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A touch of non-linearity in fluid fields: where spheres 鈥渢hink鈥� 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...

Feedback-based online algorithms for time-varying network optimization The talk focuses on the synthesis and analysis of online algorithmic solutions to control networked systems based on performance objectives and engineering constraints that may evolve over time. The time-varying optimization formalism is leveraged to model optimal trajectories of the networked systems, as...

Finite-Horizon Approximate Linear Programs for an Infinite-Horizon Revenue Management Problem Approximate linear programs have been used extensively to approximately solve stochastic dynamic programs that suffer from the well-known curse of dimensionality. Due to canonical results establishing the optimality of stationary value functions and policies for infinite-horizon dynamic programs, the literature...

Inference on Winners Many empirical questions can be cast as inference on a parameter selected through optimization. For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data. Such settings give rise to a...

Spectral Problems in Inverse Scattering for Inhomogeneous Media The inverse scattering problem for inhomogeneous (possibly anisotropic) media amounts to solving a nonlinear ill-posed equation, thus presenting difficulties in arriving at a solution. Furthermore, in the case of anisotropic media, the matrix value refractive index may not be uniquely determined from...

Granular flow: Particle Size Segregation and New Constitutive Laws The segregation of particles of different sizes can be achieved by vibration or by shear flow. I describe a nonlinear conservation law that captures the main features of segregation under shear flow, such as occurs in an avalanche. Predictions of the...

Differential imaging of evolution in elastic backgrounds with unknown microstructure Major components of nuclear power plants e.g., reactors, fuel cells and containment vessels are comprised of highly heterogeneous composites that (a) their topology and properties at micro- and meso- scales are uncertain or in most cases unknown, and (b) their...

Fairest edge usage in spanning trees This talk will explore several interesting and interrelated optimization problems involving the spanning trees of a graph. Each problem will be connected to a single fundamental question: How should we choose a probability distribution on the spanning trees of a graph that treats the...

On the dynamics of coupled Morris-Lecar Neurons In recent years, the study of computational neuronal dynamics has made remarkable progress has been made by on the nonlinear study of artificial neural networks. This approach relies on using models of single neurons as building blocks of a much larger network ensemble...