Department of Mathematics

Interdisciplinary Seminar on Mathematical and Computational Modeling

Interdisciplinary Seminar on Mathematical & Computational Modeling

Contact: Dr. Mark Albermalber@ucr.edu 


Upcoming Talks

April 24, 2017
12:10 - 1:10 p.m. Surge 268

Oleg Kim, UC Riverside Department of Mathematics

Title: "Combined modeling and experimental study of fibrin networks"

Abstract: Fibrin network is a major structural component of protective hemostatic clots and pathological obstructive thrombi that largely determines their mechanical stability in response to external loads including shear and compressive forces. In particular, fibrin networks reveal a unique nonlinear mechanical behavior characterized by a dual softening-stiffening transition as the networks are exposed to compressive loads, with softening occurring at small and intermediate compressive strains, while hardening developing at larger degrees of compression. Using a combination of confocal microscopy and rheological measurements, we demonstrate that these non-linear mechanical properties originated from structural rearrangements of the entire fibrin network, as well as alterations of individual fibers including fiber buckling, bending and reorientation. The network hardening strongly correlates with an increase in the number of intersecting fibers, resulting from densification of the compressed network and reorientation of the whole fibrillar network toward a planar structural architecture perpendicular to the direction of negative strain.We model this nonlinear behavior using a continuum theory of phase transitions and analytically predicted the storage and loss moduli which were in good agreement with the experimental data. We also demonstrate that permeability of the fibrin network and protein diffusivity are important factors determining the transport of blood proteins inside the thrombus.



Recent Talks

April 17, 2017
12:10 - 1:10 p.m. Surge 268

Dr. Russell Rockne Director, Division of Mathematical Oncology, Department of Information Sciences, City of Hope

Title: "Using Mathematical Models to Define Cancer Phenotypes"

Abstract: In this talk, I will show how mathematical models have been used to predict tumor growth and response to therapy. In particular, I will focus on partial differential equation models for brain tumors that are parameterized from MRI data. I will show how the clinical motivations for these models, and how the use of mathematical models is starting to impact cancer research and treatment at City of Hope.

April 3, 2017
12:10 - 1:10 p.m. Surge 268

Ali Nematbakhsh, Department of Bioengineering, UC Riverside

Title: "Multi-scale computational model for studying mechanics of epithelial cells"

Abstract: Multicellular development depends in large part on the growth, patterning and morphogenesis of epithelial sheets. How individual epithelial cells coordinate tissue-scale processes is still poorly understood due to the inherent complexity of emergent systems-level behavior. Testing hypothetical novel biophysical mechanisms across spatial scales requires computational models that can span subcellular to tissue levels. We will describe in this talk novel multi-scale modeling environment called Epi-Scale for simulating epithelial tissue mechanics based on the Subcellular Element (SCE) modeling approach. Epi-Scale explicitly simulates the separate mechanical contributions of multiple cellular components. Computational implementation of the model is based on an efficient parallelization algorithm that utilizes clusters of Graphical Processing Units (GPUs) for simulating large numbers of cells within a reasonable computational time. As an example of predictive power of the model we have studied mitotic rounding (MR) before cell division which ss critical for the robust segregation of chromosomes into daughter cells, and is frequently perturbed in cancerous cells. Regression analysis of parameters involved in mitotic rounding reveals relative contributions of osmotic pressure, cell-cell adhesion and cortical stiffness to the roundness and expansion of cells before division.

*March 20, 2017
12:10 - 1:10 p.m. Surge 268

Dimitrios Morikis, Department of Bioengineering, UC Riverside

Title: "Computational Modeling of Protein Dynamics and Interactions"

Abstract: We will present our recent work on the dynamics of protein-protein interactions at different scales. The common theme in our presentation is modeling of components of the immune system. First, we will discuss our ODE system that describes biochemical reactions of the activation pathways of the complement system, a component of the innate immune system and a link between innate and adaptive immunity. Second, we will discuss our computational framework AESOP for the analysis of Poisson-Boltzmann electrostatic potentials to determine the role of electrostatics in protein-protein recognition and binding for families of related proteins. Third, we will discuss the analysis of microsecond molecular dynamics simulations of a chemokine receptor in its free and ligand-bound states to delineate functional local and global conformational transitions in response to biased ligand binding. We will discuss applications in modeling disease states and personalized medicine, and in protein design and drug discovery.

