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

Dynamics of magnetic assembly of binary colloidal structures

"This is an author-created, un-copyedited version of an article published in Europhysics Letters. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1209/0295-5075/111/37002."Magnetic field (MF)-directed assembly of colloidal particles provides a step towards the bottom-up manufacturing of smart materials whose properties can be precisely modulated by non-contact forces. Here, we study the MF-directed assembly in binary colloids made up of strong ferromagnetic and diamagnetic microparticles dispersed in ferrofluids. We present observations of the aggregation of pairs and small groups of particles to build equilibrium assemblies. We also develop a theoretical model capable of solving the aggregation dynamics and predicting the particle trajectories, a key factor to understand the physics governing the MF-directed assembly.The project MINECO FIS2013-41821-R (Spain) is acknowledged for financial support

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

A Systematic Analysis of Temporal Trends in the Handgrip Strength of 2,216,320 Children and Adolescents Between 1967 and 2017

Objective: To estimate national and international temporal trends in handgrip strength for children and adolescents, and to examine relationships between trends in handgrip strength and trends in health-related and sociodemographic indicators. Methods: Data were obtained through a systematic search of studies reporting temporal trends in the handgrip strength for apparently healthy 9–17 year-olds, and by examining large national fitness datasets. Temporal trends at the country-sex-age level were estimated by sample-weighted regression models relating the year of testing to mean handgrip strength. International and national trends were estimated by a post-stratified population-weighting procedure. Pearson’s correlations quantified relationships between trends in handgrip strength and trends in health-related/sociodemographic indicators. Results: 2,216,320 children and adolescents from 13 high-, 5 upper-middle-, and 1 low-income countries/special administrative regions between 1967 and 2017 collectively showed a moderate improvement of 19.4% (95%CI: 18.4 to 20.4) or 3.8% per decade (95%CI: 3.6 to 4.0). The international rate of improvement progressively increased over time, with more recent values (post-2000) close to two times larger than those from the 1960s/1970s. Improvements were larger for children (9–12 years) compared to adolescents (13–17 years), and similar for boys and girls. Trends differed between countries, with relationships between trends in handgrip strength and trends in health-related/sociodemographic indicators negligible-to-weak and not statistically significant. Conclusions: There has been a substantial improvement in absolute handgrip strength for children and adolescents since 1967. There is a need for improved international surveillance of handgrip strength, especially in low- and middle-income countries, to more confidently determine true international trends. PROSPERO registration number: CRD42013003657

Impact of health warning labels and calorie labels on selection and purchasing of alcoholic and non-alcoholic drinks: A randomized controlled trial

AIMS: To estimate the impact on selection and actual purchasing of (a) health warning labels (text-only and image-and-text) on alcoholic drinks and (b) calorie labels on alcoholic and non-alcoholic drinks. DESIGN: Parallel-groups randomised controlled trial. SETTING: Drinks were selected in a simulated online supermarket, before being purchased in an actual online supermarket. PARTICIPANTS: Adults in England and Wales who regularly consumed and purchased beer or wine online (n = 651). Six hundred and eight participants completed the study and were included in the primary analysis. INTERVENTIONS: Participants were randomized to one of six groups in a between-subjects three [health warning labels (HWLs) (i): image-and-text HWL; (ii) text-only HWL; (iii) no HWL] × 2 (calorie labels: present versus absent) factorial design (n per group 103-113). MEASUREMENTS: The primary outcome measure was the number of alcohol units selected (with intention to purchase); secondary outcomes included alcohol units purchased and calories selected and purchased. There was no time limit for selection. For purchasing, participants were directed to purchase their drinks immediately (although they were allowed up to 2 weeks to do so). FINDINGS: There was no evidence of main effects for either (a) HWLs or (b) calorie labels on the number of alcohol units selected (HWLs: F(2,599)  = 0.406, P = 0.666; calorie labels: F(1,599)  = 0.002, P = 0.961). There was also no evidence of an interaction between HWLs and calorie labels, and no evidence of an overall difference on any secondary outcomes. In pre-specified subgroup analyses comparing the 'calorie label only' group (n = 101) with the 'no label' group (n = 104) there was no evidence that calorie labels reduced the number of calories selected (unadjusted means: 1913 calories versus 2203, P = 0.643). Among the 75% of participants who went on to purchase drinks, those in the 'calorie label only' group (n = 74) purchased fewer calories than those in the 'no label' group (n = 79) (unadjusted means: 1532 versus 2090, P = 0.028). CONCLUSIONS: There was no evidence that health warning labels reduced the number of alcohol units selected or purchased in an online retail context. There was some evidence suggesting that calorie labels on alcoholic and non-alcoholic drinks may reduce calories purchased from both types of drinks

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