3rd Annual TX-LA Undergraduate Mathematics Conference
Texas A&M University, College Station, TX
October 19-20, 2019
The TX-LA Undergraduate Mathematics Conference is a forum for sharing undergraduate research activities in mathematics among Louisiana State University, Texas A&M University, and the University of Houston. A primary goal of the conference is for students to present and share mathematics, as part of preparation for post-graduate studies or employment in research laboratories or industry.
Basic Information
October 19-20, 2019 — the Conference will start on Satuday morning and end around lunch on Sunday.
Department of Mathematics at Texas A&M University
College Station, TX
Previous TX-LA Undergraduate Mathematics Conferences
University of Houston, November 11-12, 2017
Louisiana State University, October 5-7, 2018
Registration
To register for the conference, send an email to Matt Young (myoung@math.tamu.edu) with the following information:
- Name & affiliation
- Dates of visit if different from October 18-20
- Suggested roommate (undergraduate participants)
- Food restrictions
For undergraduate students presenting at the conference, include also
- Research Advisor (if applicable)
- Title of poster and presentation (if presenting)
- Abstract of poster and presentation (if presenting)
The registration deadline is October 11, 2019.
Support
Some support is available for undergraduate students. The conference will book hotel rooms for funded undergraduate students who requested financial aid. Students and postdocs may need to share a double room.
Plenary Speaker
Ivan Ivanov, Department of Veterinary Physiology and Pharmacology, Texas A&M University.
Panel Discussion
Weston Baines, Department of Mathematics, Texas A&M University
Irina Gaynanova, Department of Statistics, Texas A&M University
Irina Holmes, Department of Mathematics, Texas A&M University
Ivan Ivanov, Department of Veterinary Physiology and Pharmacology, Texas A&M University
Jeff Lovering, Customer Marketing Group (to be confirmed)
Schedule and Abstracts
All conference activities will be held at the Blocker Building on the Texas A&M University campus.
- Registration and breaks will be held in Blocker 140, 141
- All talks will be held in Blocker 166
Click each title to reveal the abstract.
Saturday, October 19, 2019
| 9:30am - 10:00am |
BLOC 141 |
Registration and Coffee |
|
| 10:00am - 11:00am |
BLOC 166 |
Ivan Ivanov, Texas A&M University |
|
|
+ Mathematical Models of Gene Regulatory Networks
|
|
|
Abstract: According to the Central Dogma of the Molecular
Biology, the information in the living cells flows from the DNA to the
functioning proteins. This information flow is facilitated by a
complex web of biochemical reactions which ultimately determine the
cell's phenotype and fate. Developing quantitative models for those
phenomena holds the promise of designing therapeutic interventions
that could steer a cell away from undesirable phenotypes such as tumor
cells. We will focus on a few of the major challenges in the field and
will outline the potential important contributions to it by the
mathematical community.
|
|
| 11:15am - 12:15pm |
BLOC 166 |
Student Presentations |
|
|
| 11:15am - 11:35am |
Cosmas Kravaris, Texas A&M University |
|
+ Calculating the growth of the wallpaper groups using cone
types
|
|
Abstract:
We define the notions of group presentations, Cayley graphs,
growth and growth series for a group. Next, we consider the wallpaper
groups (2 dimensional crystallographic groups) and describe the method of
cone types. Finally, we use cone types to compute the growth of the
wallpaper groups.
|
|
| 11:45am - 12:05pm |
Clinten Graham and Claire Pearson, Louisiana State University |
|
+ Computational representation of prefractals and their attractors in R2
|
|
Abstract:
Using the Wolfram Language's symbolic geometry tools, we have
developed a user interface that allows iterative function
systems on regions to be described with concise notation and
rendered as geometric attractors. The geometric transformation
is described by the software in homogeneous coordinates
allowing the prefractals to be computed efficiently as a
region. From the geometric description of the IFS, the
software computes rules to draw orbits on the system's
attractor through the Chaos Game. This representation of the
attractor allows the user to modify the rules of the system
and simulate its limit in real time. The software is ideal as
a discovery tool for students in driving useful conjecture
about phase transition, fractal boundary, and convergence.
|
|
| 12:15pm - 1:30pm |
BLOC 141 |
Lunch |
| 1:30pm - 3:30pm |
BLOC 166 |
Student Presentations |
|
|
| 1:30pm - 1:50pm |
Jacob Bradley and Sean Campbell, University of Houston |
|
+ Delay-induced dynamics of protein production in resource-limited environments
|
|
Abstract:
In recent years, work has been done on understanding delay-induced phenomena
in gene networks. However, most models assume constant delay times, which
does not accurately reflect the noisy environment in a cell. Using a simple
framework from queueing theory, researchers have found interesting behavior
in signaling times while tuning variance in delay times. We extended this
study by including an assumption of limited cell resources and found that
this interesting behavior still occurs in more realistic conditions. We also
examined the effects of characteristic statistical information other than
variance on the signaling dynamics.
