Interdisciplinary Seminar on Mathematical & Computational Modeling
Contact: Dr. Mark Alber, malber@ucr.edu
Upcoming Talks
*November 20, 2017  
12:10  1:10  *Surge 268 
Dr. Leonid Berlyand, University of Pennsylvania, Department of Mathematics Title: "Phase Field and Free Boundary Models of Cell Motility" Abstract: We study two types of models describing the motility of eukaryotic cells on substrates. The first, a phasefield model, consists of the AllenCahn equation for the scalar phase field function coupled with a vectorial parabolic equation for the orientation of the actin filament network. The key properties of this system are (i) presence of gradients in the coupling termsand (ii) mass (volume) preservation constraints. We pass to the sharp interface limit to derive the equation of the motion of the cell boundary, which is mean curvature motion modified by a novel nonlinear term. We establish the existence of two distinct regimes of the physical parameters and prove existence of traveling waves in the supercritical regime. The traveling waves describe persistent motion of the cell without external cues or stimuli which is a signature of cell motility. The second model is a nonlinear free boundary problem. It consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convectiondiffusion PDE for the density of myosin motors. The key properties of this problem are (i) presence of the cross diffusion as in the classical KellerSegel problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from a family of radially symmetric steady states. We also study breaking of symmetry by proving existence of nonradial steady states. Existence of both traveling waves and nonradial steady states is established via LeraySchauder degree theory applied to a Liouvilletype equation (which is obtained via a reduction of the original system) in a free boundary setting. These results were obtained in collaboration with J. Fuhrmann, M. Potomkin, and V. Rybalko 
Past Talks
November 14, 2017  
2:10  3:10  Surge 284 
Title: "Interactions of the platelet integrin alphaIIbbeta3 with fibrin" Abstract: Although the integrin aIIbb3 mediates platelet spreading on surfaces artificiallycoated with fibrinogen, the physiologic relevance of this phenomenon is not clear. By contrast, the interaction of aIIbb3 with fibrin is responsible for clot retraction, an event important for efficient hemostasis in the hemodynamic environment of flowing blood. Moreover, whereas resting aIIbb3 can interact with immobilized fibrinogen, plateletfibrin interactions are mediated by activated aIIbb3. Lastly, the efficacy of aIIbb3 antagonists with regard to clot contraction versus platelet aggregation mediated by aIIbb3 binding to fibrinogen interactions is different, perhaps because additional aIIbb3 binding sites are exposed when fibrinogen is converted to fibrin. Here, we have compared nanomechanical measurements of the direct interaction of aIIbb3 with fibrin and fibrinogen in order to explain these differential effects. We used optical laser tweezersbased force spectroscopy for these measurements. Briefly, a bead covalently coated with purified aIIbb3 was captured by a focused laser beamand repeatedly brought into contact with surfaceattached fibrinogen, monomeric fibrin, or a naturallyformed hydrated fibrin fiber at the edge of a plasma clot. When an aIIbb3ligand complex was detected, the nanomechanical force required to dissociate the complex was measured at piconewton resolution. By analyzing distributions of these rupture forces, we were able to determine the overall reactivity and the strength of the interactions between the interacting protein pairs. Beside native fibrinogen, experiments were performed with recombinant fibrinogen variants as well. Monomeric fibrin displayed higher cumulative probability of interacting with aIIbb3 (a greater forcefree onrate) and binding strength (a smaller forced offrate). aIIbb3fibrin interactions were less sensitive to the effects of abciximab and eptifibatide compared to fibrinogen, suggesting that they had different binding specificity. Both fibrinogen and fibrinintegrin interactions were partially blocked by the RGDcontaining peptides, suggesting the existence of common RGD integrinbinding sites. This assumption was supported using fibrin variants αD97E or αD574E with impaired RGD motifs, which were less reactive with aIIbb3 than the wild type fibrin. Monomeric fibrin made from a homodimeric fibrinogen splice variant of the g chain (g´) that lacks the γC aIIbb3 site was more reactive with aIIbb3 than the parent fibrinogen, suggesting that this binding site is less important in fibrin. Polymeric fibrin displayed a rupture force profile similar to fibrinogen and monomeric fibrin with moderate (2060 pN) and strong (>60 pN) forces that peaked at 7080 pN. Interactions forces >60 pN were more effectively reduced by EDTA than by any of the inhibitory peptides, indicating their dependence on the structural integrity and functionality of aIIbb3. The free γC dodecapeptide was less efficient than the cRGD peptides or integrilin in preventing the stronger interactions. Taken together, these data demonstrate that surfacebound fibrinogen and monomeric as well as polymeric fibrin are highly reactive with the aIIbb3. Fibrin is more reactive than fibrinogen in terms of binding probability and has higher binding strength. FibrinaIIbb3 binding is less sensitive to specific b3 integrin inhibitors, suggesting that fibrin and fibrinogen have distinct specificities towards aIIbb3. . 
