Georgia Institute of Technology College of Sciences

Active scalars appear in many problems of fluid dynamics. The most common examples of active scalar equations are 2D Euler, Burgers, and 2D surface quasi-geostrophic (SQG) equations. Many questions about regularity and properties of solutions of these equations remain open. I will discuss the recently introduced idea of nonlocal maximum principle, which helped prove global regularity of solutions to the critical SQG equation. I will describe some further recent developments on regularity and blowup of solutions to active scalar equations.

A discussion of the paper "Boolean network models of cellular regulation: prospects and limitations" by Bornholdt (2008).

In this talk, I will present two examples of the application of wavelet analysis to the understanding of mild Traumatic Brain Injury (mTBI). First, the talk will focus on how wavelet-based features can be used to define important characteristics of blast-related acceleration and pressure signatures, and how these can be used to drive a Naïve Bayes classifier using wavelet packets. Later, some recent progress on the use of wavelets for data-driven clustering of brain regions and the characterization of functional network dynamics related to mTBI will be discussed. In particular, because neurological time series such as the ones obtained from an fMRI scan belong to the class of long term memory processes (also referred to as 1/f-like processes), the use of wavelet analysis guarantees optimal theoretical whitening properties and leads to better clusters compared to classical seed-based approaches.