3D Ionospheric Effects on HF Propagation and Heating

The thesis uses a three-dimensional, first-principles model of the ionosphere in combination with High Frequency (HF) raytracing model to address key topics related to the physics of HF propagation and artificial ionospheric heating. In particular: 1. Explores the effect of the ubiquitous electron density gradients caused by Medium Scale Traveling Ionospheric Disturbances (MSTIDs) on high-angle of incidence HF radio wave propagation. Previous studies neglected the all-important presence of horizontal gradients in both the cross- and down-range directions, which refract the HF waves, significantly changing their path through the ionosphere. The physics-based ionosphere model SAMI3/ESF is used to generate a self-consistently evolving MSTID that allows for the examination of the spatio-temporal progression of the HF radio waves in the ionosphere. 2. Tests the potential and determines engineering requirements for ground- based high power HF heaters to trigger and control the evolution of Equatorial Spread F (ESF). Interference from ESF on radio wave propagation through the ionosphere remains a critical issue on HF systems reliability. Artificial HF heating has been shown to create plasma density cavities in the ionosphere similar to those that may trigger ESF bubbles. The work explores whether HF heating may trigger or control ESF bubbles. 3. Uses the combined ionosphere and HF raytracing models to create the first self-consistent HF Heating model. This model is utilized to simulate results from an Arecibo experiment and to provide understanding of the physical mechanism behind observed phenomena. The insights gained provide engineering guidance for new artificial heaters that are being built for use in low to middle latitude regions. In accomplishing the above topics: (i) I generated a model MSTID using the SAMI3/ESF code, and used a raytrace model to examine the effects of the MSTID gradients on radio wave propagation observables; (ii) I implemented a three- dimensional HF heating model in SAMI3/ESF and used the model to determine whether HF heating could artificially generate an ESF bubble; (iii) I created the first self-consistent model for artificial HF heating using the SAMI3/ESF ionosphere model and the MoJo raytrace model and ran a series of simulations that successfully modeled the results of early artificial heating experiments at Arecibo.

Data-Driven Wildfire Propagation Modeling with FARSITE-EnKF

The goal of this study is to provide a framework for future researchers to understand and use the FARSITE wildfire-forecasting model with data assimilation. Current wildfire models lack the ability to provide accurate prediction of fire front position faster than real-time. When FARSITE is coupled with a recursive ensemble filter, the data assimilation forecast method improves. The scope includes an explanation of the standalone FARSITE application, technical details on FARSITE integration with a parallel program coupler called OpenPALM, and a model demonstration of the FARSITE-Ensemble Kalman Filter software using the FireFlux I experiment by Craig Clements. The results show that the fire front forecast is improved with the proposed data-driven methodology than with the standalone FARSITE model.

Mathematical Programming Models for Influence Maximization on Social Networks

In this dissertation, we apply mathematical programming techniques (i.e., integer programming and polyhedral combinatorics) to develop exact approaches for influence maximization on social networks. We study four combinatorial optimization problems that deal with maximizing influence at minimum cost over a social network. To our knowl- edge, all previous work to date involving influence maximization problems has focused on heuristics and approximation. We start with the following viral marketing problem that has attracted a significant amount of interest from the computer science literature. Given a social network, find a target set of customers to seed with a product. Then, a cascade will be caused by these initial adopters and other people start to adopt this product due to the influence they re- ceive from earlier adopters. The idea is to find the minimum cost that results in the entire network adopting the product. We first study a problem called the Weighted Target Set Selection (WTSS) Prob- lem. In the WTSS problem, the diffusion can take place over as many time periods as needed and a free product is given out to the individuals in the target set. Restricting the number of time periods that the diffusion takes place over to be one, we obtain a problem called the Positive Influence Dominating Set (PIDS) problem. Next, incorporating partial incentives, we consider a problem called the Least Cost Influence Problem (LCIP). The fourth problem studied is the One Time Period Least Cost Influence Problem (1TPLCIP) which is identical to the LCIP except that we restrict the number of time periods that the diffusion takes place over to be one. We apply a common research paradigm to each of these four problems. First, we work on special graphs: trees and cycles. Based on the insights we obtain from special graphs, we develop efficient methods for general graphs. On trees, first, we propose a polynomial time algorithm. More importantly, we present a tight and compact extended formulation. We also project the extended formulation onto the space of the natural vari- ables that gives the polytope on trees. Next, building upon the result for trees---we derive the polytope on cycles for the WTSS problem; as well as a polynomial time algorithm on cycles. This leads to our contribution on general graphs. For the WTSS problem and the LCIP, using the observation that the influence propagation network must be a directed acyclic graph (DAG), the strong formulation for trees can be embedded into a formulation on general graphs. We use this to design and implement a branch-and-cut approach for the WTSS problem and the LCIP. In our computational study, we are able to obtain high quality solutions for random graph instances with up to 10,000 nodes and 20,000 edges (40,000 arcs) within a reasonable amount of time.