Posts

Zoom Link for the Fall Semester 2024

the physical seminar is either in MW154 or MW100a (inside the reception office)

Join Zoom Meeting

https://osu.zoom.us/j/99158238170?pwd=S1I0MCsrczcrRW1qUUF1SmRaZVV2UT09

Meeting ID: 991 5823 8170

Password: 314159

Abstracts

Edriss Titi

Title: On Recent Advances of the 3D Euler Equations by Means of Examples

Abstract: Euler-Loss-Regularity

Daozhou Gao

Title: Effects of Human Movement on Disease Spread: Persistence versus Prevalence

Abstract: Human movement not only facilitates disease spread but also poses a serious challenge to disease control and eradication. It is common to use patch models to describe the spatial spread of infectious diseases in a discrete space. The basic reproduction number R0 usually serves as a threshold for disease extinction and persistence. Thus, it is desirable to control population dispersal such that R0 is reduced to less than 1 to achieve disease eradication. However, in reality, disease eradication is extremely difficult or even impossible for most infectious diseases. Reducing disease prevalence (proportion of people being infected) to a low level is a more feasible and cost-effective goal. In this talk, based on an SIS patch model initially proposed and analyzed by Allen et al. (SIAM J Appl Math, 2007), I will explore the influence of dispersal intensity and dispersal asymmetry on the disease persistence and disease prevalence. Our study highlights the necessity of evaluating control measures with other quantities besides the basic reproduction number.

Timur Akhunov

Title: Modified energy method for illposedness of dispersive equations

Abstract: Korteweg and de Vries in 1890s derived an equation that bears their name to elucidate unusual behavior of water waves. They discovered solitons that behave like billiard balls when interacting. Can solitons be made compactly supported? Rosenau-Hyman in 93 proposed partial differential equations with such solutions that they dubbed “compactons”. Wellposedness of compacton equations is poorly understood. A plausible avenue to prove illposedness results is a modified energy method.

Vlad Kobzar (Sep 17)

Title: PDE-Based Analysis of Prediction with Expert Advice and Two-Armed Bandit

Abstract: This talk addresses the classic online learning problem of prediction with expert advice (the expert problem): at each round until the final time, the predictor (player) uses guidance from a collection of experts with the goal of minimizing the difference (regret) between the player’s loss and that of the best performing expert in hindsight. The experts’ losses are determined by the environment (adversary). Using verification arguments from optimal control theory, we view the task of finding lower and upper bounds on the value of the expert problem (regret) as the problem of finding sub- and supersolutions of certain partial differential equations (PDEs). These sub- and supersolutions serve as the potentials for player and adversary strategies, which lead to the corresponding bounds. To get explicit bounds, we use closed-form solutions of specific PDEs. In certain regimes, these bounds improve upon the previous state of the art. We will also briefly discuss our subsequent work generalizing this analysis to the two-armed bandit problem, which is a partial information counterpart of the corresponding expert problem. This talk is based on joint work with Robert Kohn and Zhilei Wang.

Chang-Hong Wu

Title:  Spreading fronts arising from the singular limit of reaction-diffusion systems

Abstract:
In this talk, we will focus on the singular limit of reaction-diffusion systems to gain insight into the formation of spreading fronts of invasive species. We will derive some free boundary problems and provide interpretations for spreading fronts from a modeling perspective. Additionally, numerical examples will be presented to facilitate discussion on invasion speed. This talk is based on joint works with Hirofumi Izuhara and Harunori Monobe.

Vlad Kobzar (Oct 29)

Title: A PDE-Based Analysis of the Symmetric Two-Armed Bernoulli Bandit

Abstract: The multiarmed bandit is one of the oldest problems in machine learning and is a foundational problem in reinforcement learning, large language modeling, adaptive medical trials, digital heath, marketing and recommendation systems, to name a few.  At each round, the predictor (player) selects a probability distribution from a finite collection of distributions (arms) with the goal of minimizing the difference (regret) between the player’s rewards sampled from the selected arms and the rewards of the arm with the highest expected reward. The player’s choice of the arm and the reward sampled from that arm are revealed to the player, and this prediction process is repeated until the final round.

Peter Takac

Title: A p(x)-Laplacian Extension of a Convexity Result and Applications to Quasi-linear Elliptic BVPs

Abstract: The main result of this work is a new extension of the well-known inequality by Dı́az and Saa which, in our case, involves an anisotropic operator, such as the p(x)-Laplacian, ∆ p(x) u ≡ div(|∇u| p(x)−2 ∇u). Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p(x)-Laplacian.

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