I want to use the assert and paralleljs modules in mobile apps developed with Titanium Appcelerator. If anyone has used these modules or similar to this, please help me to use these too. Thanks in advance.
That would be great! The problem I think is that javascript (at least at it's current version) isn't multi-threaded. it's built to be event driven - and if you use event driven well, you can get pretty good performance. What paralleljs does is using web-workers which are not available in Titanium.
What you might be able to to is write some kind of webview that will run the work inside it and report back to Titanium.
Take a look at the following:
How to create multithreading in mobile sdk
You'll have to test it and see if it's memory/performance efficient.