Groups of order p^3 are mixed Tate

A natural place to study the Chow ring of the classifying space BG, for G a linear algebraic group, is Voevodsky's triangulated category of motives, inside which Morel and Voevodsky, and Totaro have defined motives M(BG) and M^c(BG), respectively. We show that, for any group G of order p^3 over a field of characteristic not p which contains a primitive p^2-th root of unity, the motive M(BG) is a mixed Tate motive. We also show that, for a finite group G over a field of characteristic zero, M(BG) is a mixed Tate motive if and only M^c(BG) is a mixed Tate motive.Comment: 17 page

MongoDB Performance In The Cloud

Web applications are growing at a staggering rate every day. As web applications keep getting more complex, their data storage requirements tend to grow exponentially. Databases play an important role in the way web applications store their information. Mongodb is a document store database that does not have strict schemas that RDBMs require and can grow horizontally without performance degradation. MongoDB brings possibilities for different storage scenarios and allow the programmers to use the database as a storage that fits their needs, not the other way around. Scaling MongoDB horizontally requires tens to hundreds of servers, making it very difficult to afford this kind of setup on dedicated hardware. By moving the database into the cloud, this opens up a possibility for low cost virtual machine instances at reasonable prices. There are many cloud services to choose from and without testing performance on each one, there is very little information out there. This paper provides benchmarks on the performance of MongoDB in the cloud

Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-It\^o integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.Comment: To appear in "Electronic Communications in Probability