About Ax 7 and Cloud I found very nice paper at Inside Microsoft Dyanmics Ax Blog. They wrote about the paper
In the paper, Mr. Greenbaum explains how the next release of Microsoft Dynamics AX, running on the Microsoft Azure, positions cloud computing for a dramatic and meaningful shift. With a starting discussion of the long-standing customer promises and pain points with regard to ERP, Greenbaum explains the basics of our cloud offering and then describes the benefits to both partners and customers.
Paper link is as follow http://blogs.msdn.com/cfs-file.ashx/__key/communityserver-components-postattachments/00-10-62-70-38/Redefing-the-potential-of-enterprise-cloud-computing-WP-final.pdf
and original post is as follow
Picture above taking from paper mentioned above link.