This kind of debugging should only be attempted if you are comfortable modifying the PHP code, and preferably done within a dedicated development copy of the system. I won’t be able to walk you through the specifics of editing the PHP files in the forum.
We can check if there are authors where there is a publication, but there isn’t a submission. This would be quite odd, but the query would be:
SELECT *
FROM authors JOIN publications ON (authors.publication_id = publications.publication_id)
LEFT JOIN submissions ON (publications.submission_id = submissions.submission_id)
WHERE submissions.submission_id IS NULL;