February 9

Hailiang Liu
(Iowa State University) 

Title: Data-driven Optimal Control of a SEIR model for COVID-19

Abstract: The rapid spread of COVID-19 has resulted in over millions of confirmed and death cases, and has a huge impact on global economy as well as everyone's daily life. In this work, we present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. This approach serves to forecast the evolution of the outbreak and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations. 
(This is based on join work with Xuping Tian). 

Link: 

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February 16

Claus Kadelka (Iowa State University)

Title: Effect of clustering and correlation of belief systems on COVID-19 and other infectious disease outbreaks

Abstract: Contact between people with similar opinions and characteristics occurs at a higher rate than among other people, a phenomenon known as homophily. The presence of clusters of unvaccinated people has been associated with increased incidence of infectious disease outbreaks despite high vaccination coverage. The epidemiological consequences of homophily regarding other beliefs and correlations among belief systems are however poorly understood. Here, we use a simple compartmental network model as well as a more complex, recently developed COVID-19 model to study how homophily and correlation of belief systems in a social interaction network affect the probability of disease outbreak and COVID-19-related mortality. We find that the current social context, characterized by the presence of homophily and correlations between who vaccinates, who engages in risk reduction, and individual risk status, corresponds to a situation with substantially worse disease burden than in the absence of heterogeneities. In the presence of an effective vaccine, relative effects of homophily and correlation of belief systems become stronger. Further, the optimal vaccination strategy depends on the degree of homophily regarding vaccination status as well as the relative level of risk mitigation high- and low-risk individuals practice. The developed methods are broadly applicable to any investigation in which node attributes in a graph might reasonably be expected to cluster or exhibit correlations. Throughout the talk, I will highlight future avenues for research in mathematical epidemiology and network science. (This is joint work with Audrey McCombs)

Link: 

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February 23

Pamela Harris (Williams College)

Title: Kostant's partition function and magic multiplex juggling sequences

Abstract: Kostant’s partition function is a vector partition function that counts the number of ways one can express a weight of a Lie algebra g as a nonnegative integral linear combination of the positive roots of g. Multiplex juggling sequences are generalizations of juggling sequences that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. Magic multiplex juggling sequences generalize further to include magic balls, which cancel with standard balls when they meet at the same height. In this talk, we present a combinatorial equivalence between positive roots of a Lie algebra and throws during a juggling sequence. This provides a juggling framework to calculate Kostant’s partition functions, and a partition function framework to compute the number of juggling sequences. This is joint work with Carolina Benedetti, Christopher R. H. Hanusa, Alejandro Morales, and Anthony Simpson.

Link: 

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March 2

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March 9

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March 16

Selenne Banuelos (California State University Channel Islands)

Title: Modeling the Long Term Effects of Thermoregulation on Human Sleep

Abstract: The connection between human sleep and energy exertion has long been regarded as part of the reasoning for the need to sleep. A recent theory proposes that during REM sleep, energy utilized for thermoregulation is diverted to other relevant biological processes. We present a mathematical model of human sleep/wake regulation with thermoregulatory functions to gain quantitative insight into the effects of ambient temperature on sleep quality. Our model extends previous models by incorporating equations for the metabolic processes that control thermoregulation during sleep. We present numerical simulations that provide a quantitative answer for how humans adjust by changing the normal sleep stage progression when it is challenged with ambient temperatures away from thermoneutral. We explore the dynamics for a single night and several nights. Our results indicate that including the effects of temperature is a vital component of modeling sleep.

Link: 

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March 23

Weimin Han (The University of Iowa)

Title: Hemivariational Inequalities: Theory and Numerical Analysis

Abstract: 

In recent years, modeling, analysis, and numerical solution of hemivariational inequalities have attracted much attention in the research communities.  Hemivariational inequalities are generalizations of variational inequalities.  Through the formulation of hemivariational inequalities, application problems involving nonmonotone, nonsmooth and multivalued constitutive laws, forces, and boundary conditions can be treated successfully. Hemivariational inequalities have been shown to be very useful across a wide variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics.

This talk provides a summary account of recent and new results on theoretical and numerical analysis of hemivariational inequalities.  It starts with a discussion of weak formulations of a model elliptic boundary value problem, followed by an introduction of variational inequalities and hemivariational inequalities.  Different from the commonly adopted approach in the literature based on the notion of pseudomonotonicity and surjectivity results for pseudomonotone operators, a new approach for the study of hemivariational inequalities is developed employing only elementary knowledge on convex minimization and Banach fixed-point theorem.  Results on convergence and optimal order error estimates are presented for numerical solutions of hemivariational inequalities.  Numerical examples are shown on the performance of the numerical methods, including numerical convergence orders.

Link: 

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March 30

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April 6

Leo Rebholz (Clemson University)

Title: Anderson acceleration and how it speeds up convergence in fixed point iterations

Abstract: Anderson acceleration (AA) is an extrapolation technique originally proposed in 1965 that recombines the most recent iterates and update steps in a fixed point iteration to improve the convergence properties of the sequence. Despite being successfully used for many years to improve nonlinear solver behavior on a wide variety of problems, a theory that explains the often-observed accelerated convergence was lacking. In this talk, we give an introduction to AA, then present a proof of AA convergence which shows that it improves the linear convergence rate based on a gain factor of an underlying optimization problem, but also introduces higher order terms in the residual error bound. We then discuss improvements to AA based on our convergence theory, and show numerical results for the algorithms applied to several application problems including Navier-Stokes, Boussinesq, and nonlinear Helmholtz systems.

Link:

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April 13

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April 20

Lorena Bociu (NC State University)

Title: Analysis and Control of Porous Media Flows with Applications in Ocular Perfusion

Abstract: Fluid flows through deformable porous media are relevant for many applications in biology, medicine and bio-engineering, including tissue perfusion and fluid flow inside cartilages and bones. We are interested in perfusion inside the eye and its connection to the development of glaucoma. Mathematically, the problem translates into the study of a nonlinear poroelastic system, which is a system of PDEs of mixed parabolic-elliptic type. We answer questions related to ocular tissue biomechanics via well-posedness, sensitivity analysis, and optimal control for the PDE coupled system applied to the eye.

Link: 

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April 27

Harbir Antil (George Mason University)

Note: Talk will start at 2.30 pm. 

Title: Part I: Fractional Operators and Applications; Part II: Simulation of Viral Propagation in Built Environment  

Abstract: Fractional calculus and its application to anomalous diffusion has recently received a tremendous amount of attention. In complex/heterogeneous material mediums, the long-range correlations or hereditary material properties are presumed to be the cause of such anomalous behavior. Owing to the revival of fractional calculus, these effects are now conveniently modeled by fractional-order differential operators and the governing equations are reformulated accordingly. 

The first part of the talk will introduce various state-of-the-art applications of fractional operators in imaging, geophysics, quantum mechanics, harmonic maps, optimal control, and machine learning.

The second part of the talk will summarize mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity will be presented. Several realistic examples of the built environments, such as TSA Queues, Hospital Rooms, Subway trains, etc. will be presented.

Link: 

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