Links :  UCR Interdisciplinary Center for Quantitative Modeling in Biology

     UCR Math Department seminar

               PDE and Applied Math Seminar

The format of the seminar is hybrid. One might join the seminars in Skye Hall 284 (unless another location is announced for a specific talk) or online through Zoom (unless the talk is joint with the departmental colloquium). Please contact Dr. Potomkin (mykhailp@ucr.edu) if you are interested in attending this seminar.

Winter 2024 

January 16, 11:30 AM Siting Liu, University of California, Los Angeles - jointly with Departmental Colloquium

January 17, 4:00 PM Herve Nganguia, Towson University - jointly with Departmental Colloquium 

January 22, 4:00 PM Mitchel Colebank, University of California, Irvine - jointly with Departmental Colloquium 

January 24, 4:00 PM Yuchi Qiu, University of California, Irvine - jointly with Departmental Colloquium 

January 25, 4:00 PM Daniel Gomez, University of Pennsylvania - jointly with Departmental Colloquium 

February 20, 2:00 PM Bo Li, University of California, San Diego - jointly with Departmental Colloquium 

February 21, 1:00 PM Stacey Finley, University of Southern California - Distinguished Lecture in Mathematical and Computational Biology

February 27, 2:00 PM, John Nardini, The College of New Jersey

March 5, 2:00 PM, Christopher E. Miles, University of California, Irvine

March 12, 2:00 PM, Daniel S. Munther, Cleveland State University 

Upcoming talks:

March 12, 2024, 2:00 PM - 2:50 PM Pacific Time

Daniel S. Munther, Cleveland State University 

Title: Modeling enteric pathogen dynamics on leafy vegetables based on weather parameters and bacterial state.

Location is 284 Skye and in zoom

Abstract: Weather affects key aspects of bacterial behavior on plants but has not been extensively investigated as a tool to assess risk of crop contamination with human foodborne pathogens. In this talk, I will discuss a newly developed mechanistic model,  informed by weather factors and bacterial state, designed to predict population dynamics on leafy vegetables. The model utilizes temperature, radiation, and dew point depression to characterize pathogen growth and decay rates. Additionally, the model incorporates the population level effect of bacterial physiological state dynamics in the phyllosphere in terms of the duration and frequency of specific weather parameters. Our results highlight the potential of a comprehensive weather-based model in predicting contamination risk in the field. Such a modeling approach would additionally be valuable for timing field sampling in quality control to ensure the microbial safety of produce. This is joint work with Maria Brandl (USDA-ARS), Renata Ivanek (Cornell U.), Ana Allende (CEBAS-CSIC, Spain).

Previous talks:

January 16, 2024, 11:30 AM - 12:20 PM Pacific Time

Siting Liu, University of California, Los Angeles

Title: Enhancing PDE computations and Score-based Generative Models through Optimization

Location is 268 Skye, preceded by Tea (11:15 - 11:30 AM) in 272 Skye

Abstract: This presentation explores optimization strategies for improving both partial differential equations (PDE) and score-based generative models (SGM). In the realm of numerical computations, we introduce a saddle point framework that capitalizes on the inherent structure of PDEs. Integrated seamlessly with existing discretization schemes, this framework eliminates the necessity for nonlinear inversions, paving the way for efficient parallelization. Shifting our focus to SGM, we delve into the mathematical foundations of the Wasserstein proximal operator (WPO). Specifically, we express it as the Wasserstein proximal operator of cross-entropy. By leveraging the PDE formulation of WPO, we propose a WPO-informed score model that demonstrates accelerated training and reduced data requirements.   

January 17, 2024, 4:00 PM - 4:50 PM Pacific Time

Herve Nganguia, Towson University

Title: Towards a multi-scale mathematical model for drug delivery systems

Location is 284 Skye, preceded by Tea (3:45 - 4:00 PM)

Abstract: Drug delivery systems (DDS) are revolutionizing modern medicine and present the most promising therapeutic alternatives to treat illnesses while minimizing side effects. In experiments and clinical trials, they have been proven particularly useful in the management of effective cancers medications and therapies that are also highly toxic for healthy cells. Beyond their biomedical potential, the design, deployment and control of DDS represent an interesting (and indeed fascinating) multi-scale mathematical modeling problem. I will start my presentation with a brief survey of laboratory experiments illustrating the range of drug delivery machines design, followed by a discussion of the various components involved in this practical application of mathematical and physical methods. The rest of the talk will be devoted to a couple of recent modeling efforts related to DDS' design and propulsion in biologically relevant flows. 

