Should I send another update letter?

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I’m currently waitlisted at 2 schools that have unranked waitlists to my understanding. I already sent a publication update/LOCI to both schools last month but just received notice of another new publication (albeit this one is minor as it is a case report). Should I send another update letter to schools? Just worried that I might come off as desperate but a publication seems like something I should let them know about…

Also, both schools are highly regarded in research if that makes a difference
 
I’m currently waitlisted at 2 schools that have unranked waitlists to my understanding. I already sent a publication update/LOCI to both schools last month but just received notice of another new publication (albeit this one is minor as it is a case report). Should I send another update letter to schools? Just worried that I might come off as desperate but a publication seems like something I should let them know about…

Also, both schools are highly regarded in research if that makes a difference
This is worthy of an update.