STAR Scholars Abstract

Constructing Jacobi Matrices from Mixed Data
Yilin Yang August 13, 2014

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 polynomial, one dimensional Schrödinger operators, the Hamburger moments problem and Sturm-Liouville problem. In the past couple of decades, constructing Jacobi matrices from different types of data was studied intensively. In this paper, we construct Jacobi matrices from a more general data type than considered before. By using the special structure of Jacobi matrix and its eigenpairs, we successfully find a method to recover Jacobi matrices from two eigenpairs by solving a nonhomogeneous linear system and show that the two eigenvalues can be replaced by any two elements of the Jacobi matrices. Meanwhile, we give the conditions of uniqueness and existence of the solution. Furthermore, we prove that different sets of parameters used to recover Jacobi matrices by other authors are equivalent by exploring the direct connections between these different types of mixed data without necessarily recovering the matrices. Also a MATLAB code was developed to compute the Jacobi matrices based on our method.

Volatile organic compounds (VOCs) are carbon-based compounds emitted by industries into the atmosphere and have been known to cause human health issues such as headaches, seizures, fatigue, along with environmental issues, such as smog, acid rain, and poor air quality. The purpose of this study is to study and develop better abatement methods for VOC compounds, specifically dichloromethane (DCM) and tetrahydrofuran (THF). These experiments also examined Pt /Al2O3 as a potential catalyst for both DCM and THF oxidation. By measuring the temperatures and speeds in which DCM and THF are oxidized, one can determine the most effective catalysts for their abatement. Catalytic oxidation tests included: two different concentrations of each compound, combining THF and DCM, addition of water to THF, and combining THF, DCM and water. The experiments were carried out over a period of 6 days, with repetitions of 3 of the tests to ensure the repeatability. Results demonstrate that THF facilitates oxidation when added to DCM, as well as an enhanced HCl yield, and that water hinders the rate of THF oxidation.  

Shape Analysis of Pediatric Thoracic Vertebra using Generalized Procrustes Analysis Spine morphology changes rapidly between birth and skeletal maturity; however, normative changes in thoracic vertebral morphology are not well understood. Hence there is a need to study age-related structural variations in the normative thoracic spine. This study quantifies vertebral shape change as a function of age for the thoracic spines of subjects 1 to 18 years old. Retrospective chest CT scans of skeletally normal subjects (55 female, 45 male) obtained from CHOP were reconstructed using MIMICS v16 (Materialise, Belgium), refined using 3-matic v8 (Materialise, Belgium), and exported to MATLAB r2011b (The MathWorks, Inc., Natick, MA). 30 landmark points were identified on all vertebrae using a custom MATLAB script. Generalized procrustes analyses were performed on landmarks at each thoracic level and gender. Data analysis suggests a correlation between landmark position and age. In the upper half of the thoracic spine, the vertebral body expands axially with age while in the lower half the vertebral body expands axially, laterally, anteriorly, and posteriorly with age. The pedicles at all thoracic levels move medially and enlarge with age as the spinous process extends towards the posterior inferiorly with age. The facets and the posterior of the spinal canal at all thoracic levels move anteriorly with age. The transverse processes above thoracic level eight move superiorly with age while at levels eight and lower the transverse processes either move insignificantly, or drift inferiorly with age. Average shape models like these may be used to aid computational modeling, and the development of patient specific parameterized models.

Slavemakers: The Comparative Neurobiology of Free and Enslaved Worker Ants  

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.

Nitric oxide (NO) is a small, but extremely important biological chemical that functions as a signaling molecule for many cellular processes. Macrophages, a type of immune system cell, secrete high concentrations of NO when attacking infectious microbes. This particular characteristic of macrophages can be simulated by semi-permeable membrane pouches filled with NO-loaded zeolites mixed with a hydrophobic ointment base. Prior research has shown that certain pouches release levels of NO that are capable of killing several types of common wound pathogens. However, literature suggests that the concentrations of NO that are capable of killing microbes, could be harmful to fibroblasts, the cells in a wound responsible for starting the healing and tissue repair processes. The goal for this research project was to expose fibroblasts to pouches known to kill bacteria in order to quantify the effect, detrimental or beneficial. This was done in vitro by submerging the NO pouches using Transwells in cell culture medium where the NO was free to diffuse across to the cell layer. Preliminary results indicate that NO concentrations high enough to kill microbes are only slightly detrimental to fibroblasts which is promising when further developing this novel method for wound care.

Presenter: Ziyin Huang (STAR Scholar 2012) Advisor: Christopher Li, Ph. D.  
Inorganic nanoparticle assemblies can enhance the properties and the performance of nanoparticles. Among the different assemblies, nanoparticle dimer formation has the advantage of producing the smallest possible nanoparticle assembly. During this experiment, silica nanoparticle dimers and Iron(II)(III) Oxide magnetic nanoparticle dimers were assembled and studied. The nanoparticles were attached on difunctionalized poly(ε-caprolactone) (PCL) single crystals formed by self-seeding in n-butanol, and then nanoparticle dimers formed when the polymer single crystals were dissolved and removed in chloroform or in acetone. Silica nanoparticle dimers were manufactured with disilane-functionalized PCL (PCL-disilane) single crystals, and dihydroxy-functionalized PCL (PCL-diol) and dithiol-functionalized PCL (PCL-dithiol) single crystals were used to form Iron(II)(III) Oxide magnetic nanoparticle dimers. Proton nuclear magnetic resonance spectroscopy (1H NMR) was used to examine the end-group functionalization of the synthesized PCL-dithiol. The PCL single crystals’ abilities of attaching nanoparticles depend on their crystallinities, sizes and thicknesses which vary with different self-seeding temperatures and crystallization temperatures. The structures of the polymer single crystals were examined with optical microscopy, and the formations of nanoparticle dimers were observed with transmission electron microscopy (TEM).            
Keywords: nanoparticle, dimer, poly(ε-caprolactone), single crystal