Tarski monoids: Matui's spatial realization theorem

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui on a class of \'etale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147

\'Etale groupoids and Steinberg algebras, a concise introduction

We give a concise introduction to (discrete) algebras arising from \'etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups also explored

Tiling groupoids and Bratteli diagrams

Let T be an aperiodic and repetitive tiling of R^d with finite local complexity. Let O be its tiling space with canonical transversal X. The tiling equivalence relation R_X is the set of pairs of tilings in X which are translates of each others, with a certain (etale) topology. In this paper R_X is reconstructed as a generalized "tail equivalence" on a Bratteli diagram, with its standard AF-relation as a subequivalence relation. Using a generalization of the Anderson-Putnam complex, O is identified with the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is built from this sequence, and its set of infinite paths dB is homeomorphic to X. The diagram B is endowed with a horizontal structure: additional edges that encode the adjacencies of patches in T. This allows to define an etale equivalence relation R_B on dB which is homeomorphic to R_X, and contains the AF-relation of "tail equivalence".Comment: 34 pages, 4 figure

The use of electronic alerts in primary care computer systems to identify the excessive prescription of short-acting beta2-agonists for people with asthma: a systematic review.

Computers are increasingly used to improve prescribing decisions in the management of long-term conditions however the effects on asthma prescribing remain unclear. We aimed to synthesise the evidence for the use of computerised alerts that identify excessive prescribing of short-acting beta2-agonists (SABAs) to improve asthma management for people with asthma. MEDLINE, CINAHL, Embase, Cochrane and Scopus databases (1990-2016) were searched for randomised controlled trials using electronic alerts to identify excessive prescribing of SABAs for people with asthma in primary care. Inclusion eligibility, quality appraisal (Cochrane risk of bias tool) and data extraction were performed by two independent reviewers. Findings were synthesised narratively. A total of 2035 articles were screened and four trials were eligible. Three studies had low risk of bias: one reported a positive effect on our primary outcome of interest, excessive SABA prescribing; another reported positive effects on the ratio of inhaled corticosteroid (ICS)-SABA prescribing, and asthma control; a third reported no effect on outcomes of interest. One study at high risk of bias reported a reduction in exacerbations and primary care consultations. There is some evidence that electronic alerts reduce excessive prescribing of SABAs, when delivered as part of a multicomponent intervention in an integrated health care system. However due to the variation in health care systems, intervention design and outcomes measured, further research is required to establish optimal design of alerting and intervening systems.The authors wish to thank Asthma UK and Queen Mary University London for funding this work as part of a PhD studentship carried out by S.M. A.D.S. is funded by a NIHR Academic Clinical Lectureship. A.B. is a National Institute for Health Research (NIHR) Senior Investigator and additionally was supported by the NIHR Respiratory Disease Biomedical Research Unit at the Royal Brompton and Harefield NHS Foundation Trust and Imperial College London. M.T. is supported by the NIHR Collaboration for Leadership in Applied Health Research and Care (CLAHRC) Wessex, NIHR School of Primary Care Research and NIHR Southampton Biomedical Research Centre. C.G. is supported by the NIHR CLAHRC North Thames at Bart’s Health NHS Trust. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health. This work is funded by Asthma UK and Queen Mary University of London

Prevalence of depression in Parkinson's disease: effects of disease stage, motor subtype and gender

Contains fulltext : 96218.pdf (publisher's version ) (Closed access)Depression is one of the most common non-motor symptoms of Parkinson's disease (PD) with a large negative impact on the quality of life. Factors such as disease stage, subtype of PD and gender might play an important role in the prevalence of depression, but a large study investigating all these factors in a within-subject design is lacking. Therefore we studied a homogeneous group of 256 Dutch PD patients (60% men, mean age=65.12 (+/-9.6) years). In total, 36.3% of the subjects had a BDI-score indicative for a minor depression, while 12.9% had a major depression. Notably, only 8.6% of the minor depressed patients and 30.3% of the major depressed patients were taking antidepressants. A higher prevalence of depression was observed in the later stages of the disease. However, this finding was absent in a smaller subsample after correction for cognitive impairment. Our data did not show a difference in the prevalence of depression between the motor subtypes and showed a trend towards higher prevalence of depression in the tremor dominant group. There was no significant difference in the prevalence of depression between men and women. We will discuss the relevance of these results in relation to the findings of other studies

Étale groupoids and Steinberg Algebras : a concise introduction

In the last couple of years, étale groupoids have become a focal point in several areas of mathematics. The convolution algebras arising from étale groupoids, considered both in analytical setting [50] and algebraic setting [23, 54], include many deep and important examples such as Cuntz algebras [27] and Leavitt algebras [40] and allowsystematic treatment of them. Partial actions and partial symmetries can also be realised as étale groupoids (via inverse semigroups), allowing us to relate convolution algebras to partial crossed products [28, 30]. Realising that the invariants long studied in topological dynamics can be modelled on étale groupoids (such as homology, full groups and orbit equivalence [41]) and that these are directly related to invariants long studied in analysis and algebra (such as K-theory) allows interaction between areas; we can use techniques developed in algebra in analysis and vice versa. The étale groupoid is the Rosetta stone