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Bridging Scales in Cell Biology: Transport, Stochasticity, and Particle Methods
Bridging Scales in Cell Biology: Transport, Stochasticity, and Particle Methods
Abstract: At the scale of a single cell, chemical processes are driven by a complex interplay of spatial transport and stochasticity. Capturing these dynamics requires mathematical models that bridge the microscopic and macroscopic worlds. In this talk, I will introduce the mesoscopic particle methods we use to investigate cellular processes, which we have applied to problems in cellular signaling and antibody-antigen interactions. I will explore several aspects of our recent research, which has included the development of accurate and efficient numerical simulation methods, the derivation and analysis of rigorous coarse-grained (PDE) limits, and applications to immune signaling. By surveying these different areas, this talk will offer a broad introduction to the mathematical and computational challenges of modeling cellular biology at the single cell scale.
Leveraging Tensor Structure in Imaging Applications
Leveraging Tensor Structure in Imaging Applications
Abstract: A tensor is a multiway array. Such objects arise naturally in imaging applications in the form of a data structure: for example, a hyperspectral data cube is a third order tensor, a digital color video is a fourth order tensor, etc. Perhaps less obvious is the role tensors can play with respect to operator representations that arise in imaging science. Recent research has shown that the use of tensors and their decompositions can be instrumental in revealing latent correlations of data and operators residing in high-dimensional spaces. Once exposed, this latent structure can translate into an expressiveness that yields superior results in applications such as compression, completion, and operator approximation, as compared to those obtained when viewing problems through the traditional matrix-based lens. In this talk, we give an overview of some popular tensor decompositions in context of imaging applications and highlight areas for future research.
How ill conditioned can submatrices of the
How ill conditioned can submatrices of the
Fourier matrix be?
Fourier matrix be?
Abstract: The discrete Fourier transform matrix, and submatrices of it, appear in a wide variety of applications. While the Fourier matrix itself is a scaled unitary matrix, its submatrices can be exponentially ill-conditioned.
In this talk, we discuss applications, prior work, and we provide tight estimates for just how ill-conditioned such matrices can be.
Bio: Dr. Samuel Isaacson received his Bachelor's degree in Applied Mathematics and Computer Science from Brown University, and his Ph.D. in Mathematics from NYU’s Courant Institute of Mathematical Sciences, working under the direction of Charles Peskin. Following a postdoctoral fellowship in the Biomathematics Research Group at the University of Utah, he joined the faculty at Boston University in 2008, where he is also affiliated with the Graduate Program in Bioinformatics and the Hariri Institute for Computing.
Dr. Isaacson’s research sits at the intersection of mathematical biology, numerical analysis, and mathematical physics. He focuses heavily on the development and numerical analysis of methods for studying biological processes at the single cell scale. His recent work addresses the rigorous coarse-grained limits of particle stochastic reaction-diffusion models, and he has developed highly accurate, efficient numerical methods to simulate these models within realistic cellular geometries. He complements this theoretical work with collaborative studies with experimentalists, investigating problems in T cell signaling and antibody-antigen interactions that combine modeling, inference, and experimental data to estimate the biophysical parameters driving ligand-receptor dynamics. In recent years he has also led the development of open source numerical libraries for the modeling and simulation of systems of reacting chemicals
His contributions to applied mathematics and biology have been recognized with numerous grants and honors, including an NSF CAREER Award, as well as recent highlighted publications in journals such as Nature Communications.
Bio: Dr. Misha Kilmer is the William Walker Professor of Mathematics at Tufts University. From 2021-2025 she served as a Deputy Director of the Institute for Computational and Experimental Research in Mathematics Brown University. She is a Class of 2026 AMS Fellow. In 2019, Prof. Kilmer was named a Fellow of the Society for Industrial and Applied Mathematics (SIAM) "for her fundamental contributions to numerical linear algebra and scientific computing, including ill-posed problems, tensor decompositions, and iterative methods.” She served as a Section Editor for SIAM Review, SIAM’s flagship journal, for five years. Prof. Kilmer had the honor of being a Kirk Distinguished Visiting Fellow at the Isaac Newton Institute for Mathematical Sciences at Cambridge University in Spring 2023. She is an inaugural member of the Tufts Chapter of the National Academy of Inventors, the 2023 recipient of the Tufts Faculty Distinguished Scholar Award and earned the unique distinction of being promoted directly from Assistant to Full Professor at Tufts in 2005.
Bio: Dr. John Urschel is the Class of 1956 Career Development Assistant Professor of Mathematics at MIT. Previously, he was a member of the Institute for Advanced Study and a Junior Fellow at the Harvard Society of Fellows. He received his Ph.D. in Mathematics from MIT in 2021 under the supervision of Michel Goemans. His main research interests include matrix analysis, numerical linear algebra, and spectral graph theory. He is the recipient of the SIAM DiPrima Prize, the SIAM Early Career Prize in Linear Algebra, and the ILAS Brualdi Early Career Prize.
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