Seminars

Induction of time inconsistency in optimal stopping problem Time inconsistency is a common phenomenon of optimal control and optimal stopping problems, especially in finance and economics. It says a player will change his optimal strategy over time. To deal with such problem, we usually search for some consistent plan (equilibrium)...

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...

Spatiotemporal Dynamics of Neocortical Seizure Activity Seizures are defined as sudden, abnormal electrical disturbances in the brain. Patients diagnosed with epilepsy have chronic, recurrent seizures and often require clinical intervention to prevent these episodes. Unfortunately, a large portion of epilepsy patients do not respond to current treatment options, in part...

Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity...

Colton Grainger, Department of Mathematics, University of Colorado Boulder On Characterizing the Capacity of Neural Networks using Algebraic Topology The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines...

Challenges and insights from the application of spectral/hp methods to problems in computation medicine Spectral/hp element methods for discretizing engineering-based PDE problems have been lauded for combining geometric (meshing) flexibility with superior convergence behavior. Since their inception in the 1980s, there has been growing interest in their development and usage...

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...

Dynamics of particles in stationary and oscillating flows The motion of small bodies in a hydrodynamic flow is a classical problem of fluid dynamics. Since 1980s-1990s the corresponding studies have been largely intensified due to the new applications, such as tracing impurities in the ocean and new biomedical applications of...

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...