Events
Department of Mathematics and Statistics
Texas Tech University
Traditional mediation analysis methods have been limited to dealing with only a few mediators, and they face challenges when the number of mediators is high-dimensional. In practice, these challenges can be compounded by outliers and the complex relationships introduced by confounders. To address these issues, we propose a novel quantile-based partially linear mediation analysis method (QMDNN) that can handle high-dimensional mediators and introduce deep neural network techniques to model complex nonlinear relationships in confounders. Unlike most existing works that focus on mediator selection, we emphasize estimation and inference on mediation effects. Theoretical analysis shows that the proposed procedure consistently selects important features in the outcome model and controls type I error rates for hypothesis testing on mediation effects. Numerical studies show that the proposed method outperforms existing approaches under a variety of settings, demonstrating the versatility and reliability of QMDNN as a modeling tool for complex data. Our application of QMDNN to study DNA methylation's mediation effect of childhood trauma on cortisol stress reactivity reveals previously undiscovered relationships by providing a comprehensive profile of the relationship at various quantiles.
Please virtually attend this week's Statistics seminar at 4:00 PM (CDT, UT-5) via this zoom link
Meeting ID: 975 5145 6676
Passcode: 356792
A real number $x$ is said to be normal if the sequence $a^n x$ is uniformly distributed modulo 1 for every integer $a≥2$. Although Lebesgue-almost all numbers are normal, the problem determining whether specific irrational numbers such as $e$ and $π$ are normal is extremely difficult. However, techniques from Fourier analysis and geometric measure theory can be used to show that certain “thin” subsets of $R$ must contain normal numbers.
 | Wednesday
Apr. 12
|
| Algebra and Number Theory
No Seminar
|
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Abstract. This presentation explores an alternate quantum framework in which the wavefunction Ψ(t, x) plays no role. Instead, quantum states are represented as ensembles of real-valued probabilistic trajectories, x(t, C), where C is a trajectory label. Quantum effects arise from the mutual interaction of different trajectories or “worlds,” manifesting as partial derivatives with respect to C. The quantum trajectory ensemble x(t, C) satisfies an action principle, leading to a dynamical partial differential equation (via the Euler-Lagrange procedure), as well as to trajectory-based symmetry and conservation laws (via Noether’s theorem). Several of these correspond to standard laws, e.g. conservation of energy. However, one such trajectory-based law (pertaining to curl-free velocity fields) appears to have no standard analog.
A full understanding of the new trajectory-based conservation law may require relativistic considerations. Whereas an earlier, non-relativistic version of the trajectory-based theory turns out to be mathematically equivalent to the time-dependent Schrödinger equation, the relativistic generalization (for single, spin-zero, massive particles) is not equivalent to the Klein-Gordon (KG) equation—and in fact, avoids certain well-known problems of the latter, such as negative (indefinite) probability density. It is precisely the new trajectory-based conservation law that makes this possible. The new relativistic quantum trajectory equations could in principle be used in quantum chemistry calculations, and otherwise could lead to new physical predictions that could be validated or refuted by experiment.
About the speaker. Dr. Bill Poirier is Chancellor’s Council Distinguished Research Professor and also Barnie E. Rushing Jr. Distinguished Faculty Member at Texas Tech University, in the Department of Chemistry and Biochemistry and also the Department of Physics. He received his Ph.D. in theoretical physics from the University of California, Berkeley, followed by a chemistry research associateship at the University of Chicago. His research interest is in understanding and solving the Schrödinger equation, from both foundational and practical perspectives. He has given well over 100 oral presentations on quantum mechanics, to both scientific and general audiences, and published over 100 papers in this field. He is also the creator of the continuous "many interacting worlds" interpretation of quantum mechanics.
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: 940 7062 3025
* Passcode: applied
Shrinking Kahler-Ricci solitons model finite-time singularities of the Kahler-Ricci flow, hence the need for their classification. I will talk about the classification of such solitons in 4 real dimensions. This is joint work with Bamler-Cifarelli-Deruelle, Cifarelli-Deruelle, and Deruelle-Sun.
We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ϵ), where ϵ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m^1.5/ϵ).
This is one of the works I published with some collaborators and my advisor during my Ph.D. at the Industrial, Manufacturing & Systems Engineering Department.
Please attend this talk for a Department Post-Doc position via this Zoom link.
Meeting ID: 991 2851 6437
Passcode: interview
Abstract pdf
Please attend this talk for a Department Post-Doc position via this Zoom link.
Meeting ID: 968 8926 6311
Passcode: interview