The name is absent

30

where hb = tb∣^tb ɪs the step size on branch b. This term arises as 1∕∕⅛ when the delta
function is discretized. Gathering the branch and soma equations together we define

/Qι

Q =

^Bi

B =

∖

Now coupling the branch conditions via the Hines matrix by A = Q + H, we arrive
at the compartmental model

z'(i) = Az(f) + Bu(t).

We view u as the input to the neuron. The neuron’s output, y, is the voltage at the
site of initiation of action potentials, which is expressed as

y(i) = Cz(i).

We suppose that the output is the soma potential, formally written as y(t) = Zjv-_m(f).
This implies C ∈ R^lx'^v where C = O except for the entry Cijv__m = 1. Together
(2.33) and (2.34) give the standard form for linear dynamical systems, where z is
called the state vector, u is the input vector, and y is the observable vector. Our

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