Digital Commons Network^™

Some Results On A Set Of Data Driven Stochastic Wildfire Models, Maxfield E. Green

Graduate College Dissertations and Theses

Across the globe, the frequency and size of wildfire events are increasing. Research focused on minimizing wildfire is critically needed to mitigate impending humanitarian and environmental crises. Real-time wildfire response is dependent on timely and accurate prediction of dynamic wildfire fronts. Current models used to inform decisions made by the U.S. Forest Service, such as Farsite, FlamMap and Behave do not incorporate modern remotely sensed wildfire records and are typically deterministic, making uncertainty calculations difficult. In this research, we tested two methods that combine artificial intelligence with remote sensing data. First, a stochastic cellular automata that learns algebraic expressions was …

Extremal/Saturation Numbers For Guessing Numbers Of Undirected Graphs, Jo Ryder Martin

Graduate College Dissertations and Theses

Hat guessing games—logic puzzles where a group of players must try to guess the color of their own hat—have been a fun party game for decades but have become of academic interest to mathematicians and computer scientists in the past 20 years. In 2006, Søren Riis, a computer scientist, introduced a new variant of the hat guessing game as well as an associated graph invariant, the guessing number, that has applications to network coding and circuit complexity. In this thesis, to better understand the nature of the guessing number of undirected graphs we apply the concept of saturation to guessing …

Reference Governors For Time-Varying Systems And Constraints, Collin Freiheit

Graduate College Dissertations and Theses

Control systems are often subject to constraints imposed by physical limitations or safety considerations, and require means of constraint management to ensure the stability and safety of the system. For real-time implementation, constraint management schemes must not carry a heavy computational burden; however many of the current solutions are computationally unattractive, especially those with robust formulations. Thus, the design of constraint management schemes with low computational loads is an important and practical problem for control engineers. Reference Governor (RG) is an efficient constraint management scheme that is attractive for real-time implementation due to its low computational complexity and ease of …

The Circuit And Cocircuit Lattices Of A Regular Matroid, Patrick Mullins

Graduate College Dissertations and Theses

A matroid abstracts the notions of dependence common to linear algebra, graph theory, and geometry. We show the equivalence of some of the various axiom systems which define a matroid and examine the concepts of matroid minors and duality before moving on to those matroids which can be represented by a matrix over any field, known as regular matroids. Placing an orientation on a regular matroid allows us to define certain lattices (discrete groups) associated to the matroid. These allow us to construct the Jacobian group of a regular matroid analogous to the Jacobian group of a graph. We then …

On The Dynamics And Structure Of Multiple Strain Epidemic Models And Genotype Networks, Blake Joseph Mitchell Williams

Graduate College Dissertations and Theses

Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as contact structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics.

This body of work first explores the role of strain-transcending immunity in mathematical disease models, …