Sequential attractors in combinatorial threshold-linear networks
Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and
central pattern generator circuits that underlie rhythmic behaviors like locomotion. While …
central pattern generator circuits that underlie rhythmic behaviors like locomotion. While …
Core motifs predict dynamic attractors in combinatorial threshold-linear networks
C Parmelee, S Moore, K Morrison, C Curto - PloS one, 2022 - journals.plos.org
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated
TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of …
TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of …
Fixed points of competitive threshold-linear networks
Threshold-linear networks (TLNs) are models of neural networks that consist of simple,
perceptron-like neurons and exhibit nonlinear dynamics determined by the network's …
perceptron-like neurons and exhibit nonlinear dynamics determined by the network's …
Nonlinear stimulus representations in neural circuits with approximate excitatory-inhibitory balance
Balanced excitation and inhibition is widely observed in cortex. How does this balance
shape neural computations and stimulus representations? This question is often studied …
shape neural computations and stimulus representations? This question is often studied …
Oscillatory networks: Insights from piecewise-linear modeling
There is enormous interest--both mathematically and in diverse applications--in
understanding the dynamics of coupled oscillator networks. The real-world motivation of …
understanding the dynamics of coupled oscillator networks. The real-world motivation of …
Diversity of emergent dynamics in competitive threshold-linear networks
Threshold-linear networks consist of simple units interacting in the presence of a threshold
nonlinearity. Competitive threshold-linear networks have long been known to exhibit …
nonlinearity. Competitive threshold-linear networks have long been known to exhibit …
Periodic solutions in threshold-linear networks and their entrainment
Threshold-linear networks (TLNs) are recurrent networks where the dynamics are threshold-
linear (linearly rectified at zero). Mathematically, they consist of coupled nonsmooth ordinary …
linear (linearly rectified at zero). Mathematically, they consist of coupled nonsmooth ordinary …
[HTML][HTML] Graph rules for recurrent neural network dynamics: extended version
C Curto, K Morrison - ArXiv, 2023 - ncbi.nlm.nih.gov
Neurons in the brain are constantly flickering with activity, which can be spontaneous or in
response to stimuli [LBH09]. Because of positive feedback loops and the potential for …
response to stimuli [LBH09]. Because of positive feedback loops and the potential for …
Predicting neural network dynamics via graphical analysis
K Morrison, C Curto - Algebraic and Combinatorial Computational Biology, 2019 - Elsevier
Neural network models in neuroscience allow one to study how the connections between
neurons shape the activity of neural circuits in the brain. In this chapter, we study …
neurons shape the activity of neural circuits in the brain. In this chapter, we study …
Diversity of emergent dynamics in competitive threshold-linear networks
Threshold-linear networks consist of simple units interacting in the presence of a threshold
nonlinearity. Competitive threshold-linear networks have long been known to exhibit …
nonlinearity. Competitive threshold-linear networks have long been known to exhibit …