|
|
| 2:00pm - 2:20pm |
Xinyue Tracy Yu, Louisiana State University |
|
+ Effect of photo-isomerization and thermal relaxation on the orientation of solid-state photoactive molecules
|
|
Abstract:
Photoactive polymers such as azobenzene are promising candidates for
actuators in the creation of soft robots. When azobenzene is exposed
to light of certain wavelengths, it undergoes photo-isomerization,
switching from a trans- to a cis-state. After continuous isomerization
and thermal relaxation, the molecules will reach thermodynamic
equilibrium and orient themselves in the direction orthogonal to the
light polarization. When there is no light, the molecules will reach
an ordered nematic state if the coupling between them is strong enough
compared to thermal fluctuation. This project presents a model that
simulates the photo-orientation process, and derives a mean field
approximation of the order parameter. We create a 2-dimensional
Heisenberg lattice of spins, and use the Metropolis Monte Carlo
algorithm to perform importance sampling of the spins. We then compare
the order parameter calculated from the simulation with those
predicted by the mean field model. These results are expected to help
research on photoactive polymers as well as potential actuators for
soft robots.
|
|
| 2:30pm - 2:50pm |
Lance Fegan, University of Houston |
|
+ Two approaches for optimal synthesis of a thin wire antenna
|
|
Abstract:
In this study, we explore a strategy for determining the
current distribution of a thin-wire antenna based on a given
radiation pattern. By this we mean seeking for a current
distribution on the antenna so that the generated radiation
pattern closely approximates a prescribed far field
pattern. The integral equation that models the relationship
between the current distribution and the generated radiation
pattern was analyzed using the method of moments. The unknown
current distribution was approximated with a truncated series
leading to a system of linear equations. This linear system is
then solved using Tikhonov regularization.This study directly
compares the results obtained from two series representations,
namely the Taylor and Fourier series. Our results show that
the accuracy of this strategy is primarily dependent upon the
approximating series used. The results from this study has
potential applications in radar and radar defense
technologies. Further research on this problem may lead to the
development of more effective techniques in terms of accuracy
and stability.
|
|
| 3:00pm - 3:20pm |
Michael Sheppard and Noah Templet, Louisiana State University |
|
+ An online GUI for EM waves in layered media
|
|
Abstract:
The goal is to make available to the community a versatile
online application for the computation of electromagnetic
fields in media with any number of layers having arbitrary
electric and magnetic tensors. The objectives are (1) to allow
scientists to explore phenomena of scattering, guided modes,
and resonance in the most general EM layered media and (2) to
provide a pedagogical tool for students and professionals to
learn EM in layered media.
|
|
| 3:30pm - 4:00pm |
BLOC 141 |
Break |
|
| 4:00pm - 5:00pm |
BLOC 166 |
Panel Discussion
- Weston Baines, Department of Mathematics, Texas A&M University
- Irina Gaynanova, Department of Statistics, Texas A&M University
- Irina Holmes, Department of Mathematics, Texas A&M University
- Ivan Ivanov, Department of Veterinary Physiology and Pharmacology, Texas A&M University
- Jeff Lovering, Customer Marketing Group (to be confirmed)
|
Sunday, October 20, 2019
| 8:30am - 9:00am |
BLOC 141 |
Coffee |
|
| 9:00am - 10:30am |
BLOC 166 |
Student Presentations |
|
|
| 9:00am - 9:20am |
Andrew Winn, Texas A&M University |
|
+ Revisiting a cutting plane method for perfect matchings
|
|
Abstract:
In 2016, Chandrasekaran, Végh, and Vempala published a method to
solve the minimum-cost perfect matching problem on an arbitrary graph
by solving a strictly polynomial number of linear programs. However,
their method requires a strong uniqueness condition, which they
imposed by using perturbations of the form $c(i)=c_0(i)+2^{-i}$. On
large graphs (roughly $m>100$), these perturbations lead to cost
values that exceed the precision of floating-point formats used by
typical linear programming solvers for numerical calculations. We
demonstrate, by a sequence of counterexamples, that perturbations are
required for the algorithm to work, motivating our formulation of a
general method that arrives at the same solution to the problem as
Chandrasekaran \textit{et al}. but overcomes the limitations described
above by solving multiple linear programs without using perturbations.
