Solution properties of the incompressible Euler system with rough path advection

We consider the Euler equations for the incompressible flow of an ideal fluid with an additional rough-in-time, divergence-free, Lie-advecting vector field. In recent work, we have demonstrated that this system arises from Clebsch and Hamilton-Pontryagin variational principles with a perturbative geometric rough path Lie-advection constraint. In this paper, we prove local well-posedness of the system in $L^2$-Sobolev spaces $H^m$ with integer regularity $m\ge \lfloor d/2\rfloor+2$ and establish a Beale-Kato-Majda (BKM) blow-up criterion in terms of the $L^1_tL^\infty_x$-norm of the vorticity. In dimension two, we show that the $L^p$-norms of the vorticity are conserved, which yields global well-posedness and a Wong-Zakai approximation theorem for the stochastic version of the equation

Variational principles for fluid dynamics on rough paths

In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynamics (RGFD) models as critical points of rough action functionals. These RGFD models characterize Lagrangian trajectories in fluid dynamics as geometric rough paths (GRP) on the manifold of diffeomorphic maps. Three constrained variational approaches are formulated for the derivation of these models. The first is the Clebsch formulation, in which the constraints are imposed as rough advection laws. The second is the Hamilton-Pontryagin formulation, in which the constraints are imposed as right-invariant rough vector fields. The third is the Euler--Poincar\'e formulation in which the variations are constrained. These variational principles lead directly to the Lie--Poisson Hamiltonian formulation of fluid dynamics on geometric rough paths. The GRP framework preserves the geometric structure of fluid dynamics obtained by using Lie group reduction to pass from Lagrangian to Eulerian variational principles, thereby yielding a rough formulation of the Kelvin circulation theorem. The rough-path variational approach includes non-Markovian perturbations of the Lagrangian fluid trajectories. In particular, memory effects can be introduced through this formulation through a judicious choice of the rough path (e.g. a realization of a fractional Brownian motion). In the special case when the rough path is a realization of a semimartingale, we recover the SGFD models in Holm (2015). However, by eliminating the need for stochastic variational tools, we retain a pathwise interpretation of the Lagrangian trajectories. In contrast, the Lagrangian trajectories in the stochastic framework are described by stochastic integrals which do not have a pathwise interpretation. Thus, the rough path formulation restores this property

Exploring the impact of the somatic method ‘Timani’ on performance quality, performance-related pain and injury, and self-efficacy in music students in Norway: an intervention study

The importance of including performance-related body mechanics into music education to improve performance quality and prevent performance-related injuries has been stressed by many researchers recently. However, it is unclear how this information could be delivered most effectively. The somatic method ‘Timani’ provides a practical solution by combining expertise in music performance and functional body mechanics with the goal of achieving a more efficient playing technique. Since no in-depth study has been conducted to assess the method before, we explored the impact of this method on young musicians’ performance through an online, 4-week-long Timani intervention with a mixed-methodology design. 17 students (mean age = 19.17 years) were recruited from the Norwegian Academy of Music. They participated in two group workshops at the beginning and the end of the project and received four individual Timani sessions administered by certified teachers. We collected survey data at the workshops about performance-related pain and self-efficacy, and qualitative feedback after each session. In addition, all sessions were observed by the researcher and semi-structured interviews were conducted with the teachers about the perceived outcomes and their experiences with teaching the method online. Our findings show that the intervention had a positive impact on a physical, professional, and to some extent, psychological and behavioral level. The improvements included better posture when playing, enhanced control and dexterity in the upper extremities, and improved breathing mechanisms. The seven students who had performance-related pain pre-intervention reported a reduction in the discomfort. The positive results were achieved by the dual expertise of the teachers in music performance and functional body mechanics, the structure of the sessions, the communication, and the pedagogical tools used. Both students and teachers felt that administering the sessions online was satisfactory and produced good results. Timani is a promising method to establish healthy playing and singing habits thus improving performance quality and preventing performance-related problems and has great potential in reducing pre-existing injuries and pain. Also, it can be effectively taught online which has further implications for the logistics of delivery

Seabirds as guides for fisheries management: European shag Phalacrocorax aristotelis diet as indicator of saithe Pollachius virens recruitment

publishedVersio

Transitions between Metastable Long-Run Consumption Behaviors in a Stochastic Peer-Driven Consumer Network

We study behavioral change - as a transition between coexisting attractors - in the context of a stochastic, non-linear consumption model with interdependent agents. Relying on the indirect approach to the analysis of a stochastic dynamic system, and employing a mix of analytical, numerical and graphical techniques, we identify conditions under which such transitions are likely to occur. The stochastic analysis depends crucially on the stochastic sensitivity function technique as it can be applied to the stochastic analoga of closed invariant curves [14], [1]. We find that in a moderate noise environment increased peer influence actually reduces the complexity of observable long-run consumer behavior. © 2021 American Institute of Mathematical Sciences. All rights reserved.Acknowledgments. Tatyana Perevalova and Jochen Jungeilges gratefully acknowledge research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2021-1387)

