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Here, we systematically describe the oscillatory regimes which a NMM of a single cortical source with extrinsic input from other cortical and subcortical areas to each subpopulation can explain.
However, the entorhinal cortex may not be the only major extrinsic input to consider, and the trisynaptic circuit may not be the only way information is processed in hippocampus.
When R is plotted as a function of the correlation time of the extrinsic input, Type II shows a local maximum while Type I gives only a monotone increase.
Furthermore, in most of the literature, the JR-NMM includes a term representing extrinsic input or background noise, which essentially is done by declaring that input function to be a stochastic process.
As noted above, η 2 is a frozen copy across trials of the stochastic part of the extrinsic input, while the intrinsic noise η 1 varies from trial to trial.
In the latter case the extrinsic input has been modelled as a deterministic periodic function (see also [25]) and with this type of input, the solution of the System (1) (or (2) or (3)) remains a deterministic function and the mathematical background to treat it is deterministic analysis.
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Our key conclusions were; (i) when forward connections, mediating bottom-up or extrinsic inputs, are sufficiently strong, nonlinear mechanisms cause a saturation of excitatory interneuron responses.
These comprise (1) parameters that mediate the influence of extrinsic inputs on the states, (2) parameters that mediate intrinsic coupling among the states, and (3) [bilinear] parameters that allow the inputs to modulate that coupling.
Experiments also explore in vitro the roles of extrinsic inputs to the superior colliculus, including cholinergic inputs from the parabigeminal and parabrachial nuclei and GABAergic inputs from the substantia nigra pars reticulata, in modulating the activity of the collicular circuitry.
Finally, once the methods to estimate state variables and unknown parameters were consolidated, we proceeded to test the methods to our ultimate goal: estimating jointly the intrinsic states of the neuron and the extrinsic inputs (i.e., the synaptic conductances).
Shifting the dampening onset to lower firing rates can result into a regime where bursting is no longer possible (even though the extrinsic inputs that originally produced this bursting may still be present).
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