94 citations · 264 across the 34 of their papers we have counts for
34 papers
Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure
Kalel L. Rossi, Antonio Mihara, Lyle E. Muller +2
We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronizatio…
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…
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…
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…
A mathematical language for linking fine-scale structure in spikes from hundreds to thousands of neurons with behaviour
Alexandra N. Busch, Roberto C. Budzinski, Federico W. Pasini +8
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, character…
A Spatiotemporal Perspective on Dynamical Computation in Neural Information Processing Systems
T. Anderson Keller, Lyle Muller, Terrence J. Sejnowski +1
Spatiotemporal flows of neural activity, such as traveling waves, have been observed throughout the brain since the earliest recordings; yet there is still little consensus on thei…
Transformers and Cortical Waves: Encoders for Pulling In Context Across Time
Lyle Muller, Patricia S. Churchland, Terrence J. Sejnowski
The capabilities of transformer networks such as ChatGPT and other Large Language Models (LLMs) have captured the world's attention. The crucial computational mechanism underlying…
Image segmentation with traveling waves in an exactly solvable recurrent neural network
Luisa H. B. Liboni, Roberto C. Budzinski, Alexandra N. Busch +4
We study image segmentation using spatiotemporal dynamics in a recurrent neural network where the state of each unit is given by a complex number. We show that this network generat…
An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network
Roberto C. Budzinski, Alexandra N. Busch, Samuel Mestern +7
We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially syn…
Theory of transient chimeras in finite Sakaguchi-Kuramoto networks
Roberto C. Budzinski, James W. C. Graham, Ján Mináč +1
Chimera states are a phenomenon in which order and disorder can co-exist within a network that is fully homogeneous. Precisely how transient chimeras emerge in finite networks of K…
Traveling Waves Encode the Recent Past and Enhance Sequence Learning
T. Anderson Keller, Lyle Muller, Terrence Sejnowski +1
Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One phy…
Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators
Priya B. Jain, Tung T. Nguyen, Ján Mináč +2
Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study…
Dynamical properties and mechanisms of metastability: a perspective in neuroscience
Kalel L. Rossi, Roberto C. Budzinski, Everton S. Medeiros +3
Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literat…
Predicting Stellar Mass Accretion: An Optimized Echo State Network Approach in Time Series Modeling
Gianfranco Bino, Shantanu Basu, Ramit Dey +3
Modeling the dynamics of the formation and evolution of protostellar disks as well as the history of stellar mass accretion typically involve the numerical solution of complex syst…
On the Paley graph of a quadratic character
Ján Mináč, Lyle Muller, Tung T. Nguyen +1
Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches…
An algebraic approach to spike-time neural codes in the hippocampus
Federico W. Pasini, Alexandra N. Busch, Ján Mináč +2
Although temporal coding through spike-time patterns has long been of interest in neuroscience, the specific structures that could be useful for spike-time codes remain highly uncl…
Broadcasting solutions on networked systems of phase oscillators
Tung T. Nguyen, Roberto C. Budzinski, Federico W. Pasini +3
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the…
Small changes at single nodes can shift global network dynamics
Kalel L. Rossi, Roberto C. Budzinski, Bruno R. R. Boaretto +2
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the bra…
On the joins of group rings
Sunil K. Chebolu, Jonathan L. Merzel, Ján Mináč +4
Given a collection of finite groups and a ring , we define a subring of the ring ( that encompasses all the individual group…
Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays
Roberto C. Budzinski, Tung T. Nguyen, Gabriel B. Benigno +4
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstra…
Joins of normal matrices, their spectrum, and applications
Jan Mináč, Lyle Muller, Tung T. Nguyen +1
Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic…
Spectral perturbation by rank one matrices
Jon Merzel, Jan Minac, Lyle Muller +2
Let be a matrix of size over an algebraically closed field and a monic polynomial of degree . In this article, we describe the necessary and sufficie…