I and many collaborators, postdocs, and students from many disciplines have explored lung mechanics and disease pathology for over 2 decades in a pan-university effort called the UNC Virtual Lung Project. In the last decade we have explored how viruses “traffic” in mucosal barriers, including the human respiratory tract (RT), in the presence of antibodies.…
Virtual Career Fair, Entrepreneurship Workshop and Industry Panel. Register for all 3 events at https://careers.dasa.ncsu.edu/data-science-career-expo/
Monsoons are significant atmospheric phenomena that manifest over various regions in the tropics and have massive social and economic consequences. We will present hybrid methods that combine ideas from dynamical systems-based nonlinear time series analysis and machine learning and analyze the dynamics of the South Asian monsoon. Specifically, we will show two sets of results,…
Presentations by: Zixuan Cang and Hangjie Ji During each 50-minute First Year Research Seminar, two faculty give our new graduate students a short (~20-25 minute), accessible talk about their research or research area.
I am going to report on recent work on the numerical optimization of tangent-point energies of curves and surfaces. After a motivation and brief introduction to the central computational tools (construction of suitable Riemannian metrics on the space of embedded manifolds, a polyhedral discretization of the energies, and fast multipole techniques), I am going to…
Zoom meeting: Link
Disordered systems are mathematical models (typically of the physical world) that are governed by random variables. These models have offered insights into a diverse array of research problems, and have also brought about a great number of powerful mathematical tools. The through line to the subject is the essential role played by probability theory, a…
Brian Adams (NCSU PhD 2005) will conduct a mathematics and statistics-specific information session including a brief overview of SNL’s mission, R&D areas, and opportunities in mathematics, statistics, and computational science. Staff and project profiles will demonstrate the ways you can contribute to high-impact problems in the national interest through fundamental math and computational science R&D, software/hardware development,…
It is a classical result that the simple algebras in the category of finite dimensional vector spaces are precisely the n x n matrix algebras. The notion of algebras in more general tensor categories is easy to formulate, and we can ask for classification results in these categories. Such classification results have broad applications to conformal field…
When dealing with large compartment models it can often be challenging to track how a small component of the model affects the overall system. This is an issue when trying to determine if a model is in its "simplest form" or if there are components that can be removed without significantly affecting the model's behavior.…
Graph associahedra are simple polytopes dual to tubing complexes based on graphs, where a tubing consists of compatible connected subgraphs of a graph G. Graph associahedra can be realized by repeatedly truncating faces of a simplex. We generalize graph associahedra to define P-graph associahedra, which can be realized by repeatedly truncating faces of a simple polyhedron P. When P is…
Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability. Gibbsian line ensembles can be thought of as collections of…
In this talk, Dr. Olivia Walch, the CEO of Arcascope, will discuss her research into the mathematics of sleep and circadian rhythms modeling, and large scale analysis of wearable data. She will also discuss her journey from being a post-doc to forming her own start-up, as well as the challenges and opportunities in taking these mathematical…
Constructing efficient numerical solution methods for the equation of radiative transfer (ERT)remains as a challenging task in scientific computing despite of the tremendous development on the subject in recent years. We present in this work a simple fast computational algorithm for solving the ERT in isotropic media in steady state setting and time-dependent setting. The algorithm we developed has two steps. In the first step, we solve a volume integral equation for the angularly-averaged ERT solution using iterative schemes such as the GMRES method.The computation in this step is accelerated with a fast multipole method (FMM). In the second step, we solve a scattering-free transport equation to recover the angular dependence of the ERT solution. The algorithm does not require the underlying medium be homogeneous. We present numerical simulations under various scenarios to demonstrate the performance of the proposed numerical algorithm for both homogeneous and heterogeneous media. Then we will…
In this talk, I will discuss the Bernstein problem for minimal surfaces, and the recent solution to the stable Bernstein problem for minimal hypersurfaces in R^4. Precisely, we show that a complete, two-sided, stable minimal hypersurface in R^4 is flat. Corollaries include curvature estimates for stable minimal hypersurfaces in 4-dimensional Riemannian manifolds, and a structural…
In the study of disordered quantum systems, it is believed that a strong dichotomy should occur between two phases: a delocalized (or conducting) phase and a localized (or insulating) phase. While this is far from being proved in all generality, the study of large symmetric random matrices, which model simple systems, allows us to describe…
A classical result due to Dobrushin (1956) yields the central limit theorem for partial sums of functionals of inhomogeneous ("sufficiently contracting'') Markov chains. In the talk we will restrict to bounded functionals of uniformly elliptic inhomogeneous Markov chains, for which we can obtain: A Berry-Esseen theorem (optimal rates in the Central limit theorem); Correction terms of…
Many inference problems relate to the dynamical system, x'=f(x). One primary problem in applications is that of system identification, i.e., how should the user accurately and efficiently identify the model f(x), including its functional family or parameter values, from discrete time-series data? One of the most successful algorithms to this end is the Sparse Identification of…
The rectangle poset and the action of rowmotion on it are two well studied objects in dynamical algebraic combinatorics, but work involving the trapezoid poset has proven more difficult. In 1983 Proctor showed that the number of reverse plane partitions of the rectangle poset and its associated trapezoid are the same. Since then it has…