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Kamala Dadashova, NC State, Parameter subset selection for a mathematical model of antibody therapies for neurological diseases

SAS 1220

A significant challenge in the development of drugs to treat central nervous system (CNS) disorders is to attain sufficient delivery of antibodies across blood-brain barriers (BBB). Since not all antibodies can pass through BBB, it is crucial to understand antibody exposure in the CNS quantitatively to construct drug characteristics and identify proper dosing regimens. We…

Alexey Miroshnikov, Discover Financial Services, Wasserstein-based fairness interpretability framework for machine learning models

SAS 4201

The objective of this talk is to introduce a fairness interpretability framework for measuring and explaining the bias in classification and regression models at the level of a regressor distribution. In our work, we measure the model bias across sub-population distributions in the model output using the Wasserstein metric. To properly quantify the contributions of…

Daniel Stern, University of Chicago, Steklov Eigenvalues on Surfaces

SAS 4201

As described in the previous week's talk by Mikhail Karpukhin, there is a rich interplay between isoperimetric problems for Laplace eigenvalues on surfaces and the study of harmonic maps and minimal surfaces in spheres. Over the last 10-15 years, a program initiated by Fraser and Schoen has revealed a similar relationship between isoperimetric problems for the…

Differential Equations and Nonlinear Analysis Seminar: Stéphane Gaubert, École Polytechnique, France, What tropical geometry tells us about linear programming and zero-sum games

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Tropical convex sets arise as ``log-limits'' of parametric families of classical convex sets. The tropicalizations of polyhedra and spectrahedra are of special interest, since they can be described in terms of deterministic and stochastic games with mean payoff. In that way, one gets a correspondence between classes of zero-sum games, with an unsettled complexity, and classes…

John Darges, NC State, Extreme learning machines for variance-based global sensitivity analysis

SAS 1220

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while…

Semyon Tsynkov, NC State, Imaging With Synthetic Aperture Radar

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Synthetic aperture radars (SAR) use microwaves to obtain images of the Earth's surface from airplanes or satellites. SAR images can be taken during nighttime and prove insensitive to the clouds or dust in the atmosphere. Therefore, SAR complements the aerial or spaceborne photography, even though there are fundamental differences between the two technologies. For example,…

Albert Chern, UCSD, Geometric approaches to infinite domain problems

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Numerical simulations on infinite domains are challenging. In this talk, we will take geometric approaches to analyze the problems and provide new solutions.  One problem we tackle is the perfectly matched layer (PML) problem for computational waves on infinite domains. PML is a theoretical wave-absorbing medium attached to the truncated domain that generates no reflection…

Differential Equations and Nonlinear Analysis Seminar: Bianchini Stefano, SISSA, ITALY, Properties of mixing BV vector fields

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We consider the density properties of divergence-free vector fields b in L^1(,BV(^2)) which are ergodic/weakly mixing/strongly mixing: this means that their Regular Lagrangian Flow X_t is an ergodic/weakly mixing/strongly mixing measure preserving map when evaluated at t=1. Our main result is that there exists a G-set U made of divergence free vector fields such that – The map T associating b with…

Sonia Kovalesky Day

SAS Hall Lobby

AWM is happy to announce that we will be bringing back our Sonia Kovalevsky (SK) Day event this year, which will take place on Saturday, April 9th from 9:15a-2:00p in SAS Hall on NCSU's campus. Sonia Kovalevsky was the first major female mathematician and, in honor of her, schools across the nation host an SK…

Gregor Kemper, Technical University of Munich, Distance geometry, algebra and drones

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Is it always possible to reconstruct a point configuration in the plane from the unlabeled set of mutual distances between the points? This and other questions translate to invariant theory and ultimately into problems about polynomial ideals. As it turns out, the following question is related: Can a drone detect the walls of a room…

Harley Hanes, NC State, Sensitivity and Identifiability Analysis of Boundary Penalties in a Galerkin Reduced Order Model.

SAS 1220

Galerkin reduced-order models (ROMs) approximate computational fluid simulations by reducing snapshot data to a basis of proper orthogonal decomposition (POD) modes and solving for modal coefficients with ordinary differential equations. Galerkin ROMs reduce computational cost and can approximate flows with alternate Reynolds numbers, while parametric reduced order models allow adjustment of other system parameters. However,…

Differential Equations and Nonlinear Analysis Seminar: Robin Neumayer, CMU, USA, Quantitative Faber-Krahn Inequalities and Applications

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Among all drum heads of a fixed area, a circular drum head produces the vibration of lowest frequency. The general dimensional analogue of this fact is the Faber-Krahn inequality: balls have the smallest principal Dirichlet eigenvalue among subsets of Euclidean space with a fixed volume. I will discuss new quantitative stability results for the Faber-Krahn…

Math Honors Presentation Session

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Some of our math honors students are giving talks on their research on  Friday, April 15, 2022 at 3 pm.   There will be nine 12 - 15 minute talks on  zoom and it would be great if you can attend this zoom session to listen to their research work. https://ncsu.zoom.us/j/96201139617?pwd=eFVadDNFOE1nQ3dyRVpvMk8yM0pOUT09 Meeting ID: 962 0113 9617 Passcode: 915393 Erick…

Differential Equations and Nonlinear Analysis Seminar: Francesca Bucci, Università degli Studi di Firenze, Italy, Riccati theory in the realm of PDE’s: state of the art and recent advances in the optimal control of evolution equations with memory

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The well-posedness of Riccati equations plays a central role in the study of the optimal control problem with quadratic functionals for linear partial differential equations (PDEs). Indeed, it allows the synthesis of the optimal control by solving the Riccati equation corresponding to the minimization problem, and then of the closed-loop equation. In this lecture I…

RESCHEDULED Thomas J. R. Hughes, University of Texas at Austin, Isogeometric Analysis: Mathematical and Engineering Perspectives

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The vision of Isogeometric Analysis (IGA) was first presented in a paper published October 1, 2005 . Since then it has become a focus of research within both the fields of Finite Element Analysis (FEA) and Computer Aided Design (CAD) and has become a mainstream analysis methodology and provided a new paradigm for geometric design…

Abhi Chowdhary, NC State, Infinite-dimensional Bayesian inversion for fault slip from surface measurements

SAS 1220

Given the inability to directly observe the conditions of a fault line, inversion of parameters describing them has been a subject of practical interest for the past couple of decades. To resolve this under a linear elasticity forward model, we consider Bayesian inference in the infinite dimensional setting given some surface displacement measurements, resulting in…