A two-parameter family of double-power-law biorthonormal potential-density expansions

Biorthonormal basis function expansions are widely used in galactic dynamics, both to study problems in galactic stability and to provide numerical algorithms to evolve collisionless stellar systems. They also provide a compact and efficient description of the structure of numerical dark matter haloes in cosmological simulations. We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley, Sanders, Evans & Erkal expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the $\gamma$ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding further examples. In the process, we also uncovered a novel integral transform solution to Poisson's equation

The super-NFW model: An analytic dynamical model for cold dark matter haloes and elliptical galaxies

An analytic galaxy model with $\rho \sim r^{-1}$ at small radii and $\rho \sim r^{-3.5}$ at large radii is presented. The asymptotic density fall-off is slower than the Hernquist model, but faster than the Navarro-Frenk-White (NFW) profile for dark matter haloes, and so in accord with recent evidence from cosmological simulations. The model provides the zeroth-order term in a biorthornomal basis function expansion, meaning that axisymmetric, triaxial and lopsided distortions can easily be added (much like the Hernquist model itself which is the zeroth-order term of the Hernquist-Ostriker expansion). The properties of the spherical model, including analytic distribution functions which are either isotropic, radially anisotropic or tangentially anisotropic, are discussed in some detail. The analogue of the mass-concentration relation for cosmological haloes is provided.EJL and JLS acknowledge financial support from the Science and Technology Facilities Council

Galaxy halo expansions: a new biorthogonal family of potential-density pairs

Efficient expansions of the gravitational field of (dark) haloes have two main uses in the modelling of galaxies: first, they provide a compact representation of numerically-constructed (or real) cosmological haloes, incorporating the effects of triaxiality, lopsidedness or other distortion. Secondly, they provide the basis functions for self-consistent field expansion algorithms used in the evolution of $N$-body systems. We present a new family of biorthogonal potential-density pairs constructed using the Hankel transform of the Laguerre polynomials. The lowest-order density basis functions are double-power-law profiles cusped like $\rho \sim r^{-2 + 1/\alpha}$ at small radii with asymptotic density fall-off like $\rho \sim r^{-3 -1/(2\alpha)}$. Here, $\alpha$ is a parameter satisfying $\alpha \ge 1/2$. The family therefore spans the range of inner density cusps found in numerical simulations, but has much shallower -- and hence more realistic -- outer slopes than the corresponding members of the only previously-known family deduced by Zhao (1996) and exemplified by Hernquist & Ostriker (1992). When $\alpha =1$, the lowest-order density profile has an inner density cusp of $\rho \sim r^{-1}$ and an outer density slope of $\rho \sim r^{-3.5}$, similar to the famous Navarro, Frenk & White (1997) model. For this reason, we demonstrate that our new expansion provides a more accurate representation of flattened NFW haloes than the competing Hernquist-Ostriker expansion. We utilize our new expansion by analysing a suite of numerically-constructed haloes and providing the distributions of the expansion coefficients.JLS and EJL acknowledge the support of the STFC

Models of Distorted and Evolving Dark Matter Halos

We investigate the ability of basis function expansions to reproduce the evolution of a Milky Way-like dark matter halo, extracted from a cosmological zoom-in simulation. For each snapshot, the density of the halo is reduced to a basis function expansion, with interpolation used to recreate the evolution between snapshots. The angular variation of the halo density is described by spherical harmonics, and the radial variation either by biorthonormal basis functions adapted to handle truncated haloes or by splines. High fidelity orbit reconstructions are attainable using either method with similar computational expense. We quantify how the error in the reconstructed orbits varies with expansion order and snapshot spacing. Despite the many possible biorthonormal expansions, it is hard to beat a conventional Hernquist-Ostriker expansion with a moderate number of terms ($\gtrsim15$ radial and $\gtrsim6$ angular). As two applications of the developed machinery, we assess the impact of the time-dependence of the potential on (i) the orbits of Milky Way satellites, and (ii) planes of satellites as observed in the Milky Way and other nearby galaxies. Time evolution over the last 5 Gyr introduces an uncertainty in the Milky Way satellites' orbital parameters of $\sim 15$ per cent, comparable to that induced by the observational errors or the uncertainty in the present-day Milky Way potential. On average, planes of satellites grow at similar rates in evolving and time-independent potentials. There can be more, or less, growth in the plane's thickness, if the plane becomes less, or more, aligned with the major or minor axis of the evolving halo

