Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Oct. 16
|
| Algebra and Number Theory
No Seminar
|
There has been a huge interest in studying human brain connectomes inferred from different imaging modalities and exploring their relationships with human traits, such as cognition. Brain connectomes are usually represented as networks, with nodes corresponding to different regions of interest (ROIs) and edges to connection strengths between ROIs. Due to networks' high-dimensionality and non-Euclidean nature, it is challenging to depict their population distribution and relate them to human traits. Building on recent advances in deep learning, this work focuses on two tasks in learning brain graphs. (1) Population distribution learning. We develop a nonlinear latent factor model to characterize the population distribution of brain graphs and infer their relationships to human traits. (2) Interpretable transfer learning for graph inference. We aim to extract and transfer the knowledge learned from large-scale studies conducted under different sources to assist the inference in the target small-scaled cases. We applied the developed approaches to two large-scale brain imaging datasets, the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP) for adults, to study the structural brain connectome and its relationship with cognition.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
Meeting ID: 922 8091 6684
Passcode: 384511
This is part 2 of a 2-part talk. The theory of matrix cocycles provides a foundation for random matrix theory in Ergodic theory - the measure theoretic study of deterministic dynamical systems. The foundational works in this field establish the existence of Lyapunov exponents and stable / unstable splittings, for general matrix cocycles. Matrix cocycles appear naturally in a wide variety of physical phenomenon. We shall first see how it arises in the context of learning a dynamical system. The performance of a learning technique can be modelled using a cocycle, and we demonstrate the application of this theory in establishing the limits of learning.
Renormalized area of minimal submanifolds of Poincaré-Einstein manifolds has been the focus of much study in conformal geometry over the past 20 years. As well as in the AdS/CFT correspondence in physics. In 2008, Alexakis and Mazzeo showed that the renormalized area of 2D minimal surfaces in hyperbolic space has many interesting functional properties. Not least of which being it’s connection to the asymptotic Plateau problem and the Willmore functional. In 2001, Anderson proved a rigidity result in terms of the renormalized volume for 4D Poincaré-Einstein spaces. More recently, Bernstein proved a rigidity result for 2D minimal surfaces in hyperbolic space. We will report on a partial rigidity result for minimal hypersurfaces of 5D hyperbolic space in terms of the renormalized area.
Abstract. Quantum entanglement is the physical phenomenon, the medium, and, most importantly, the resources that enable quantum technologies. In this talk, we discuss recent results in estimating the degree of entanglement over major models of generic states as measured by different entanglement entropies, where the case of von Neumann entropy will be studied in some detail. Main ingredients leading to our results are random matrix theory, orthogonal polynomials, and the observed anomaly cancellation phenomena.
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
Oct. 18
7 PM
MA 108
|
| Mathematics Education
Math Circle
Álvaro Pámpano
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
Abstract pdf