Events
Department of Mathematics and Statistics
Texas Tech University
In this talk, we discuss the elements of non-abelian homological
algebra in the framework of Quillen's model category theory. We
briefly explain a direct algebraic approach to the model structure of
simplicial commutative algebras. Then we describe the construction of
the cotangent complex and Andre-Quillen (co)homology. As for
applications, we recall the characterizations of some classes of rings
and ring homomorphisms by Andre-Quillen (co)homology. Finally, we
discuss exceptional complete intersection maps and some recent results
on detecting them by bounded homological dimensions where
Andre-Quillen homology is exploited implicitly.
Follow the talk via this Zoom link
Meeting ID: 913 0074 4693
Passcode: 586188
The rapid advancement of functional data in various application fields has increased the demand for advanced statistical approaches that can incorporate complex structures and nonlinear associations. In this talk, I will present a functional random forests (FunFor) approach to model the functional data response that is densely and regularly measured, as an extension of the landmark work of Breiman, who introduced traditional random forests for a univariate response. The FunFor approach is able to predict curve responses for new observations and selects important variables from a large set of scalar predictors. The FunFor approach inherits the efficiency of the traditional random forest approach in detecting complex relationships, including nonlinear and high-order interactions. Additionally, it is a non-parametric approach without the imposition of parametric and distributional assumptions. Multiple simulation settings and one real-data analysis consistently demonstrate the excellent performance of the FunFor approach in various scenarios. In particular, FunFor successfully ranks the true predictors as the most important variables, while achieving the most robust variable sections and the smallest prediction errors when comparing it with three other relevant approaches. Although motivated by a biological leaf shape data analysis, the proposed FunFor approach has great potential to be widely applied in various fields due to its minimal requirement on tuning parameters and its distribution-free and model-free nature.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
This is the continuation of the previous talk. We study the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear operator $A$ and a positively homogeneous scalar function $H$ of a negative degree $-\alpha$. Then any solution with an extinction time $T_*$ behaves like $(T_*-t)^{1/\alpha}\xi_*$ as time $t\to T_*^-$, where $\xi_*$ is an eigenvector of $A$. The proof first establishes the asymptotic behaviors of the "Dirichlet" quotient and the normalized solution. They are then combined with a perturbation technique that requires the function $H$ to satisfy some pointwise H\"older-like condition. The result allows the higher order terms to be general and the nonlinear function $H$ to take very complicated forms.
Abstract. Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Galerkin (DLR-DG) method for the space homogeneous kinetic equation with a relaxation operator, modeling the emission and absorption of particles by a background medium. Both DLRA and the DG scheme can be formulated as Galerkin equations. To ensure their consistency, a weighted DLRA is introduced so that the resulting DLR-DG solution is a solution to the fully discrete DG scheme in a subspace of the classical DG solution space. Similar to the classical DG method, we show that the proposed DLR-DG method is well-posed. We also identify conditions such that the DLR-DG solution converges to the equilibrium. Numerical results are presented to demonstrate the theoretical findings. This is a joint work with Eirik Endeve, Cory Hauck, and Stefan Schnake.
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: 968 6501 7586
* Passcode: Applied
 | Wednesday
Sep. 20
7 PM
MA 108
|
| Mathematics Education
Math Circle
Hung Tran
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
Abstract pdf
abstract 2 PM CDT (UT-5)