Events
Department of Mathematics and Statistics
Texas Tech University
Let \((\mathcal{A},\mathcal{E})\) be an exact category. We establish
basic results that allow one to identify sub(bi)functors of
\(\operatorname{Ext}_{\mathcal{E}}(-,-)\) using additivity of numerical
functions and restriction to subcategories. We also study a small
number of these new functors over commutative local rings in detail
and find a range of applications from detecting regularity to
understanding Ulrich modules. Time permitting, we also see how one can
define the notion of Ulrich Sprit rings naturally arising from a class
of such subfunctors and demonstrate some basic properties of Ulrich
Split rings.
Follow the talk via this Zoom link
Meeting ID: 913 0074 4693
Passcode: 586188
The complicated interaction between the host and its resident microbial communities has spurred investigations into microbiome-associated diseases, unveiling novel insights on pathogenesis and help developing targeted interventions. While existing studies have interesting statistical findings of alternation of certain microbiome communities or metabolites in such disease, the underlying mechanisms through which the microbiome influences such diseases remain elusive. In this paper, we explore the metabolites pathogenesis on microbiome-related disease via data integration. Specifically, we develop a novel framework to enrich pathway finding of unobserved metabolites or increase the power of detecting the causal metabolites. We demonstrate the strength of our method via simulation studies and a real data application in inflammatory bowel disease.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday the 25th via this Zoom link.
Meeting ID: 938 2030 4393
Passcode: 986036
Abstract. Inverse source scattering problems are essential in various fields, including antenna synthesis, medical imaging, and earthquake monitoring. In many applications, it is necessary to consider uncertainties in the model, and such problems are known as stochastic inverse problems. Traditional methods require a large number of realizations and information on medium coefficients to achieve accurate reconstruction for inverse random source problems.
To address this issue, we propose a data-assisted approach that uses boundary measurement data to reconstruct the statistical properties of the random source with fewer realizations. We compare the performance of different data-driven algorithms under this framework to enhance the initial approximation obtained from integral equations. Our numerical experiments demonstrate that the data-assisted approach achieves better reconstruction with only 1/10 of the realizations required by traditional methods.
Among the various Image-to-Image translation algorithms that we tested, the pix2pix method outperforms others in reconstructing well-separated inclusions with accurate positions. Our proposed approach results in stable reconstruction with respect to the observation data noise.
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. 27
7 PM
MA 108
|
| Mathematics Education
Math Circle
Hung Tran
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster