Dry eye disease is caused by a breakdown of a uniform tear film, which occurs when the layer of tears experiences breakup. To better understand this ocular condition, the dynamics of the tear film can be studied using fluorescence imaging. Many parameters affect tear film thickness and fluorescent intensity distributions over time; exact values or…
In this talk I will introduce a geometric inverse problem that is motivated by geophysical imaging and seismology. Specifically, I will reconstruct a compact Riemannian manifold with strictly convex boundary from wave-based data on the boundary. The given data assumes the knowledge of an open measurement region on the boundary, and that for every point…
We study problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of alarge class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems.…
Jared finished his Ph.D. in Applied Math at NC State two years ago and since then has been working at Teledyne Technologies in their Intelligent Systems Lab. During that time he primarily worked on DARPA contracts, but also worked on internal research and development projects. He will be discussing his work on a power lines detection…
In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either only one vertex or only one hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed.…
The capability of using imperfect statistical reduced-order models to capture crucial statistics in complex turbulent systems is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent dynamical equations using both parameterization and machine learning strategies. A systematic framework of correcting model errors with empirical information theory is…
Waists and widths measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds, as well as applications to quantitative symplectic camels. Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact Peter McGrath…
A nonlinear model is developed for fluid-poroelastic structure interaction with quasi-Newtonian fluids that exhibit a shear-thinning property. The flow in the fluid region is described by the Stokes equations and in the poroelastic medium by the quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting…
Advisor Ernest Stitzinger, contact for Zoom access
Advisor Ilse Ipsen (ipsen@ncsu.edu contact for Zoom access)
Advisor Kailash Misra (misra@ncsu.edu contact for Zoom access)
Advisor Alen Alexanderian (alexanderian@ncsu.edu, contact for Zoom access)
Gaussian processes (GPs) are popular models for random functions in computational and applied mathematics, statistics, machine learning and data science. However, GP methodology scales poorly to large data-sets due to the need to factorize a dense covariance matrix. In spatial statistics, a standard approach to surmount this challenge is to represent Matérn GPs using finite…
Advisor Hien Tran (tran@ncsu.edu, contact for Zoom access)
The Laplacian is a canonical second order elliptic operator defined on any Riemannian manifold. The study of optimal upper bounds for its eigenvalues is a classical problem of spectral geometry going back to J. Hersch, P. Li and S.-T. Yau. It turns out that the optimal isoperimetric inequalities for Laplacian eigenvalues are closely related to…
Advisor Seth Sullivant (smsulli2@ncsu.edu, contact for Zoom access)
In recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based…
Advisor Pierre Gremaud, contact for Zoom access
In this talk we will discuss the connection between invariant evolutions of polygons and completely integrable discrete systems via polygonal geometric invariants. We will give examples and show how some open problems for bi-Hamiltonian structures of discrete systems were made easier and solved using this correspondence. If time allows we will discuss some open problems.…