On the first page of The Problem of Consciousness (1991), Colin McGinn asks "How is it possible for conscious states to depend on brain states? How can technicolour phenomenology arise from soggy grey matter?" Many philosophers feel that questions like these pose an unanswerable challenge to physicalism. They argue that there is no way of bridging the "explanatory gap" between the material brai...

We present a new identity involving compositions (i.e. ordered partitions of natural numbers). The formula has its origin in complex dynamical systems and appears when counting, in the polynomial family {fc : z 7→ z d + c}, periodic critical orbits with equivalent itineraries. We present two proofs of the identity; one following the original approach in dynamics and another coming from the clas...

In the first half of this paper, a Fubini type identity in law which was previously developed by two of the authors between quadratic functionals of Brownian motion is extended in two directions: an analogue of this identity in law holds when Brownian motion is replaced by a symmetric stable process of any order a E (0,2), provided the function: x -* x2 is replaced by: x -> I x la; such Fubini ...

Smith, J. Allegra (B. A., M. A., Psychology) The Tug-of-War Within: Oppositional Affirmation, Parent Versus Professional Identification, and Gender Thesis directed by Professor Bernadette Park The self-affirmation literature suggests focusing on other important identities after a failure can repair self-integrity and maintain motivation. In the current research, however, I introduce Oppositiona...

A Rogers-Ramanujan (R-R) type identity is a q-hypergeometric identity in the form of an infinite (possibly multiple) series equals an infinite product. The series is the generating function of partitions whose parts satisfy certain difference conditions, whereas the product is the generating function of partitions whose parts usually satisfy certain congruence conditions. For a discussion of a ...