Student Posters at the SACNAS 2003 Meeting
The 2003 SACNAS Undergraduate Poster Award winner was A Mathematical Model for Photoreceptor Interactions (Poster 396), presented by Daniel J. Hernandez, Jon Van Laarhoven, Ubaldo Rodríguez Bernier and Miguel Angel Cólón Vélez (Carlos Castillo-Chavez, advisor), Los Alamos National Laboratory, Los Alamos, NM
The abstract published in the SACNAS conference program:
The retina is arguably the single most important component of the vision process. It is responsible for converting electromagnetic radiation into a chemical signal understandable by the brain. The interactions between photoreceptor cells in the retina have been the focus of innumerable biological studies in previous decades, yet this interaction has not yet been completely understood. In an effort to gain insight, this paper takes a different approach: we investigate the rod-cone interactions from a mathematical perspective. We develop models which address the possibility of direct photoreceptor interactions via horizontal and amacrine cells as well as investigating indirect interactions via an intermediary trophic factor. A time delay is incorporated into the governing equations and the model is adapted for degenerative diseases, specifically Retinitis Pigmentosa. The model without disease contains Hopf bifurcations, and the model with disease contains even more interesting dynamic behavior. The dynamic behaviors of these models are interpreted to point out possibilities in treatment for degenerative retinal diseases.
Listed below are the other student posters on mathematics presented in the exhibit hall on Friday afternoon and Saturday morning. The presenter's name is in bold:
The Greenhouse Effect, An Applied Mathematical Model. Poster 386. Christina N. Alva (Gregory Wene, advisor), University of Texas at San Antonio, TX
Other Dispersion Properties of Some Interleavers for Turbo Codes. Poster 387. Carlos F. Avenancio (Ivelisse Rubio, advisor), University of Puerto Rico-Humacao, PR
Parallel Transport and Curvature in Differential Geometry and in Theoretical Physics. Poster 388. Kamal K. Barley (Anthony Phillips, advisor), SUNY-Stony Brook, NY
Global Predictions of HIV Infection by Subtype in 2004 and 2010. Poster 389. Brandon J. Brown (Louxin Zhang, advisor), National University of Singapore
Numerical Integration of the Levy Motion Driven Stochastic Differential Equation with Drift and Sticky Boundaries for Motile Microbes. Poster 390. Adele M. Douglin (John H. Cushman, advisor), Purdue University, West Lafayette, IN
The Effects of Student-Teacher Ratio on Student and Faculty Performance in High School Scenarios. Poster 391. Cassie J. Fett, Griselle Torres-Garcia and Katie Diaz (Carlos Castillo-Chavez, advisor), Mathematical and Theoretical Biology Institute, Cornell University, Ithaca, NY
A Numerical Simulation of Flagellar Motion. Poster 392. Heather A. Flores, Stefan Mendez-Diez and Edgar Lobaton (Ricardo Cortez, advisor), Tulane University, New Orleans, LA
Change in Host Behavior and Its Impact on the Co-Evolution of Dengue. Poster 393. Chad P. Gonzales, David Murillo and Karen M. Herman (Carlos Castillo-Chavez, advisor), Los Alamos National Laboratory, Los Alamos, NM
Scaling Laws and the Dynamics of Interracial and Multi-Ethnic Mixing. Poster 394. Magdaliz Gorritz, Gloria Martinez and Jorge Bracamonte (Carlos Castillo-Chavez, advisor), Los Alamos National Laboratory, Los Alamos, NM
On Lower Bounds for the Independence Number of a Graph. Poster 395. Iride V. Gramajo (Ermelinda G. DeLaViña, advisor), University of Houston-Downtown, Houston, TX
Properties of a Type of Permutations Over Finite Fields. Poster 397. Yara B. Luis and Luis O. Perez (Ivelisse Rubio, advisor), University of Puerto Rico at Humacao, Humacao, PR
Dynamical Systems Over Finite Rings. Poster 398. José G. Miranda-Negron and Aida Liz González (Maria A. Aviñó-Diaz, advisor), Agosto University of Puerto Rico at Cayey, Cayey, PR
Zeros of Littlewood Polynomials. Poster 399. Sonny Mohammadzadeh and Juan Carlos Trujillo (Kevin G. Hare, advisor), University of Califoirnia Berkeley, CA
Modeling Bacterial Conjugation. Poster 400. Maria Osorio (John H. Cushman, advisor), Purdue University, West Lafayette, IN
Semi-Parametric Mass Estimates for the Milky Way and Andromeda Halos. Poster 401. Neeraj B. Pradhan, Ivan Barrientos, Anne McIntyre and David Wilkerson (Javier Rojo, advisor), Rice University, Houston, TX
An Integrated Model of a Swimming Sunfish. Poster 402. Tiffany M. Psemeneki (Rob Root, advisor), Mathematics Summer REU, Lafayette College, Easton, PA
Wallpaper: The Mathematics of Art. Poster 403. Nancy Rodriguez and Maya Johnson, Miami University, Oxford, OH
Semiclassical Wave-Packet Scattering in One and Two Dimension. Poster 404. Ivan D. Rothstein (George A. Hagedorn, advisor), Virginia Tech, Blacksburg, VA
A Comparison of the Effect of Genotyping Error on the Power of Armitage Trend Test and the 2X3 Chi-Squared Test in Di-Allelic Genetic Association Studies. Poster 405. Rose Saint Fleur, Sun J. Kang and Derek Gordon (Stephen J. Finch, advisor), SUNY-Stony Brook, Stony Brook, NY
Comparison of Temperature Variations in the Earth's Mesopause. Poster 406. Tamara D. Singleton (Maura Hagan, advisor), National Center for Atmospheric Research, Boulder, CO
A Deterministic Approach to the Spread of Rumors. Poster 407. Keinan A. Thompson, Darryl T. Daugherty and Reynaldo Castro Estrada (Carlos Castillo-Chavez, advisor), Los Alamos national Laboratory, Los Alamos, NM
The kaplan-Meier Estimator, A Look at Bias in the Small-Sample Case. Poster 408. Sarah J. Williams, Karl Calderon and Tollie Thigpen (Javier Rojo, advisor), Rice University, Houston, TX
Visit the AMS Careers and Education web pages or email prof-serv@ams.org for more information on graduate studies in mathematics.
Read more about Mathematics at the 2002 SACNAS Meeting and a report on the 2001 SACNAS Meeting.