Events
Department of Mathematics and Statistics
Texas Tech University
Abstract pdf
Many species have a consumer-resource relationship in which the resource species serve as food to the consumer species, causing death for the resource and growth for the consumer species. This relationship can involve a consumer and a resource, or multiple consumers and a resource. In the case of multiple consumers, competition for a resource is possible, and this can lead to death in any of the consumers. These processes can be continuous (which monitors populations of the consumer and resource at every time), or discrete (which monitors the populations yearly). Models that are only continuous or discrete may fail to take on the various workings of the species. Hence, this work combines continuous and discrete approaches to model consumer-resource interactions. For this model, it is vital to understand what leads to the death of the species, the survival of either, or the coexistence of both. However, identifying and understanding the behaviors possible require careful analysis and computations due to the model approach. In the case of competing consumers, we establish necessary conditions on model parameters for the existence of a coexistence fixed point. For the rest of our parameter space, we use a numerical approach to create a bifurcation-like image that shows the possible behaviors this model can exhibit. This is accomplished by testing the model over a wide span of parameters and varying initial conditions using Latin Hypercube Sampling. We identify parameters and initial conditions that produce the persistence of both species. In the case of a single consumer, we compare the behavior in different regions to existing bifurcation curves and obtain a better understanding of parameter regions without analytic results.
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Estimation of heterogeneous treatment effects is an essential component of precision medicine. Model and algorithm-based methods have been developed within the causal inference framework to achieve valid estimation and inference. Existing methods such as the A-learner, R-learner, modified covariates method (with and without efficiency augmentation), inverse propensity score weighting, and augmented inverse propensity score weighting have been proposed mostly under the square error loss function. The performance of these methods in the presence of data irregularity and high dimensionality, such as that encountered in electronic health record (EHR) data analysis, has been less studied. In this research, we describe a general formulation that unifies many of the existing learners through a common score function. The new formulation allows the incorporation of least absolute deviation (LAD) regression and dimension reduction techniques to counter the challenges in EHR data analysis. We show that under a set of mild regularity conditions, the resultant estimator has an asymptotic normal distribution. Within this framework, we proposed two specific estimators for EHR analysis based on weighted LAD with penalties for sparsity and smoothness simultaneously. Our simulation studies show that the proposed methods are more robust to outliers under various circumstances. We use these methods to assess the blood pressure-lowering effects of two commonly used antihypertensive therapies.
Please virtually attend this week's Statistics seminar at 4:00 PM (CDT, UT-5) via this zoom link
In this talk I will discus a recognition principle for iterated suspensions as coalgebras over the little cubes operad. This is joint work with Oisín Flynn-Connolly and José Moreno-Fernádez. arXiv:2210.00839.
Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Steklov eigenvalue problem is an eigenvalue problem for an operator which is defined in the boundary of a domain. Since the operator is nonlocal, the eigenvalues depend on both the geometries of the interior and the boundary of the domain. In this talk, we consider the Steklov-Dirichlet eigenvalue problem in eccentric annuli. We investigate the first eigenvalue if the distance between the boundary components are sufficiently close. This is based on joint work with Jiho Hong and Mikyoung Lim (KAIST).
Two classical problems in commutative algebra are the classification
of the (perfect) ideals of a (regular local) ring in terms of their
minimal free resolutions, and the description of their linkage
classes. In particular one would like to describe all the ideals in
the linkage class of a complete intersection. In this seminar we deal
with these two problems for perfect ideals of codimension 3. The main
tools that we use are sequences of linear maps that can be defined
over an exact complex of length 3 and that generalize the well-known
multiplicative structure (Joint work with Xianglong Ni and Jerzy
Weyman).
Abstract. Continuum plasma physics models are used to study important phenomena in astrophysics and in technology applications such as magnetic confinement (e.g. tokamak), and pulsed inertial confinement (e.g. NIF, Z-pinch) fusion devices. The computational simulation of these systems requires solution of the governing PDEs for conservation of mass, momentum, and energy, along with various approximations to Maxwell's equations. The resulting systems are characterized by strong nonlinear coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that these interactions produce. For effective long-time-scale integration of these systems some aspect of implicit time integration is required. These characteristics make scalable and efficient parallel iterative solution, of the resulting poorly conditioned discrete systems, extremely difficult.
This talk will discuss the structure of the implicit continuum fluid models that we are employing for MFC type applications. These include resistive magnetohydrodynamics (MHD), and a partially ionized multifluid electromagnetic (EM) plasma formulation. After discretization by stabilized finite element type methods the strongly coupled highly nonlinear algebraic system is achieved with a fully-coupled Newton nonlinear iterative method. The resulting large-scale sparse linear systems are iteratively solved by a GMRES Krylov method, preconditioned by approximate block factorization (ABF) and physics-based preconditioning approaches. These methods reduce the coupled multiphysics system to a set of simplified sub-systems to which scalable algebraic multilevel methods (AMG) can be applied. A critical aspect of these preconditioners is the development of approximate Schur complement operators that encode the critical cross-coupling physics of the system. To demonstrate the flexibility and performance of these methods we consider application of these techniques to various challenging prototype plasma problems. These include computational results relevant to aspects of magnetic confinement fusion applications. Results are presented on robustness, efficiency, and the parallel and algorithmic scaling of the solution methods. This work is collaborative with Jesus Bonilla, Edward Phillips, Peter Ohm, Michael Crockatt, Ignacio Tomas, Roger P. Pawlowski, R. Tuminaro, Jonathan Hu, Xinazhu-Tang, and Luis Chacon.
About the speaker. John Shadid is a Distinguished Member of the Technical Staff in the Computational Mathematics Department at Sandia National Laboratories, and has an appointment as a National Lab Professor in the Mathematics Department at the University of New Mexico. Dr. Shadid received his Ph.D. in Mechanical Engineering from the University of Minnesota in 1989. John has contributed to the areas of applied math, numerical methods, computational algorithms, and software development, for solution methods of highly-nonlinear coupled multiple-time-scale PDE systems. John was co-PI for the Aztec software library that received a 1997 R&D100 award and was one of the very first scalable parallel iterative solver libraries. He has also been lead-PI for several projects developing robust, scalable, implicit finite element reacting flow, MHD, and multifluid electromagnetic plasma system simulation capabilities in support of DOE Office of Science oriented scientific applications.
In 2018, he was elected as a SIAM Fellow, and in 2019 he received the United States Association of Computational Mechanics (USACM) Thomas J.R. Hughes Medal for Computational Fluid Mechanics.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
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* Meeting ID: 940 7062 3025
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