Events
Department of Mathematics and Statistics
Texas Tech University
As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and difficulty of interpretation, especially for high-dimensional time series. We propose a novel sparse infinite-order VAR model for high-dimensional time series, which avoids all above drawbacks while inheriting essential temporal patterns of the VARMA model. As another attractive feature, the temporal and cross-sectional structures of the VARMA-type dynamics captured by this model can be interpreted separately, since they are characterized by different sets of parameters. This separation naturally motivates the sparsity assumption on the parameters determining the cross-sectional dependence. As a result, greater statistical efficiency and interpretability can be achieved with little loss of temporal information. As the final part of this talk, we will discuss how this idea can inspire a Recurrent Neural Network based model for high-dimensional time series, which fits naturally within the multivariate Granger causality framework, allowing for network discovery under nonlinear dynamics.
The Statistics seminar may be attended online at 4:00 PM CST (UTC-6) via this Zoom link.
Meeting ID: 925 6793 0900
Passcode: 223682
We investigate various properties of Ricci, hyperbolic Ricci, hyperbolic Yamabe, and Riemann solitons on certain semi-Riemannian manifolds. Additionally, we study soliton submanifolds that are isometrically immersed in a semi-Riemannian manifold equipped with a torse-forming vector field. Special attention is given to the cases where the submanifolds are minimal, totally umbilical, or totally geodesic, as well as to situations where the ambient manifold has constant sectional curvature.
This Differential Geometry, PDE and Mathematical Physics seminar is available over zoom.
 | Wednesday
Nov. 5
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| Algebra and Number Theory
No Seminar
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Abstract. We present a brief overview of Nonstandard Finite Difference (NSFD) methods, focusing on their application to autonomous dynamical systems. Special attention is given to the development and analysis of Elementary Stable Nonstandard (ESN) and Positive Elementary Stable Nonstandard (PESN) schemes. These methods are designed to preserve key qualitative features of the underlying continuous models, including positivity of solutions and local stability near equilibria. The proposed schemes utilize a non-local discretization of the right-hand side and a nonstandard treatment of the time derivative, resulting in significant improvements in the qualitative behavior of numerical solutions. Their explicit formulation makes them computationally efficient and well-suited for simulating complex biological, chemical, and physical systems. We illustrate the effectiveness of these methods through a series of biological case studies, demonstrating their superior performance compared to classical numerical schemes. These results highlight the potential of NSFD techniques as robust tools for modeling and simulation in applied sciences.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 915 2866 2672
* Passcode: applied
Math Circle Fall Flyer
Combination immunotherapy, which integrates immune checkpoint inhibition with immune stimulation, has shown great promise in cancer treatment but remains highly sensitive to patient-specific conditions. We present a mathematical model that captures the essential mechanisms of tumor–immune interactions under combination therapy. Using bifurcation analysis, we identify distinct dynamical regimes, including tumor eradication, partial control, oscillations, and immune escape, and derive analytical conditions for transitions between these regimes within a hierarchical parametric framework. Interestingly, higher-codimension Hopf and Bogdanov–Takens bifurcations emerge, revealing rich and complex dynamics. Numerical simulations further illustrate various clinical outcomes across different parameter regions. Finally, sensitivity analysis demonstrates how parameters correlate with outcomes in partially controlled and oscillatory regimes. The results agree with simulations and further reveal dual effects of key parameters: factors that promote tumor suppression in partially controlled states may destabilize immune dynamics in oscillatory regimes. Together, these findings illustrate how nonlinear dynamics and parameter sensitivity shape treatment outcomes, providing insights into the design of immunotherapy strategies.
abstract 2 PM CST (UTC-6)
Zoom link available from Dr. Brent Lindquist upon request.