Canonical formalism for simplicial gravity

We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in particular.Comment: 4 pages, 5 figures, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

Complex Networks on Hyperbolic Surfaces

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties. This method provides a new perspective to classify network-complexity both on local and global scale. We demonstrate by means of several examples that there is a strong relation between the network properties and the embedding surface.Comment: 8 Pages 3 Figure

Crumpled triangulations and critical points in 4D simplicial quantum gravity

This is an expanded and revised version of our geometrical analysis of the strong coupling phase of 4D simplicial quantum gravity. The main differences with respect to the former version is a full discussion of singular triangulations with singular vertices connected by a subsingular edge. In particular we provide analytical arguments which characterize the entropical properties of triangulations with a singular edge connecting two singular vertices. The analytical estimate of the location of the critical coupling at k_2\simeq 1.3093 is presented in more details. Finally we also provide a model for pseudo-criticality at finite N_4(S^4).Comment: 44 page

Risk and Protective Factors of Dementia Among Adults With Post-Traumatic Stress Disorder: A Systematic Review Protocol

INTRODUCTION: Post-traumatic stress disorder (PTSD) is associated with an increased risk of dementia. Individual epidemiological studies have controlled for several confounders of the relationship between PTSD and increased dementia risk, yet particular risk factors underlying this relationship have not been determined. This systematic review protocol aims to identify risk and protective factors of dementia among adults with PTSD. METHODS AND ANALYSIS: We will conduct an electronic search of the databases: PubMed, CINAHL, PsychINFO, The Cochrane Library, Scopus and ProQuest Dissertation and Theses Global. After screening the studies, quantitative synthesis will be performed, if possible. Otherwise, a narrative synthesis will be performed. We will include randomised controlled trials and other types of research evidence including longitudinal cohort studies. Strength of evidence will be assessed using the Grading of Recommendations, Assessment, Development and Evaluations method. Examples of variables that will be extracted are: year of PTSD diagnosis, comorbid conditions, health behaviours, pharmacological treatments and year of mild cognitive impairment or dementia diagnosis. We developed this systematic review protocol according to the Preferred Reporting Items for Systematic Review and Meta-Analysis Protocols 2015 statement. ETHICS AND DISSEMINATION: The proposed study will not collect individual-level data and, therefore, does not require ethical approval. Results of this study will provide current evidence on risk and protective factors of dementia in adults with PTSD. Findings will be disseminated in peer-reviewed publications and conference presentations. PROSPERO REGISTRATION NUMBER: CRD42019128553

Polyhedra in loop quantum gravity

Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in Euclidean space: a polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: we give formulas for the edge lengths, the volume and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner with the state of a quantum polyhedron, thus generalizing the notion of quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spinfoams with non-simplicial graphs.Comment: 32 pages, many figures. v2 minor correction

A matrix solution to pentagon equation with anticommuting variables

We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative, this provides a "more quantum" topological field theory than in our previous works

Nonperturbative dynamics for abstract (p,q) string networks

We describe abstract (p,q) string networks which are the string networks of Sen without the information about their embedding in a background spacetime. The non-perturbative dynamical formulation invented for spin networks, in terms of causal evolution of dual triangulations, is applied to them. The formal transition amplitudes are sums over discrete causal histories that evolve (p,q) string networks. The dynamics depend on two free SL(2,Z) invariant functions which describe the amplitudes for the local evolution moves.Comment: Latex, 12 pages, epsfig, 7 figures, minor change

Observables in 3-dimensional quantum gravity and topological invariants

In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model. Instead of giving a formal description of the observables, we just formulate the paper by examples. This means that we just show how an idea works with particular cases and give a way to compute 'expectation values' in general by a topological procedure.Comment: 24 pages, 47 figure