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Full-Text Articles in Physical Sciences and Mathematics
Tropical Linear Algebra: Notions Of Rank Over The Tropical Semiring, William D. Wise
Tropical Linear Algebra: Notions Of Rank Over The Tropical Semiring, William D. Wise
Honors Papers
Three formulations of the rank of a matrix that are equivalent in classical linear algebra give rise to distinct notions of rank over the tropical semiring. This paper explores these three concepts of tropical rank and their relationships with one another, working up to a proof of the inequality that relates the three.
Pillars And Buttes: A Petrologic Comparison Of Modern And Ancient Hydrocarbon Seep Rock, Erica C. Morelli
Pillars And Buttes: A Petrologic Comparison Of Modern And Ancient Hydrocarbon Seep Rock, Erica C. Morelli
Honors Papers
Purpose: Literature on the formation of authigenic rock at cold seeps focuses on the role of microbes in creating geochemically favorable environment for the precipitation of carbonate and barite minerals. Less understood is the pathway that lithified microbial patches of seafloor sediment follow to become rock formations that are identified in strata dating back to the Silurian. In this study I will compare Holocene seep rock from the Gulf of Mexico to Cretaceous carbonates that have been identified as seep rock. Through the study of rock in its early stages of formation to rock that has likely undergone multiple phases …
Selfish Routing On Dynamic Flows, Christine Marie Antonsen
Selfish Routing On Dynamic Flows, Christine Marie Antonsen
Honors Papers
Selfish routing on dynamic flows over time is used to model scenarios that vary with time in which individual agents act in their best interest. In this paper we provide a survey of a particular dynamic model, the deterministic queuing model, and discuss how the model can be adjusted and applied to different real-life scenarios. We then examine how these adjustments affect the computability, optimality, and existence of selfish routings.
Chaos And Learning In Discrete-Time Neural Networks, Jess M. Banks
Chaos And Learning In Discrete-Time Neural Networks, Jess M. Banks
Honors Papers
We study a family of discrete-time recurrent neural network models in which the synaptic connectivity changes slowly with respect to the neuronal dynamics. The fast (neuronal) dynamics of these models display a wealth of behaviors ranging from simple convergence and oscillation to chaos, and the addition of slow (synaptic) dynamics which mimic the biological mechanisms of learning and memory induces complex multiscale dynamics which render rigorous analysis quite difficult. Nevertheless, we prove a general result on the interplay of these two dynamical timescales, demarcating a regime of parameter space within which a gradual dampening of chaotic neuronal behavior is induced …
Arrow: A Modern Reversible Programming Language, Eli Rose
Arrow: A Modern Reversible Programming Language, Eli Rose
Honors Papers
Reversible programming languages are those whose programs can be run backwards as well as forwards. This condition impacts even the most basic constructs, such as =, if and while. I discuss Janus, the first imperative reversible programming language, and its limitations. I then introduce Arrow, a reversible language with modern features, including functions. Example programs are provided.