Events
Department of Mathematics and Statistics
Texas Tech University
Recent developments of convex integration technique led to many non-uniqueness results of various PDEs. I will try to describe the mechanism of how this technique works for a simple case, specifically a construction of a solution to the 3D Euler equations that does not conserve its energy (although it is well-known that the classical approach yields local unique solution that conserves energy). Afterwards, if time permits, I will describe related open problems of my interest. This talk is intended to be accessible to graduate students.
 | Monday
Oct. 3
4 PM
online
|
| Biomathematics
TBA
Mohammadi Ain
Department of Mathematics and Statistics, Texas Tech University
|
Discrete data such as the microbiome taxa count data resulting from 16S rRNA sequencing are routinely encountered in bioinformatics. Taxa count data in microbiome studies are typically high-dimensional, overdispersed, and can only reveal relative abundance, therefore are treated as compositional. Analyzing compositional data presents challenges because they are restricted on a simplex. Additionally, these microbiome taxa compositions are affected by other biological and/or environmental covariates such as age, gender, diet, etc. Here, we develop regression-based mixtures of logistic normal multinomial models for clustering microbiome data. These models partition samples into homogeneous subpopulations and allow for investigation of the relationship between bacterial abundance and biological and/or environmental covariates within each inferred group. In this project, we utilize an efficient framework for parameter estimation using variational Gaussian approximations (VGA). The performance of the proposed method is illustrated on both simulated and real datasets.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
Meeting ID: 948 7629 6935
Passcode: 602422
| Wednesday
Oct. 5
|
| Algebra and Number Theory
No Seminar
|
We will report on a result within the holographic study of conformal geometry initiated by Fefferman and Graham. We will first cover some background and history of this area. Then we will discuss the result which can be contextualized as follows:
In 1999 Graham and Witten showed that one can define a notion of renormalized area for properly embedded minimal submanifolds of Poincare-Einstein spaces. For even-dimensional submanifolds, this quantity is a global invariant of the embedded submanifold. In 2008 Alexakis and Mazzeo wrote a paper on this quantity for surfaces in a 3-dimensional PE manifold, getting an explicit formula and studying its functional properties. We will look at a formula for the renormalized area of a minimal hypersurface of a 5-dimensional Poincare-Einstein space in terms of a Chern-Gauss-Bonnet formula.
Watch online via this Zoom link.
Whether or not the solution to the $2\frac{1}{2}$-dimensional Hall-magnetohydrodynamics system starting from any smooth initial data preserves its regularity for all time remains a challenging open problem. Although the research direction on component reduction of regularity criteria for Navier-Stokes equations and magnetohydrodynamics system has caught much attention recently, the Hall term has presented many difficulties. In this manuscript we discover a certain cancellation within the Hall term and obtain various new regularity criteria: first, in terms of a gradient of only the third component of the magnetic field; second, in terms of only the third component of the current density; third, in terms of only the third component of the velocity field; fourth, in terms of only the first and second components of the velocity field. As another consequence of the cancellation that we discovered, we are able to prove the global well-posedness of the $2\frac{1}{2}$-dimensional Hallmagnetohydrodynamics system with hyper-diffusion only for the magnetic field in the horizontal direction; we also obtained an analogous result in the 3-dimensional case via the discovery of additional cancellations. These results extend and improve various previous works. This is the joint work with Prof. Kazuo Yamazaki.
Please attend this week's Applied Math seminar at 4 PM Wednesday via this Zoom link.
Meeting ID: 976 3095 1027
Passcode: applied
We systematically investigate the links between price returns and ESG features.
We propose a cross-validation scheme with random company-wise validation to mitigate the relative
initial lack of quantity and quality of ESG data, which allows us to use most of the latest and
best data to both train and validate our models.
Boosted trees successfully explain a single bit of annual price returns not accounted for in the
traditional market factor.
We check with benchmark features that ESG features do contain significantly more information than
basic fundamental features alone.
The most relevant sub-ESG feature encodes controversies.
Finally, we find opposite effects of better ESG scores on the price returns of small and large
capitalization companies: better ESG scores are generally associated with larger price returns for the latter,
and reversely for the former.