Getting from B to A: The Inverse Curl Problem — Zachary Silberman
Many different numerical codes are employed in studies of highly relativistic magnetized accretion flows around black holes. Based on the formalisms each uses, some codes evolve the magnetic field vector B, while others evolve the magnetic vector potential A, the two being related by the curl: B=curl(A). Here, we discuss how to generate vector potentials corresponding to specified magnetic fields on staggered grids, a surprisingly difficult task on finite cubic domains. The code we have developed solves this problem via a cell-by-cell method, whose scaling is nearly linear in the number of grid cells, and here we discuss the success this algorithm has in generating smooth vector potential configurations.
Deep Machine Learning: Overview and Applications — Christopher Kanan
Over the past four years, deep machine learning has transformed artificial intelligence. With some caveats, these systems now surpass humans at some specialized tasks, such as identifying people in photos, classifying objects in images, and playing board games, such as Go. In this talk, I describe the technologies behind deep learning, along with the computer hardware necessary to run these algorithms. I discuss applications for these algorithms in which performance now rivals humans. Lastly, I describe ongoing work in my lab to apply deep learning algorithms to new problems and to fix its limitations.
Periodic orbits of a neuron model with a periodic internal decay rate — Michael Radin
It is our goal to study the existence of periodic solutions, existence of eventually periodic solutions and the study of boundedness nature of solutions depending on the relationship between the periodic terms of the sequence of our neuron model; in particular, it is our objective to study which particular periodic cycles of various periods will exist, the patterns of these periodic cycles and their stability character as well. Furthermore, we will investigate which particular periodic cycles of our neuron model can be eventually periodic and why only particular ones be eventually periodic; we will analyze this behavior together with a bifurcation diagram as well. Moreover, we study different patterns of the transient terms of eventually periodic solutions to understand the phenomena more precisely.