Interacting spin-2 fields in three dimensions

Using the frame formulation of multi-gravity in three dimensions, we show that demanding the presence of secondary constraints which remove the Boulware-Deser ghosts restricts the possible interaction terms of the theory and identifies invertible frame field combinations whose effective metric may consistently couple to matter. The resulting ghost-free theories can be represented by theory graphs which are trees. In the case of three frame fields, we explicitly show that the requirement of positive masses and energies for the bulk spin-2 modes in AdS$_3$ is consistent with a positive central charge for the putative dual CFT$_2$.Comment: 26 pages, 3 figures, v2: minor changes, matches published versio

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE

Parallel approach to sliding window sums

Sliding window sums are widely used in bioinformatics applications, including sequence assembly, k-mer generation, hashing and compression. New vector algorithms which utilize the advanced vector extension (AVX) instructions available on modern processors, or the parallel compute units on GPUs and FPGAs, would provide a significant performance boost for the bioinformatics applications. We develop a generic vectorized sliding sum algorithm with speedup for window size w and number of processors P is O(P/w) for a generic sliding sum. For a sum with commutative operator the speedup is improved to O(P/log(w)). When applied to the genomic application of minimizer based k-mer table generation using AVX instructions, we obtain a speedup of over 5X.Comment: 10 pages, 5 figure

A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities

We consider a manifold endowed with two different vielbeins $E^{A}{}_{\mu}$ and $L^{A}{}_{\mu}$ corresponding to two different metrics $g_{\mu\nu}$ and $f_{\mu\nu}$. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation $g^{\mu\nu} E^{A}{}_{\mu} L^{B}{}_{\nu} = g^{\mu\nu} E^{B}{}_{\mu} L^{A}{}_{\nu}$ can be imposed (or the "Deser-van Nieuwenhuizen" gauge chosen). We clarify and correct various statements which have been made about this issue.Comment: 20 pages. Section 7, prop. 6 and 7. added. Some results made more precis

Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model

In this note we investigate the anomalous breaking of anisotropic scaling symmetry in a non-relativistic field theory with dynamical exponent z=2. On general grounds, one can show that there exist two possible "central charges" which characterize the breaking of scale invariance. Using heat kernel methods, we compute these two central charges in the quantum Lifshitz model, a free field theory which is second order in time and fourth order in spatial derivatives. We find that one of the two central charges vanishes. Interestingly, this is also true for strongly coupled non-relativistic field theories with a geometric dual described by a metric and a massive vector field.Comment: 26 pages; major revision (results were unaffected), published versio

Bridging flavour violation and leptogenesis in SU(3) family models

We reconsider basic, in the sense of minimal field content, Pati-Salam x SU(3) family models which make use of the Type I see-saw mechanism to reproduce the observed mixing and mass spectrum in the neutrino sector. The goal of this is to achieve the observed baryon asymmetry through the thermal decay of the lightest right-handed neutrino and at the same time to be consistent with the expected experimental lepton flavour violation sensitivity. This kind of models have been previously considered but it was not possible to achieve a compatibility among all of the ingredients mentioned above. We describe then how different SU(3) messengers, the heavy fields that decouple and produce the right form of the Yukawa couplings together with the scalars breaking the SU(3) symmetry, can lead to different Yukawa couplings. This in turn implies different consequences for flavour violation couplings and conditions for realizing the right amount of baryon asymmetry through the decay of the lightest right-handed neutrino. Also a highlight of the present work is a new fit of the Yukawa textures traditionally embedded in SU(3) family models.Comment: 26 pages, 5 figures, Some typos correcte

Bimetric Gravity from Ghost-free Massive Gravity

Generically, non-linear bimetric theories of gravity suffer from the same Boulware-Deser ghost instability as non-linear theories of massive gravity. However, recently proposed theories of massive gravity have been shown to be ghost-free. These theories are formulated with respect to a flat, non-dynamical reference metric. In this work we show that it is possible to give dynamics to the reference metric in such a way that the consistency of the theory is maintained. The result is a non-linear bimetric theory of a massless spin-2 field interacting with a massive spin-2 field that is free of the Boulware-Deser ghost. To our knowledge, this is the first construction of such a ghost-free bimetric theory.Comment: results extended, version accepted for publicatio

Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

Reliability and validity of three questionnaires measuring context-specific sedentary behaviour and associated correlates in adolescents, adults and older adults

BACKGROUND: Reliable and valid measures of total sedentary time, context-specific sedentary behaviour (SB) and its potential correlates are useful for the development of future interventions. The purpose was to examine test-retest reliability and criterion validity of three newly developed questionnaires on total sedentary time, context-specific SB and its potential correlates in adolescents, adults and older adults. METHODS: Reliability and validity was tested in six different samples of Flemish (Belgium) residents. For the reliability study, 20 adolescents, 22 adults and 20 older adults filled out the age-specific SB questionnaire twice. Test-retest reliability was analysed using Kappa coefficients, Intraclass Correlation Coefficients and/or percentage agreement, separately for the three age groups. For the validity study, data were retrieved from 62 adolescents, 33 adults and 33 older adults, with activPAL as criterion measure. Spearman correlations and Bland-Altman plots (or non-parametric approach) were used to analyse criterion validity, separately for the three age groups and for weekday, weekend day and average day. RESULTS: The test-retest reliability for self-reported total sedentary time indicated following values: ICC = 0.37-0.67 in adolescents; ICC = 0.73-0.77 in adults; ICC = 0.68-0.80 in older adults. Item-specific reliability results (e.g. context-specific SB and its potential correlates) showed good-to-excellent reliability in 67.94%, 68.90% and 66.38% of the items in adolescents, adults and older adults respectively. All items belonging to sedentary-related equipment and simultaneous SB showed good reliability. The sections of the questionnaire with lowest reliability were: context-specific SB (adolescents), potential correlates of computer use (adults) and potential correlates of motorized transport (older adults). Spearman correlations between self-reported total sedentary time and the activPAL were different for each age group: rho = 0.02-0.42 (adolescents), rho = 0.06-0.52 (adults), rho = 0.38-0.50 (older adults). Participants over-reported total sedentary time (except for weekend day in older adults) compared to the activPAL, for weekday, weekend day and average day respectively by +57.05%, +46.29%, +53.34% in adolescents; +40.40%, +19.15%, +32.89% in adults; +10.10%, -6.24%, +4.11% in older adults. CONCLUSIONS: The questionnaires showed acceptable test-retest reliability and criterion validity. However, over-reporting of total SB was noticeable in adolescents and adults. Nevertheless, these questionnaires will be useful in getting context-specific information on SB