7 papers
Phase-based spatial ordinal patterns for characterizing oscillatory dynamics
Robison J. Santos-Silva, Bruno R. R. Boaretto, Thiago L. Prado +1
The emergence of organized spatiotemporal patterns is ubiquitous in oscillatory systems, from neural populations to engineered networks. Identifying these patterns and tracking how…
Delay coordinates synchronization and induces abrupt transition in excitable networks
Bruno R. R. Boaretto, Kalel L. Rossi, Lyle E. Muller +2
Neuronal communication is inherently time-delayed, due to the finite speed of signal propagation. Although often considered challenging or disruptive, such time delays can also end…
Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Arthur S. Powanwe, Luisa H. B. Liboni, Anif N. Shikder +7
We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption…
An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling
Anif N. Shikder, Ramit Dey, Sayantan Auddy +6
We establish a mathematical correspondence between state space models, a state-of-the-art architecture for capturing long-range dependencies in data, and an exactly solvable nonlin…
Traveling Waves Integrate Spatial Information Through Time
Mozes Jacobs, Roberto C. Budzinski, Lyle Muller +2
Traveling waves of neural activity are widely observed in the brain, but their precise computational function remains unclear. One prominent hypothesis is that they enable the tran…
Geometric perspective of linear stability in finite networks of nonlinear oscillators
Yashee Sinha, Priya B. Jain, Antonio Mihara +4
We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematic…