Wednesday 10:00 -10:50 am, https://ucr.zoom.us/j/97606227247
Organizers : Weitao Chen / Heyrim Cho / Yat Tin Chow / Qixuan Wang / Jia Gou / Mykhailo Potomkin / Yiwei Wang / Maziar Raissi / Siting Liu
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam
Archives: Fall 2019 / Winter 2020 / Spring 2020 / Fall 2020 / Winter 2021 / Spring 2021 / Fall 2021 / Winter 2022 / Spring 2022 / Fall 2022 / Winter 2023 / Spring 2023 / Fall 2023 / Winter 2024 / Spring 2024 /Fall 2024 / Winter 2025
Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar
In Winter 2025, the PDE & Applied Math seminar will be held through Zoom or in person (Skye 268). Specific information about the format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Maziar Raissi (maziarr@ucr.edu) and Dr. Yiwei Wang (yiweiw@ucr.edu).
Winter 2025 Schedule
Jan 8 04:00 PM (Wed) Dr. Thomas Bury (McGill University)
Jan 9 04:00 (Thu) Dr. Lingxia Qiao (UCSD)
Jan 10 04:00 (Fri) Dr. Mintao Xia (Courant Institute of Mathematical Sciences)
Jan 15 04:00 PM (Wed) Dr. Tingwei Meng (UCLA)
Jan 16 04:00 PM (Thu) Dr. Changhan He (UCI)
Jan 22 10:00 AM (Wed) Dr. Yuan Gao (Purdue University)
Jan 29 10:00 AM (Wed) Dr. Hengrong Du (UCI)
Feb 5 10:00 AM (Wed) Dr. Liping Deng (UCR)
Feb 12 10:00 AM (Wed) Dr. Hussain Ibdah (UCR)
Feb 19 10:00 AM (Wed) Dr. Aparna Chandramowlishwaran (UCI) Canceled
Feb 26 10:00 AM (Wed) Dr. Linfeng Li (UCLA)
Mar 5 10:00 AM (Wed) Dr. Yuebin Guo (Rutgers University)
Mar 12 10:00 AM (Wed) Dr. Ramin Bostanabad (UCI) Canceled, reschedule to April 30
Upcoming Talks:
Jan 29th, 2025, 10:00 AM - 11:00 AM PT
Hengrong Du (UCI)
Title: On the convergence of approximate Schrödinger Bridge
Abstract: The Schrödinger bridge has demonstrated promising applications in generative models. It is an entropy-regularized optimal-transport (EOT) approach that employs the iterative proportional fitting (IPF) algorithm to solve an alternating projection problem. However, due to the complexity of finding precise solutions for the projections, approximations are often required. In our study, we study the convergence of the IPF algorithm using approximated projections with a bounded cost or on a bounded domain. Our results demonstrate an approximate linear convergence with bounded perturbations. This is a joint work with Wei Deng, Yu Chen, Nicole Tianjiao Yang, Qi Feng, and Ricky TQ Chen.
Past Talks:
Jan 9th, 2025, 04:00 PM - 05:00 PM PT
Lingxiao Qiao (UCSD)
Title: Network Design Principle for Biological Functions
Abstract: The proper functioning of the organism relies on various cell behaviors, such as chemotaxis, circadian rhythms, and cell migration. The execution of these biological functions is closely related to biochemical processes within the cell. Specifically, receptors on the cell membrane sense change in the environment and transmit signals to downstream signaling molecules, regulating gene expression levels. Proteins translated from gene transcription can further regulate signaling pathways and metabolic networks. Moreover, biochemical molecules involved in the above cellular networks are usually not uniformly distributed within the cell, and many of them can form assemblies. Given the complexity of these cellular networks, mathematical models are widely used to model the cellular network and reveal the principles behind biological functions. By building mathematical models of signaling pathways, gene networks, and molecular assemblies, we have studied the mechanisms of biological functions including adaptation, noise resistance, oscillations, pattern formation, cell migration, and anti-phase oscillation. These studies have revealed the formation mechanisms of complex biological phenomena and provided an important theoretical foundation for biomedicine.
Jan 14th, 2025, 03:00 PM - 04:00 PM PT
Thomas M Bury (McGill University)
Title: Deep Learning for Predicting Critical Transitions in Natural Systems
Abstract: Critical transitions---abrupt, qualitative changes in a system's dynamics---occur in a wide range of natural systems, from the human heart to the Earth's climate. In recent years, substantial research has focussed on identifying early warning signals for these transitions using insights from dynamical systems theory and stochastic processes. In the first part of my talk, I will present our work on combining deep learning with dynamical systems to signal impending critical transitions. I will showcase our approach using data from various disciplines, including physiology, geology, engineering, and paleoclimatology.
In the second part of my talk, we will explore the dynamics of cardiac arrhythmia, a condition that poses many challenges in prediction and risk evaluation. I will present our research that combines mathematical modeling, deep learning, clinical data, and laboratory experiments to gain insight into the dynamics associated with the onset of cardiac arrhythmia. I will highlight how advancements in cardiac monitoring technologies are opening up exciting opportunities at the interface of cardiology and mathematics.
Jan 22th, 2025, 10:00 AM - 11:00 AM PT
Yuan Gao (Purdue University)
Title: Macroscopic Dynamics for Chemical Reactions: Large Deviation and Wasserstein Diffusion Approximation
Abstract: At a mesoscopic scale, the molecular count of each species in biochemical reactions can be modeled by random time-changed Poisson processes. To characterize the macroscopic behavior in the large-volume limit, the law of large numbers (LLN) in path space determines a mean-field limit ODE. Simultaneously, the WKB expansion leads to a Hamilton-Jacobi equation (HJE), with the corresponding Lagrangian providing the good rate function in the large deviation principle (LDP). A rigorous proof can be achieved by recasting Varadhan’s discrete nonlinear semigroup as a monotone scheme that approximates the limiting first-order HJE. The convergence of Varadhan’s discrete nonlinear semigroup (the monotone scheme) to the continuous Lax-Oleinik semigroup establishes the LDP for the chemical reaction process at any single time. Consequently, the macroscopic mean-field limit reaction rate equation is recovered. Moreover, the LDP for invariant measures can be used to construct the global energy landscape, enabling the dissipative-conservative decomposition of the reaction rate equation. For the diffusion approximation in the reversible (gradient flow) case, we also propose a canonical construction of diffusion on the probability simplex based on the discrete Wasserstein metric. In the two-species case, this Wasserstein diffusion approximation is equivalently transformed into the one-dimensional Wright-Fisher diffusion.