265 research outputs found
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
Impact of wine bottle and glass sizes on wine consumption at home: a within- and between- households randomized controlled trial
Background and aims: Reducing alcohol consumption across populations would decrease the risk of a range of diseases, including many cancers, cardiovascular disease and Type 2 diabetes. The aim of the current study was to estimate the impact of using smaller bottles (37.5- versus 75-cl) and glasses (290 versus 370 ml) on consuming wine at home. Design: Randomized controlled trial of households with cross-over randomization to bottle size and parallel randomization to glass size. Setting: UK households. Participants: A total of 260 households consuming at least two 75-cl bottles of wine each week, recruited from the general population through a research agency. The majority consisted of adults who were white and of higher socio-economic position. Intervention: Households were randomized to the order in which they purchased wine in 37.5- or 75-cl bottles, to consume during two 14-day intervention periods, and further randomized to receive smaller (290 ml) or larger (350 ml) glasses to use during both intervention periods. Measurements: Volume (ml) of study wine consumed at the end of each 14-day intervention period, measured using photographs of purchased bottles, weighed on study scales. Findings: Of the randomized households, 217 of 260 (83%) completed the study as per protocol and were included in the primary analysis. There was weak evidence that smaller bottles reduced consumption: after accounting for pre-specified covariates, households consumed on average 145.7 ml (3.6%) less wine when drinking from smaller bottles than from larger bottles [95% confidence intervals (CI) = –335.5 to 43. ml; −8.3 to 1.1%; P = 0.137; Bayes factor (BF) = 2.00]. The evidence for the effect of smaller glasses was stronger: households consumed on average 253.3 ml (6.5%) less wine when drinking from smaller glasses than from larger glasses (95% CI = –517 to 10 ml; −13.2 to 0.3%; P = 0.065; BF = 2.96). Conclusions: Using smaller glasses to drink wine at home may reduce consumption. Greater uncertainty remains around the possible effect of drinking from smaller bottles
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
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
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
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
On Symmetries of Extremal Black Holes with One and Two Centers
After a brief introduction to the Attractor Mechanism, we review the
appearance of groups of type E7 as generalized electric-magnetic duality
symmetries in locally supersymmetric theories of gravity, with particular
emphasis on the symplectic structure of fluxes in the background of extremal
black hole solutions, with one or two centers. In the latter case, the role of
an "horizontal" symmetry SL(2,R) is elucidated by presenting a set of
two-centered relations governing the structure of two-centered invariant
polynomials.Comment: 1+13 pages, 2 Tables. Based on Lectures given by SF and AM at the
School "Black Objects in Supergravity" (BOSS 2011), INFN - LNF, Rome, Italy,
May 9-13 201
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 prevalence of vertebral fracture amongst patients presenting with non-vertebral fractures
INTRODUCTION: Despite vertebral fracture being a significant risk factor for further fracture, vertebral fractures are often unrecognised. A study was therefore conducted to determine the proportion of patients presenting with a non-vertebral fracture who also have an unrecognised vertebral fracture. METHODS: Prospective study of patients presenting with a non-vertebral fracture in South Glasgow who underwent DXA evaluation with vertebral morphometry (MXA) from DV5/6 to LV4/5. Vertebral deformities (consistent with fracture) were identified by direct visualisation using the Genant semi-quantitative grading scale. RESULTS: Data were available for 337 patients presenting with low trauma non-vertebral fracture; 261 were female. Of all patients, 10.4% were aged 50–64 years, 53.2% were aged 65–74 years and 36.2% were aged 75 years or over. According to WHO definitions, 35.0% of patients had normal lumbar spine BMD (T-score −1 or above), 37.4% were osteopenic (T-score −1.1 to −2.4) and 27.6% osteoporotic (T-score −2.5 or lower). Humerus (n=103, 31%), radius–ulna (n=90, 27%) and hand/foot (n=53, 16%) were the most common fractures. For 72% of patients (n=241) the presenting fracture was the first low trauma fracture to come to clinical attention. The overall prevalence of vertebral deformity established by MXA was 25% (n=83); 45% (n=37) of patients with vertebral deformity had deformities of more than one vertebra. Of the patients with vertebral deformity and readable scans for grading, 72.5% (58/80) had deformities of grade 2 or 3. Patients presenting with hip fracture, or spine T-score ≤−2.5, or low BMI, or with more than one prior non-vertebral fracture were all significantly more likely to have evidence of a prevalent vertebral deformity (p<0.05). However, 19.8% of patients with an osteopenic T-score had a vertebral deformity (48% of which were multiple), and 16.1% of patients with a normal T-score had a vertebral deformity (26.3% of which were multiple). Following non-vertebral fracture, some guidelines suggest that anti-resorptive therapy should be reserved for patients with DXA-proven osteoporosis. However, patients who have one or more prior vertebral fractures (prevalent at the time of their non-vertebral fracture) would also become candidates for anti-resorptive therapy—which would have not been the case had their vertebral fracture status not been known. Overall in this study, 8.9% of patients are likely to have had a change in management by virtue of their underlying vertebral deformity status. In other words, 11 patients who present with a non-vertebral fracture would need to undergo vertebral morphometry in order to identify one patient who ought to be managed differently. CONCLUSIONS: Our results support the recommendation to perform vertebral morphometry in patients who are referred for DXA after experiencing a non-vertebral fracture. Treatment decisions will then better reflect any given patient’s future absolute fracture risk. The 'Number Needed to Screen' if vertebral morphometry is used in this way would be seven to identify one patient with vertebral deformity, and 14 to identify one patient with two or more vertebral deformities. Although carrying out MXA will increase radiation exposure for the patient, this increased exposure is significantly less than would be obtained if X-rays of the dorso-lumbar spine were obtained
- …