11 Coupling Functions in Neuroscience
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surrogate time series which have similar statistical properties to those of the original
data. Also one should be careful when analysing neural coupling functions as it has
been shown that they can be time-varying [19, 65, 73], hence this should be taken
into account in the analysis.
11.4 Conclusions and Discussions
In summary, this chapter gives an overview of how coupling functions are relevant and
useful in neuroscience. They bring an additional dimension—the form of coupling
function—which revels the mechanism of the neural interactions. This is relevant in
neuroscience, as it can describe and be linked to the many different brain functions.
Two largely studied levels of neural interactions were discussed, the low-level
individual neurons and the high-level systemic processes like the brainwave oscillations. Of course, these two levels are not exclusive but they are closely related, i.e. the
brainwaves are like mean-field averages of the activities of billions of neurons. In fact
studies exist where the brainwave oscillations are modeled as Kuramoto ensembles
but the large-scale cross-frequency couplings for the modelling are inferred from
data [5, 62]. Needless to say, coupling functions have implications for other levels
and depths of the brain other than the two discussed here.
The focus was on phase coupling functions, though the interactions can be in
amplitude, or combine phase-amplitude based domains [8, 29, 30]. Many modeling
methods used in neuroscience actually inferred dynamical systems where coupling
functions were an integral part [15, 28]. In such cases coupling functions were
implicit, and they were not treated as separate entities, nor were they assesses and
analysed separately. These tasks are yet to be developed properly for the amplitude
and the phase-amplitude domains.
As an outlook, with all their advantages one could expect that coupling functions
will continue to play an important role in future neuroscience studies, maybe even to
extend their current use. The ever demanding computational power for calculations
on large populations of neuron interactions will be more accessible in future, as new
improved and faster methods will be developed. The artificial neural networks take
on increasing importance recently, with many application across different disciplines
and industries [22, 85]. The coupling function theory and the different findings in
many neuroscience studies could play an important role in establishing improved
and more efficient artificial neural networks. Also, the models could be extended
and generalized further for easier applications on amplitude and phase-amplitude
domains. The theory needs to follow closer the new discoveries from neural coupling
functions analysis. The coupling function developments in other fields, especially in
physics, could play an important role for neuroscience tasks, and vice versa.
185
surrogate time series which have similar statistical properties to those of the original
data. Also one should be careful when analysing neural coupling functions as it has
been shown that they can be time-varying [19, 65, 73], hence this should be taken
into account in the analysis.
11.4 Conclusions and Discussions
In summary, this chapter gives an overview of how coupling functions are relevant and
useful in neuroscience. They bring an additional dimension—the form of coupling
function—which revels the mechanism of the neural interactions. This is relevant in
neuroscience, as it can describe and be linked to the many different brain functions.
Two largely studied levels of neural interactions were discussed, the low-level
individual neurons and the high-level systemic processes like the brainwave oscillations. Of course, these two levels are not exclusive but they are closely related, i.e. the
brainwaves are like mean-field averages of the activities of billions of neurons. In fact
studies exist where the brainwave oscillations are modeled as Kuramoto ensembles
but the large-scale cross-frequency couplings for the modelling are inferred from
data [5, 62]. Needless to say, coupling functions have implications for other levels
and depths of the brain other than the two discussed here.
The focus was on phase coupling functions, though the interactions can be in
amplitude, or combine phase-amplitude based domains [8, 29, 30]. Many modeling
methods used in neuroscience actually inferred dynamical systems where coupling
functions were an integral part [15, 28]. In such cases coupling functions were
implicit, and they were not treated as separate entities, nor were they assesses and
analysed separately. These tasks are yet to be developed properly for the amplitude
and the phase-amplitude domains.
As an outlook, with all their advantages one could expect that coupling functions
will continue to play an important role in future neuroscience studies, maybe even to
extend their current use. The ever demanding computational power for calculations
on large populations of neuron interactions will be more accessible in future, as new
improved and faster methods will be developed. The artificial neural networks take
on increasing importance recently, with many application across different disciplines
and industries [22, 85]. The coupling function theory and the different findings in
many neuroscience studies could play an important role in establishing improved
and more efficient artificial neural networks. Also, the models could be extended
and generalized further for easier applications on amplitude and phase-amplitude
domains. The theory needs to follow closer the new discoveries from neural coupling
functions analysis. The coupling function developments in other fields, especially in
physics, could play an important role for neuroscience tasks, and vice versa.