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networks that serves as our guide throughout; we also list related model classes as
well as biophysically more detailed models. Section 13.4 gives an overview of basic
states and important collective phenomena in recurrent spiking neural networks. In
Section 13.5 we present recent approaches to characterize the emergence of patterns
of coordinated, precisely timed spikes in neural network models. Finally, in Section
13.6, we conclude and highlight some open questions. To keep this overview concise,
we focus on conceptual questions and theoretical challenges throughout, sometimes
passing over technical subtleties and smaller (yet not unimportant) problems.
13.2. Feed-Forward Mechanisms: Synre Chains
The synre chain hypothesis states that precisely timed spiking in cortical networks
is due to the existence of anatomical feed-forward structures that are part of cortical
circuits [4, 5]. Thinking abstractly, such a feed-forward structure can be separated
into groups of neurons or `layers', such that neurons in one layer receive many
synaptic connections from neurons in the previous layer (Fig. 13.1a). In its sim-
plest setting, the connectivity between layers is uni-directional and global, i.e. each
neuron in a layer receives an excitatory synapse from every neuron in the previous
layer. In general, this connectivity between layers is diluted and only predominantly
excitatory; still, when many spikes are received from a suciently synchronized pre-
synaptic group of neurons, the likelihood that a post-synaptic neuron generates a
spike is increased.
If now some initial layer of neurons emits spikes synchronously, i.e. with only
small inter-neuronal variations (on the order of one millisecond) each of the post-
synaptic neurons in the next layer receives an almost synchronous collection of
spikes (`volley') after an eective transmission delay [79]. Collectively, this may
initiate synchronous spiking activity generated by that next layer. Depending on
the temporal spread of the spikes, on the inter-connectivity between layers and on
the total number of synchronously ring neurons in a group, this may lead to the
persistent (or decaying) propagation of synchronous activity along the chain [38, 62],
(Fig. 13.1b). The feed-forward anatomy underlying synre chains is viewed as
an embedded part of a larger recurrent circuit such that each neuron receives in
addition many synaptic inputs from outside the chain; as the basic state of the entire
circuit is often asynchronous and irregular [33, 138, 140, 162], this additional input
is typically regarded as noise that adds to the propagating synchronous activity [4,
5, 38, 53, 61, 62, 83, 101, 159].
Already in 1963 Grith [56] suggested that densely coupled feed-forward
anatomy may have a functional role in the brain. He investigated the capabil-
ity of what he calls `transmission lines' to reliably transmit information in a non-
trivial way along feed-forward chains of abstract units. This idea was rened by
Abeles [4, 5] to account for the appearance of precise spiking sequences of neu-
rons. Diesmann and others showed that both fully connected and randomly diluted
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