### Implementing a signature-based characterization up to isometry of smooth surfaces

**Advisor:** Cheri Shakiban

**Abstract:** The goal of this research project is to implement a signature-based characterization up to isometry of smooth surfaces. This project iintegrates ideas of using structure and surface geometry to approximately characterize a surface. Our signature characterization is called an anatomical signature curve, which is parametrized by the intrinsic Gaussian curvature of a surface. The signature is calculated along the geodesic path determined by dissecting a surface with respect to its underlying skeleton. In addition, we will also implement a histogram based characterization. In this project, students will work with geometric skeletons, surface geometry, geometric invariants, geodesics, graphs, tessellations, and programming in Matlab.

**Course Work Required**: Calculus III and CISC 130

**Student Researchers**: Robert Klemm, Cassandra Carter, Carol Mikhael

### Matrix Representations of Wavelet Transforms

**Advisor:** Pat Van Fleet

**Abstract:** Orthogonal wavelet transforms act on matrix A by the product W A W^T where W is an orthogonal matrix. Thus, since W^T = W^(-1), the transform is actually a similarity transform. It is easy to see that the wavelet transform T is linear and as such, it should be represented by a single matrix multiplication (T(A) = MA. In this project, we will start by deriving M for the Haar wavelet transformation. Once complete, we will consider finding M for the iterated Haar wavelet transform, other orthogonal families of wavelet transforms, and wavelet packet transforms.

**Background**: The student should have taken MATH 240 and have a good understanding of matrix representations of linear transformations.

**Student Researchers**: Madeline Schuster, Sam Van Fleet

**Final Research Paper**: In Place Computation of Discrete Haar Wavelet

### Hierarchy in Herds: Modeling Dominance and Subordinance

**Advisor:** Paul Ohmann

**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.

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**: Hierarchy in Cow Herds

### Image De-Blurring for Spacecraft Navigation

**Advisor:** Thomas Höft

**Abstract:** Interplanetary spacecraft, including NASA's New Horizons on its recent mission to Pluto, use images of distant stars to aid in navigation correction. Due to the high speed of the spacecraft and dim intensity of the star, these images are corrputed by motion blur. This project will develop inverse problem methods to de-blur such images, with the goal of enabling more accurate and noise-stable navigation correction for future spacecraft.

**Background**: MATH 240 and Matlab programming experience.

**Student Researchers**: Liam Coulter

**Final Research Paper**: Image Deblurring

### Modeling Actin Activation in Moving Cells

**Advisor:** Magda Stolarska

**Abstract:** The polymerization of actin, a filamentous protein that is part of a cell's cytoskeleton, is the driving force behind cell movement. The localization of actin and the speed with which it polymerizes distinguishes between different movements, such as cell spreading and directed cell motility toward an attractant. This localization is controlled by a host of accessory proteins. The goal of this project is to write a mathematical model describing the interaction of the accessory proteins that control actin during cell spreading. In addition, we will solve this model using the finite element method programmed in Matlab and run simulations that allow us to predict the local concentrations of actin and its accessory proteins in a moving cell.

**Background**: MATH 200 and some programming experience

**Student Researchers**: Nick Sheridan

**Final Research Paper**: Modeling Biochemical Interacitons

### Calculating the Probability of a Data Breach

**Advisor:** Arkady Shemyakin

**Abstract:** The goal of this project is to develop a tool that will allow experts in data security, such as Gary Stanull from Optum Inc., to determine the probability of a data breach given certain properties of the data record. One example of such a property is the record size. One approach to this problem is to develop and analyze a statistical model based on various input parameters that can be determined through historical data. Understanding what aspects of security most reduce the probability of a data breach will allow companies to reduce unnecessary spending on security measures that do little to benefit information security. The development of such a model will be beneficial to health care management companies and similar organizations that store large amounts of confidential data. This project falls under the CAMIO program, and students will be working directly with Gary, who will advise them on their progress.

**Student Researchers**: Meghan Anthony, Maria Ishmael, Erik Santa, Natalie Vandeweghe

**Final Research Paper**: Estimating Probability of a Data Breach

### Learning Sasaki's theory of tornado genesis.

**Advisor:** Doug Dokken

**Abstract:** Students will learn Sasaki's theory of tornado genesis. They will run numerical simulations of supercell thunderstorms at UST and MSI. Then analyze the output using visualization tools, such as vis5D. The students will look for evidence supporting Sasaki's theory of tornado genesis. The students will also explore interpretations of Sasaki's path - integral inthe supercel tornado context.

**Background**: Multivariable calculus, Linear algebra, some programming experience.

**Student**: Will Frost

**Final Research Paper**: Sasaki's Entropic Balance Tornadogenesis