Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and
central pattern generator circuits that underlie rhythmic behaviors like locomotion. While …

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 …

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 …

Balanced excitation and inhibition is widely observed in cortex. How does this balance
shape neural computations and stimulus representations? This question is often studied …

There is enormous interest--both mathematically and in diverse applications--in
understanding the dynamics of coupled oscillator networks. The real-world motivation of …

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 …

Threshold-linear networks (TLNs) are recurrent networks where the dynamics are threshold-
linear (linearly rectified at zero). Mathematically, they consist of coupled nonsmooth ordinary …

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 …

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 …

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 …