Events
Department of Mathematics and Statistics
Texas Tech University
This talk asks questions that arise in ecosystem models but have implications throughout math and engineering. We ask what are the solution properties that hold for "almost every" equation F(X)=C where X and C are finite dimensional. What does "almost every" F mean? "Almost every" is defined so as to be useful to the scientist. I think of this as pure math for the applied scientist. Systems of M equations in N unknowns are ubiquitous in mathematical modeling. These systems, often nonlinear, are used to identify equilibria of dynamical systems in ecology, genomics, control, and many other areas. Our goal is to describe the properties that will hold for "almost every" F that has some structure, and in particular the global properties of solutions for structured systems of smooth functions. As an application of these ideas I will show examples of Lotka-Volterra systems of differential equations. One example has 14 species. We show that 3 must die out exponentially fast. The technique is rather unique. We produce a "team" of 24 Lyapunov functions, each of which gives different information about which species will die out and all of which are essential.
References
[1] arXiv.org/abs/2203.01432 Extinction of multiple populations and a team of Die-out Lyapunov functions Akhavan & Yorke
[2] arXiv.org/abs/2203.00503 Robustness of solutions of almost every system of equations Jahedi, Sauer & Yorke
[3] arXiv/abs/2008.12140 Structured Systems of Nonlinear Equations Jahedi, Sauer & Yorke
This week's Analysis seminar may be attended at 4:00 PM CST (UT-6) via this Zoom link.
Meeting ID: 976 4978 7908
Passcode: 973073
Local extrema of a function are often the focus in various applications. However, inferring these extrema with noise present can be challenging because (i) the number of local extrema may be unknown, and (ii) the induced shape constraints associated with local extrema are highly irregular. In this talk I will introduce a strategy that eliminates the need to specify the number of local extrema, resulting in a fast and simple Bayesian approach for inference on local extrema. The posterior measure converges to a mixture of Gaussians with the number of components matching the underlying truth, enabling posterior exploration that accounts for multi-modality. Point and interval estimates with frequentist properties will also be provided. The proposed method will be demonstrated through an application to analyzing event-related potentials in cognitive science.
BIO:
Dr. Meng Li is the Noah Harding Assistant Professor of Statistics at Rice University. He was previously a Visiting Assistant Professor in the Department of Statistical Science at Duke University. He received his PhD from the Department of Statistics at North Carolina State University. His research focuses on structured high-dimensional and nonparametric inference on complex data with theoretical guarantees and scalable implementation. To this end, he is particularly interested in variable selection, post-selection inference, symbolic regression, nonparametric Bayes, quantile regression, image processing, functional data analysis, and materials informatics. He serves as an Associate Editor of Bayesian Analysis and on the Scientific Oversight Committee of Extracorporeal Life Support Organization (ELSO). He has supervised 8 PhD students and 1 postdoc. His work is funded by NSF, NIH, ORAU, and QuesTek.
Please virtually attend this week's Statistics seminar at 4:00 PM (CST, UT-6) Monday the 27th via this zoom link
Meeting ID: 978 8596 5193
Passcode: 037287
No abstract.
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Enhancing the correspondence between ideals and varieties
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
The derived category \(D(A)\) of a ring \(A\) is an important example of a
triangulated category in algebra; indeed, this category is the right
setting for the study of complexes "up to homology".
A complex can be viewed as a representation of a certain quiver with
relations, \(Q^{cpx}\). The vertices in this quiver are the integers,
there is an arrow \(q \to q-1\) for each integer \(q\), and the relations are
that consecutive arrows compose to 0. Hence the (classic) derived
category \(D(A)\) can be viewed as a category of representations of
\(Q^{cpx}\).
It is an insight of Iyama and Minamoto that the reason \(D(A)\) is well
behaved is that \(Q^{cpx}\) has a so-called Serre functor. We prove that
if \(Q\) is any quiver with relations that has a Serre functor, then the
category of \(A\)-module valued representations of \(Q\) has a "derived
category" \(D_Q(A)\), which we call the \(Q\)-shaped derived category of the
ring \(A\). For \(Q\) equal to \(Q^{cpx}\) the category \(D_Q(A)\) coincides with the
classic derived category \(D(A)\). In the talk we will demonstrate that
the \(Q\)-shaped derived category \(D_Q(A)\) has many similarities with the
classic derived category \(D(A)\) and the theory will be illustrated by
several concrete examples.
Follow the talk via this Zoom link
Meeting ID: 979 3375 1447
Passcode: 136297
Abstract. Although turbulence affects natural and engineered systems from sub-meter to planetary scales, fundamental understanding and predictive modeling of turbulence continue to defy and bedevil scientists and engineers. This talk summarizes our work during the past decade in leveraging disparate data (ranging from sparse observations to full-field data) to enhance Reynolds-averaged Navier-Stokes (RANS) turbulence models in a physics-informed framework. Specifically, I will present (1) using sparse data to infer Reynolds stress fields based on ensemble data assimilation for reducing RANS model uncertainties, and (2) our ongoing work in unifying data assimilation and neural networks for parallel learning of turbulence models with quantified uncertainties.
About the speaker. Dr. Heng Xiao is Professor at the University of Stuttgart, Germany. He holds a bachelor’s degree from Zhejiang University, China, a master’s degree from the Royal Institute of Technology (KTH), Sweden, and a Ph.D. degree from Princeton University, USA. From 2009 to 2012, he worked as a postdoctoral researcher at ETH Zurich, Switzerland. Between 2013 and 2022, he was a faculty member in the Department of Aerospace and Ocean Engineering at Virginia Tech. In 2013 he moved to Stuttgart to take the chaired professorship in Data-Driven Fluid Dynamics. His current research focus on turbulence modeling with data-driven methods, including data assimilation, machine learning, and uncertainty quantification..
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room MATH 011 (basement)
ZOOM details:
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* Meeting ID: 940 7062 3025
* Passcode: applied
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