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patterns have been derived [102{105]. The stability properties are of particular
interest, e.g. because they determine the computational capabilities of a network
(where computation is not only possible with stable states [10, 11, 72, 95] ) and be-
cause motifs that exhibit patterns which are stable (or unstable) might, if embedded
in a larger network, inuence the entire network's function in a specic way.
The theory of coupled phase oscillators suggests so-called chimera states as
a possible link [118] between a fully synchronous state and asynchronous states.
Chimera states were originally found [85] in rings of coupled identical limit-cycle
oscillators with translation-invariant, non-local coupling. In chimera states, one sub-
population of neighboring oscillators is phase-locked whereas oscillators in a second
sub-population are asynchronous and neither locked with the rst sub-population
nor with each other. Such chimera states are thus similar to the partially synchro-
nized states [154] described above. However, they are signicantly dierent as they
occur also in homogeneous, translation invariant systems ([8, 85, 137], Ref. [118]
introduces a location-dependent stimulation that breaks this symmetry), whereas
the partial locking found in pulse-coupled systems [154] was induced by inhomo-
geneities [154].
Since in each biological neural system one particular network is selected that
generates a desired dynamics (and function) an open question is whether and in
which aspects networks may be optimized, for instance structurally. First examples
[103, 104] show that even very sparse heterogeneously coupled networks and very
dense, homogeneously coupled networks may be capable of generating the same
predened pattern, cf. Fig. 13.7.
13.6. Conclusions and Open Questions
The currently debated question under which conditions and how patterns of pre-
cisely timed spikes and microscopic synchrony may emerge in neural circuits is still
far from being answered and also their potential functional role is explored further.
On the path towards a nal conclusion, experimental and theoretical ndings need
to be jointly evaluated in a critical way in order to generate and conrm (or reject)
key hypotheses. We have here presented two major hypotheses for the mechanism
underlying the generation of spike patterns; one where feed-forward anatomy is
crucial, and one asserting that spike patterns may emerge collectively in recurrent
networks. Up to now, both hypotheses have been neither conrmed nor rejected
experimentally and on theoretical grounds, both seem possible.
The hypotheses on synre and recurrent mechanisms mark only the extreme
starting points for such investigations, working in the limits of strong feed-forward
chains and of no particular coarse structure, respectively. Intermediate possibil-
ities need to be explored as well. For instance, what is the impact of observed
non-random topology, such as motifs present in otherwise apparently randomly
connected, spatially extended circuits [103, 107, 123, 141, 142]?