January 22, 2024, 4:00 PM - 4:50 PM Pacific Time

Mitchel Colebank, University of California, Irvine

Title: Computational Modeling and Statistical Inference for Cardiovascular Digital Twins

Location is 284 Skye, preceded by Tea (3:45 - 4:00 PM)

Abstract: Cardiovascular disease is the leading cause of death in the modern world and acts on multiple spatial and temporal scales. Computational models have had notable success in simulating cardiovascular function and integrating multimodal data from either pre-clinical or clinical studies. The development of subject-specific models informed by these data sources are necessary for establishing cardiovascular digital twins for clinical patient management. However, functional data (e.g., invasive hemodynamics) as well as structural imaging data are both subjected to measurement error but are necessary for model calibration and parameter inference. Thus, cardiovascular digital twins must include mathematical models of multiscale, physiological mechanisms, as well as robust statistical methods for parameter inference and uncertainty quantification. Surrogate modeling is also necessary to overcome the computational expense of these multiscale models and enable nearly real time predictions. In this talk, I will discuss innovations in image-based models of blood flow (described by partial differential equations), multiscale systems-level models of cardiac function (systems of ordinary differential equations), and the statistical tools necessary for inverse problems and uncertainty quantification in cardiovascular research. While a majority of the work will focus on pulmonary vascular and right heart function, these methods collectively build the necessary tools for developing digital twins for multiple cardiac and vascular sub-units of the full cardiovascular system.  

January 24, 2024, 4:00 PM - 4:50 PM Pacific Time

Yuchi Qiu, University of California, Irvine

Title: Multiscale modeling and topological data analysis in artificial intelligence-driven biology

Location is 284 Skye, preceded by Tea (3:45 - 4:00 PM)

Abstract: Artificial intelligence (AI) has emerged as a pivotal tool in biology, revolutionizing data analysis at both large-scale and single-cell levels. However, the lack of interpretability in Al poses challenges in extracting intricate functions and dynamics from high-dimensional, complex heterogeneous, and noisy biological data. In this talk, we aim to address these challenges by investigating dynamics and topology of data via multiscale modeling and topological data analysis. First, we will discuss our approaches for deciphering cellular spatio-temporal dynamics, focusing on the interplay between gene regulation, spatial signals, and intercellular mechanical interactions. Our approaches include stochastic simulations, the subcellular element method, and reaction-diffusion equations. Building upon this foundation, we have developed a deep learning-based dynamical model using unbalanced dynamic optimal transport to connect time-course single-cell transcriptomic snapshots and interrogate underlying gene regulatory networks. Lastly, we will discuss AI models designed to expedite protein design that incorporate a persistent spectral Laplacian method, large language models, and a hierarchical clustering-based Bayesian optimization approach.   

January 25, 2024, 4:00 PM - 4:50 PM Pacific Time

Daniel Gomez, University of Pennsylvania 

Title: Asymptotic Analysis of Localized and Singular Perturbations with Lévy Flights

Location is 284 Skye, preceded by Tea (3:45 - 4:00 PM)

Abstract: How long will a confined Brownian particle take to hit an exceedingly small target? It is a classical result that the expected value of this first hitting time (FHT) blows up as the size of the target vanishes in two or more spatial dimensions. This is an example of a "strongly localized perturbation" in the sense that small geometric defects have large global effects. If Brownian motion is replaced with Lévy flights, a spatially discontinuous jump process, then the FHT has the potential to blow up even in the case of one spatial dimension. In this talk, I will discuss how matched asymptotic expansions yield a computationally inexpensive method for computing the FHT in the case of Lévy flights by reducing the problem to that of solving a linear system of equations. Moreover, we will see that depending on the fractional order of the Lévy flight, the FHT is qualitatively similar to that for Brownian motion in one or more spatial dimensions. In addition to analyzing FHT problems, matched asymptotic expansions have also been highly successful in studying localized solutions to singularly perturbed reaction diffusion systems. I will conclude by outlining how matched asymptotic expansions similarly yield nonlinear algebraic systems, globally coupled eigenvalue problems, and differential algebraic equations that describe the structure and dynamical properties of localized solutions. 

