Events
Department of Mathematics and Statistics
Texas Tech University
We study the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but coherent way. We prove that every decaying solution admits an asymptotic expansion of a new type. This expansion contains a new variable that allows it to be established in a closed-form, but does not affect the meaning and precision of the expansion. This second talk will focus on the proofs, especially, the construction of the expansions.
The emergence of nonlocal theories as promising models in different areas of science (continuum mechanics, biology, image processing) has led the mathematical community to conduct varied investigations of systems of integro-differential equations. In this talk I will present results for systems of integral equations with weakly singular kernels, flux-type boundary conditions, as well as some recent results on nonlocal Helmholtz-Hodge type decompositions with applications at both theoretical and applied levels.
Today's seminar begins at 1 PM (CST UT-6).
Please watch online via this Zoom link.
In this talk, we start providing a friendly introduction to Cryptography, focusing on the (Generalized) Diffie-Hellman Key Exchange. Building on this foundation, we present a novel cryptographic protocol that utilizes the semigroup of oriented knots under the connected sum operation. The shared secret key is derived from a knot invariant, computed from two distinct representations of the same knot. The security of this protocol relies on two computationally hard problems: the Decomposition Problem, which involves determining the prime decomposition of a knot, and the Recognition Problem, which asks whether two knot diagrams represent the same knot. This is a joint work with Arno Wildi.
Join the Zoom Meeting at 3 PM (CST UT-6)
Meeting ID: 958 5298 7437
Passcode: 922447
Deep learning algorithms have recently inspired innovative strategies to address computational bottlenecks in traditional solvers for high-dimensional differential equations (DEs). Neural network (NN)-based solvers, which approximate the DE solutions using NNs, have gained significant popularity. However, achieving high accuracy with these solvers remains a challenge, and their black-box nature often limits the interpretability of their solutions.
In this talk, I will introduce the finite expression method (FEX), a symbolic approach for discovering accurate and interpretable mathematical expression solutions to DEs. FEX leverages reinforcement learning to tackle the combinatorial optimization problems inherent in solving DEs. Numerical examples of high-dimensional DEs demonstrate that FEX achieves highly accurate solutions, with relative errors approaching single-precision machine epsilon. Moreover, FEX provides interpretable insights into DE solutions, which enhances understanding of physical systems and guides the development of postprocessing techniques for refined results. By combining accuracy with interpretability, FEX offers a promising alternative to NN-based solvers for high-dimensional DEs.
This presentation may be viewed in the TTU Mediasite catalog via eraider login.
In this talk, we will discuss two applications of mathematical modeling to sexually transmitted diseases, a compartmental model and an agent-based model. In the first part of the talk, we will propose four compartmental models to examine the interactions between host immune responses and the monkey(mpox) virus across three distinct infection routes (intravenous, intradermal, and intrarectal). The models are calibrated using viral load data from macaques infected through each of these three infection routes. The infectiousness of each infected macaque is calculated to uncover specific characteristics driving the 2022-2023 outbreak. In the second part of the talk, we will discuss an agent-based model with a dynamically sexual contact network that was developed to simulate the individual-level dynamics of Chlamydia trachomatis (CT) infection. With the calibrated model, we then evaluate the impact of different vaccine program on the CT burden and its long-term sequalae.
The Biomath seminar may be attended Friday at 11:00 AM CST (UT-6) via this Zoom link.
Meeting ID: 948 8777 3344
Passcode: 872069
abstract noon CST (UT-6)
Zoom link available from Dr. Brent Lindquist upon request.