Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity

One would often like to know when two a priori distinct extremal black p-brane solutions are in fact U-duality related. In the classical supergravity limit the answer for a large class of theories has been known for some time. However, in the full quantum theory the U-duality group is broken to a discrete subgroup and the question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of N=8 supergravity in four, five and six dimensions. The purpose of this note is to present and clarify what is currently known about these discrete orbits while at the same time filling in some of the details not yet appearing in the literature. To this end we exploit the mathematical framework of integral Jordan algebras and Freudenthal triple systems. The charge vector of the dyonic black string in D=6 is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. The situation in four dimensions is less clear: while black holes preserving more than 1/8 of the supersymmetries may be fully classified by known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes a complete classification is known. All projective black holes are E_{7(7)}(Z) related to a four or five charge canonical form determined uniquely by the set of known arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to appear in Class. Quantum Gra

The global impact of tobacco control policies on smokeless tobacco use: a systematic review

BACKGROUND: Smokeless tobacco, used by more than 300 million people globally, results in substantial morbidity and mortality. For smokeless tobacco control, many countries have adopted policies beyond the WHO Framework Convention on Tobacco Control, which has been instrumental in reducing smoking prevalence. The impact of these policies (within and outside the Framework Convention on Tobacco Control) on smokeless tobacco use remains unclear. We aimed to systematically review policies that are relevant to smokeless tobacco and its context and investigate their impact on smokeless tobacco use. METHODS: In this systematic review, we searched 11 electronic databases and grey literature between Jan 1, 2005, and Sept 20, 2021, in English and key south Asian languages, to summarise smokeless tobacco policies and their impact. Inclusion criteria were all types of studies on smokeless tobacco users that mentioned any smokeless tobacco relevant policies since 2005, except systematic reviews. Policies issued by organisations or private institutions were excluded as well as studies on e-cigarettes and Electronic Nicotine Delivery System except where harm reduction or switching were evaluated as a tobacco cessation strategy. Two reviewers independently screened articles, and data were extracted after standardisation. Quality of studies was appraised using the Effective Public Health Practice Project's Quality Assessment Tool. Outcomes for impact assessment included smokeless tobacco prevalence, uptake, cessation, and health effects. Due to substantial heterogeneity in the descriptions of policies and outcomes, data were descriptively and narratively synthesised. This systematic review was registered in PROSPERO (CRD42020191946). FINDINGS: 14 317 records were identified, of which 252 eligible studies were included as describing smokeless tobacco policies. 57 countries had policies targeting smokeless tobacco, of which 17 had policies outside the Framework Convention on Tobacco Control for smokeless tobacco (eg, spitting bans). 18 studies evaluated the impact, which were of variable quality (six strong, seven moderate, and five weak) and reported mainly on prevalence of smokeless tobacco use. The body of work evaluating policy initiatives based on the Framework Convention on Tobacco Control found that these initiatives were associated with reductions in smokeless tobacco prevalence of between 4·4% and 30·3% for taxation and 22·2% and 70·9% for multifaceted policies. Two studies evaluating the non-Framework policy of sales bans reported significant reductions in smokeless tobacco sale (6·4%) and use (combined sex 17·6%); one study, however, reported an increased trend in smokeless tobacco use in the youth after a total sales ban, likely due to cross-border smuggling. The one study reporting on cessation found a 13·3% increase in quit attempts in individuals exposed (47·5%) to Framework Convention on Tobacco Control policy: education, communication, training, and public awareness, compared with non-exposed (34·2%). INTERPRETATION: Many countries have implemented smokeless tobacco control policies, including those that extend beyond the Framework Convention on Tobacco Control. The available evidence suggests that taxation and multifaceted policy initiatives are associated with meaningful reductions in smokeless tobacco use. FUNDING: UK National Institute for Health Research

Freudenthal triple classification of three-qubit entanglement

We show that the three-qubit entanglement classes: (0) Null, (1) Separable A-B-C, (2a) Biseparable A-BC, (2b) Biseparable B-CA, (2c) Biseparable C-AB, (3) W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a Freudenthal triple system defined over the Jordan algebra C+C+C. We also compute the corresponding SLOCC orbits.Comment: 11 pages, 2 figures, 6 tables, revtex; minor corrections, references added; version appearing in Phys. Rev.

Spatial and temporal facies evolution of a Lower Jurassic carbonate platform, NW Tethyan margin (Mallorca, Spain)

The variety of depositional facies of a Lower Jurassic carbonate platform has been investigated on the island of Mallorca along a transect comprising six stratigraphic profiles. Twenty-nine facies and sub-facies have been recognized, grouped into seven facies associations, ranging in depositional environment from supratidal/terrestrial and peritidal to outer platform. Spatial and temporal (2D) facies distribution along the transect reflects the evolution of the carbonate platform with time showing different facies associations, from a broad peritidal platform (stage 1) to a muddy open platform (stage 2), and finally to a peritidal to outer carbonate platform (stage 3). Stage 1 (early Sinemurian to earliest late Sinemurian) corresponds to a nearly-flat peritidal-shallow subtidal epicontinental platform with facies belts that shifted far and fast over the whole study area. The evolution from stage 1 to stage 2 (late Sinemurian) represents a rapid flooding of the epicontinental shallow platform, with more open-marine conditions, and the onset of differential subsidence. During stage 3 (latest Sinemurian), peritidal and shallow-platform environments preferentially developed to the northeast (Llevant Mountains domain) with a rapid transition to middle-outer platform environments toward the northwest (Tramuntana Range domain). Stages 1 and 3 present facies associations typical of Bahamian-type carbonates, whereas stage 2 represents the demise of the Bahamian-type carbonate factory and proliferation of muddy substrates with suspension-feeders. The described platform evolution responded to the interplay between the initial extensional tectonic phases related to Early Jurassic Tethyan rifting, contemporaneous environmental perturbations, and progressive platform flooding related to the Late Triassic–Early Jurassic worldwide marine transgression and associated accommodation changes

