,981 total trainable parameters. Chapter 3, Waste Multi-Class Vision Transformer (WMC-ViT), introduces the usefulness of mindful algorithm design for the realm of multi-class classification on a mutually exclusive dataset. WMC-ViT shows that the task oriented design strategy allowed for a network to achieve an accuracy score of 94.27\% on a five class problem while still maintaining a tiny parameter count of 35,492. The final chapter demonstrates that by utilizing functional blocks of BC-ViT, a simple and effective target detection algorithm for infrared images can be created. The Edge Infrared Vision Transformer (EIR-ViT) showed admirable results with a high IoU …

In the era of big data, it is essential to implement practical security and privacy measures to ensure the lawful use of data and provide users with trust and assurance. In the dissertation, I address this issue through several key steps. Firstly, I delve into the problem of conditional secret disclosure, representing it using graphs to determine the most efficient approach for storing and disclosing secrets. Secondly, I extend the conditional disclosure of secrets problem from a single secret to multiple secrets and from a bipartite graph to an arbitrary graph. Thirdly, I remove security constraints to observe how they affect the efficiency of storage and recovery. In our final paper, I explore the secure summation problem, aiming to determine the capacity of total noise. Throughout the dissertation, I leverage information-theoretic tools to address security and privacy concerns.

Air corridors are an integral part of the advanced air mobility infrastructure. They are the virtual highways in the sky for transportation of people and cargo in the controlled airspace at an altitude of around 1000 ft. to 2000 ft. above the ground level. This paper presents fundamental insights into the design of air corridors with high operational efficiency as well as zero collisions. It begins with the definitions of air cube, skylane or track, intersection, vertiport, gate, and air corridor. Then, a multi-layered air corridor model is proposed. Traffic at intersections is analyzed in detail with examples of vehicles turning in different directions. The concept of capacity of an air corridor is introduced along with the nature of distribution of locations of vehicles in the air corridor and collision probability inside the corridor are discussed. Finally, the results of simulations of traffic flows are presented.