On the codimension growth of G-graded algebras

Let W be an associative PI-affine algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W_e) denote the codimension growth of W and of the identity component W_e, respectively. We prove: exp(W) \leq |G|^2 exp(W_e). This inequality had been conjectured by Bahturin and Zaicev.Comment: 9 page

Hamiltonian Gravity and Noncommutative Geometry

A version of foliated spacetime is constructed in which the spatial geometry is described as a time dependent noncommutative geometry. The ADM version of the gravitational action is expressed in terms of these variables. It is shown that the vector constraint is obtained without the need for an extraneous shift vector in the action.Comment: 22 pages, AMS-LaTeX. Some improvements - mainly to sections 8 and 9. Typographical errors to equations in appendix correcte

Perceiving deviance

I defend the claim that we have the capacity to perceptually represent objects and events in experience as deviating from an expectation, or, for short, as deviant. The rival hypothesis is that we may ascribe the property of deviance to a stimulus at a cognitive level, but that property is not a representational content of perceptual experience. I provide empirical reasons to think that, contrary to the rival hypothesis, we do perceptually represent deviance