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

UCR Math Department seminar

Winter 2020 Schedule

Jan 08 13:00 (Wed) Organizing meeting

Jan 15 13:00 (Wed) Dr. Xin Yang (Virginia Tech) (Zhang, Qi)

Jan 22 13:00 (Wed) Dr. Mykhailo Potomkin (UC Riverside)

Jan 29 13:00 (Wed) Dr. Mykhailo Potomkin (UC Riverside)

Feb 03 11:00 (Mon) Dr. Padmini Rangamani (UCSD) (Chen)

Feb 12 15:30 (Wed) Dr. Jingyi (Jessica) Li (UCLA) (Chen)

Feb 19 13:00 (Wed) Dr. Jasper Weinburd (Harvey Mudd College) (Cho) -> next quarter!

Feb 21 11:00 (Fri) Dr. Sebastien Motsch (Arizona State University) (Cho)

Feb 26 13:00 (Wed) Dr. Dong Zhou (CSU LA) (Chen)

Mar 04 13:00 (Wed) Dr. Derdei Bichara, (CSU Fullerton) (Chen)

Mar 06 11:00 (Fri) Dr. Dongwook Lee (UCSC) (Cho)

Mar 11 13:00 (Wed) Dr. Rodrigo Platte (Arizona State University) (Cho) -> After covid

Title and Abstracts

Mar 06 11:00 (Fri), 2020, Skye 284

Dr. Dongwook Lee (UCSC, Department of Applied Mathematics)

Title: Variable high-order multidimensional GP-WENO

Abstract: A new class of high-order numerical algorithms for compressible flow simulations is introduced. The method is based on the Gaussian Processes (GP) modeling that generalizes the standard Gaussian probability distribution to a probabilistic distribution over function space. This work is an extension of our previous work on the GP-WENO methods [Reyes et al., Journal of Scientific Computing, 76(1): 443-480, 2018; Reyes et al., Journal of Computational Physics, 381: 189--217, 2019] to multiple spatial dimensions using the finite volume formulation. The numerical solutions of GP-WENO provide a variable order of accuracy as a function of the GP stencil radius in multidimensional cases. The new approach is to adopt GP prediction techniques, which utilize GP covariance kernel functions to interpolate/reconstruct high-order approximations of flow variables in shock-dominant compressible flows. The nonlinear stability of the scheme is afforded by the GP fitting, which designs smoothness indicators through a measure of the likelihood. The resulting GP-WENO scheme remains robust in the vicinity of shocks, while delivers a selectable high order of solution accuracy on smooth flows. This GP-WENO method furnishes a new direction for the design of high-order finite volume methods in multiple spatial dimensions, particularly with reduced algorithmic complexity and greater flexibility, compared to conventional polynomial-based high-order approaches.

Mar 04 13:00 (Wed), 2020

Dr. Derdei Bichara, (CSU Fullerton)

Title: Global dynamics across interacting networks: A complete characterization

Abstract: The role of heterogeneity in populations has long been recognized as a driving force in the spread of infectious diseases. Indeed, populations differ in their propensity to transmit or acquire infectious agents in terms of activities, socio-economic or genetic groups. Oftentimes, mathematical models in population dynamics that incorporate such heterogeneities use network to describe the interactions between the units of the model. For many models that describe such phenomena, the complete global behavior of these systems have been open questions. In this talk, I provide a complete characterization of the some these problems.

Feb 26 13:00 (Wed), 2020

Dr. Dong Zhou (CSU LA)

Title: Order reduction in Runge-Kutta time-stepping for initial boundary value problems

Abstract: When advancing a time-dependent PDE forward via high-order Runge-Kutta methods, one may observe a convergence order less than the formal order of the scheme. This order reduction phenomenon is a fundamental problem in PDE initial-boundary-value-problems (IBVPs), and as well as in stiff ODEs. For such IBVPs, geometric structures arise that do not have an analog in ODE initial-value-problems: boundary layers appear, induced by a mismatch between the approximation error in the interior and at the boundaries. We present a modal analysis that explains under which circumstances boundary layers persist over many time steps. Base on this, two remedies are proposed and studied: (1) a new condition on the Butcher tableau, called weak stage order, which is compatible with diagonally implicit Runge-Kutta schemes; (2) a systematic derivation of modified boundary conditions.

Feb 21 11:00 (Fri), 2020, at Skye 284

Dr. Sebastien Motsch (Arizona State University)

Title: Tumor growth: from agent-based model to free-boundary problem

Abstract: In this talk, we investigate the large time behavior of a agent based model modeling tumor growth. This microscopic model combines short-range repulsion and cell division. We derive the associated macroscopic dynamics leading to a porous media type equation. In order to capture the long-time behavior of the microscopic model, we have to modify the porous media in order to include a density threshold for the repulsion. The main difficulty is then to investigate the limit as the repulsion between cells becomes singular (modeling non-overlapping constraint). We show formally that such asymptotic limit leads to a free-boundary problem (Hele-Shaw type). Numerical results confirm the relevance of such limit.

