Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl

Toeplitz operators on symplectic manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.Comment: 40 page

Large N limit of SO(N) gauge theory of fermions and bosons

In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to a Majorana field and a real scalar field in 1+1 dimensions extending ideas of Rajeev. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp_1(H|H )/U(H_+|H_+), where H|H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H_+|H_+ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only (the purely bosonic case is treated in our earlier work). In the Majorana fermion case the phase space is given by O_1(H)/U(H_+), where H refers to the complex one-particle states and H_+ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the 't Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known 't Hooft equation.Comment: 27 pages, no figure

The role of interleukin-1β as a predictive biomarker and potential therapeutic target during clinical ex vivo lung perfusion

BACKGROUND: Extended criteria donor lungs deemed unsuitable for immediate transplantation can be reconditioned using ex vivo lung perfusion (EVLP). Objective identification of which donor lungs can be successfully reconditioned and will function well post-operatively has not been established. This study assessed the predictive value of markers of inflammation and tissue injury in donor lungs undergoing EVLP as part of the DEVELOP-UK study. METHODS: Longitudinal samples of perfusate, bronchoalveolar lavage, and tissue from 42 human donor lungs undergoing clinical EVLP assessments were analyzed for markers of inflammation and tissue injury. Levels were compared according to EVLP success and post-transplant outcomes. Neutrophil adhesion to human pulmonary microvascular endothelial cells (HPMECs) conditioned with perfusates from EVLP assessments was investigated on a microfluidic platform. RESULTS: The most effective markers to differentiate between in-hospital survival and non-survival post-transplant were perfusate interleukin (IL)-1β (area under the curve = 1.00, p = 0.002) and tumor necrosis factor-α (area under the curve = 0.95, p = 0.006) after 30 minutes of EVLP. IL-1β levels in perfusate correlated with upregulation of intracellular adhesion molecule-1 in donor lung vasculature (R(2) = 0.68, p < 0.001) and to a lesser degree upregulation of intracellular adhesion molecule-1 (R(2) = 0.30, p = 0.001) and E-selectin (R(2) = 0.29, p = 0.001) in conditioned HPMECs and neutrophil adhesion to conditioned HPMECs (R(2) = 0.33, p < 0.001). Neutralization of IL-1β in perfusate effectively inhibited neutrophil adhesion to conditioned HPMECs (91% reduction, p = 0.002). CONCLUSIONS: Donor lungs develop a detectable and discriminatory pro-inflammatory signature in perfusate during EVLP. Blocking the IL-1β pathway during EVLP may reduce endothelial activation and subsequent neutrophil adhesion on reperfusion; this requires further investigation in vivo

A Conformally Invariant Holographic Two-Point Function on the Berger Sphere

We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at its conformal infinity. Using basic notions from conformal geometry and the theory of boundary value problems, in particular the Dirichlet-to-Robin operator, we establish that our two-point correlation function is conformally invariant and corresponds to a boundary operator of conformal dimension one. It is plausible that the methods we use could have more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte

Standardised data on initiatives—STARDIT: Beta version

Background and objective: There is currently no standardised way to share information across disciplines about initiatives, including fields such as health, environment, basic science, manufacturing, media and international development. All problems, including complex global problems such as air pollution and pandemics require reliable data sharing between disciplines in order to respond effectively. Current reporting methods also lack information about the ways in which different people and organisations are involved in initiatives, making it difficult to collate and appraise data about the most effective ways to involve different people. The objective of STARDIT (Standardised Data on Initiatives) is to address current limitations and inconsistencies in sharing data about initiatives. The STARDIT system features standardised data reporting about initiatives, including who has been involved, what tasks they did, and any impacts observed. STARDIT was created to help everyone in the world find and understand information about collective human actions, which are referred to as ‘initiatives’. STARDIT enables multiple categories of data to be reported in a standardised way across disciplines, facilitating appraisal of initiatives and aiding synthesis of evidence for the most effective ways for people to be involved in initiatives. This article outlines progress to date on STARDIT; current usage; information about submitting reports; planned next steps and how anyone can become involved. Method: STARDIT development is guided by participatory action research paradigms, and has been co-created with people from multiple disciplines and countries. Co-authors include cancer patients, people affected by rare diseases, health researchers, environmental researchers, economists, librarians and academic publishers. The co-authors also worked with Indigenous peoples from multiple countries and in partnership with an organisation working with Indigenous Australians. Results and discussion: Over 100 people from multiple disciplines and countries have been involved in co-designing STARDIT since 2019. STARDIT is the first open access web-based data-sharing system which standardises the way that information about initiatives is reported across diverse fields and disciplines, including information about which tasks were done by which stakeholders. STARDIT is designed to work with existing data standards. STARDIT data will be released into the public domain (CC0) and integrated into Wikidata; it works across multiple languages and is both human and machine readable. Reports can be updated throughout the lifetime of an initiative, from planning to evaluation, allowing anyone to be involved in reporting impacts and outcomes. STARDIT is the first system that enables sharing of standardised data about initiatives across disciplines. A working Beta version was publicly released in February 2021 (ScienceforAll.World/STARDIT). Subsequently, STARDIT reports have been created for peer-reviewed research in multiple journals and multiple research projects, demonstrating the usability. In addition, organisations including Cochrane and Australian Genomics have created prospective reports outlining planned initiatives. Conclusions: STARDIT can help create high-quality standardised information on initiatives trying to solve complex multidisciplinary global problems

The prevalence and incidence of mental ill-health in adults with autism and intellectual disabilities

The prevalence, and incidence, of mental ill-health in adults with intellectual disabilities and autism were compared with the whole population with intellectual disabilities, and with controls, matched individually for age, gender, ability-level, and Down syndrome. Although the adults with autism had a higher point prevalence of problem behaviours compared with the whole adult population with intellectual disabilities, compared with individually matched controls there was no difference in prevalence, or incidence of either problem behaviours or other mental ill-health. Adults with autism who had problem behaviours were less likely to recover over a two-year period than were their matched controls. Apparent differences in rates of mental ill-health are accounted for by factors other than autism, including Down syndrome and ability level