Dynamics for a 2-vertex Quantum Gravity Model

We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N) invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.Comment: 28 pages, v2: typos correcte

Loop quantum gravity and Planck-size black hole entropy

The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.Comment: 21 pages, 5 figures. Contribution to the Proceedings of the NEB XII International Conferenc

Classical Setting and Effective Dynamics for Spinfoam Cosmology

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasize

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. This way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.Comment: 6 page

One vertex spin-foams with the Dipole Cosmology boundary

We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework.Comment: 23 pages, 30 figure

Effective Hamiltonian Constraint from Group Field Theory

Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition amplitudes over all possible (discretized) geometries and topologies. The issue remains, however, of explicitly relating the specific form of the group field theory action and the canonical Hamiltonian constraint. Here, we suggest an avenue for addressing this issue. Our strategy is to expand group field theories around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin network wave functions. We apply our procedure to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss the relevance of understanding the spectrum of this Hamiltonian operator for the renormalization of group field theories.Comment: 14 page

Geno-and cytotoxicity induced on Cyprinus carpio by aluminum, iron, mercury and mixture thereof.

Metals such as Al, Fe and Hg are used in diverse anthropogenic activities. Their presence in water bodies is due mainly to domestic, agricultural and industrial wastewater discharges and constitutes a hazard for the organisms inhabiting these environments. The present study aimed to evaluate geno- and cyto- toxicity induced by Al, Fe, Hg and the mixture of these metals on blood of the common carp Cyprinus carpio. Specimens were exposed to the permissible limits in water for human use and consumption according to the pertinent official Mexican norm [official Mexican norm NOM-127-SSA1-1994] Al (0.2 mg L 1), Fe (0.3 mg L 1), Hg (0.001 mg L 1) and their mixture for 12, 24, 48, 72 and 96 h. Bio- markers of genotoxicity (comet assay and micronucleus test) and cytotoxicity (caspase-3 activity and TUNEL assay) were evaluated. Significant increases relative to the control group (po0.05) were observed in all biomarkers at all exposure times in all test systems; however, damage was greater when the metals were present as a mixture. Furthermore, correlations between metal concentrations and biomarkers of geno- and cytotoxicity were found only at certain exposure times. In conclusion, Al, Fe, Hg and the mixture of these metals induce geno- and cytotoxicity on blood of C. carpio.CONACyT-Mexico, Project 18154

From the discrete to the continuous - towards a cylindrically consistent dynamics

Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum gravity we propose a coarse graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme towards this end. A crucial role in this coarse graining scheme is played by embedding maps that allow the interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as a choice of embedding maps will determine a truncation of the renormalization flow.Comment: 22 page

Vascular Inflammation in Subclinical Atherosclerosis Detected by Hybrid PET/MRI

BACKGROUND: Atherosclerosis is a chronic inflammatory disease, but data on arterial inflammation at early stages is limited. OBJECTIVES: The purpose of this study was to characterize vascular inflammation by hybrid 18F-fluorodeoxyglucose (18F-FDG) positron emission tomography/magnetic resonance imaging (PET/MRI). METHODS: Carotid, aortic, and ilio-femoral 18F-FDG PET/MRI was performed in 755 individuals (age 40 to 54 years; 83.7% men) with known plaques detected by 2-/3-dimensional vascular ultrasound and/or coronary calcification in the PESA (Progression of Early Subclinical Atherosclerosis) study. The authors evaluated the presence, distribution, and number of arterial inflammatory foci (increased 18F-FDG uptake) and plaques with or without inflammation (coincident 18F-FDG uptake). RESULTS: Arterial inflammation was present in 48.2% of individuals (24.4% femorals, 19.3% aorta, 15.8% carotids, and 9.3% iliacs) and plaques in 90.1% (73.9% femorals, 55.8% iliacs, and 53.1% carotids). 18F-FDG arterial uptakes and plaques significantly increased with cardiovascular risk factors (p < 0.01). Coincident 18F-FDG uptakes were present in 287 of 2,605 (11%) plaques, and most uptakes were detected in plaque-free arterial segments (459 of 746; 61.5%). Plaque burden, defined by plaque presence, number, and volume, was significantly higher in individuals with arterial inflammation than in those without (p < 0.01). The number of plaques and 18F-FDG uptakes showed a positive albeit weak correlation (r = 0.25; p < 0.001). CONCLUSIONS: Arterial inflammation is highly prevalent in middle-aged individuals with known subclinical atherosclerosis. Large-scale multiterritorial PET/MRI allows characterization of atherosclerosis-related arterial inflammation and demonstrates 18F-FDG uptake in plaque-free arterial segments and, less frequently, within plaques. These findings suggest an arterial inflammatory state at early stages of atherosclerosis. (Progression of Early Subclinical Atherosclerosis [PESA]; NCT01410318).The PESA study is cofunded equally by the Centro Nacional de Investigaciones Cardiovasculares (CNIC) and Banco Santander. The study also receives funding from the Instituto de Salud Carlos III (PI15/02019) and the European Regional Development Fund (ERDF) “A way to make Europe.” The CNIC is supported by the Ministerio de Ciencia, Innovación y Universidades, and the Pro CNIC Foundation, and is a Severo Ochoa Center of Excellence (SEV-2015-0505). Dr. Sanchez-González is an employee of Philips Healthcare. Dr. Bueno has received research funding from the Instituto de Salud Carlos III, Spain (PIE16/00021 & PI17/01799), AstraZeneca, Bristol-Myers Squibb, Janssen, and Novartis; has received consulting fees from AstraZeneca, Bayer, Bristol-Myers Squibb-Pfizer, and Novartis; and has received speaking fees or support for attending scientific meetings from AstraZeneca, Bayer, Bristol-Myers Squibb-Pfizer, Novartis, and MEDSCAPE-the heart.org.S

Genetic Diversity of Pinus nigra Arn. Populations in Southern Spain and Northern Morocco Revealed By Inter-Simple Sequence Repeat Profiles †

Eight Pinus nigra Arn. populations from Southern Spain and Northern Morocco were examined using inter-simple sequence repeat markers to characterize the genetic variability amongst populations. Pair-wise population genetic distance ranged from 0.031 to 0.283, with a mean of 0.150 between populations. The highest inter-population average distance was between PaCU from Cuenca and YeCA from Cazorla, while the lowest distance was between TaMO from Morocco and MA Sierra Mágina populations. Analysis of molecular variance (AMOVA) and Nei’s genetic diversity analyses revealed higher genetic variation within the same population than among different populations. Genetic differentiation (Gst) was 0.233. Cuenca showed the highest Nei’s genetic diversity followed by the Moroccan region, Sierra Mágina, and Cazorla region. However, clustering of populations was not in accordance with their geographical locations. Principal component analysis showed the presence of two major groups—Group 1 contained all populations from Cuenca while Group 2 contained populations from Cazorla, Sierra Mágina and Morocco—while Bayesian analysis revealed the presence of three clusters. The low genetic diversity observed in PaCU and YeCA is probably a consequence of inappropriate management since no estimation of genetic variability was performed before the silvicultural treatments. Data indicates that the inter-simple sequence repeat (ISSR) method is sufficiently informative and powerful to assess genetic variability among populations of P. nigra