Collective Behavior: Macroscopic versus Kinetic Descriptions

Sampling and Computation in High Dimensions

Ron DeVore

Texas A&M University

It is well known that computation in high spatial dimensions suffers from the curse of dimensionality if the objects to be computed are modeled only by smoothness. This has led to various new models based on sparsity, variable reduction, tensor formats, etc., in order to make high dimensional computation more amenable. This talk will discuss some of these notions and the form sampling or computation should take to avoid the curse. The talk will also briefly discuss whether these models are realistic in real world applications