October 18, 2017  
1:10  2:00 p.m.  Surge 268 
Junping Shi, Margaret Hamilton Professor of Mathematics, College of William and Mary Title: "Modeling Chesapeake Bay oyster population" Abstract: Native oyster populations in Chesapeake Bay have been the focus of three decades of restoration attempts, which have generally failed to rebuild the populations and oyster reef structure. Recent restoration successes and field experiments indicate that the vertical relief of reefs is critical to reef persistence. I will describe an interdisciplinary research effort on oyster population and related problems. More specifically, I will talk about (i) ordinary differential equation models of live oysters, dead oyster shells, and sediment, (ii) ordinary differential equation model of multiple reefs displaying bistability, and (iii) partial differential equation models of oyster or mussel shoreline pattern formation.

June 5, 2017  
12:10  1:10 p.m.  Surge 268 
Sakhrat Khizroev, Florida International University Title: "Applications of Magnetoelectric Nanoparticles in Cancer Research" Abstract: In regard to cancer therapy, magnetoelectric nanoparticles (MENs) have proven to be in a class of its own when compared to any other nanoparticle type. Like conventional magnetic nanoparticles, they can be used for externally controlled drug delivery via application of a magnetic field gradient and imageguided delivery. However unlike conventional nanoparticles, due to the presence of a nonzero magnetoelectric effect, MENs provide a unique mix of important properties to address key challenges in modern cancer therapy: (i) a targeting mechanism driven by a physical force rather than antibody matching, (ii) a highspecificity delivery to enhance the cellular uptake of therapeutic drugs across the cancer cell membranes only, while sparing normal cells, (iii) an externally controlled mechanism to release drugs on demand, and (iv) a capability for image guided precision medicine. These properties separate MENsbased targeted delivery from traditional biotechnology approaches and lay a foundation for the complementary approach of technobiology. The biotechnology approach stems from the underlying biology and exploits bioinformatics to find the right therapy. In contrast, the technobiology approach is geared towards using the physics of molecularlevel interactions between cells and nanoparticles to treat cancer at the most fundamental level and thus can be extended to all the cancers. This presentation gives an overview of the MENsbased underlying physics of potential cancer therapy. 
May 22, 2017  
12:10  1:10 p.m.  Surge 268 
Dr. Roya Zandi, Department of Physics, UC Riverside Title: "The selfassembly of viruslike particles: From small symmetric nanoshells to conical HIV structures" Abstract: Viruses infect all kinds of hosts (bacteria, plants, and animals) of these viruses involve a spherical shell (capsid), that protects their genome. Amazingly enough, despite the tremendous diversity in the protein building blocks of these capsids, the structures they adopt almost always have icosahedral symmetry. Many studies have shown that symmetric shells appear in nature as a result of the free energy minimization of a generic interaction between their constituent subunits. Here, we study the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. I will also discuss the structure of conical viruses. I will show that the continuum theory of elastic shells combined with the nonequilibrium assembly process is able to predict the formation of structures pertinent to retroviruses (such as HIV). Our minimal model of assembly yields a unified onedimensional phase diagram in which the appearance of spherical, irregular, conical and cylindrical structures of retroviruses are seen to be governed by the spontaneous curvature of protein subunits. 