We then give an explicit algorithm that exploits are method, and show
that this new algorithm still runs in strongly polynomial time.
|
|
| 9:30am - 9:50am |
Larry Guan, University of Houston |
|
+ Defect analysis of 1D spring-mass systems via Laplace transform and asymptotics
|
|
Abstract:
Spring-mass systems have seen utility for decades in modeling
multiple physical phenomena like elastic deformation and wave
propagation. Our focus is on linear spring-mass systems and
the use of experimental data to analytically locate and
characterize defects ("error" masses) along the
chain. Asymptotics within the Laplace domain enabled us to
numerically trial each block for defect status using the
vibrational data of only the first block in the chain while
simultaneously counting the number of defects. However,
despite the theoretical soundness, this process works only for
data without measurement/numerical noise and any defects
beyond the first are undetectable.
|
|
| 10:00am - 10:20am |
Rohin Gilman, Louisiana State University |
|
+ Two approaches for optimal synthesis of a thin wire antenna
|
|
Abstract:
Using Koopman's global linearization approach, we demonstrate
how the Chernoff Product Formula can be used to approximate
solutions of initial value problems for fully non-linear
differential equations of the form $x'(t)=F(t,x(t))$. We
demonstrate that the rates of convergence of these non-linear
approximations show the same qualitative behavior as their
linear counterparts; namely, the Strang Product type
approximations appear to be of order $\frac{1}{n^2}$, whereas
the Lie-Totter Product type approximations are of order
$\frac{1}{n}$. Joint work with Amy Adair, Arun Banjara, and
Logan Hart.
|
|
|
| 10:30am - 11:00am |
BLOC 141 & BLOC 1st Floor Lobby |
Break & set-up for Poster Session
|
|
| 11:00am - 12:30pm |
BLOC 1st Floor Lobby |
Poster Session
- • Jacob Bradley and Sean Campbell, University of Houston
- • Lance Fegan, University of Houston
- • Rohin Gilman, Louisiana State University
- • Clinten Graham and Claire Pearson, Louisiana State University
- • Larry Guan, University of Houston
- • Cosmas Kravaris, Texas A&M University
- • Michael Sheppard and Noah Templet, Louisiana State University
- • Alexandra Vaughn, University of Houston & Michael E. DeBakey High School
- • Andrew Winn, Texas A&M University
- • Xinyue Tracy Yu, Louisiana State University
|
|
| 12:30pm |
BLOC 141 |
Lunch
|
Location, Transportation, Parking
All activities will be held at the Blocker Building on
the campus of Texas A&M University.
The Northside Garage (NSG) is located directly across from the Blocker Building (BLOC) and has space for visitor parking. During the weekend, you can also park for free at any un-reserved space in a numbered lot, such as Lot 50 and Lot 51. The interactive campus map also lists available parking lots.
Texas A&M University is located in College Station, Texas, which by automobile lies about 1 hour and 45 minutes northwest of Houston, 1 hour and 45 minutes east of Austin, and 3 hours south of Dallas.
Hotels
Hotel reservations for registered participants who receive financial support will be arranged and billed through the Mathematics Department. Details of your reservation will be sent to the provided email address at least one week prior to the conference.
Funded participants will be housed at the Hampton Inn, 320 Texas Ave., College Station, TX 77840, which is within walking distance of campus.
If you are not receiving financial support from the conference, you can stay in any hotel in town. Below are some hotels that are within walking distance to the conference site. Please check the rate and availability with the hotels directly.
- Hampton Inn, 320 Texas Ave., College Station, TX 77840
- Home2 Suites, 300 Texas Ave., College Station, TX 77840
- Embassy Suites, 201 University Dr. East, College Station, TX 77840
- La Quinta Inn, 607 Texas Ave, College Station, TX 77840
- Fairfield Inn & Suites , 4613 Texas Ave, Bryan, TX 77802
- Econo Lodge, 104 Texas Ave. South, College Station, TX 77840
- The George, 180 Century Court, College Station, TX 77840
Resources
Acknowledgment
This conference is supported in part by a grant from the Simons Foundation and the Department of Mathematics at Texas A&M University.
Local Organizers
Michael Anshelevich (Texas A&M University)
Matt Papanikolas (Texas A&M University)
Matt Young (Texas A&M University)
Organizers at Large
Daniel Onofrei (University of Houston)
William Ott (University of Houston)
Stephen Shipman (Louisiana State University)
Andrew Török (University of Houston)
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