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February 2021

Applied Math. Talk: Modeling and Simulation of Ultrasound-mediated Drug Delivery to the Brain by Peter Hinow, University of Wisconsin, Milwaukee

February 15 @ 3:00 pm - 4:00 pm
Zoom meeting United States

We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound. Thereupon, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier. We present a compartmental model of a capillary that is able to capture the complex binding and transport processes the drug undergoes in the…

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Applied math. talk: Heatmap centrality: a new measure to identify super-spreader nodes in scale-free networks by Christina Duron, the University of Arizona

February 22 @ 3:00 pm - 4:00 pm
Zoom meeting United States

Abstract: The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the “shortest path” between two nodes, this talk will explore the properties of the recently proposed measure, the heatmap centrality, by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often…

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March 2021

Applied math. talk: Blowup rate estimates of a singular potential in the Landau-de Gennes theory for liquid crystals by Xiang Xu, Old Dominion University.

March 1 @ 3:00 pm - 4:00 pm
Zoom meeting United States

Abstract: The Landau-de Gennes theory is a type of continuum theory that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. In the free energy, there is a singular bulk potential which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. In this talk we shall discuss some analytic properties related to this singular potential. More specifically, we provide precise estimates of both this singular potential and its…

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Applied math. talk: Optimal control of the SIR model in the presence of transmission and treatment uncertainty by Henry Schellhorn, CGU

March 8 @ 3:00 pm - 4:00 pm
Zoom meeting United States

Abstract The COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency of treatments is subject to uncertainty. We consider two different regimes, or submodels, of the stochastic SIR model, where the population consists of three groups: susceptible, infected and recovered. In the first regime the proportion of infected is very low, and the proportion of susceptible is very close to 100%. …

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Applied math. talk: Periodic travelling waves in nonlinear wave equations: modulation instability and rogue waves by Dmitry Pelinovsky, McMaster University, Canada

March 22 @ 3:00 pm - 4:00 pm
Zoom meeting United States

Abstract:     I will overview the following different wave phenomena in integrable nonlinear wave equations: (1) universal patterns in the dynamics of fluxon condensates in the semi-classical limit; (2) modulational instability of periodic travelling waves; (3) rogue waves on the background of periodic and double-periodic waves. Main examples include the sine-Gordon equation, the nonlinear Schroedinger equation, and the derivative nonlinear Schroedinger equation. For the latter equation, in collaboration with Jinbing Chen (South East University, China) and Jeremy Upsal (University…

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Applied math. talk: Hyperbolicity-Preserving Stochastic Galerkin Method for Shallow Water Equations by Dihan Dai, Department of Mathematics, University of Utah

March 29 @ 3:00 pm - 4:00 pm
Zoom meeting United States

Abstract: The system of shallow water equations and related models are widely used in oceanography to model hazardous phenomena such as tsunamis and storm surges. Unfortunately, the inherent uncertainties in the system will inevitably damage the credibility of decision-making based on the deterministic model. The stochastic Galerkin (SG) method seeks a solution by applying the Galerkin method to the stochastic domain of the equations with uncertainty. However, the resulting system may fail to preserve the hyperbolicity of the original model.…

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April 2021

Applied math. talk: Large Eddy Simulation Reduced Order Models by Traian Iliescu, Virginia Tech

April 12 @ 3:00 pm - 4:00 pm
Zoom meeting United States

In this talk, we present reduced order models (ROMs) for turbulent flows, which are constructed by using ideas from large eddy simulation (LES) and variational multiscale (VMS) methods.  First, we give a general introduction to reduced order modeling and emphasize the connection to classical Galerkin methods (e.g., the finite element method) and the central role played by data.  Then, we describe the closure problem, which represents one of the main obstacles in the development of ROMs for realistic, turbulent flows. …

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Applied math. talk: Adversarially robust classification via geometric flows, by Ryan Murray, North Caroline State University

April 19 @ 3:00 pm - 4:00 pm
Zoom meeting United States

Abstract: Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However, recently there have been a number of works demonstrating that these improved algorithms can be "fooled" using specially constructed adversarial examples. In turn, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks. In this talk I will describe a recently…

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Applied Math. Talk: Balancing Geometry and Density: Path Distances on High-Dimensional Data by Anna Little, University of Utah

April 26 @ 3:00 pm - 4:00 pm
Zoom meeting United States

 Abstract: This talk discusses multiple methods for clustering high-dimensional data, and explores the delicate balance between utilizing data density and data geometry. I will first present path-based spectral clustering, a novel approach which combines a density-based metric with graph-based clustering. This density-based path metric allows for fast algorithms and strong theoretical guarantees when clusters concentrate around low-dimensional sets. However, the method suffers from a loss of geometric information, information which is preserved by simple linear dimension reduction methods such as…

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