Abstract Submitted for Presentation

The current standard of care for breast cancer screening is a combination ofmammography, clinical breast exams, and magnetic resonance imaging (MRI).MRI imaging is extremely valuable in cases with dense or scarred breast tissue;however, the integration of MRI is often not covered by insurance for screeningpurposes and is, therefore, often not conducted. Radiographic alternatives toMRI are avoided due to the risk associated with the increase exposure dose.Volumetric ultrasound imaging, while inadequate for standalone screening, is apotential solution for complex screening cases if the modality can be fused withmammography projections. The additional information provided by volumetricultrasound allows for clearer discrimination between soft tissues possessing sim-ilar radiographic density. This project aims to fuse volumetric ultrasound withmammography projections by developing a new registration algorithm. Thisalgorithm reduces the dimensionality of the volumetric ultrasound to that ofthe target mammography projection and subsequently employs a mutual in-formation based similarity metric to frame the data fusion as an optimizationproblem.

On some Jacobi Matrix Inverse Eigenvalue Problems with Mixed Given Data
CN-04

Yilin Yang
Advisor(s): Lei Cao

Undergraduate Student
College of Arts and Sciences
Mathematics

Jacobi matrices (real symmetric tridiagonal matrices) have a wide range of applications in physics and engineering, and are closely and non-trivially linked with many other mathematical objects, such as orthogonal polynomials, one dimensional Schrödinger operators, and the Sturm-Liouville problem. In the past couple of decades, constructing Jacobi matrices from different types of data was studied intensively. In this research, we construct Jacobi matrices from two new types of data, and thus providing some new methods for solving inverse eigenvalue problem of Jacobi matrices. Using its special structure, we firstly show that a Jacobi matrix can be reconstructed from two eigenpairs by solving a nonhomogeneous linear system. Secondly, we show that a unique Jacobi matrix J could be determined by the eigenvalues of J, the eigenvalues of the submatrix obtained by removing the first two rows and columns from J and an arbitrary entry of J. Furthermore, we summarize equivalent sets of parameters used to recover Jacobi matrices and show some direct connections among these sets.

Event: Drexel University College of Medicine Discovery Day 
Date: October 3rd, 2013
Type: Poster 
Title: Slavemakers: The Comparative Neurobiology of Free and Enslaved Worker Ants

Abstract:
Ants are social insects with thousands of species worldwide. Some ants establish complex symbiotic relationships with other ant species, such as the unique behavior of slavemaking. This study focuses on the socially parasitic slavemaster behavior of ant species, Formica fusca and Polyergus. Polyergus ants, the “slavemakers”, depend on enslaved F. fusca ants, which they steal as unhatched pupae from their parent colonies and raise as workers in their own colony. We predict that Polyergus brain functions have diminished because they have become so dependent on their slaves. This result suggests that slaves are actually “smarter” than their Polyergus masters. Yet not all F. fusca individuals are slaves, and differences in slave status may be reflected in sensory brain investment. By using sectioning and imaging methods, we quantified brain volumes of free and enslaved F. fusca. By comparing the brain volumes of the optic and antennal sensory regions, we determined to what extent slave or free individuals were visually or chemically oriented. Little is known about these ant species and these results may lead to further insight into their social behavior.