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Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar

UCR Math Department seminar

Fall 2020 Schedule

Oct 07 10:00 (Wed) Organizing Meeting

Oct 14 10:00 (Wed) Dr. Jia Gou (University of California, Riverside) (Gou)

Oct 21 10:00 (Wed) Dr. Zheng Chen (University of Massachusetts) (Chen)

Oct 28 10:00 (Wed) Dr. Wing Tat Leung (University of California, Irvine) (Chow)

Nov 04 10:00 (Wed) Dr. Michael Lindstrom (University of California, Los Angeles) (Gou)

Nov 12 11:00 (Thr) Dr. Huan Lei (Michigan State University) (Cho)

Nov 18 10:00 (Wed) Dr. Levon Nurbekyan (University of California, Los Angeles) (Chow)

Nov 25 10:00 (Wed) Dr. Qiliang Wu (Ohio University) (Chen)

Dec 02 10:00 (Wed) Dr. Ali Pakzad (Indiana University) (Chow)

Dec 09 10:00 (Wed) Tony Li (University of California, Riverside) (Tentative)

Upcoming talks:

Title and Abstracts

October 14 10:00 (Wed), 2020 (online)

Dr. Jia Gou (University of California, Riverside)

Title: Theoretical and Computational Studies of Mathematical Models in Biology

Abstract: Mathematical models have been widely used to understand biological mechanisms and dynamics underlying experimental observations. In this talk, I will first introduce a model of spatially-segregated dynamically-active cells coupled by bulk diffusion and provide a theoretical investigation of this kind of coupling mechanism between small cells in a 2D bounded domain at different diffusion rates. Our analysis shows that such coupling is a robust mechanism for the initiation of synchronized oscillatory dynamics in the segregated cells. Results in one-dimensional domains will also be discussed.

The second problem is related to the growth control in the Drosophila wing disc. Growth control in the disc involves various local signals, including signaling pathways, mechanical signals, etc. We develop a model of the Hippo pathway, which is the core regulatory pathway that mediates cell proliferation and apoptosis and is highly conserved in mammals. We investigate the regulatory role of two upstream components Fat and Ds on the downstream mediator Yki of the pathway, and provide explanations to some of the seemingly contradictory experimental results. In the third part I will also briefly talk about our current work on morphogen transport in the wing disc.

October 21 10:00 (Wed), 2020 (online)

Dr. Zheng Chen (University of Massachusetts)

Title: Boundary condition splitting strategies for hybrid methods on linear kinetic equations

Abstract: Numerical simulations for linear kinetic models defined over position-velocity phase-space are computationally costly. Especially when the collision frequencies vary much over the domain, and multiscale phenomena exhibit. A collision-based hybrid method introduced by Hauck and McClarren [3] is proposed to save computational cost for collisional models but keep the accuracy in the meantime. The method separates the kinetic equation into a system of two equations for collided and uncollided components of the distribution function. The collided equation is simulated with a low-resolution angular discretization, and the uncollided equation is simulated with a high-resolution angular discretization. Proper mapping between the two components is required after each time stepping. One of the interesting questions about this hybrid method is how to assign the boundary condition to the two components to keep it accurate. Numerical results show putting all boundary data on the uncollided component leads to non-physical solutions. In this project, the splitting methods for boundary data are investigated. Inspired by the boundary layer problem for linear kinetic models discussed in Bensoussan, Lions, and Papanicolaou [1] and Golse, Jin, and Levermore [2], an interior-boundary splitting strategy is proposed and analyzed. Numerical results will be shown to validate the analysis. An adaptive splitting method is also discussed for the multiscale setting.

References:
[1] Alain Bensoussan, Jacques L Lions, and George C Papanicolaou. “Boundary layers and homogenization of transport processes.” Publications of the Research Institute for Mathematical Sciences 15.1 (1979), pp. 53–157.
[2] Francois Golse, Shi Jin, and C David Levermore. “The convergence of numerical transfer schemes in diffusive regimes i: discrete-ordinate method.” SIAM journal on numerical analysis 36.5 (1999), pp. 1333–1369.
[3] Cory D Hauck and Ryan G McClarren. “A collision-based hybrid method for time-dependent, linear, kinetic transport equations.” Multiscale Modeling & Simulation 11.4 (2013), pp. 1197–1227.

October 28 10:00 (Wed), 2020 (online)

Dr. Wing Tat Leung (University of California, Irvine)

Title: Multi-scale model of tissue and tumor growth

Abstract: Due to complexness, multiscale feature, and full of feedback of the tumor model, it is difficult to relate to the cell-scale tumor model and tissue-scale tumor model. Moreover, until recently, it was not easy to collect the amount of data needed to connect the tumor model in these scales. In many applications, it is essential to understand the connection between cell-scale behavior and tissue-scale behavior.

