VIRTUAL SHADOW MODULES AND THEIR LINK INVARIANTS

We introduce an algebra ℤ[X, S] associated to a pair X, S of a virtual birack X and X-shadow S. We use modules over ℤ[X, S] to define enhancements of the virtual birack shadow counting invariant, extending the birack shadow module invariants to virtual case. We repeat this construction for the twisted virtual case. As applications, we show that the new invariants can detect orientation reversal and are not determined by the knot group, the Arrow polynomial and the Miyazawa polynomial, and that the twisted version is not determined by the twisted Jones polynomial.

CORRELATES OF PERCEPTIVE INSTABILITIES IN EVENT-RELATED POTENTIALS

The study of instabilities in perception has attracted much interest in recent decades. The investigations presented here focus on electrophysiological correlates of orientation reversals of both ambiguous visual stimuli and alternating nonambiguous stimuli, representing the two options of the ambiguous version. Based on a refined experimental setup, significant features in the event-related potentials associated with the perception of orientation reversal were found in both cases. Their occipital location, their early occurrence (200–250 ms), and their latency difference (50 ms) offer interesting perspectives for an understanding of unstable brain states in terms of basic concepts of dynamical systems.

Integral modular categories and integrality of quantum invariants at roots of unity of prime order

It is shown how to deduce integrality properties of quantum 3-manifold invariants from the existence of integral subcategories of modular categories. The method is illustrated in the case of the invariants associated to classical Lie algebras constructed in [42], showing that the invariants are algebraic integers provided the root of unity has prime order. This generalizes a result of [31], [32] and [29] in the sl2-case. We also discuss some details in the construction of invariants of 3-manifolds, such as the S-matrix in the PSUk case, and a local orientation reversal principle for the colored Homfly polynomial.