Interesting identities involving weighted representations of integers as sums of arbitrarily many squares.

We consider the number of ways to write an integer as a sum of squares, a problem with a long history going back at least to Fermat. The previous studies in this area generally fix the number of squares which may occur and then either use algebraic techniques or connect these to coefficients of certain complex analytic functions with many symmetries known as modular forms, from which one may use techniques in complex and real analysis to study these numbers. In this paper, we consider sums with arbitrarily many squares, but give a certain natural weighting to each representation.

Effect of Aging on Taurine Transporter (TauT) Expression in the Mouse Brain Cortex.

Taurine content in an older brain is decreased compared to a younger brain and is associated with cognitive deficits. It is not yet known whether the decrease in taurine content is associated with decreased expression of taurine inflow mediating transporters during the aging process. In this study, we investigated whether aging affects taurine transporter and glycine transporter 1 expression in the brain cortex of the mouse.