February 20, 2024, 2:00 PM - 2:50 PM Pacific Time

Bo Li, University of California, San Diego

Title: Variational Implicit Solvation and Fast Algorithms for Biolecular Binding and Unbinding

Location is 284 Skye

Abstract: Ligand-receptor binding and unbinding are fundamental molecular processes, whereas water fluctuations impact strongly their thermodynamics and kinetics. We develop a variational implicit-solvent model (VISM) and a fast binary level-set method to calculate the potential of mean force and the molecule-water interfacial structures for dry and wet states. Monte Carlo simulations with our model and method provide initial configurations for efficient molecular dynamics simulations. Moreover, combined with the string method and stochastic simulations of ligand molecules, our hybrid approach enables the prediction of the transition paths and rates for the dry-wet transitions and the mean first-passage times for the ligand-pocket binding and unbinding. Without any explicit description of individual water molecules, our predictions are in a very good, qualitative and semi-quantitative, agreement with existing explicit-water molecular dynamics simulations. This talk reviews a series of works done in collaboration with L.-T. Cheng, S. Zhou, Z. Zhang, S. Liu, H.-B. Cheng, J. Dzubiella, C. Ricci, and J. A. McCammon.

February 21, 2024, 1:00 PM - 1:50 PM Pacific Time

Stacey Finley, University of Southern California

Title: Exploring the Tumor-Immune Ecosystem Using Computational Modeling

Location is Multidisciplinary Research Building 1 - Seminar Room (first floor)

Abstract: My research group works in the area of mathematical oncology, where we use mathematical models to decipher the complex networks of reactions inside of cancer cells and interactions between cells. We have combined detailed, mechanistic and data-driven modeling to study these networks and predict ways to control tumor growth. Our recent work is aimed at predicting metabolism and signaling in the tumor microenvironment. In this talk, I will present our recent work aimed at predicting signaling-mediated interactions between tumor and immune cells using agent-based models. Our models generate novel mechanistic insight into cell behavior and predict the effects of strategies aimed at inhibiting tumor growth. We have also developed methods of calibrating the models to tumor image data to generate reliable predictive frameworks.

February 27, 2024, 2:00 PM - 2:50 PM Pacific Time

John Nardini, The College of New Jersey

Title: Forecasting and predicting stochastic agent-based models of cell migration with biologically-informed neural networks

Location is 284 Skye and in zoom

Abstract: Collective migration, or the coordinated movement of many individuals, is an important component of many biological processes, including  wound healing,  tumorigenesis, and embryo development. Spatial agent-based models (ABMs) are often used to model collective migration, but it is challenging to thoroughly study these models' behavior due to their random and computational nature. Modelers often overcome these obstacles by coarse-graining discrete ABM rules into continuous mean-field partial differential equation (PDE) models. These models are advantageous because they are fast to simulate; unfortunately, these PDE models can poorly predict ABM behavior (or even be ill-posed) at certain parameter values. In this work, we describe how biologically-informed neural networks (BINNs) can be used to learn BINN-guided PDE models that are capable of accurately predicting ABM behavior. In particular, we show that BINN-guided PDE simulations can forecast future ABM data not seen during model training. Additionally, we demonstrate how to predict ABM data at previously-unexplored parameter values by combining BINN-guided PDE simulations with multivariate interpolation. We highlight these results using three separate ABMs that consist of rules on agent pulling and/or adhesion. Surprisingly, BINN-guided PDEs can accurately forecast and predict ABM data with a one-compartment PDE when the mean-field PDE is ill-posed or requires two compartments. While we focus our presentation on the biological applications, this work is broadly applicable to studying many systems that exhibit the collective migration of individuals.

March 5, 2024, 2:00 PM - 2:50 PM Pacific Time

Christopher E. Miles, University of California, Irvine

Title: Decoding spatial stochastic RNA dynamics from static imaging data with point process inference

Location is 284 Skye and in zoom

Abstract: Advances in microscopy can now provide snapshot images of individual RNA molecules within a nucleus. Decoding the underlying spatiotemporal dynamics is important for understanding gene expression, but challenging due to the static, heterogeneous, and stochastic nature of the data. I will write down a stochastic reaction-diffusion model and show that observations of this process follow a spatial point (Cox) process constrained by a reaction-diffusion PDE. Inference on this data resembles a classical inverse problem but differs in the observations of individual particles rather than concentrations. We perform inference using variational Bayesian Monte Carlo with promising results. However, many open computational and modeling challenges remain in the development of scalable and extendable techniques for this inverse problem. This work is in collaboration with the Fangyuan Ding lab of Biomedical Engineering at UCI.