$3\mathrm{.}2$ How would a Self$-$Organizing Map behave if the Gaussian or the Mexican Hat neighbourhood influence function $.)$ were to be replaced by a Dirac Delta function?

a$)$ then the influence function would be purely flat, i$.$e$.$ be constant over all output nodes

b$)$ the influence would become similar as for a Gaussian function in the limit as the learning rate parameter gradually reduces to zero over iterations

c$)$ influence of the Best Matching Unit would be $\text{'}1\text{'}$ for itself and $\text{'}0\text{'}$ on all other output nodes

d$)$ the influence of the BMU will be $\text{'}0\text{'}$ for itself and gradually increase towards $\text{'}1\text{'}$ for nodes that are farther away.