March 13, 2017
12:10 - 1:10 p.m. Surge 268

Steve Cook, Computer Science & Engineering, UC Riverside

Title: "A Micro-Macro Framework for Analyzing Steric and Hydrodynamic Interactions in Gliding Assays"

Abstract: Macroscopic flows of filament-motor mixtures, driven by the hydrolysis of ATP, are important to many cellular processes such as cytoplasmic streaming in Drosophila oocytes and cortical flow in the first cell division of C.~elegans. Gliding assays, reduced in vitro model systems where motor proteins adsorbed onto a planar substrate bind to and move filaments, recreate large-scale dynamic patterns like coherent swarming motion and density waves. These systems are sensitive to the microscopic behavior such as the motor protein binding and unbinding dynamics, which take place on a faster timescale than the direct and fluid-mediated filament interactions. In this work, we present a multiscale modeling and simulation framework for gliding assays that allows detailed microscopic motor modeling as well as both steric and hydrodynamic interactions between filaments. Our model is based on continuum kinetic theory, and our implementation utilizes CPU and GPU parallelism to track the sparse but high-dimensional state space arising from the microscopic motor protein configurations. We find that steric interactions play a role in the formation of spatiotemporally coherent flow structures, and qualitatively reproduce experimentally observed behaviors including filament crossover and alignment, and clump formation, merging, and splitting.

February 27, 2017
12:10 - 1:10 p.m. Surge 268

Juan Carlos del Alamo, Department of Mechanical and Aerospace Engineering, UCSD

Title: "Quantifying Intracardiac Flow in the Clinical Setting"


Recent advances in imaging techniques now allow physicians to obtain robust measurements of intracardiac flows in the clinical setting.  Flow patterns inside the normal left ventricle (LV) are characterized by the formation of diastolic vortices, generated during filling that eventually last until the aortic valve is opened. In the failing LV, progressive adverse remodeling leads to abnormal vortex patterns that may vary the pumping efficiency. This talk will summarize recent clinical research about the contribution of intraventricular flow to LV function via three mechanisms 1) In diastole: by facilitating fluid transport and constraining the inflow to minimize pressure loss. 2) In systole: although currently being debated, by efficiently transferring kinetic energy from diastole to ejection. 3) In transport and mixing: by minimizing the number of cardiac cycles that blood stays in ventricular transit. We will illustrate how intraventricular flow quantification can be used to characterize and optimize the impact of clinical interventions and device implantation on intraventricular flow. Finally, we will provide an example of a prospective clinical study in which clinical analysis of intraventricular flow has been used predict intracardiac thrombus formation with the aim of guiding the prescription of anticoagulant therapy.

February 13, 2017
12:10 - 1:10 p.m. Surge 268

Presentations by Graduate Students

Titles/Abstracts: TBA


February 6, 2017
12:10 - 1:10 p.m. Surge 268

Amir Moradifam, Department of Mathematics, UC Riverside

Title: "Imaging electrical conductivities from their induced current and network tomography for random walks on graphs" 


January 30, 2017
12:10 - 1:10 p.m. Surge 268

Wenlong Jin, Department of Civil and Environmental Engineering, Calit2

Title: "Nonstandard second-order formulation of the LWR model" 


The seminal LWR model (Lighthill and Whitham, 1955; Richards, 1956) has many equivalent first-order formulations in both Eulerian and Lagrangian coordinates. In this study, we present a second-order formulation of the LWR model based on Phillips’ model (Phillips, 1979); but the model is nonstandard with a hyperreal infinitesimal relaxation time. Since the original Phillips model is unstable with three different definitions of stability in both Eulerian and Lagrangian coordinates, we cannot use traditional methods to prove the equivalence between the second-order model, which can be considered the zero-relaxation limit of Phillips’ model, and the LWR model, which is the equilibrium counterpart of Phillips’ model. Instead, we resort to a nonstandard method based on the equivalence relationship between second-order continuum and car-following models established in (Jin, 2016) and prove that the nonstandard model and the LWR model are equivalent, since they have the same anisotropic car-following model and stability property. We further derive conditions for the nonstandard model to be forward-traveling and collision-free, prove that the collision-free condition is consistent with but more general than the CFL condition (Courant et al., 1928), and demonstrate that only anisotropic and symplectic Euler discretization methods lead to physically meaningful solutions. We numerically solve the lead-vehicle problem and show that the nonstandard second-order model has the same shock and rarefaction wave solutions as the LWR model for both Greenshields and triangular fundamental diagrams; for a non-concave fundamental diagram we show that the collision-free condition, but not the CFL condition, yields physically meaningful results. Finally we present a correction method to eliminate negative speeds and collisions in general second-order models, and verify the method with a numerical example. Together with (Jin, 2016), this study presents a new approach to address the two critiques on second-order continuum models in (Daganzo, 1995a) and can help to guide the development and discretization of more physically meaningful second-order continuum and car-following models.
December 5, 2016
12:10 - 1:10 p.m. Surge 268

