String bit models of two-dimensional quantum gravity coupled with matter

We extend the formalism of Hamiltonian string bit models of quantum gravity type in two spacetime dimensions to include couplings to particles. We find that the single-particle closed and open universe models respectively behave like empty open and closed universes, and that a system of two distinguishable particles in a closed universe behaves like an empty closed universe. We then construct a metamodel that contains all such models, and find that its transition amplitude is exactly the same as the sl(2) gravity model.Comment: 24 pages, LaTeX2e; typos corrected, references adde

Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables

We prove a conjecture of Kontsevich, which asserts that the iterations of the noncommutative rational map $F_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1})$ are given by noncommutative Laurent polynomials with nonnegative integer coefficients.Comment: 13 pages; This paper supersedes the first author's preprint "A step towards the cluster positivity conjecture" (arXiv:1103.2726). The main improvement is that we give expressions in terms of subpaths of certain lattice path

A String Bit Hamiltonian Approach to Two-Dimensional Quantum Gravity

Motivated by the formalism of string bit models, or quantum matrix models, we study a class of simple Hamiltonian models of quantum gravity type in two space-time dimensions. These string bit models are special cases of a more abstract class of models defined in terms of the sl(2) subalgebra of the Virasoro algebra. They turn out to be solvable and their scaling limit coincides in special cases with known transfer matrix models of two-dimensional quantum gravity.Comment: 24 pages, no figure; LaTeX2

On Inhomogeneity of a String Bit Model for Quantum Gravity

We study quantum gravitational effect on a two-dimensional open universe with one particle by means of a string bit model. We find that matter is necessarily homogeneously distributed if the influence of the particle on the size of the universe is optimized.Comment: 16 pages, LaTeX2

Attachment styles as predictors of Facebook-related jealousy and surveillance in romantic relationships

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsFacebook has become ubiquitous over the past five years, yet few studies have examined its role within romantic relationships. In two studies, we tested attachment anxiety and avoidance as predictors of Facebook-related jealousy and surveillance (i.e., checking a romantic partner’s Facebook page). Study 1 found that anxiety was positively associated, and avoidance negatively associated, with Facebook jealousy and surveillance. The association of anxiety with Facebook jealousy was mediated in part by lower trust. Study 2 replicated this finding, and daily diary results further showed that over a one-week period, anxiety was positively associated, and avoidance negatively associated, with Facebook surveillance. The association of anxiety with greater surveillance was mediated in part by daily experiences of jealousy

Neutrino oscillations and Big Bang Nucleosynthesis

We outline how relic neutrino asymmetries may be generated in the early universe via active-sterile neutrino oscillations. We discuss possible consequences for big bang nucleosynthesis, within the context of a particular 4-neutrino model.Comment: 6 pages. Talk given at NuFACT'01 workshop, Tsukuba, Japan (May 2001

The abelian projection revisited

Abelian projection is reanalysed in the frame of the SU(N) Higgs model. The extension to QCD is discussed. It is shown that dual superconductivity of the vacuum is an intrinsic property independent of the choice of the abelian projection.Comment: 3 pages, 1 figure, Lattice2003(topology

Short-duration lensing events: I. wide-orbit planets? free-floating low-mass objects? or high-velocity stars?

Short duration lensing events tend to be generated by low-mass lenses or by lenses with high transverse velocities. Furthermore, for any given lens mass and speed, events of short duration are preferentially caused by nearby lenses (mesolenses) that can be studied in detail, or else by lenses so close to the source star that finite-source-size effects may be detected, yielding information about both the Einstein ring radius and the surface of the lensed star. Planets causing short-duration events may be in orbits with any orientation, and may have semimajor axes smaller than an AU, or they may reach the outer limits of their planetary systems, in the region corresponding to the Solar System's Oort Cloud. They can have masses larger than Jupiter's or smaller than Pluto's. Lensing therefore has a unique potential to expand our understanding of planetary systems. A particular advantage of lensing is that it can provide precision measurements of system parameters, including the masses of and projected separation between star and planet. We demonstrate how the parameters can be extracted and show that a great deal can be learned. For example, it is remarkable that the gravitational mass of nearby free-floating planet-mass lenses can be measured by complementing observations of a photometric event with deep images that detect the planet itself. A fraction of short events may be caused by high-velocity stars located within a kpc. Many high-velocity lenses are likely to be neutron stars that received large natal kicks. Other high-speed stars may be members of the halo population. Still others may be hypervelocity stars that have been ejected from the Galactic Center, or runaway stars escaped from close binaries, possibly including the progenitor binaries of Type Ia supernovae.Comment: 17 pages; 2 figures; submitted to ApJ 3 July 200