The origin and composition of carbonatite-derived carbonate-bearing fluorapatite deposits

Carbonate-bearing fluorapatite rocks occur at over 30 globally distributed carbonatite complexes and represent a substantial potential supply of phosphorus for the fertiliser industry. However, the process(es) involved in forming carbonate-bearing fluorapatite at some carbonatites remain equivocal, with both hydrothermal and weathering mechanisms inferred. In this contribution, we compare the paragenesis and trace element contents of carbonate-bearing fluorapatite rocks from the Kovdor, Sokli, Bukusu, Catalão I and Glenover carbonatites in order to further understand their origin, as well as to comment upon the concentration of elements that may be deleterious to fertiliser production. The paragenesis of apatite from each deposit is broadly equivalent, comprising residual magmatic grains overgrown by several different stages of carbonate-bearing fluorapatite. The first forms epitactic overgrowths on residual magmatic grains, followed by the formation of massive apatite which, in turn, is cross-cut by late euhedral and colloform apatite generations. Compositionally, the paragenetic sequence corresponds to a substantial decrease in the concentration of rare earth elements (REE), Sr, Na and Th, with an increase in U and Cd. The carbonate-bearing fluorapatite exhibits a negative Ce anomaly, attributed to oxic conditions in a surficial environment and, in combination with the textural and compositional commonality, supports a weathering origin for these rocks. Carbonate-bearing fluorapatite has Th contents which are several orders of magnitude lower than magmatic apatite grains, potentially making such apatite a more environmentally attractive feedstock for the fertiliser industry. Uranium and cadmium contents are higher in carbonate-bearing fluorapatite than magmatic carbonatite apatite, but are much lower than most marine phosphorites

Case Reports1. A Late Presentation of Loeys-Dietz Syndrome: Beware of TGFβ Receptor Mutations in Benign Joint Hypermobility

Background: Thoracic aortic aneurysms (TAA) and dissections are not uncommon causes of sudden death in young adults. Loeys-Dietz syndrome (LDS) is a rare, recently described, autosomal dominant, connective tissue disease characterized by aggressive arterial aneurysms, resulting from mutations in the transforming growth factor beta (TGFβ) receptor genes TGFBR1 and TGFBR2. Mean age at death is 26.1 years, most often due to aortic dissection. We report an unusually late presentation of LDS, diagnosed following elective surgery in a female with a long history of joint hypermobility. Methods: A 51-year-old Caucasian lady complained of chest pain and headache following a dural leak from spinal anaesthesia for an elective ankle arthroscopy. CT scan and echocardiography demonstrated a dilated aortic root and significant aortic regurgitation. MRA demonstrated aortic tortuosity, an infrarenal aortic aneurysm and aneurysms in the left renal and right internal mammary arteries. She underwent aortic root repair and aortic valve replacement. She had a background of long-standing joint pains secondary to hypermobility, easy bruising, unusual fracture susceptibility and mild bronchiectasis. She had one healthy child age 32, after which she suffered a uterine prolapse. Examination revealed mild Marfanoid features. Uvula, skin and ophthalmological examination was normal. Results: Fibrillin-1 testing for Marfan syndrome (MFS) was negative. Detection of a c.1270G > C (p.Gly424Arg) TGFBR2 mutation confirmed the diagnosis of LDS. Losartan was started for vascular protection. Conclusions: LDS is a severe inherited vasculopathy that usually presents in childhood. It is characterized by aortic root dilatation and ascending aneurysms. There is a higher risk of aortic dissection compared with MFS. Clinical features overlap with MFS and Ehlers Danlos syndrome Type IV, but differentiating dysmorphogenic features include ocular hypertelorism, bifid uvula and cleft palate. Echocardiography and MRA or CT scanning from head to pelvis is recommended to establish the extent of vascular involvement. Management involves early surgical intervention, including early valve-sparing aortic root replacement, genetic counselling and close monitoring in pregnancy. Despite being caused by loss of function mutations in either TGFβ receptor, paradoxical activation of TGFβ signalling is seen, suggesting that TGFβ antagonism may confer disease modifying effects similar to those observed in MFS. TGFβ antagonism can be achieved with angiotensin antagonists, such as Losartan, which is able to delay aortic aneurysm development in preclinical models and in patients with MFS. Our case emphasizes the importance of timely recognition of vasculopathy syndromes in patients with hypermobility and the need for early surgical intervention. It also highlights their heterogeneity and the potential for late presentation. Disclosures: The authors have declared no conflicts of interes