Neuronal Parameter Sensitivity

Definition

Sensitivity of a quantity to a parameter at a fixed point of the parameter space measures the relative change of the quantity in relation to a relative change of the parameter. There are two interrelated formal definitions of sensitivity.

Consider a real-valued function C = C(p) of a real variable p. Let C(p) be defined for the two values of p, p = p ₀ and p = p ₀ + Δp, where Δp is some number. Then sensitivity S of C = C(p) to the change of p from p ₀ to p ₀ + Δp is defined as

$$ S=\frac{C\left({p}_0+\Delta p\right)-C\left({p}_0\right)}{C\left({p}_0\right)}\div \frac{\Delta p}{p_0}. $$

(1)

For example, S = 2 means that the relative increase of C(p) from C(p ₀) to C(p ₀ + Δp) is two times the relative increase of p from p ₀ to p ₀ + Δp. Notice that in Eq. 1, the value of S depends on p ₀ and Δp and there are no other requirements to C(p) except for it being defined for p = p ₀ and p = p ₀ + Δp.

If the function C = C(p) is differentiable at p ₀, then S is defined as

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