Abstract of Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice, by Rebecca Santorella Ph.D., Brown University, May 2022. As data becomes …
Domain exchange transformations (DETs) are dynamical systems of piecewise translations defined on piecewise smooth Jordan domains. DETs are two-dimensional generalizations of interval exchange transformations which …
Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been …
The FitzHugh-Nagumo equations are known to admit fast traveling pulses that have monotone tails and arise as the concatenation of Nagumo fronts and backs in …
The zebrafish (Danio rerio), a widely-studied model organism, is a small fish with distinctive black and yellow stripes on its body and fins. Numerous experimental …
Solitary waves are localized disturbances that maintain their shape as they propagate at a constant velocity. They have applications in diverse fields such as fluid …
Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can …
It is argued that convolutional neural networks (CNNs) struggle to represent the relations among items in a visual scene efficiently. We claim this is a …
Solutions of reaction-diffusion systems exhibit a wide variety of patterns like spirals, stripes and Turing patterns. In particular, the Belousov-Zhabotinsky (BZ) reaction produces spiral patterns, …
