Learning about Quantum Gravity with a Couple of Nodes

Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the U(N) framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory

U(N) and holomorphic methods for LQG and Spin Foams

The U(N) framework and the spinor representation for loop quantum gravity are two new points of view that can help us deal with the most fundamental problems of the theory. Here, we review the detailed construction of the U(N) framework explaining how one can endow the Hilbert space of N-leg intertwiners with a Fock structure. We then give a description of the classical phase space corresponding to this system in terms of the spinors, and we will study its quantization using holomorphic techniques. We take special care in constructing the usual holonomy operators of LQG in terms of spinors, and in the description of the Hilbert space of LQG with the different polarization given by these spinors.Comment: 16 pages. Proceedings for the 3rd Quantum Geometry and Quantum Gravity School in Zakopane (2011

U(N) tools for Loop Quantum Gravity: The Return of the Spinor

We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wave-functions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the spin network states. We conclude by applying explicitly our framework to states living on the simple 2-vertex graph and discuss the properties of the resulting Hamiltonian.Comment: 23 page

New tools for Loop Quantum Gravity with applications to a simple model

Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field at large scales. Here we will review the recent U(N) framework for Loop Quantum Gravity and the new spinor representation (that provides a classical setting for the U(N) framework). Then, we will apply these techniques to a simple model in order to propose a dynamics for a symmetry reduced sector of the theory. Furthermore, we will explore certain analogies of this model with Loop Quantum Cosmology.Comment: 4 pages, to appear in Proceedings of Spanish Relativity Meeting 2011 (ERE 2011) held in Madrid, Spai

Mechanisms of induction of regulatory B cells in the tumour microenvironment and their contribution to immunosuppression and pro-tumour responses

The presence of tumour-infiltrating immune cells was originally associated with the induction of anti-tumour responses and good a prognosis. A more refined characterization of the tumour microenvironment has challenged this original idea and evidence now exists pointing to a critical role for immune cells in the modulation of anti-tumour responses and the induction of a tolerant pro-tumour environment. The coordinated action of diverse immunosuppressive populations, both innate and adaptive, shapes a variety of pro-tumour responses leading to tumour progression and metastasis. Regulatory B cells have emerged as critical modulators and suppressors of anti-tumour responses. As reported in autoimmunity and infection studies, Bregs are a heterogeneous population with diverse phenotypes and different mechanisms of action. Here we review recent studies on Bregs from animal models and patients, covering a variety of types of cancer. We describe the heterogeneity of Bregs, the cellular interactions they make with other immune cells and the tumour itself, and their mechanism of suppression that enables tumour escape. We also discuss the potential therapeutic tools that may inhibit Bregs function and promote anti-tumour responses

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

The influence of skull shape modularity on internal skull structures: a 3D-Pilot study using bears

In order to capture the phenotypic variation of the internal skull structures, such as the sinuses or the brain, it is necessary to perform CT scans in a large number of specimens, which is difficult and expensive. Therefore, while the external morphology of the mammalian cranium has been the subject of many morphometric studies, the internal structures of the cranium have been comparatively less studied. Here, we explore how the variation of external shape reflects the morphology of internal structures. We use the family Ursidae (Carnivora, Mammalia) as a case study because bears have a wide variability of cranial morphologies in part associated with different trophic ecologies. To do this, we digitized a set of landmarks in 3D with a Microscribe G2X from the external surface of the cranium in a wide sample of bears. Additionally, the crania of seven bear species were CT-scanned and prepared digitally to visualize the 3D models of the external cranium morphology and of internal structures. Subsequently, we divided the landmarks into two modules, splanchnocranium and neurocranium, and we perform a two-block partial least squares analysis (2B PLS) to explore the intraspecific (static) morphological changes associated with the covariation between them. These morphological changes were visualized using the morphing technique with the 3D models, looking at both the external shape and the internal structures. In addition, we inferred the volume of the sinuses and of the brain in each hypothetical model. Our results show that the first two PLS axes are associated externally with changes in the basicranial angle, face length and cranium height and width. Concerning the internal structures, there are parallel changes in dorso-ventral and medio-lateral expansion of sinuses and brain, accompanied by their corresponding changes in volume. In contrast, the third PLS axis is related to opposite changes in the volume of sinuses and brain. These preliminary results suggest that the opposite relationship between sinuses and brain volumes in the bear cranium is not as evident as expected, at least at intraspecific level.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech