@user_name... It only seems like everyone has analysis if you read the boards here. When you get into a program, you'll be surprised that several people have never taken analysis. It's definitely true in my program, and I think Antichron said it's true of at least one or two in his class. Not a great dataset, but it's something.
@wendyecon
I think your chances largely depend on your
LORs and whether your school has sent prior applicants to the US (which I would assume it has if it's a top university). If you've published in two journals and done some RA work, you should have better than "moderate"
LORs.
The simple answer is that strong
LORs from a well-known university means I think you have a good list and will likely end up in a top 30 (though an extra safety or two never hurt anyone). Depending on the quality of the publications and the
LORs, you could possibly do very well.