Seminars

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...

"Don't go with the flow -- – A new tensor algebra for Neural Networks" Multi-dimensional information often involves multi-dimensional correlations that may remain latent by virtue of traditional matrix-based learning algorithms. In this study, we propose a tensor neural network framework that offers an exciting new paradigm for supervised machine...

In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full order model. One approach to model reduction is to find reduced order models that are locally optimal approximations...

A Stochastic Model of Optimal Debt Management and Bankruptcy We consider a problem of optimal debt management which is modeled as a non-cooperative game between a borrower and a pool of risk-neutral lenders. Since the debtor may go bankrupt, lenders charge a higher interest rate to offset the possible loss...

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...

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...

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...

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...