Dyad is the centre of the DNA that is wrapped around the nucleosome core (It basically is the centre of symmetry of the nucleosome). It is a common practice to set it at 0 thereby making incoming DNA half, negative and outgoing DNA half, positive.
By oscillations the authors mean that there is a periodic repeat of A/T dinucleotide. IMO it is actually not correct to call it oscillation which is mostly used in a time course dynamical sense.
I guess this is what is meant by the **3-nt moving average** :
You have conditional dinucleotide probabilities for each position (As shown in the figure). Now you calculate the A/T dinucleotide probability which is:
P[A/T] = PAA + PAT + PTT + PTA
Now you find the moving average for 3 steps:
MA(n) = (1/3)×(PA/T + PA/T + PA/T)
_where **n** is the nth position of the DNA_