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1)PsiBlast is used to derive sequence profile for the query. The whole query sequence is involved in PsiBlast search. The query profile is prepared in the same manner as a sequence profile for each sequence in the database (the source of fragments) had been made.
When it comes to rank fragments, each residue position is treated separately, i.e. a fragment score is a sum of per-position components. E.g. for nine-mers it is a sum of 9 values describing the fit between a profile column (20 probabilities) from the query and a column from a database entry. The positions within a fragment are treated independently.
2) If there are no homologous sequences, then the sequence profile is just the query sequence. Performance of PsiPred is obviously worse. Fragment picker uses three independent secondary structure predictions, which may help getting the right secondary structure prediction
3) I am not sure, but as far as I remember Rosetta uses all 9-mers in stage 1, then only top 25 ninemers. Always ALL 3-mers are used.