Jianzhong Wu, Department of Chemical Engineering, UC Riverside

Title: "Bayesian Statistics for Many-Body Systems" 


Both classical and quantum mechanics have been well established in terms of the temporal evolutions of the dynamic variables of individual particles. Whereas the equations of motion are equally applicable to one-body as well as many-body systems, the numerical complexity rises rapidly as the number of particles increases yet dynamic uncertainty makes it imperative to describe the properties of many-body systems from a statistical perspective. In this lecture, I outline a generic and computationally efficient procedure to predict the properties of many-body systems based on Bayesian statistics in conjunction with the Hohenberg-Kohn-Mermin theorem.  Illustrative examples will be discussed for many-body systems consisting of the Langevin particles, hard spheres, fermions, and hybrid mixtures with both quantum and classical components.  
November 28, 2016
12:10 - 1:10 p.m. Surge 268

Jim Kelliher, Department of Mathematics, UC Riverside

Title: "High-Reynolds number fluid flow and the accumulation of vorticity on the boundary: Prandtl, Chorin, and Kato" 


Though the equations describing the motion of a viscous classical incompressible fluid have been studied for almost 200 years, the behavior of such a fluid as it interacts with a solid boundary is still poorly understood, in particular at low viscosity. Three theories of this behavior are those initiated by Ludwig Prandtl in 1904, Alexander Chorin in 1973, and Tosio Kato in 1983. Prandtl's and Chorin's theories are heuristic, making appealing and reasonable-seeming assumptions about the behavior of the fluid near the boundary. In their simplest form, they are expected to apply only to laminar flows, but even for such flows they have never been proved to hold (or to fail to hold). Kato's theory is mathematically precise, but conditional by nature; nonetheless, it can be used as a "probe" into the validity of the other two theories. I will give a brief overview of the three theories and describe the beginning of a synthesis of them, in particular the three different, though potentially complementary, ways in which they depict the accumulation of vorticity on the boundary in the limit as the viscosity is taken to zero.
November 21, 2016
12:10 - 1:10 p.m. Surge 268

Craig Schroeder, Department of Computer Sciences & Engineering, UC Riverside

Title: "Hybrid Simulation Methods: Simulating the World Around You" 


Hybrid particle/grid numerical methods have been around for a long time, and their usage is common in some fields, from plasma physics to artist-directed fluids. I will explore the use of hybrid methods to simulate many different complex phenomena occurring all around you, from wine to shaving foam and from sand to the snow in Disney's Frozen. I will also talk about some of the practical advantages and disadvantages of hybrid methods and how one of the weaknesses that has long plagued them can now be fixed.
November 14, 2016
12:10 - 1:10 p.m. Surge 268

Venugopala Gonehal, Department of Botany & Plant Sciences, UC Riverside

Title: "Regulation and Interpretation of Stem Cell Promoting Transcription Factor Gradient" 


Stem cells located in growing tips, the shoot apical meristems, of plants provide cells for the development of all above-ground plant parts/biomass. The shoot meristem development and function is being studied for nearly a century. However, recent developments in live imaging have provided unprecedented view of growth patterns at cellular and organ level. These studies have revealed that stem cell number control does not involve mechanisms such as asymmetric cell division, cell death and cell migration. Instead the tissue homeostasis is achieved only through regulated cell expansion, cell division and cell displacement. Recent developments in single cell type genomics are augmenting classical genetics experiments in exploring how cells interpret genetic code to regulate stem cell division, growth and differentiation patterns.   My lab has developed these methods and combining them with transient gene manipulations to understand the molecular and cellular basis of stem cell homeostasis. I will provide overview of our work on transcriptional mechanisms that underlie stem cell control which has taken us into a new area of dose-dependent regulation of gene expression. We have shown that WUSCHEL (WUS), a stem cell promoting transcription factor accumulates at a higher level in the niche and a lower level in stem cells.  This concentration differential allows it to function as a transcriptional repressor at higher level and as an activator at lower levels. I will talk about our work on cis-regulatory logic underlying this behavior. I will also talk about a related topic on how cells regulate WUS concentration. This involves regulation at the level of DNA binding, nuclear-cytoplasmic partitioning and diffusivity of WUS into adjacent cells. I will discuss the importance of dose-dependent transcriptional regulation and the regulation of WUS concentration in the control of stem cell division and the differentiation of stem cell descendants. 


