On the Spectrum of the Derangement Graph

We derive several interesting formulae for the eigenvalues of the derangement graph and use them to settle affirmatively a conjecture of Ku regarding the least eigenvalue

On the diffeomorphism commutators of lattice quantum gravity

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a variety of different discretizations of the continuum constraints, and thus generalizes an earlier calculation by Renteln.Comment: 16 pages, Te

NON-PERTURBATIVE SOLUTIONS FOR LATTICE QUANTUM GRAVITY

We propose a new, discretized model for the study of 3+1-dimensional canonical quantum gravity, based on the classical SL(2,\C)-connection formulation. The discretization takes place on a topological $N^3$- lattice with periodic boundary conditions. All operators and wave functions are constructed from one-dimensional link variables, which are regarded as the fundamental building blocks of the theory. The kinematical Hilbert space is spanned by polynomials of certain Wilson loops on the lattice and is manifestly gauge- and diffeomorphism- invariant. The discretized quantum Hamiltonian $\hat H$ maps this space into itself. We find a large sector of solutions to the discretized Wheeler-DeWitt equation $\hat H\psi=0$, which are labelled by single and multiple Polyakov loops. These states have a finite norm with respect to a natural scalar product on the space of holomorphic SL(2,\C)-Wilson loops. We also investigate the existence of further solutions for the case of the $1^3$-lattice. - Our results provide for the first time a rigorous, regularized framework for studying non-perturbative quantum gravity.Comment: 26 pages, 2 figures (postscript, compressed and uuencoded), TeX, Jan 9

On diffeomorphism invariance for lattice theories

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider $2+1$ gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known --for both the continuum and the lattice-- and can be compared.Comment: 11 Pages, Revtex, 3 figure

Simplifying the spectral analysis of the volume operator

The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis, for quantum states that can be realized on a cubic three-dimensional lattice. This involves a decomposition of Hilbert space into sectors transforming according to the irreducible representations of a subgroup of the cubic group. As an application, we determine the complete spectrum for a class of states with six-valent intersections.Comment: 19 pages, TeX, to be published in Nucl. Phys.

Polyp Resection - Controversial Practices and Unanswered Questions

Detection and complete removal of precancerous neoplastic polyps are central to effective colorectal cancer screening. The prevalence of neoplastic polyps in the screening population in the United States is likely 450%. However, most persons with neoplastic polyps are never destined to develop cancer, and do not benefit for finding and removing polyps, and may only be harmed by the procedure. Further 70–80% of polyps are diminutive (≤5 mm) and such polyps almost never contain cancer. Given the questionable benefit, the high-cost and the potential risk changing our approach to the management of diminutive polyps is currently debated. Deemphasizing diminutive polyps and shifting our efforts to detection and complete removal of larger and higher-risk polyps deserves discussion and study. This article explores three controversies, and emerging concepts related to endoscopic polyp resection. First, we discuss challenges of optical resect-and-discard strategy and possible alternatives. Second, we review recent studies that support the use of cold snare resection for ≥ 5 mm polyps. Thirdly, we examine current evidence for prophylactic clipping after resection of large polyps

Criminal law as a security project

This paper asks how criminal might be understood as a security project. Following Valverde’s lead, it does this not by trying to define the concept of security, but by looking at the operation of the temporal and spatial logics of the criminal law. It looks first at the basic logics of time and space in conceptions of criminal liability and jurisdiction, before reviewing some recent developments which challenge these practices and what these might mean for criminal law as a security project