- ... AMPA-receptors
^{2.1} - AMPA is short for
-amino-3-hydroxy-5-methyl-4-isoxalone propionic acid.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
obtain
^{2.2} - We want outward currents to be positive, hence the
change in the sign of
*i*_{ext}and*i*_{syn}.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... normally
^{3.1} - Exceptions
are the rare cases where the function
*F*or*G*is degenerate; e.g.,*F*(*u*,*w*) =*w*^{2}.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... potential
^{4.1} - Note that in Eq. (4.20) we consider the synaptic current as
an
*external*current whereas in Chapter 2 we have considered it as a membrane current and therefore used a different sign convention. In both cases, an excitatory input increases the membrane potential.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... currents
^{5.1} - We
neglect here intrinsically bursting and chaotic neurons.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... independent
^{6.1} - In a simulation, spike arrival
could for example be simulated by independent Poisson processes
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... past
^{6.2} - Neurons which have never fired before
are assigned a formal firing time
= - .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... noise
^{7.1} - It is called white noise
because the power spectrum
(i.e. the Fourier transform of the autocorrelation)
is flat. A Poisson process is an example of
a statistical process with autocorrelation (7.73);
cf. Chapter 5.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
out
^{9.1} - The decay of the activity is exponential in
*n*if < 1; for = 1 the decay is polynomial in*n*.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
parameters
^{9.2} - We use a tilde in order to identify parameters
that describe the time course of the membrane potential. Parameters
without a tilde refer to the firing-time distribution.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
analogously
^{10.1} - Note that
*w*_{ij}is a step function of time with discontinuities whenever a presynaptic spike arrives or a postsynaptic action potential is triggered. In order to obtain a well-defined differential equation we specify that the amplitude of the step depends on the value of*w*_{ij}immediately*before*the spike. In mathematical terms, we impose the condition that*w*_{ij}(*t*) is continuous from left, i.e., that*w*_{ij}(*t*^{(f)}-*s*) =*w*_{ij}(*t*^{(f)}).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... Aristoteles
^{10.2} - Aristoteles, "De memoria et reminiscentia": There is no need to
consider how we remember what is distant, but only what is neighboring, for
clearly the method is the same. For the changes follow each other by habit,
one after another. And thus, whenever someone wishes to recollect he will do
the following: He will seek to get a starting point for a change after which
will be the change in question.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .