A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation desc...

Oppression operates at various levels, with varying degrees of negativity, and groups respond in markedly different ways. In this paper, the in-between status of the colored South African group is used to illustrate issues of identity and oppression under the Apartheid system-and differing ways in which oppression was experienced and used. The colored group had many social advantages over Black...

We determine the generic degrees of cyclotomic Hecke algebras attached to exceptional finite complex reflection groups. The results are used to introduce the notion of spetsial reflection group, which in a certain sense is a generalization of the finite Weyl group. In particular, to spetsial W there is attached a set of unipotent degrees which in the case of a Weyl group is just the set of degr...

The threat sensitivity hypothesis predicts that organisms will evaluate the relative danger of and respond differentially to varying degrees of predation threat. Doing so allows potential prey to balance the costs and benefits of anti-predator behaviors. Threat sensitivity has undergone limited testing in the auditory modality, and the relative threat level of auditory cues from different sourc...

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Sch...

(Current Biology 21, R493–R494; July 12, 2011) In this Correspondence, we reported a training efficacy advantage for attempts to grasp subjectively ‘‘invisible’’ stimuli, relative to verbal descriptions. The reported statistical analyses for Experiments 1–3 used inappropriate degrees of freedom. We thank Ludwig and colleagues for bringing this to our attention (see http://www.cell.com/current-b...

A generalized transformation theory which leads to a non-Hamiltonian description of dynamics is introduced. The transformation is such that all averages of observables remain invariant. However, the time evolution of the density matrix can no longer be expressed in terms of a commutator with the Hamiltonian. Therefore such transformations are not canonical in the usual sense. An explicit "two c...

In this note we prove that every closed orientable 3-manifold has a triangulation in which each edge has degree 4, 5 or 6.

This article explores how health inequalities are constructed as an object for policy intervention by considering four framings: politics, audit, evidence and treatment. A thematic analysis of 197 interviews conducted with local managers in England, Scotland and Wales is used to explore how these framings emerge from local narratives. The three different national policy regimes create contrasti...

This paper uses the distribution and interpretation of antonymous adjectives in comparative constructions as an empirical basis to argue that abstract representations of measurement, or ‘degrees’, must be modeled as intervals on a scale, rather than as points, as commonly assumed. I begin by demonstrating that the facts in this domain must be accounted for in terms of the interaction of the sem...