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Is theta_j just the jth element of theta_head_k in 3.23?

the shooting alg. from the paper

after the kth iteration of the whole algorithm (algorithm 5) i get the new kth estimate of my parameter vector theta. All other things that are dependent on this estimate are depicted as ...(theta_head_k) but in the shooting algorithm (3.23) there is x(theta_head_k) and theta_j. Is theta_j just the jth element of theta_head_k? But that would be kind of inconsistent with the notation in the rest of the paper. Or do I miss anything here? The whole algorithm is and it starts with defining theta_head_k

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