Numerical loop quantum cosmology: an overview

A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key prediction of the bounce at the Planck scale in different models, and the numerical methods used to analyze the properties of the quantum difference operator and the von Neumann stability issues. Using the quantization of a massless scalar field in an isotropic spacetime as a template, an attempt is made to highlight the complementarity of different methods to gain understanding of the new physics emerging from the quantum theory. Open directions which need to be explored with more refined numerical methods are discussed.Comment: 33 Pages, 4 figures. Invited contribution to appear in Classical and Quantum Gravity special issue on Non-Astrophysical Numerical Relativit

Spherically Symmetric Quantum Geometry: Hamiltonian Constraint

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed.Comment: 33 page

Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies

The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows to consider the dynamics including the role of small non-symmetric degrees of freedom for the symmetric evolution. This serves as a model for the general situation of perturbative degrees of freedom in a background independent quantization such as loop quantum gravity, and for the more complicated addition of perturbative inhomogeneities. While being crucial for cosmological phenomenology, it is shown that perturbative non-symmetric degrees of freedom do not allow definitive conclusions for the singularity issue and in such a situation could even lead to wrong claims.Comment: 32 page

Acute kidney disease and renal recovery : consensus report of the Acute Disease Quality Initiative (ADQI) 16 Workgroup

Consensus definitions have been reached for both acute kidney injury (AKI) and chronic kidney disease (CKD) and these definitions are now routinely used in research and clinical practice. The KDIGO guideline defines AKI as an abrupt decrease in kidney function occurring over 7 days or less, whereas CKD is defined by the persistence of kidney disease for a period of > 90 days. AKI and CKD are increasingly recognized as related entities and in some instances probably represent a continuum of the disease process. For patients in whom pathophysiologic processes are ongoing, the term acute kidney disease (AKD) has been proposed to define the course of disease after AKI; however, definitions of AKD and strategies for the management of patients with AKD are not currently available. In this consensus statement, the Acute Disease Quality Initiative (ADQI) proposes definitions, staging criteria for AKD, and strategies for the management of affected patients. We also make recommendations for areas of future research, which aim to improve understanding of the underlying processes and improve outcomes for patients with AKD

On (Cosmological) Singularity Avoidance in Loop Quantum Gravity

Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical General Relativity to spatially homogeneous situations which is then quantized by the methods of LQG. Thus, LQC is a quantum mechanical toy model (finite number of degrees of freedom) for LQG(a genuine QFT with an infinite number of degrees of freedom) which provides important consistency checks. However, it is a non trivial question whether the predictions of LQC are robust after switching on the inhomogeneous fluctuations present in full LQG. Two of the most spectacular findings of LQC are that 1. the inverse scale factor is bounded from above on zero volume eigenstates which hints at the avoidance of the local curvature singularity and 2. that the Quantum Einstein Equations are non -- singular which hints at the avoidance of the global initial singularity. We display the result of a calculation for LQG which proves that the (analogon of the) inverse scale factor, while densely defined, is {\it not} bounded from above on zero volume eigenstates. Thus, in full LQG, if curvature singularity avoidance is realized, then not in this simple way. In fact, it turns out that the boundedness of the inverse scale factor is neither necessary nor sufficient for curvature singularity avoidance and that non -- singular evolution equations are neither necessary nor sufficient for initial singularity avoidance because none of these criteria are formulated in terms of observable quantities.After outlining what would be required, we present the results of a calculation for LQG which could be a first indication that our criteria at least for curvature singularity avoidance are satisfied in LQG.Comment: 34 pages, 16 figure

Current therapy of granulomatosis with polyangiitis and microscopic polyangiitis: the role of rituximab.

Granulomatosis with polyangiitis and microscopic polyangiitis are anti-neutrophil cytoplasmic antibody-associated vasculitides (AAVs) that are prone to cycles of remission and relapse. The introduction of cytotoxic therapy has changed the prognosis for these diseases from typically fatal to manageable chronic illnesses with a relapsing course. Despite improvements in outcomes, recurrence of disease and drug-related toxicity continue to produce significant morbidity and mortality. Better understanding of the pathogenesis of AAV and the mechanism of action of cyclophosphamide has led to investigation of therapies that target B cells. Two randomized controlled trials have shown that rituximab is not inferior to cyclophosphamide for induction of remission in severe AAV, with no significant difference in the incidence of overall adverse events in rituximab- versus cyclophosphamide-treated patients. Data from ongoing clinical trials will determine the role of rituximab in the maintenance of remission

Loop Quantum Cosmology

Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.Comment: 104 pages, 10 figures; online version, containing 6 movies, available at http://relativity.livingreviews.org/Articles/lrr-2005-11