Interventions to reduce consumption of sugar-sweetened beverages or increase water intake: evidence from a systematic review and meta-analysis

A systematic review and meta-analyses were conducted to evaluate the effects of interventions to reduce sugar-sweetened beverages (SSB) or increase water intakes and to examine the impact of behaviour change techniques (BCTs) in consumption patterns. Randomized and nonrandomized controlled trials published after January 1990 and until December 2016 reporting daily changes in intakes of SSB or water in volumetric measurements (mL d¯¹) were included. References were retrieved through searches of electronic databases and quality appraisal followed Cochrane principles. We calculated mean differences (MD) and synthesized data with random-effects models. Forty studies with 16 505 participants were meta-analysed. Interventions significantly decreased consumption of SSB in children by 76 mL d¯¹ (95% confidence interval [CI] −105 to −46; 23 studies, P < 0.01), and in adolescents (−66 mL d¯¹, 95% CI −130 to −2; 5 studies, P = 0.04) but not in adults (−13 mL d¯¹, 95% CI −44 to 18; 12 studies, P = 0.16). Pooled estimates of water intakes were only possible for interventions in children, and results were indicative of increases in water intake (MD +67 mL d¯¹, 95% CI 6 to 128; 7 studies, P = 0.04). For children, there was evidence to suggest that modelling/demonstrating the behaviour helped to reduce SSB intake and that interventions within the home environment had greater effects than school-based interventions. In conclusion, public health interventions – mainly via nutritional education/counselling – are moderately successful at reducing intakes of SSB and increasing water intakes in children. However, on average, only small reductions in SSBs have been achieved by interventions targeting adolescents and adults. Complementary measures may be needed to achieve greater improvements in both dietary behaviours across all age groups

Morphology of Mouse Anterior Cruciate Ligament-Complex Changes Following Exercise During Pubertal Growth

Postnatal development and the physiological loading response of the anterior cruciate ligament (ACL) complex (ACL proper, entheses, and bony morphology) is not well understood. We tested whether the ACL-complex of two inbred mouse strains that collectively encompass the musculoskeletal variation observed in humans would demonstrate significant morphological differences following voluntary cage-wheel running during puberty compared with normal cage activity controls. Female A/J and C57BL/6J (B6) 6-week-old mice were provided unrestricted access to a standard cage-wheel for 4 weeks. A/J-exercise mice showed a 6.3% narrower ACL (p-=-0.64), and a 20.1% more stenotic femoral notch (p-<-0.01) while B6-exercise mice showed a 12.3% wider ACL (p-=-0.10), compared with their respective controls. Additionally, A/J-exercise mice showed a 5.3% less steep posterior medial tibial slope (p-=-0.07) and an 8.8% less steep posterior lateral tibial slope (p-=-0.07), while B6-exercise mice showed a 9.8% more steep posterior medial tibial slope (p-<-0.01) than their respective controls. A/J-exercise mice also showed more reinforcement of the ACL tibial enthesis with a 20.4% larger area (p-<-0.01) of calcified fibrocartilage distributed at a 29.2% greater depth (p-=-0.02) within the tibial enthesis, compared with their controls. These outcomes suggest exercise during puberty significantly influences ACL-complex morphology and that inherent morphological differences between these mice, as observed in their less active genetically similar control groups, resulted in a divergent phenotypic outcome between mouse strains. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:1910-1919, 2019Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151297/1/jor24328.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151297/2/jor24328_am.pd

Three-dimensional cephalometric evaluation of maxillary growth following in utero repair of cleft lip and alveolar-like defects in the mid-gestational sheep model

Objective: To evaluate maxillary growth following in utero repair of surgically created cleft lip and alveolar (CLA)-like defects by means of three-dimensional (3D) computer tomographic (CT) cephalometric analysis in the mid-gestational sheep model. Methods: In 12 sheep fetuses a unilateral CLA-like defect was created in utero (untreated control group: 4 fetuses). Four different bone grafts were used for the alveolar defect closure. After euthanasia, CT scans of the skulls of the fetuses, 3D re-constructions, and a 3D-CT cephalometric analysis were performed. Results: The comparisons between the operated and nonoperated skull sides as well as of the maxillary asymmetry among the experimental groups revealed no statistically significant differences of the 12 variables used. Conclusions: None of the surgical approaches used for the in utero correction of CLA-like defects seem to affect significantly postsurgical maxillary growth; however, when bone graft healing takes place, a tendency for almost normal maxillary growth can be observed. Copyright (c) 2006 S. Karger AG, Basel

