Transformers and cortical waves: encoders for pulling in context across time
The capabilities of transformer networks such as ChatGPT and other large language models
(LLMs) have captured the world's attention. The crucial computational mechanism …
(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
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 …
areas in awake animals. These traveling waves modulate the excitability of local networks …
Synchrony for weak coupling in the complexified Kuramoto model
We present the finite-size Kuramoto model analytically continued from real to complex
variables and analyze its collective dynamics. For strong coupling, synchrony appears …
variables and analyze its collective dynamics. For strong coupling, synchrony appears …
[HTML][HTML] Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
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 …
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
We introduce an analytical approach that allows predictions and mechanistic insights into
the dynamics of nonlinear oscillator networks with heterogeneous time delays. We …
the dynamics of nonlinear oscillator networks with heterogeneous time delays. We …
Joins of circulant matrices
Joins of circulant matrices - ScienceDirect Skip to main contentSkip to article Elsevier logo
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Synchronized states of power grids and oscillator networks by convex optimization
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 …
power grid must rotate with fixed relative phases to enable a steady flow of electric power …
Equilibria in Kuramoto oscillator networks: An algebraic approach
Kuramoto networks constitute a paradigmatic model for the investigation of collective
behavior in networked systems. Despite many advances in recent years, many open …
behavior in networked systems. Despite many advances in recent years, many open …
Theory of transient chimeras in finite Sakaguchi-Kuramoto networks
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 …
that is fully homogeneous. Precisely how transient chimeras emerge in finite networks of …
On the joins of group rings
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 …
n (R)(n=∑ i= 1 d| G i|) that encompasses all the individual group rings R [G i] along the …