# Current Research Projects

Below is a list of our summer 2017 student research projects. For more information click on the title of the project.

### 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, Annelia Anderson

Final Research Paper: 2017 CAM Klemm Tucker Anderson

### 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

Final Research Paper: 2017 CAM 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

Final Research Paper: 2017 CAM 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:Mitch Perila, Kristen Rutschke

Final Research Paper: 2017 CAM Rutschke Perila

### 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: George McGivern, Brad Walton

Final Research Paper: 2017 CAM McGivern Walton

### Error Correction and QR Codes

Abstract: Ever wonder how information is stored on your latest Blu-ray disc? How are you able to connect almost instantaneously with your friends through text messaging? How is it possible to scan a QR code with your cell phone and be brought immediately to a website? The answer is coding theory. In this project, students will be introduced to coding theory and, in particular, explore how QR codes are encoded. In addition, students will research encrypted QR codes.

Background: Linear algebra and programming experience is preferred.

Student Researchers: Grant Barland

Final Research Paper: 2017 CAM Barland

### Using numerical modeling to constrain the timing and duration of faulting in the Ama Drime Range, southernmost Tibet.

Abstract: The Ama Drime Range, located ~ 70 kilometers to the northeast of Mt. Everest, is bound on both the east and west by N-S striking extensional faults. Numerous time-temperature datasets exist to help constrain the timing and duration of slip along the range bounding faults, but the data alone cannot confidently differentiate between continuous slip on single fault strands or phased slip on multiple faults. The goal of the project is to use a thermo-kinematic finite-element numerical model (Pecube) to test for tectonic scenarios consistent with the time-temperature data.

Background: (1) an introductory geology course (Geol 1xx), (2) Calculus I or higher with a grade of at least a C.

Student Researchers: Claire Rubio

Final Research Paper: 2017 CAM Summer McDermott

### Estimating the Probability of Cybersecurity Breach

Abstract: This project is a continuation of the cybersecurity study carried out as CAM projects in 2015-2017. An important variable in cybersecurity studies effecting probability and severity of a breach is the size (number of records) of a database application. The value of this variable is not always available and has to be estimated. The goal of the project is to analyze proxy variables for database application size (company revenue, total assets and total employment) with the emphasis on financial and medical companies. Tools of the study include regression and correlation analysis. UST library provides assistance with data collection and clean-up.

Background:

Student Researchers:Christina Dau, Maria Ishmael. Also Matt Ehren (Washington University, St. Louis). Co-advisor Gary Stanull, Optum.

Final Report Paper: Cybersecurity Risk CAM 2017

### Copula Models of Economic Capital for Insurance Companies

Abstract:  Financial and economic variables have proven notoriously difficult to forecast, and a perfect example of the necessities of accurate predictions is the financial crisis in 2008. We model one such financial variable, economic capital, particularly for life insurance companies.

Economic capital is defined as the amount of capital that a firm, usually in financial services, needs to ensure that the company stays solvent given its risk profile. Economic capital implies a deeper examination of correlation and distribution of risks and assets, as opposed to the more formulaic risked based capital.

The novelty in our approach is the application of copula models, or a multivariate probability distribution used to describe non-linear and tail dependence between random variables forming asset/liability portfolio of a life insurance company, particularly in the low interest environment insurance companies currently face.

In summer we concentrate on the asset variables defined with the help of Bloomberg indices. The work requires access to UST Bloomberg terminal. The continuation of the project under research grant of the Society of Actuaries is planned for the academic year 2017/2018 and will expand to liability variables as well.

Background:

Student Researchers:Jessica Mohr, Thomas Vlasak.

Final Report Paper: 2017 CAM Mohr Vlasak