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Hi Jessica Hutchinson,

I do not know of any parallel corpus for different notations.

There is a wealth of data available for SignWriting.

You may be interested in the ASL Gospel site 
(http://www.aslgospel.org/).  It has ASL translations for all 4 Gospels 
of the Bible (Matthew, Mark, Luke, and John).  You can find the data 
behind this text in the ASL Bible in SignPuddle: 
http://www.signbank.org/signpuddle2.0/index.php?ui=1&sgn=28

Go to the export page and click the download link.  You will get a XML 
file that contains all of the data that you need. 
http://www.signbank.org/signpuddle2.0/export.php?ui=1&sgn=28

The sign data will be in the format called Formal SignWriting (FSW).  
This format is documented in the Modern SignWriting specification, 
section 9.  You can download the document or view it online.

Download: https://github.com/Slevinski/msw/raw/master/MSW.pdf
View online: http://signpuddle.com

SignWriting is different than HamNoSys and Stokoe because SignWriting is 
2-dimensional.  The character encoding model for SignWriting is based on 
mathematics.  The 2-dimensional nature of SignWriting has unique 
challenges, such as the built-in variability of the script: 
http://signpuddle.com/wiki/index.php/MSW:Mathematical_Model#4.D._Variability 


The variability of SignWriting necessitates a searching scheme that is 
not based on exact string matches, but on approximate matching with 
regular expressions.

The open source project (the SignWriting Image Server) can be found on 
Github.  It is an implementation of the Modern SignWriting 
specification. https://github.com/Slevinski/swis

Regards,
-Steve