Admissible semi-linear representations

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described

Are 21st-century citizens grieving for their loss of privacy?

Although much research exists that examines cognitive events leading up to information disclosure, such as risk-benefit analysis and state-based and trait-based attributes, minimal research exists that examines user responses after a direct or indirect breach of privacy. The present study examines 1,004 consumer responses to two different high-profile privacy breaches using sentiment analysis. Our findings indicate that individuals who experience an actual or surrogate privacy breach exhibit similar emotional responses, and that the pattern of responses resembles well-known reactions to other losses. Specifically, we present evidence that users contemplating evidence of a privacy invasion experience and communicate very similar responses as individuals who have lost loved ones, gone through a divorce or who face impending death because of a terminal illness. These responses parallel behavior associated with the Kübler-Ross’s five stages of grief

Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo

Exact results for strongly-correlated fermions in 2+1 dimensions

We derive exact results for a model of strongly-interacting spinless fermions hopping on a two-dimensional lattice. By exploiting supersymmetry, we find the number and type of ground states exactly. Exploring various lattices and limits, we show how the ground states can be frustrated, quantum critical, or combine frustration with a Wigner crystal. We show that on generic lattices, the model is in an exotic ``super-frustrated'' state characterized by an extensive ground-state entropy.Comment: 4 pages, 2 figures. v2: added discussion of "super-frustrated" state; to appear in PR

The effect of negative polarity items on inference verification

The scalar approach to negative polarity item (NPI) licensing assumes that NPIs are allowable in contexts in which the introduction of the NPI leads to proposition strengthening (e.g., Kadmon & Landman 1993, Krifka 1995, Lahiri 1997, Chierchia 2006). A straightforward processing prediction from such a theory is that NPI’s facilitate inference verification from sets to subsets. Three experiments are reported that test this proposal. In each experiment, participants evaluated whether inferences from sets to subsets were valid. Crucially, we manipulated whether the premises contained an NPI. In Experiment 1, participants completed a metalinguistic reasoning task, and Experiments 2 and 3 tested reading times using a self-paced reading task. Contrary to expectations, no facilitation was observed when the NPI was present in the premise compared to when it was absent. In fact, the NPI significantly slowed down reading times in the inference region. Our results therefore favor those scalar theories that predict that the NPI is costly to process (Chierchia 2006), or other, nonscalar theories (Giannakidou 1998, Ladusaw 1992, Postal 2005, Szabolcsi 2004) that likewise predict NPI processing cost but, unlike Chierchia (2006), expect the magnitude of the processing cost to vary with the actual pragmatics of the NPI

Non-Abelian Gravity and Antisymmetric Tensor Gauge Theory

A non-abelian generalisation of a theory of gravity coupled to a 2-form gauge field and a dilaton is found, in which the metric and 3-form field strength are Lie algebra-valued. In the abelian limit, the curvature with torsion is self-dual in four dimensions, or has SU(n) holonomy in $2n$ dimensions. The coupling to self-dual Yang-Mills fields in 4 dimensions, or their higher dimensional generalisation, is discussed. The abelian theory is the effective action for (2,1) strings, and the non-abelian generalisation is relevant to the study of coincident branes in the (2,1) string approach to M-theory. The theory is local when expressed in terms of a vector pre-potential.Comment: 14 pages, phyzzx macro. Minor correction

Wilson surfaces and higher dimensional knot invariants

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.Comment: 31 pages, 9 figure