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I just discovered some mistake after the online publication? There are two mistakes- instead of figure S4A (supplementary figure), it says Figure S3A at two places. It's very embarrassing, should I write to the editor about this?

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This sort of typographical error should be handled with a "Correction". You'd say something like "In the article such-and-such (citation) the text on line x, page y should read "Figure 4A" instead of "Figure 3A". The online text has been corrected."

The details of how that's done depends on the journal, so you should discuss with the editor.

It's quite common to have to issue corrections, it's not a big deal, and aside from being a minor embarrassment an occasional Correction doesn't reflect on you in any way. I suppose if it were a regular thing it might get noticed, but this should not be a big deal.

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    This might be field dependent. In my field, errors of this magnitude abound in every paper and are rarely formally corrected. Occasionally someone puts a list on their webpage. If a reader (who will necessarily be an expert in order even just make heads or tails of the paper) would not be able to figure out the appropriate correction after a bit of effort, then perhaps a correction is issued. – Alexander Woo Aug 20 '16 at 1:32
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    Sure, I think that's probably true in my fields as well, the author would be fine in letting it go, but since they seemed upset about it a correction is fine too – iayork Aug 20 '16 at 1:40
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You should inform your coauthors, use this opportunity to search for other misprints and finally write to the editor.

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