Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde

Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity

In this work we investigate the canonical quantization of 2+1 gravity with cosmological constant $\Lambda>0$ in the canonical framework of loop quantum gravity. The unconstrained phase space of gravity in 2+1 dimensions is coordinatized by an SU(2) connection $A$ and the canonically conjugate triad field $e$. A natural regularization of the constraints of 2+1 gravity can be defined in terms of the holonomies of $A+=A + \sqrt\Lambda e$. As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection $A_{\lambda}=A+\lambda e$ on the kinematical Hilbert space of loop quantum gravity. The holonomy operator associated to a given path acts non trivially on spin network links that are transversal to the path (a crossing). We provide an explicit construction of the quantum holonomy operator. In particular, we exhibit a close relationship between the action of the quantum holonomy at a crossing and Kauffman's q-deformed crossing identity. The crucial difference is that (being an operator acting on the kinematical Hilbert space of LQG) the result is completely described in terms of standard SU(2) spin network states (in contrast to q-deformed spin networks in Kauffman's identity). We discuss the possible implications of our result.Comment: 19 pages, references added. Published versio

Comparison of 5-year progression of retinitis pigmentosa involving the posterior pole among siblings by means of SD-OCT: a retrospective study

The blockchain technology promises to transform finance, money and evengovernments. However, analyses of blockchain applicability and robustness typicallyfocus on isolated systems whose actors contribute mainly by running the consensusalgorithm. Here, we highlight the importance of considering trustless platformswithin the broader ecosystem that includes social and communication networks. Asan example, we analyse the flash-crash observed on 21st June 2017 in the Ethereumplatform and show that a major phenomenon of social coordination led to acatastrophic cascade of events across several interconnected systems. We proposethe concept of “emergent centralisation” to describe situations where a single systembecomes critically important for the functioning of the whole ecosystem, and arguethat such situations are likely to become more and more frequent in interconnectedsocio-technical systems. We anticipate that the systemic approach we propose willhave implications for future assessments of trustless systems and call for the attentionof policy-makers on the fragility of our interconnected and rapidly changing world

A pragmatic cluster randomised trial evaluating three implementation interventions

Background Implementation research is concerned with bridging the gap between evidence and practice through the study of methods to promote the uptake of research into routine practice. Good quality evidence has been summarised into guideline recommendations to show that peri-operative fasting times could be considerably shorter than patients currently experience. The objective of this trial was to evaluate the effectiveness of three strategies for the implementation of recommendations about peri-operative fasting. Methods A pragmatic cluster randomised trial underpinned by the PARIHS framework was conducted during 2006 to 2009 with a national sample of UK hospitals using time series with mixed methods process evaluation and cost analysis. Hospitals were randomised to one of three interventions: standard dissemination (SD) of a guideline package, SD plus a web-based resource championed by an opinion leader, and SD plus plan-do-study-act (PDSA). The primary outcome was duration of fluid fast prior to induction of anaesthesia. Secondary outcomes included duration of food fast, patients' experiences, and stakeholders' experiences of implementation, including influences. ANOVA was used to test differences over time and interventions. Results Nineteen acute NHS hospitals participated. Across timepoints, 3,505 duration of fasting observations were recorded. No significant effect of the interventions was observed for either fluid or food fasting times. The effect size was 0.33 for the web-based intervention compared to SD alone for the change in fluid fasting and was 0.12 for PDSA compared to SD alone. The process evaluation showed different types of impact, including changes to practices, policies, and attitudes. A rich picture of the implementation challenges emerged, including inter-professional tensions and a lack of clarity for decision-making authority and responsibility. Conclusions This was a large, complex study and one of the first national randomised controlled trials conducted within acute care in implementation research. The evidence base for fasting practice was accepted by those participating in this study and the messages from it simple; however, implementation and practical challenges influenced the interventions' impact. A set of conditions for implementation emerges from the findings of this study, which are presented as theoretically transferable propositions that have international relevance. Trial registration ISRCTN18046709 - Peri-operative Implementation Study Evaluation (POISE

Effective Theory Approach to the Spontaneous Breakdown of Lorentz Invariance

We generalize the coset construction of Callan, Coleman, Wess and Zumino to theories in which the Lorentz group is spontaneously broken down to one of its subgroups. This allows us to write down the most general low-energy effective Lagrangian in which Lorentz invariance is non-linearly realized, and to explore the consequences of broken Lorentz symmetry without having to make any assumptions about the mechanism that triggers the breaking. We carry out the construction both in flat space, in which the Lorentz group is a global spacetime symmetry, and in a generally covariant theory, in which the Lorentz group can be treated as a local internal symmetry. As an illustration of this formalism, we construct the most general effective field theory in which the rotation group remains unbroken, and show that the latter is just the Einstein-aether theory.Comment: 45 pages, no figures

Loop Quantum Gravity

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. The research in loop quantum gravity forms today a vast area, ranging from mathematical foundations to physical applications. Among the most significative results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume; which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, overcompleteness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34 page

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Behavioural activation by mental health nurses for late-life depression in primary care: a randomized controlled trial

Background: Depressive symptoms are common in older adults. The effectiveness of pharmacological treatments and the availability of psychological treatments in primary care are limited. A behavioural approach to depression treatment might be beneficial to many older adults but such care is still largely unavailable. Behavioural Activation (BA) protocols are less complicated and more easy to train than other psychological therapies, making them very suitable for delivery by less specialised therapists. The recent introduction of the mental health nurse in primary care centres in the Netherlands has created major opportunities for improving the accessibility of psychological treatments for late-life depression in primary care. BA may thus address the needs of older patients while improving treatment outcome and lowering costs.The primary objective of this study is to compare the effectiveness and cost-effectiveness of BA in comparison with treatment as usual (TAU) for late-life depression in Dutch primary care. A secondary goal is to explore several potential mechanisms of change, as well as predictors and moderators of treatment outcome of BA for late-life depression. Methods/design: Cluster-randomised controlled multicentre trial with two parallel groups: a) behavioural activation, and b) treatment as usual, conducted in primary care centres with a follow-up of 52 weeks. The main inclusion criterion is a PHQ-9 score > 9. Patients are excluded from the trial in case of severe mental illness that requires specialized treatment, high suicide risk, drug and/or alcohol abuse, prior psychotherapy, change in dosage or type of prescribed antidepressants in the previous 12 weeks, or moderate to severe cognitive impairment. The intervention consists of 8 weekly 30-min BA sessions delivered by a trained mental health nurse. Discussion: We expect BA to be an effective and cost-effective treatment for late-life depression compared to TAU. BA delivered by mental health nurses could increase the availability and accessibility of non-pharmacological treatments for late-life depression in primary care. Trial registration: This study is retrospectively registered in the Dutch Clinical Trial Register NTR6013on August 25th 2016. © 2017 The Author(s)