In this talk, we are going to introduce an upscaling technic using the Biological Dynamic Density Function Theory(DDFT). In the DDFT, instead of considering a discrete model for the interaction of the cells (agent-based model), we consider a continuum model for the noise-averaged density of the cells. In the classical DDFT, the model is still in cell-scale where the noise-averaged density is oscillating with a period of cell length. To obtain a tissue-scale model for tumor growth, we use a one-mode approximated model and consider the asymptotic behavior of this one-mode approximated model when the ratio of cell length and domain size converging to zero. In this talk, we will also provide a numerical example to demonstrate our proposed upscaling model.

November 4 10:00 (Wed), 2020 (online)

Dr. Michael Lindstrom (University of California, Los Angeles)

Title: Two Mathematical Models of Disease: Alzheimer's Disease at the Protein Scale and COVID-19 at the Population Level

Abstract: In this talk, we'll look into mathematical models of two different diseases, Alzheimer's Disease and COVID-19. For Alzheimer's, we will build and analyze a mathematical model of oligomers, unstable formations of the amyloid beta protein that is continuously produced in the brain, and their toxicity toward neurons and examine the accordance between such a model and various clinical manifestations of the illness. Then we'll switch gears and examine a network model of COVID-19 based on data from Ottawa, Canada, paying particular attention to disease mitigation strategies upon disabled people and their caregivers.

November 12 11:00 (Thr), 2020 (online)

Dr. Huan Lei (Michigan State University)

Title: Machine learning based modeling of non-Newtonian fluids with molecular fidelity

Abstract: Predictive modeling of the macroscale hydrodynamics of the non-Newtonian fluids relies on the faithful constitutive closures. In practice, accurate modeling of the closure equations poses a major challenge. In this talk, I will present a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics models directly from a micro-scale description. To faithfully retain the molecular-level fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized with deep neural networks. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. The overall scheme is an end-to-end learning procedure of both the conformation tensors and the relevant constitutive terms in their dynamics at the same time. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative, and with some terms represented by neural network models. Contrary to the conventional wisdom about machine learning, the model we obtained has a clear physical interpretation. Numerical results for both steady-state and dynamic flows demonstrate the accuracy of this machine learning-based model in comparison with direct molecular dynamics simulations, where models based on empirical closures show limitations. This a joint work with Dr. Lei Wu and Dr. Weinan E at Princeton University.

November 18 10:00 (Wed), 2020 (online)

Dr. Levon Nurbekyan (University of California, Los Angeles)

Title: Machine-learning methods for solving optimal control, mean-field games, and related problems

Abstract: I will present some of the recent developments in solution methods for high-dimensional optimal control and related problems such as mean-field games and normalizing flows.

November 25 10:00 (Wed), 2020 (online)

Dr. Qiliang Wu (Ohio University)

Title: Pearling and Localized Undulation of Bilayers in Amphiphilic Morphology

Abstract: Amphiphiles, such as lipids and functionalized polymers, plays a central role in the self-assembly of solvent accessible, intricately structured nano-scaled network structures, which are vital in cell functionality and offer wide applications to drug delivery, detergent production, emulsion stabilization and energy conversion devices. We study amphiphilic morphology in the framework of the functionalized Cahn-Hilliard (FCH) energy. The FCH is a continuum model accommodating various co-dimensional structures such as bilayers (co-dim 1), filaments (co-dim 2) and micelles (co-dim 3). We focus on defect structures that break the dimensional reduction and include endcaps that terminate filaments or bilayers and Y junctions. More specifically, we show the existence of pearled bilayer solutions via a spatial dynamics formulation, in combination with center manifold reduction and a fixed point argument. In addition, we also show via a functional analytic framework that in the presence of spatial inhomogeneity, localized undulation appears under proper functionalization terms. More interestingly, both the pearling and localized undulation are shown to be a manifesitation of a degenerate 1:1 resonance Hopf bifurcation encoded in a reduced ODE system from the FCH energy.

December 02 10:00 (Wed), 2020 (online)

Dr. Ali Pakzad (Indiana University)

Title: Data assimilation; effects of the higher order interpolation

Abstract: Data assimilation refers to a class of techniques that inject spatially coarse observational data into mathematical models to obtain better forecasts of physical systems. We discuss an approach which adds a feedback control term at the PDE level to synchronize the computed solution with the true solution corresponding to the observed data.

In this talk, after a survey of recent rigorous results supporting this method for fluid dynamics, we discuss using higher order finite elements to interpolate data on a coarse grid. We then demonstrate computationally that the synchronization is achieved at better rate than with linear interpolation. This is part of a joint work with Michael Jolly.

December 09 10:00 (Wed), 2020 (online) (Tentative)

Tony Li (University of California, Riverside)

Title: Modeling interaction between CAR T and cancer cells based on deterministic and stochastic approach

Abstract: Effective adoptive T cell therapy (ACT), comprising the killing of cancer cells through the therapeutic use of transferred T cells, has played an important role in immunotherapy of cancer. One of the approaches is chimeric antigen receptor (CAR) T cell therapy. In this talk, we will first simply introduce an old model given by Kuznetsov. We shall further discuss another ODE model, based on the Kuznetsov Model, that describes a more complicated dynamics between CAR-T cells and cancer cells. Meanwhile, we also built a stochastic model to compare the results from two different approaches. Our conclusions were drawn according to the comparison of different models.