Physical Sciences and Mathematics Commons^™

Design And Analysis Of Strategic Behavior In Networks, Sixie Yu

McKelvey School of Engineering Theses & Dissertations

Networks permeate every aspect of our social and professional life.A networked system with strategic individuals can represent a variety of real-world scenarios with socioeconomic origins. In such a system, the individuals' utilities are interdependent---one individual's decision influences the decisions of others and vice versa. In order to gain insights into the system, the highly complicated interactions necessitate some level of abstraction. To capture the otherwise complex interactions, I use a game theoretic model called Networked Public Goods (NPG) game. I develop a computational framework based on NPGs to understand strategic individuals' behavior in networked systems. The framework consists of three …

Model-Based Deep Learning For Computational Imaging, Xiaojian Xu

McKelvey School of Engineering Theses & Dissertations

This dissertation addresses model-based deep learning for computational imaging. The motivation of our work is driven by the increasing interests in the combination of imaging model, which provides data-consistency guarantees to the observed measurements, and deep learning, which provides advanced prior modeling driven by data. Following this idea, we develop multiple algorithms by integrating the classical model-based optimization and modern deep learning to enable efficient and reliable imaging. We demonstrate the performance of our algorithms by validating their performance on various imaging applications and providing rigorous theoretical analysis.

The dissertation evaluates and extends three general frameworks, plug-and-play priors (PnP), regularized …

Geometric Algorithms For Modeling Plant Roots From Images, Dan Zeng

McKelvey School of Engineering Theses & Dissertations

Roots, considered as the ”hidden half of the plant”, are essential to a plant’s health and pro- ductivity. Understanding root architecture has the potential to enhance efforts towards im- proving crop yield. In this dissertation we develop geometric approaches to non-destructively characterize the full architecture of the root system from 3D imaging while making com- putational advances in topological optimization. First, we develop a global optimization algorithm to remove topological noise, with applications in both root imaging and com- puter graphics. Second, we use our topology simplification algorithm, other methods from computer graphics, and customized algorithms to develop a high-throughput …

Continuous-Time And Complex Growth Transforms For Analog Computing And Optimization, Oindrila Chatterjee

McKelvey School of Engineering Theses & Dissertations

Analog computing is a promising and practical candidate for solving complex computational problems involving algebraic and differential equations. At the fundamental level, an analog computing framework can be viewed as a dynamical system that evolves following fundamental physical principles, like energy minimization, to solve a computing task. Additionally, conservation laws, such as conservation of charge, energy, or mass, provide a natural way to couple and constrain spatially separated variables. Taking a cue from these observations, in this dissertation, I have explored a novel dynamical system-based computing framework that exploits naturally occurring analog conservation constraints to solve a variety of optimization …

Machine Learning Morphisms: A Framework For Designing And Analyzing Machine Learning Work Ows, Applied To Separability, Error Bounds, And 30-Day Hospital Readmissions, Eric Zenon Cawi

McKelvey School of Engineering Theses & Dissertations

A machine learning workflow is the sequence of tasks necessary to implement a machine learning application, including data collection, preprocessing, feature engineering, exploratory analysis, and model training/selection. In this dissertation we propose the Machine Learning Morphism (MLM) as a mathematical framework to describe the tasks in a workflow. The MLM is a tuple consisting of: Input Space, Output Space, Learning Morphism, Parameter Prior, Empirical Risk Function. This contains the information necessary to learn the parameters of the learning morphism, which represents a workflow task. In chapter 1, we give a short review of typical tasks present in a workflow, as …

A General Framework Of Large-Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques, Soysal Degirmenci

McKelvey School of Engineering Theses & Dissertations

In a world where data rates are growing faster than computing power, algorithmic acceleration based on developments in mathematical optimization plays a crucial role in narrowing the gap between the two. As the scale of optimization problems in many fields is getting larger, we need faster optimization methods that not only work well in theory, but also work well in practice by exploiting underlying state-of-the-art computing technology.

In this document, we introduce a unified framework of large-scale convex optimization using Jensen surrogates, an iterative optimization method that has been used in different fields since the 1970s. After this general treatment, …