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Convergence to the Mean Field Game Limit: A Case Study Mean field games are used as approximations to n-player games with large n. Indeed, n-player Nash equilibria are known to converge to their mean field counterpart when the latter is unique. In this talk we study a specific stochastic game...

QUBO Models in Optimization, Machine Learning, and Quantum Computing The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as...

Set Values for Nonzero Sum Games With Multiple Equilibriums Nonzero sum games typically have multiple Nash equilibriums (or no equilibriums), and unlike zero sum games, they may have different values at different equilibriums. While most works in the literature focus on the existence of individual equilibriums, we propose instead to...

Cluster Synchronization in Networks with Symmetries We first review the master stability function (MSF) approach to synchronization of networks of coupled identical oscillators. The original formulation proposed by Pecora and Carroll applies to the case that all the oscillators in the network converge on the same time-evolution (complete synchronization) and...

Optimal transport for seismic inversion: tackling the nonlinearity. Full waveform inversion (FWI) is a seismic imaging method which is now part of the conventional imaging workflow in the industry. It is also used for global and regional scale imaging in seismology. Its primary interest compared to tomography is its high-resolution...

Computational Complexity, Dynamical Systems, and Non-Convex Optimization For a given computational problem, computational complexity asks the question of the resources needed - such as time, space, energy - by any algorithm which solves the problem. Despite algorithms being a form of discrete dynamical system (in both time & space), the...

Using Survival Information in Truncation by Death Problems Without the Monotonicity Assumption In some randomized clinical trials, patients may die before the measurements of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes...

Nancy Rodriguez, Department of Applied Mathematics, 精品SM在线影片 "Mathematical Biology and Sociology: a Buff's Perspective" Daniel Appel枚 , Department of Applied Mathematics, 精品SM在线影片 鈥淐omputational Mathematics at 精品SM在线影片鈥�

ontrolling oscillations in high-order accurate methods through neural networks While discontinuous Galerkin methods have proven themselves to be powerful computational methods, capable of accurately solving a variety of PDE's, the combination of high-order accuracy and discontinuous solutions remain a significant challenge. Traditional methods such as TVB limiting or artificial viscosity...

Neuroendocrine stress response and PTSD The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions are correlated with stress-related diseases such as PTSD and major depression. We characterize normal and diseased states of the HPA axis as basins of attraction of a dynamical system describing the...