Events
Department of Mathematics and Statistics
Texas Tech University
The last few decades have witnessed a significant development in statistical methods for genetic data analysis, owing to the massive amount of data generated with high-throughput technologies. Identifying gene-environment (GxE) interactions has been one of the central foci along the line, given the importance of GxE interactions in determining the variation of many complex disease traits such as Parkinson disease, type 2 diabetes and cardiovascular diseases. However, the underlying machinery of GxE is still poorly understood due to the lack of powerful statistical methods. Epidemiological evidence suggested that disease risks can be modified by simultaneous exposure to multiple environmental agents with effects larger than the simple addition of individual factors acting alone. Motivated by this, we proposed a semi-parametric partial linear model to assess how multiple environmental factors acting jointly to interact with genetic variants to affect disease risk. We further extended this framework to longitudinal traits to study dynamic GxE interactions. In this talk, I will spend more time on this work and present a functional varying-index coefficients model to study dynamic GxE interactions with longitudinal traits. We developed a rigorous testing procedure to assess the synergistic GxE interactions under the quadratic inference framework (QIF). The utility of the method is demonstrated through extensive simulations and a case study.
This is a joint work with Jingyi Zhang, Honglang Wang and Xu Liu.
Bio: Dr. Yuehua Cui is a Professor and Graduate Program Director in the Department of Statistics and Probability at Michigan State University (MSU). He earned his Ph.D. in Statistics from the University of Florida in 2005 and has been a faculty member at MSU since then. Dr. Cui's research focuses on developing statistical and computational methods for genetic and genomic data analysis, with expertise in mediation analysis, causal inference with Mendelian randomization, spatial transcriptomics, multi-omics data integration, and applied functional and longitudinal data analysis. His work has been supported by the NSF, NIH, and other funding agencies, and he has authored over 100 journal articles, making significant contributions to statistical genetics and genomics. Dr. Cui serves on the editorial boards of several journals, including Statistics and Probability Letters, BMC Genomics Data, and Computational and Structural Biotechnology Journal. He is an elected Fellow of the American Statistical Association (ASA) and an elected member of the International Statistical Institute (ISI).
Please virtually attend this week's Statistics seminar at 4:00 PM via this zoom link
Meeting ID: 957 8837 8218
Passcode: 644866
In this talk I will discuss the differential topology of non-linear proper Fredholm mappings. In applications these mappings arise as non-linear PDE problems (of elliptic type). I will discuss work with Lauran Toussaint that relates these mappings to the stable homotopy groups of spheres, and if time permits, I will discuss an ongoing project on defining a new homology theory of singular type for infinite dimensional spaces. This is joint work with Alberto Abbondandolo, Michael Jung and Lauran Toussaint.Let k ≥ 2 be an even integer. Let q be a prime power such that q ≡ k+1 (mod 2k). We define the k-th power Paley digraph of order q, Gk(q), as the graph with vertex set 𝔽q where a → b is an edge if and only if b−a is a k-th power residue. We provide a formula, in terms of finite field hypergeometric functions, for the number of transitive subtournaments of order four contained in G_k(q), 𝒦4(Gk(q)), which holds for all k. We also provide a formula, in terms of Jacobi sums, for the number of transitive subtournaments of order three contained in Gk(q), 𝒦3(G_k(q)). In both cases, we give explicit determinations of these formulae for small k. We show that zero values of 𝒦4(Gk(q)) (resp. 𝒦3(Gk(q))) yield lower bounds for the multicolor directed Ramsey numbers Rk⁄2(4)=R(4,4,...,4) (resp. Rk⁄2(3)). We state explicitly these lower bounds for k ≤ 10 and compare to known bounds, showing improvement for R2(4) and R3(3). Combining with known multiplicative relations we give improved lower bounds for Rt(4), for all t ≥ 2, and for Rt(3), for all t ≥ 3.
Abstract. We present an overview of sharp interface limits ($\Gamma$-limits) of bulk energies and of their gradient flows that yield classes of sharp interface energies and their gradient flows. We develop a formalism to take variational derivatives of sharp interface energies and apply this to sharp interface energies that are not trivially in the range of the bulk energy $\Gamma$-limit. This applications to faceting in brine inclusions and to membrane self-adhesion and folding without self-intersection. We show that the resulting gradient flows have a rich structure which we exploit to simplify the stability analysis. For simplicity all discussion is posed in R^2.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room Math 011 (Math 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
Mar. 13
6:30 PM
MA 108
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| Mathematics Education
Math Circle
Aaron Tyrrell
Mathematics and Statistics, Texas Tech University
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Math Circle Spring Poster
abstract noon CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.