Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Oct. 14
|
| Algebra and Number Theory
No Seminar
|
The Muskat problem (also known as the Hele-Shaw problem with gravity) models the evolution of the interface between two different fluids in porous media. We introduce a mathematical model for this problem using viscosity solutions theory for integro-differential equations, and discuss a new result on the global well-posedness of the corresponding Hamilton-Jacobi-Bellmann equation with bounded, uniformly continuous initial data, in all dimensions. This is a joint work with Russell Schwab and Olga Turanova.
This Analysis seminar may be attended at 4:00 PM CDT (UT-5) via this Zoom link.
Meeting ID: 966 4439 4032
Passcode: 946975
We present the fourth fundamental form and curvature formulas for hypersurfaces in four-dimensional Euclidean space. These quantities are defined and computed for rotational hypersurfaces. Furthermore, we investigate rotational hypersurfaces that satisfy a specific relation involving the fourth Laplacian and a 4X4 matrix.
This seminar may be viewed in the TTU Mediasite Catalog and the slideshow pdf is available.
Abstract. Vector autoregressive (VAR) models are popular in econometrics due to their flexibility in capturing dynamic relationships between variables. The fact that VARs are also
tailor-made for the determination of Granger-causal relationships, has recently sparked great interest in neuroscience, which seeks to understand how regional brain activation signals connect with complex functional circuitry. In such applications, high-dimensional models are the norm; however these tend to exhibit an inherent sparsity structure. In this study, we propose two different
types of algorithm for sparse VAR model identification, which are able to handle situations where the number of parameters ($m$) is comparable to the sample size ($n$). Both methods rely on individual coefficient p-values as the basis for sparsification. The thresholding method (TLSE) simply declares as non-active those coefficients whose p-value exceeds a cuttoff. The information criterion based method (BLSE), uses the initial p-value ranking as the basis for fitting increasingly larger models in a stepwise manner, identifying as optimal the model with smallest BIC value. We show both methods enjoy an asymptotic oracle property whereby active coefficients are correctly identified in the limit as $n\rightarrow\infty$. Simulations comparing these to existing methods (mostly lasso variants), suggest that the new methods are better at sparsity pattern recovery. The methodology is illustrated on high-dimensional econometric and neuroscience real datasets with the aim of unveiling the strength of Granger-causal flow between nodes.
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")
 | Thursday
Oct. 17
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Aaron Tyrrell
Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
abstract 1 PM CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.