Using coloured filters to reduce the symptoms of visual stress in children with reading delay

Background: Meares Irlen Syndrome (MIS), otherwise known as “visual stress”, is one condition that can cause difficulties with reading. Aim: This study aimed to compare the effect of two coloured-filter systems on the symptoms of visual stress in children with reading delay. Methods: The study design was a pre-test, post-test, randomized head-to-head comparison of two filter systems on the symptoms of visual stress in school children. A total of 68 UK mainstream schoolchildren with significant impairment in reading ability completed the study. Results: The filter systems appeared to have a large effect on the reported symptoms between pre and post three-month time points (d = 2.5, r = 0.78). Both filter types appeared to have large effects (Harris d = 1.79, r = 0.69 and DRT d = 3.22, r = 0.85). Importantly, 35% of participants’ reported that their symptoms had resolved completely; 72% of the 68 children appeared to gain improvements in three or more visual stress symptoms. Conclusion and significance: The reduction in symptoms, which appeared to be brought about by the use of coloured filters, eased the visual discomfort experienced by these children when reading. This type of intervention therefore has the potential to facilitate occupational engagement

Evaluation of the impact of a school gardening intervention on children's fruit and vegetable intake: a randomised controlled trial.

Background: Current academic literature suggests that school gardening programmes can provide an interactive environment with the potential to change children’s fruit and vegetable intake. This is the first cluster randomised controlled trial (RCT) designed to evaluate whether a school gardening programme can have an effect on children’s fruit and vegetable intake. Methods: The trial included children from 23 schools; these schools were randomised into two groups, one to receive the Royal Horticultural Society (RHS)-led intervention and the other to receive the less involved Teacher-led intervention. A 24-hour food diary (CADET) was used to collect baseline and follow-up dietary intake 18 months apart. Questionnaires were also administered to evaluate the intervention implementation. Results: A total of 641 children completed the trial with a mean age of 8.1 years (95% CI: 8.0, 8.4). The unadjusted results from multilevel regression analysis revealed that for combined daily fruit and vegetable intake the Teacher-led group had a higher daily mean change of 8 g (95% CI: −19, 36) compared to the RHS-led group -32 g (95% CI: −60, −3). However, after adjusting for possible confounders this difference was not significant (intervention effect: −40 g, 95% CI: −88, 1; p = 0.06). The adjusted analysis of process measures identified that if schools improved their gardening score by 3 levels (a measure of school gardening involvement - the scale has 6 levels from 0 ‘no garden’ to 5 ‘community involvement’), irrespective of group allocation, children had, on average, a daily increase of 81 g of fruit and vegetable intake (95% CI: 0, 163; p = 0.05) compared to schools that had no change in gardening score. Conclusions: This study is the first cluster randomised controlled trial designed to evaluate a school gardening intervention. The results have found very little evidence to support the claims that school gardening alone can improve children’s daily fruit and vegetable intake. However, when a gardening intervention is implemented at a high level within the school it may improve children’s daily fruit and vegetable intake by a portion. Improving children’s fruit and vegetable intake remains a challenging task

Cavalier King Charles Spaniels with Chiari-like malformation and Syringomyelia have increased variability of spatio-temporal gait characteristics

Abstract Background Chiari-like malformation in the Cavalier King Charles Spaniel is a herniation of the cerebellum and brainstem into or through the foramen magnum. This condition predisposes to Syringomyelia; fluid filled syrinxes within the spinal cord. The resulting pathology in spinal cord and cerebellum create neuropathic pain and changes in gait. This study aims to quantify the changes in gait for Cavalier King Charles Spaniel with Chiari-like malformation and Syringomyelia. Methods We compared Cavalier King Charles Spaniel with Chiari-like malformation with (n = 9) and without (n = 8) Syringomyelia to Border Terriers (n = 8). Two video cameras and manual tracking was used to quantify gait parameters. Results and conclusions We found a significant increase in coefficient of variation for the spatio-temporal characteristics and ipsilateral distance between paws and a wider base of support in the thoracic limbs but not in the pelvic limbs for Cavalier King Charles Spaniels compared with the border terrier