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1. Given Figure 1, what is the smallest common subtree that includes both t1 (Troops) and t2 (near)?
2. Section 5: “Therefore, d(a)=l(a).” When is this true and why? (Assume this holds for the following questions.)
3. Let \phi_m = {general-pos-tag, entity-type, relation-arguments} (in accordance with the paper).
Let \phi_s = \phi_m (unlike in the paper). Based on Figure 2 and Section 5, compute the following matching functions and similarity functions: m(t0,u0)=? m(t1,u1)=? m(t2,u2)=? s(t0,u0)=? s(t1,u1)=? s(t2,u2)=?
4. Let \lambda=0.5. Compute (derive and explain) the contiguous kernel for the two trees in Figure 2:
K_1(T,U)=? Provide the final "number" and some counts along the way, so its clear how you got the number. Optionally, compute also the sparse kernel K_0(T,U).
5. Let DT be a function that assigns the correct augmented dependency tree to a sentence.
Compute (estimate) contiguous kernel and bag-of-words kernel for the following sentences:
K_1(DT("Peter sleeps"), DT("Bob runs"))=?
K_2(DT("Peter sleeps"), DT("Bob runs"))=?
6. Lets have a pair of sentences:
"Bob saw US troops that moved towards Baghdad" "US troops that moved towards Baghdad were seen by Bob" You want to check the relation between entities "US" and "Baghdad". Compute (estimate) K_1 and K_2.