Modeling the brain as a dynamical network
DateFriday, November 16, 2018 - 3:00pm
AbstractSeeking to understand how the brain processes visual information, my collaborators and I have built a model of the monkey visual cortex, which is quite similar to our own. We have focused on an early part of the visual pathway called the primary visual cortex (V1), and have modeled it as a large network of neurons that interact dynamically to compute the model's response to stimuli, mimicking the way neurons compute in the real cortex. I will report on our model's capabilities thus far, including its response to drifting gratings varying in orientation, spatial frequency and contrast. Dynamical mechanisms will be discussed, as will emergent phenomena such as gamma-band rhythms, which are ubiquitous throughout cortex. This work was carried out jointly with Robert Shapley (Center for Neural Science, NYU) and Logan Chariker (CNS/Courant).
Reduced order model for active array data processing in inverse scattering.
DateFriday, November 30, 2018 - 3:00pm
AbstractI will discuss an inverse problem for the wave equation, where an array of sensors probes an unknown, heterogeneous medium with pulses and measures the scattered waves. The goal in inversion is to determine from these measurements scattering structures in the medium, modeled mathematically by a reflectivity function. Most imaging methods assume a linear mapping between the unknown reflectivity and the array data. The linearization, known as the Born (single scattering) approximation is not accurate in strongly scattering media, so the reconstruction of the reflectivity may be poor. We show that it is possible to remove the multiple scattering (nonlinear) effects from the data using a reduced order model (ROM). The ROM is defined by an orthogonal projection of the wave propagator operator on the subspace spanned by the time snapshots of the solution of the wave equation. The snapshots are known only at the sensor locations, which is enough information to construct the ROM. The main result discussed in the talk is a novel, linear-algebraic algorithm that uses the ROM to map the data to its Born approximation. I will discuss how it applies to imaging with sound, electromagnetic and elastic waves.