Matching Items (3)

152943-Thumbnail Image.png

A two strain spatiotemporal mathematical model of cancer with free boundary condition

Description

In a 2004 paper, John Nagy raised the possibility of the existence of a hypertumor \emph{i.e.}, a focus of aggressively reproducing parenchyma cells that invade part or all of a tumor. His model used a system of nonlinear ordinary differential

In a 2004 paper, John Nagy raised the possibility of the existence of a hypertumor \emph{i.e.}, a focus of aggressively reproducing parenchyma cells that invade part or all of a tumor. His model used a system of nonlinear ordinary differential equations to find a suitable set of conditions for which these hypertumors exist. Here that model is expanded by transforming it into a system of nonlinear partial differential equations with diffusion, advection, and a free boundary condition to represent a radially symmetric tumor growth. Two strains of parenchymal cells are incorporated; one forming almost the entirety of the tumor while the much more aggressive strain

appears in a smaller region inside of the tumor. Simulations show that if the aggressive strain focuses its efforts on proliferating and does not contribute to angiogenesis signaling when in a hypoxic state, a hypertumor will form. More importantly, this resultant aggressive tumor is paradoxically prone to extinction and hypothesize is the cause of necrosis in many vascularized tumors.

Contributors

Agent

Created

Date Created
2014

157856-Thumbnail Image.png

Undergraduate Students’ Conceptions of Multiple Analytic Representations of Systems (of Equations)

Description

The extent of students’ struggles in linear algebra courses is at times surprising to mathematicians and instructors. To gain insight into the challenges, the central question I investigated for this project was: What is the nature of undergraduate students’ conceptions

The extent of students’ struggles in linear algebra courses is at times surprising to mathematicians and instructors. To gain insight into the challenges, the central question I investigated for this project was: What is the nature of undergraduate students’ conceptions of multiple analytic representations of systems (of equations)?

My methodological choices for this study included the use of one-on-one, task-based clinical interviews which were video and audio recorded. Participants were chosen on the basis of selection criteria applied to a pool of volunteers from junior-level applied linear algebra classes. I conducted both generative and convergent analyses in terms of Clement’s (2000) continuum of research purposes. The generative analysis involved an exploration of the data (in transcript form). The convergent analysis involved the analysis of two student interviews through the lenses of Duval’s (1997, 2006, 2017) Theory of Semiotic Representation Registers and a theory I propose, the Theory of Quantitative Systems.

All participants concluded that for the four representations in this study, the notation was varying while the solution was invariant. Their descriptions of what was represented by the various representations fell into distinct categories. Further, the students employed visual techniques, heuristics, metaphors, and mathematical computation to account for translations between the various representations.

Theoretically, I lay out some constructs that may help with awareness of the complexity in linear algebra. While there are many rich concepts in linear algebra, challenges may stem from less-than-robust communication. Further, mathematics at the level of linear algebra requires a much broader perspective than that of the ordinary algebra of real numbers. Empirically, my results and findings provide important insights into students’ conceptions. The study revealed that students consider and/or can have their interest piqued by such things as changes in register.

The lens I propose along with the empirical findings should stimulate conversations that result in linear algebra courses most beneficial to students. This is especially important since students who encounter undue difficulties may alter their intended plans of study, plans which would lead them into careers in STEM (Science, Technology, Engineering, & Mathematics) fields.

Contributors

Agent

Created

Date Created
2019

161274-Thumbnail Image.png

Energy Use Scaling and Alarm Spread in Social Ants: An Investigation Using Multi-agent Simulation and Object Tracking

Description

Social insect groups, such as bees, termites, and ants, epitomize the emergence of group-level behaviors from the aggregated actions and interactions of individuals. Ants have the unique advantage that whole colonies can be observed in artificial, laboratory nests, and each

Social insect groups, such as bees, termites, and ants, epitomize the emergence of group-level behaviors from the aggregated actions and interactions of individuals. Ants have the unique advantage that whole colonies can be observed in artificial, laboratory nests, and each individual's behavior can be continuously tracked using imaging software. In this dissertation, I study two group behaviors: (1) the spread of alarm signals from three agitated ants to a group of 61 quiescent nestmates, and (2) the reduction in per-capita energy use as colonies scale in size from tens of ants to thousands. For my first experiment, I track the motion of Pogonomyrmex californicus ants using an overhead camera, and I analyze how propagation of an initial alarm stimulus affects their walking speeds. I then build an agent-based model that simulates two-dimensional ant motion and the spread of the alarmed state. I find that implementing a simple set of rules for motion and alarm signal transmission reproduces the empirically observed speed dynamics. For the second experiment, I simulate social insect colony workers that collectively complete a set of tasks. By assuming that task switching is energetically costly, my model recovers a metabolic rate scaling pattern, known as hypometric metabolic scaling. This relationship, which predicts an organism's metabolic rate from its mass, is observed across a diverse set of social insect groups and animal species. The results suggest an explicit link between the degree of workers' task specialization and whole-colony energy use.

Contributors

Agent

Created

Date Created
2021