November 7, 2016
12:10 - 1:10 p.m. Surge 268

Hoori Ajami, Department of Environmental Sciences, UC Riverside

Title: "A Hydrologist Perspective on Mathematical Modeling of Terrestrial Hydrologic Process" 


Hydrologists often rely on mathematical models to test various hypothesis about watershed response and function at large scales, and make projections about future water availability as a result of climate variability and human use. Increases in greenhouse gas concentrations are expected to impact the terrestrial hydrologic cycle through changes in precipitation and temperature and vegetation dynamics. As a result, projections of future changes in water resources are complex due to the tight coupling between the biosphere and terrestrial hydrologic cycle. In this talk, I will 1) provide an overview of hydrologic model development while focusing on differences in model conceptualization and formulation, 2) discuss issues related to model coupling such as coupling of surface water models with groundwater models and ecologic models, 3) discuss sources of uncertainty in model predictions, and 4) present case studies from USA, Denmark and Australia using different numerical models.


October 31, 2016
12:10 - 1:10 p.m. Surge 268

Kurt E. Anderson, Department of Biology, UC Riverside

Title: "Ecological dynamics on river networks" 


I will review current and recent work in my lab exploring dynamics of natural populations and communities on river networks. Using advances in graph theory, we will explore how the structure of river networks influences important ecological outcomes such as population persistence, ecological stability, and community asynchrony


October 24, 2016
12:10 - 1:10 p.m. Surge 268

Larry Li, Department of Botany & Plant Sciences, UC Riverside

Title: "Patch invasion: impact of dimensionality on dynamic regimes" 


Spatially explicit models have become widely used in today’s mathematical ecology to study persistence of populations. For the sake of simplicity, population dynamics is often analyzed with 1-D models.

An important question is: how adequate is such 1-D simplification of 2-D (or 3-D) dynamics for predicting species persistence. Here we show that dimensionality of the environment can play a critical role in the persistence of predator–prey interactions.

We consider 1-D and 2-D dynamics of a predator–prey model with the prey growth damped by the Allee effect. We show that adding a second space coordinate into the 1-D model results in a pronounced increase of size of the domain in the parametric space where predator–prey coexistence becomes possible. This result is due to the possibility of formation of a number of 2-D patterns, which is impossible in the 1-D model. The 1-D and the 2-D models exhibit different qualitative responses to variations of system parameters. We show that in ecosystems having a narrow width (e.g. mountain valleys, vegetation patterns along canals in dry areas, etc.), extinction of species is more probable compared to ecosystems having a pronounced second dimension. In particular, the width of a long narrow natural reserve should be large enough to guarantee nonextinction of species via interaction of 2-D population patches.


October 17, 2016
12:10 - 1:10 p.m. Surge 268

Richard James Arnott, Department of Economics, UC Riverside

Title: "Solving for Equilibrium in the Basic Bathtub Model" 


The talk will provide background for a paper in progress with Josh Buii, a Ph.D. in mathematics at UCR, which has the same title as the talk. The talk will discuss the state of the art in the transportation economics approach to modeling downtown rush-hour traffic congestion. In the process, it will introduce the method of economic model building.


October 10, 2016
12:10 - 1:10 p.m. Surge 268

Mark Alber, Department of Mathematics, UC Riverside

Title: "Stochastic cellular automata"


Cellular automata are mathematical finite state machines which change the state of their cells step by step. Each cell has several possible states: 0,1,...,(p-1). To run cellular automata one needs initial distribution of states for all cells and a set of rules. An example of 2-state cellular automata will be provided as a basic introduction. 

October 3, 2016
12 - 1:30 p.m. Surge 268 *Organization meeting

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