Seminars

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, University of Colorado Boulder "Mathematical Biology and Sociology: a Buff's Perspective" Daniel Appelö , Department of Applied Mathematics, University of Colorado Boulder “Computational Mathematics at CU Boulder”

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...

A touch of non-linearity in fluid fields: where spheres “think” collectively and swim together From crawling cells to orca whales, swimming in nature occurs at different scales. The study of swimming across length scales can shed light onto the biological functions of natural swimmers or inspire the design of artificial...

Practical and Theoretical Questions in Network Synchronization: Optimization and Control Collective behavior in large ensembles of network-coupled dynamical systems remains an active area of research in the nonlinear dynamics and networks science communities. Example applications stem from both naturally-occurring to man-made systems, e.g., cardiac pacemaker cells, mammalian circadian rhythms, Josephson...