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

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra "dilatonic" coordinate, whose rotation, Lorentz and conformal groups are SO(d-1), SO(d-1,1) XSO(1,1) and SO(d,2)XSO(2,1), respectively. The generalized spacetimes described by simple Jordan algebras of degree three correspond to extensions of Minkowskian spacetimes in the critical dimensions (d=3,4,6,10) by a dilatonic and extra (2,4,8,16) commuting spinorial coordinates, respectively. The Freudenthal triple systems defined over these Jordan algebras describe conformally covariant phase spaces. Following hep-th/0008063, we give a unified geometric realization of the quasiconformal groups that act on their conformal phase spaces extended by an extra "cocycle" coordinate. For the generic Jordan family the quasiconformal groups are SO(d+2,4), whose minimal unitary realizations are given. The minimal unitary representations of the quasiconformal groups F_4(4), E_6(2), E_7(-5) and E_8(-24) of the simple Jordan family were given in our earlier work hep-th/0409272.Comment: A typo in equation (37) corrected and missing titles of some references added. Version to be published in JHEP. 38 pages, latex fil

Developing Digital Tools for Remote Clinical Research:How to Evaluate the Validity and Practicality of Active Assessments in Field Settings

The ability of remote research tools to collect granular, high-frequency data on symptoms and digital biomarkers is an important strength because it circumvents many limitations of traditional clinical trials and improves the ability to capture clinically relevant data. This approach allows researchers to capture more robust baselines and derive novel phenotypes for improved precision in diagnosis and accuracy in outcomes. The process for developing these tools however is complex because data need to be collected at a frequency that is meaningful but not burdensome for the participant or patient. Furthermore, traditional techniques, which rely on fixed conditions to validate assessments, may be inappropriate for validating tools that are designed to capture data under flexible conditions. This paper discusses the process for determining whether a digital assessment is suitable for remote research and offers suggestions on how to validate these novel tools

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

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

The impact of introducing alcohol‐free beer options in bars and public houses on alcohol sales and revenue: a randomised crossover field trial

Aims: The study aimed to estimate the impact of introducing a draught alcohol‐free beer, thereby increasing the relative availability of these products, on alcohol sales and monetary takings in bars and pubs in England. Design: Randomised crossover field trial. Setting: England. Participants: Fourteen venues that did not previously sell draught alcohol‐free beer. Intervention and comparator: Venues completed two intervention periods and two control periods in a randomised order over 8 weeks. Intervention periods involved replacing one draught alcoholic beer with an alcohol‐free beer. Control periods operated business as usual. Measurements: The primary outcome was mean weekly volume (in litres) of draught alcoholic beer sold. The secondary outcome was mean weekly revenue [in GBP (£)] from all drinks. Analyses adjusted for randomised order, special events, season and busyness. Findings: The adjusted mean difference in weekly sales of draught alcoholic beer was −20 L [95% confidence interval (CI) = −41 to +0.4], equivalent to a 4% reduction (95% CI = 8% reduction to 0.1% increase) in the volume of alcoholic draught beer sold when draught alcohol‐free beer was available. Excluding venues that failed at least one fidelity check resulted in an adjusted mean difference of −29 L per week (95% CI = −53 to −5), equivalent to a 5% reduction (95% CI = 8% reduction to 0.8% reduction). The adjusted mean difference in weekly revenue was +61 GBP per week (95% CI = −328 to +450), equivalent to a 1% increase (95% CI = 5% decrease to 7% increase) when draught alcohol‐free beer was available. Conclusions: Introducing a draught alcohol‐free beer in bars and pubs in England reduced the volume of draught alcoholic beer sold by 4% to 5%, with no evidence of the intervention impacting net revenue

Morphology of the first instar larva of obligatory traumatic myiasis agents (Diptera: Calliphoridae, Sarcophagidae)

There are only three fly species that are obligate agents of traumatic myiasis of humans and livestock: a single species of flesh fly, Wohlfahrtia magnifica (Sarcophagidae), and two species of blow flies, Chrysomya bezziana and Cochliomyia hominivorax (Calliphoridae). The morphology of their first instar larvae is thoroughly and consistently documented here with light microscopy photographs and scanning electron microscopy micrographs. The following morphological structures are documented: pseudocephalon, antennal complex, maxillary palpus, oral ridges, thoracic and abdominal spinulation, spiracular field, posterior spiracles and cephaloskeleton. New diagnostic features drawn from the cephaloskeleton and the spinulation of abdominal segments, including the anal pad, are discovered and extensively described. Earlier descriptions in the literature are revisited, and major discrepancies between these and the results of the current study are discussed. The present results allow clarification, correction and, especially, complementation of information provided by earlier authors. The relatively distant taxonomic position of all three species is evidence that obligatory myiasis has arisen independently, and the extensively similar morphology in the first instar larvae of Chrysomya bezziana, Cochliomyia hominivorax and W. magnifica in comparison to necrophagous species, especially the enhancement of the anterior part of the cephaloskeleton and the segmental spinulation, is therefore best interpreted as homoplasic adaptations to a life strategy as obligate vertebrate parasites. An identification key for first instar larvae of all obligatory traumatic myiasis agents of mammals is provided.Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited

Screen-based media use clusters are related to other activity behaviours and health indicators in adolescents

Background: Screen-based media (SBM) occupy a considerable portion of young peoples’ discretionary leisure time. The aim of this paper was to investigate whether distinct clusters of SBM use exist, and if so, to examine the relationship of any identified clusters with other activity/sedentary behaviours and physical and mental health indicators.Methods: The data for this study come from 643 adolescents, aged 14 years, who were participating in the longitudinal Western Australian Pregnancy Cohort (Raine) Study through May 2003 to June 2006. Time spent on SBM, phone use and reading was assessed using the Multimedia Activity Recall for Children and Adults. Height, weight, muscle strength were measured at a clinic visit and the adolescents also completed questionnaires on their physical activity and psychosocial health. Latent class analysis (LCA) was used to analyse groupings of SBM use.Results: Three clusters of SBM use were found; C1 ‘instrumental computer users’ (high email use, general computer use), C2 ‘multi-modal e-gamers’ (both high console and computer game use) and C3 ‘computer e-gamers’ (high computer game use only). Television viewing was moderately high amongst all the clusters. C2 males took fewer steps than their male peers in C1 and C3 (-13,787/week, 95% CI: -4619 to -22957, p = 0.003 and -14,806, 95% CI: -5,306 to -24,305, p = 0.002) and recorded less MVPA than the C1 males (-3.5 h, 95% CI: -1.0 to -5.9, p = 0.005). There was no difference in activity levels between females in clusters C1 and C3.Conclusion: SBM use by adolescents did cluster and these clusters related differently to activity/sedentary behaviours and both physical and psychosocial health indicators. It is clear that SBM use is not a single construct and future research needs to take consideration of this if it intends to understand the impact SBM has on health