# CAM Research Projects Available to Students

Below is a list of CAM Research projects with current openings. If you are interested please apply. It is possible that projects - other than those listed below - are available.

If you have any questions regarding these projects, or the CAM Summer Research program, please send an email to Prof. Magda Stolarska: mastolarska@stthomas.edu

### Extending the method of signature curve to 3D surfaces and develop algorithms to characterize and recognize images corresponding to solid 3D objects.

Abstract: We would like to extend the method of signature curve to 3D surfaces and develop algorithms to characterize and recognize images corresponding to solid 3D objects. In order to extend this method to 3D, we must understand the topology of the three-dimensional objects and introduce new tools.  One such tool is topological skeleton, which is a line-like representation of the shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Together with the distance of its points to the shape boundary, the skeleton can also serve as a representation of the shape.   The topological skeleton when combined with signature curves will give rise to a new method that we will call Skeletal Signature Curve. Skeletal Signature Curve will definitely have applications in medical imaging such as characterizing cancer cells in solid tumors and we plan to investigate these applications.

Course Work Required: MATH 200 and knowledge of Matlab and Mathematica

Student Researchers: Robert Klemm, Lucas Tucker

Skeletal Signature Curves

### This project includes working with Simpson College's differential analyzer.

Abstract: A research student and I will be working on Simpson College’s differential analyzer first to make sure it is working properly then analyzing a particular differential equation(s) on the machine. If time allows, we will develop lesson plans to use the differential analyzer in calculus classes such as Math 108/109.

Background: The student should have knowledge of Differential Equations.

Student Researchers: Abby Sunberg

### Hierarchy in Herds: Modeling Dominance and Subordinance

Abstract: Many studies and observations suggest that animals congregate in herds because of the protective quality that grouping confers. At the same time, individuals in these herds also need to forage or travel to other locations. This study seeks to model the movement of cattle herds by constructing separate algorithms describing dominant and subordinate individuals, using guidance from the following sources:

Radka Sarova, et. al: (2010), "Graded leadership by dominant animals in a herd of female beef cattle on pasture," Animal Behaviour 79: 1037-1045.
Viscido et. al. (2002), "The dilemma of the Selfish Herd: The Search for a Realistic Movement Rule," Journal of Theoretical Biology 217:183-194.

Background: Students should have completed PHYS 112 as well as CISC 130 (or have Matlab experience), along with a good GPA and an ability to work independently with faculty guidance.

Student Researchers: Taryn Kay

### Exploring what happens to propagation time of a directed graph when the orientation of one edge of graph is reversed.

Abstract: An oriented graph is a set of vertices and edges on which one can choose and orientation or direction on each edge, thus creating a directed graph. The zero-forcing game on directed graphs is similar to that on undirected graphs in that any filled vertex is allowed to fill a neighbor vertex if the filled vertex has only one unfilled out neighbor.  The propagation time is how many steps are required to fill the entire graph.  In this project the student will explore what happens to the propagation time when the orientation of one edge is reversed.

Background: There are no prerequisites.

Student Researchers:

### Modeling non-equilibrium properties of a tornado layer.

Abstract:The goal of this project is to use meteorological data for modeling non-equilibrium properties of a tornado layer.

Course Work Required: MATH 114 is required. MATH 200 and/or MATH 210 is/are preferred.

Student Researchers: