Transformers and cortical waves: encoders for pulling in context across time

L Muller, PS Churchland, TJ Sejnowski - Trends in neurosciences, 2024 - cell.com
The capabilities of transformer networks such as ChatGPT and other large language models
(LLMs) have captured the world's attention. The crucial computational mechanism …

Waves traveling over a map of visual space can ignite short-term predictions of sensory input

GB Benigno, RC Budzinski, ZW Davis… - Nature …, 2023 - nature.com
Recent analyses have found waves of neural activity traveling across entire visual cortical
areas in awake animals. These traveling waves modulate the excitability of local networks …

Synchrony for weak coupling in the complexified Kuramoto model

M Thümler, SGM Srinivas, M Schröder, M Timme - Physical Review Letters, 2023 - APS
We present the finite-size Kuramoto model analytically continued from real to complex
variables and analyze its collective dynamics. For strong coupling, synchrony appears …

[HTML][HTML] Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks

RC Budzinski, TT Nguyen, J Đoàn, J Mináč… - … Journal of Nonlinear …, 2022 - pubs.aip.org
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto
model, which describes synchronization in systems from swarms of insects to …

Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays

RC Budzinski, TT Nguyen, GB Benigno, J Đoàn… - Physical Review …, 2023 - APS
We introduce an analytical approach that allows predictions and mechanistic insights into
the dynamics of nonlinear oscillator networks with heterogeneous time delays. We …

Joins of circulant matrices

J Đoàn, J Mináč, L Muller, TT Nguyen… - Linear Algebra and its …, 2022 - Elsevier
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Synchronized states of power grids and oscillator networks by convex optimization

C Hartmann, PC Böttcher, D Gross, D Witthaut - PRX Energy, 2024 - APS
Synchronization is essential for the operation of ac power systems: all generators in the
power grid must rotate with fixed relative phases to enable a steady flow of electric power …

Equilibria in Kuramoto oscillator networks: An algebraic approach

TT Nguyen, RC Budzinski, J Ðoàn, FW Pasini… - SIAM Journal on Applied …, 2023 - SIAM
Kuramoto networks constitute a paradigmatic model for the investigation of collective
behavior in networked systems. Despite many advances in recent years, many open …

Theory of transient chimeras in finite Sakaguchi-Kuramoto networks

RC Budzinski, JWC Graham, J Mináč… - arXiv preprint arXiv …, 2023 - arxiv.org
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 …

On the joins of group rings

SK Chebolu, JL Merzel, J Mináč, L Muller… - Journal of Pure and …, 2023 - Elsevier
Given a collection {G i} i= 1 d of finite groups and a ring R, we define a subring of the ring M
n (R)(n=∑ i= 1 d| G i|) that encompasses all the individual group rings R [G i] along the …