Feb 19 13:00 (Wed), 2020

Dr. Jasper Weinburd (Harvey Mudd College)

Title: Agent-based and PDE Models for Foraging Locust Swarms

Abstract: Locusts are devastating pests that aggregate in large swarms, destroying crops, pasture, and wild vegetation. The shape of a swarm is correlated with its other macroscopic qualities including density, average speed, and how much food is left uneaten. But individual insects are governed by microscopic behaviors, primarily social interaction with other locusts and attraction to nearby food resources. In this talk, we’ll start to unravel the relationships between macroscopic swarm qualities and microscopic individual behaviors. We’ll look in depth at two models: a set of partial differential equations (PDE) governing the mean-field density of locusts, and an agent-based model (ABM) that tracks the behavior of each individual insect. Traveling wave solutions in the PDE characterize collective swarming, feeding, and marching observable in the ABM. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations.

Feb 12 15:30 (Wed), 2020

Dr. Jingyi Li (UCLA, Department of Statistics)

Title: Statistical methods for single-cell RNA sequencing data imputation and experimental design

Abstract: Single-cell RNA sequencing (scRNA-seq) has revolutionized biological sciences by revealing genome-wide gene expression levels within individual cells. In this talk, I will introduce two recent statistical methods we have developed, scImpute and scDesign, for addressing challenges in scRNA-seq data analysis and experimental design. First, scRNA-seq data analysis is complicated by excess zeros, the so-called dropouts due to low amounts of mRNA sequenced within individual cells. scImpute is the first statistical method that automatically identifies likely dropouts and only imputes them by borrowing information from similar cells. We will show that scImpute is able to enhance the clustering of cell subpopulations, improve the accuracy of differential expression analysis, and aid the study of gene expression dynamics. Second, experimental researchers often face a critical question on how to optimize the choices of scRNA-seq platforms, sequencing depths, and cell numbers in designing scRNA-seq experiments, so as to balance the exploration of the depth and breadth of transcriptome information. scDesign is a flexible simulator and the first statistical framework for researchers to quantitatively assess practical scRNA-seq experimental design in the context of differential gene expression analysis. scDesign also assists computational method development by generating high-quality synthetic scRNA-seq datasets under customized experimental settings. We will show that scDesign leds to rational and reproducible experimental designs and that scDesign is a useful tool for benchmarking scRNA-seq computational methods.

Feb 03 11:00 (Mon), 2020

Dr. Padmini Rangamani (UC San Diego, Department of Mechanical and Aerospace Engineering)

Title: Modeling structural plasticity of postsynaptic spines

Abstract: The ability of the brain to encode and store information depends on the plastic nature of the individual synapses. The increase and decrease in synaptic strength, mediated through the structural plasticity of the spine, are important for learning, memory, and cognitive function. Dendritic spines are small structures that contain the synapse. They come in a variety of shapes (stubby, thin, or mushroom-shaped) and a wide range of sizes that protrude from the dendrite. These spines are the regions where the postsynaptic biochemical machinery responds to the neurotransmitters. Spines are dynamic structures, changing in size, shape, and number during development and aging. While spines and synapses have inspired neuromorphic engineering, the biophysical events underlying synaptic and structural plasticity of single spines remain poorly understood.

Our current focus is on understanding the biophysical events underlying structural plasticity. I will discuss recent efforts from my group — first, a systems biology approach to construct a mathematical model of biochemical signaling and actin-mediated transient spine expansion in response to calcium influx caused by NMDA receptor activation and a series of spatial models to study the role of spine geometry and organelle location within the spine for calcium and cyclic AMP signaling. Second, I will discuss how mechanics of membrane-cytoskeleton interactions can give insight into spine shape region. And I will conclude with some new efforts in using reconstructions from electron microscopy to inform computational domains. I will conclude with how geometry and mechanics plays an important role in our understanding of fundamental biological phenomena and some general ideas on bio-inspired engineering.

Jan 22 13:00 (Wed), 2020

Dr. Mykhailo Potomkin (UC Riverside)

Title: A PDE model of micro-swimmer in liquid crystal

Abstract: Recent experimental and modeling results have shown that the interaction between orientation order of liquid crystal and activity of micro-swimmers, such as bacteria, leads to novel optical, hydrodynamical, and electrical properties of liquid crystals, as well as emergence of intriguing patterns.

To understand how the orientation order of liquid crystal affects the motion of an individual active swimmer, a nonlinear PDE system coupling liquid crystal hydrodynamics with a model of active swimmer is introduced. In this talk, I will present this PDE system and show that it reveals how the shape of the swimmer and surface properties affect swimming direction.

Jan 15 13:00 (Wed), 2020

Dr. Xin Yang (Virginia Tech)

Title: Well-Posedness for the Coupled KdV-KdV Systems

Abstract: The KdV equation is a mathematical model for the waves on shallow water surfaces. The coupled KdV-KdV systems are usually applied to describe the interaction of two long waves with different dispersion coefficients. The well-posedness of the Cauchy problem of both the single equation and the coupled systems are of fundamental importance. In particular, people are asking what is the least regularity requirement for the initial data such that the Cauchy problem is well-posed? Recently, this task for the single KdV equation has been completely accomplished. Inspired by this success, we will discuss the situation for the coupled KdV-KdV systems. This talk is based on joint works with Bing-Yu Zhang.

Upcoming talks: