Representations of the Weyl Algebra in Quantum Geometry

The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. Additional assumptions concern the dimension of the underlying analytic manifold (at least three), the finite wide triangulizability of surfaces in it to be used for the fluxes and the naturality of the action of diffeomorphisms -- but neither any domain properties of the represented Weyl operators nor the requirement that the diffeomorphisms act by pull-backs. For this, the general behaviour of C*-algebras generated by continuous functions and pull-backs of homeomorphisms, as well as the properties of stratified analytic diffeomorphisms are studied. Additionally, the paper includes also a short and direct proof of the irreducibility of A.Comment: 71 pages, 1 figure, LaTeX. Changes v2 to v3: previous results unchanged; some addings: inclusion of gauge transforms, several comments, Subsects. 1.5, 3.7, 3.8; comparison with LOST paper moved to Introduction; Def. 2.5 modified; some typos corrected; Refs. updated. Article now as accepted by Commun. Math. Phy

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Transcranial pulsed ultrasound facilitates brain uptake of laronidase in enzyme replacement therapy for Mucopolysaccharidosis type I disease

[[abstract]]BACKGROUND: Mucopolysaccharidosis type I (MPS I) is a debilitating hereditary disease characterized by alpha-L-iduronidase (IDUA) deficiency and consequent inability to degrade glycosaminoglycans. The pathological accumulation of glycosaminoglycans systemically results in severe mental retardation and multiple organ dysfunction. Enzyme replacement therapy with recombinant human alpha-L-iduronidase (rhIDU) improves the function of some organs but not neurological deficits owing to its exclusion from the brain by the blood-brain barrier (BBB). METHODS: We divided MPS I mice into control group, enzyme replacement group with rhIDU 2.9 mg/kg injection, enzyme replacement with one-spot ultrasound treatment group, and enzyme replacement with two-spot ultrasound treatment group, and compare treatment effectiveness between groups. All ultrasound treatments were applied on left side brain. Evans blue was used to simulate the distribution of rhIDU in the brain. RESULTS: Transcranial pulsed weakly focused ultrasound combined with microbubbles facilitates brain rhIDU delivery in MPS I mice receiving systemic enzyme replacement therapy. With intravenously injected rhIDU 2.9 mg/kg, the IDUA enzyme activity on the ultrasound treated side of the cerebral hemisphere raised to 7.81-fold that on the untreated side and to 75.84% of its normal value. Evans blue simulation showed the distribution of the delivered drug was extensive, involving a large volume of the treated cerebral hemisphere. Two-spot ultrasound treatment scheme is more efficient for brain rhIDU delivery than one-spot ultrasound treatment scheme. CONCLUSIONS: Transcranial pulsed weakly focused ultrasound can open BBB extensively and facilitates brain rhIDU delivery. This novel technology may provide a new MPS I treatment strategy

The landscape of genomic alterations across childhood cancers

Pan-cancer analyses that examine commonalities and differences among various cancer types have emerged as a powerful way to obtain novel insights into cancer biology. Here we present a comprehensive analysis of genetic alterations in a pan-cancer cohort including 961 tumours from children, adolescents, and young adults, comprising 24 distinct molecular types of cancer. Using a standardized workflow, we identified marked differences in terms of mutation frequency and significantly mutated genes in comparison to previously analysed adult cancers. Genetic alterations in 149 putative cancer driver genes separate the tumours into two classes: small mutation and structural/copy-number variant (correlating with germline variants). Structural variants, hyperdiploidy, and chromothripsis are linked to TP53 mutation status and mutational signatures. Our data suggest that 7-8% of the children in this cohort carry an unambiguous predisposing germline variant and that nearly 50% of paediatric neoplasms harbour a potentially druggable event, which is highly relevant for the design of future clinical trials