Events
Department of Mathematics and Statistics
Texas Tech University
Using homological algebra, Serre defined and studied an intersection
multiplicity for finitely generated modules over a regular local
ring. He did this by using the Euler characteristic, and showed that
it satisfied many properties one would expect with an intersection
theory. The goal of this talk is to give an introduction to the
partial Euler characteristics and share a result about an Ext analog
of the partial Euler characteristics.
There has been a growing interest in hybrid dynamical systems in recent years. Such systems often undergo vector field switching and/or state jumps. By introducing the notions of persistent limit set and persistent mode, we extend the classical LaSalle's invariance principle to hybrid systems exhibiting both impulses and switching. A weak invariance principle is established for such systems, under a weak dwell-time condition on the impulsive and switching signals. This weak invariance principle is then applied to derive asymptotic stability criteria for impulsive switched systems. As an application, we investigate a switched SEIR epidemic model with pulse treatment and establish sufficient conditions for the global asymptotic stability of the disease-free solution under weak dwell-time signals.
This seminar is co-sponsored with the BioMath group.
Zoom link
Meeting ID: 968 5126 2664
Passcode: TTU
We explore the Enneper family of real maximal surfaces using Weierstrass data in three-dimensional Minkowski space. Our focus is on deriving the algebraic surfaces within this family and analyzing their class and degree.
Watch online Tuesday at 4 PM via this Zoom link.
Abstract. Finite element methods for H(curl) interface equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential obstacle for almost all the interface-unfitted mesh methods in the literature regarding the application to H(curl) interface problems. In this talk, we will present a novel immersed virtual element method (IVEM) for solving a 3D H(curl) interface problems. The motivation is to combine the conformity of virtual element spaces and robust approximation capabilities of immersed finite element spaces. The proposed method is able to achieve optimal convergence for a class of 3D H(curl) interface problem. To develop a systematic framework, a de Rham complex for H1, H(curl), and H(div) interface problems will be established based on which the Hiptmair-Xu (HX) preconditioner can be adapted to develop a fast solver for the H(curl) interface problem. An efficient polyhedral mesh generator is also provided to generate a polyhedral mesh with an interface fitted boundary triangulation.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (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: 979 1333 6658
* Passcode: Applied (Note the capital letter "A")
In this work, we revisited the evaluation of the effectiveness of the COVID-19 vaccination campaign in 2021, as measured by the number of deaths averted. The published estimates differ a lot: from one widely referenced paper by Watson et alia (2022) estimating 0.5-0.6% of the USA population being saved, to average-level estimates of 0.15-0.2%, and to some estimates as low as 0.0022%. For other countries, Watson et al. gave much higher estimates than all other works too. We reviewed 30 relevant papers, carried out an in-depth analysis of the model by Watson et al. and of several other studies, and provided our own regression-based analysis of the US county-level data. The model by Watson et al. is very sophisticated and has many features; some of them that make it more realistic (age-structured epidemiology, elderly first vaccination, healthcare overload effects), but others that are likely inaccurate (substantial reinfection rates (i.e., immunity loss) for the Alpha and Delta variants, possible overfitting due to overly flexible time-dependent infection transmission rate) or questionable (45% increase in fatality rate for the Delta variant). Yet, the main argument is that Watson et al.’s model does not reproduce the trends observed in the county-level US data. Eventually, we concluded that Watson et al.'s 0.5-0.6% is an overestimate, and 0.15-0.2% of the US population saved by vaccination — as estimated by regression studies on subnational-level data (e.g., Suthar et al. (2022) and by He et al. (2022)) — is much more plausible value.
In our view, in order to be considered reliable, mathematical models should be tested on more detailed real data that was not used in model fitting. On the other hand, detailed data bring about new challenges in statistical modelling and uncertainties in data reliability.
Zoom link
Meeting ID: 953 8930 8090
Passcode: Biomath
abstract 2 PM CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.