May 15, 2017  
12:10  1:10 p.m.  Surge 268 
Title: "Quantifying Intracardiac Flow in the Clinical Setting" Abstract: 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. 
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 softeningstiffening 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 nonlinear 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. 
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: "Multiscale 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 tissuescale processes is still poorly understood due to the inherent complexity of emergent systemslevel 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 multiscale modeling environment called EpiScale for simulating epithelial tissue mechanics based on the Subcellular Element (SCE) modeling approach. EpiScale 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, cellcell 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 proteinprotein 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 PoissonBoltzmann electrostatic potentials to determine the role of electrostatics in proteinprotein 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 ligandbound 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 MicroMacro Framework for Analyzing Steric and Hydrodynamic Interactions in Gliding Assays" Abstract: Macroscopic flows of filamentmotor 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 largescale 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 fluidmediated 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 highdimensional 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" Abstract: 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 secondorder formulation of the LWR model" Abstract: The seminal LWR model (Lighthill and Whitham, 1955; Richards, 1956) has many equivalent firstorder formulations in both Eulerian and Lagrangian coordinates. In this study, we present a secondorder 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 secondorder model, which can be considered the zerorelaxation 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 secondorder continuum and carfollowing models established in (Jin, 2016) and prove that the nonstandard model and the LWR model are equivalent, since they have the same anisotropic carfollowing model and stability property. We further derive conditions for the nonstandard model to be forwardtraveling and collisionfree, prove that the collisionfree 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 leadvehicle problem and show that the nonstandard secondorder model has the same shock and rarefaction wave solutions as the LWR model for both Greenshields and triangular fundamental diagrams; for a nonconcave fundamental diagram we show that the collisionfree condition, but not the CFL condition, yields physically meaningful results. Finally we present a correction method to eliminate negative speeds and collisions in general secondorder 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 secondorder continuum models in (Daganzo, 1995a) and can help to guide the development and discretization of more physically meaningful secondorder continuum and carfollowing models.

December 5, 2016  
12:10  1:10 p.m.  Surge 268 
Jianzhong Wu, Department of Chemical Engineering, UC Riverside Title: "Bayesian Statistics for ManyBody Systems" Abstract: 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 onebody as well as manybody systems, the numerical complexity rises rapidly as the number of particles increases yet dynamic uncertainty makes it imperative to describe the properties of manybody systems from a statistical perspective. In this lecture, I outline a generic and computationally efficient procedure to predict the properties of manybody systems based on Bayesian statistics in conjunction with the HohenbergKohnMermin theorem. Illustrative examples will be discussed for manybody 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: "HighReynolds number fluid flow and the accumulation of vorticity on the boundary: Prandtl, Chorin, and Kato" Abstract: 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 reasonableseeming 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" Abstract: Hybrid particle/grid numerical methods have been around for a long time, and their usage is common in some fields, from plasma physics to artistdirected 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" Abstract: Stem cells located in growing tips, the shoot apical meristems, of plants provide cells for the development of all aboveground 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 dosedependent 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 cisregulatory 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, nuclearcytoplasmic partitioning and diffusivity of WUS into adjacent cells. I will discuss the importance of dosedependent 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" Abstract: 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" Abstract: 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" Abstract: 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 1D models. An important question is: how adequate is such 1D simplification of 2D (or 3D) 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 1D and 2D 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 1D 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 2D patterns, which is impossible in the 1D model. The 1D and the 2D 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 2D 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" Abstract: 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 rushhour 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" Abstract: 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,...,(p1). To run cellular automata one needs initial distribution of states for all cells and a set of rules. An example of 2state cellular automata will be provided as a basic introduction. 
October 3, 2016  
12  1:30 p.m.  Surge 268  *Organization meeting 