Thermodynamic Properties near the onset of Loop-Current Order in high-TcT_c superconducting cuprates

We have performed large-scale Monte Carlo simulations on a two-dimensional generalized Ashkin-Teller model to calculate the thermodynamic properties in the critical region near its transitions. The Ashkin-Teller model has a pair of Ising spins at each site which interact with neighboring spins through pair-wise and 4-spin interactions. The model represents the interactions between orbital current loops in $Cu O_2$-plaquettes of high-$T_c$ cuprates, which order with a staggered magnetization \Mso inside each unit-cell in the underdoped region of the phase diagram below a temperature $T^*(x)$ which depends on doping. The pair of Ising spins per unit-cell represent the directions of the currents in the links of the current loops. The generalizations are the inclusion of anisotropy in the pair-wise nearest neighbor current-current couplings consistent with the symmetries of a square lattice and the next nearest neighbor pair-wise couplings. We use the Binder cumulant to estimate the correlation length exponent $\nu$ and the order parameter exponent $\beta$. Our principal results are that in a range of parameters, the Ashkin-Teller model as well as its generalization has an order parameter susceptibility which diverges as $T \to T^*$ and an order parameter below $T^*$. Importantly, however, there is no divergence in the specific heat. This puts the properties of the model in accord with the experimental results in the underdoped cuprates. We also calculate the magnitude of the "bump" in the specific heat in the critical region to put limits on its observability. Finally, we show that the staggered magnetization couples to the uniform magnetization $M_0$ such that the latter has a weak singularity at $T^*$ and also displays a wide critical region, also in accord with recent experiments.Comment: 14 pages, 19 figures, to appear in Physical Review

Computer vision enables short- and long-term analysis of <i>Lophelia pertusa</i> polyp behaviour and colour from an underwater observatory

An array of sensors, including an HD camera mounted on a Fixed Underwater Observatory (FUO) were used to monitor a cold-water coral (Lophelia pertusa) reef in the Lofoten-Vesterålen area from April to November 2015. Image processing and deep learning enabled extraction of time series describing changes in coral colour and polyp activity (feeding). The image data was analysed together with data from the other sensors from the same period, to provide new insights into the short- and long-term dynamics in polyp features. The results indicate that diurnal variations and tidal current influenced polyp activity, by controlling the food supply. On a longer time-scale, the coral’s tissue colour changed from white in the spring to slightly red during the summer months, which can be explained by a seasonal change in food supply. Our work shows, that using an effective integrative computational approach, the image time series is a new and rich source of information to understand and monitor the dynamics in underwater environments due to the high temporal resolution and coverage enabled with FUOs

Fall risk in an active elderly population – can it be assessed?

BACKGROUND: Falls amongst elderly people are often associated with fractures. Training of balance and physical performance can reduce fall risk; however, it remains a challenge to identify individuals at increased risk of falling to whom this training should be offered. It is believed that fall risk can be assessed by testing balance performance. In this study a test battery of physiological parameters related to balance and falls was designed to address fall risk in a community dwelling elderly population. RESULTS: Ninety-four elderly males and females between 70 and 80 years of age were included in a one year follow-up study. A fall incidence of 15% was reported. The test battery scores were not different between the fallers and non-fallers. Test scores were, however, related to self-reported health. In spite of inclusion of dynamic tests, the test battery had low fall prediction rates, with a sensitivity and specificity of 50% and 43% respectively. CONCLUSION: Individuals with poor balance were identified but falls were not predicted by this test battery. Physiological balance characteristics can apparently not be used in isolation as adequate indicators of fall risk in this population of community dwelling elderly. Falling is a complex phenomenon of multifactorial origin. The crucial factor in relation to fall risk is the redundancy of balance capacity against the balance demands of the individuals levels of fall-risky lifestyle and behavior. This calls for an approach to fall risk assessment in which the physiological performance is evaluated in relation to the activity profile of the individual

Differences in Walking Pattern during 6-Min Walk Test between Patients with COPD and Healthy Subjects

BACKGROUND: To date, detailed analyses of walking patterns using accelerometers during the 6-min walk test (6MWT) have not been performed in patients with chronic obstructive pulmonary disease (COPD). Therefore, it remains unclear whether and to what extent COPD patients have an altered walking pattern during the 6MWT compared to healthy elderly subjects. METHODOLOGY/PRINCIPAL FINDINGS: 79 COPD patients and 24 healthy elderly subjects performed the 6MWT wearing an accelerometer attached to the trunk. The accelerometer features (walking intensity, cadence, and walking variability) and subject characteristics were assessed and compared between groups. Moreover, associations were sought with 6-min walk distance (6MWD) using multiple ordinary least squares (OLS) regression models. COPD patients walked with a significantly lower walking intensity, lower cadence and increased walking variability compared to healthy subjects. Walking intensity and height were the only two significant determinants of 6MWD in healthy subjects, explaining 85% of the variance in 6MWD. In COPD patients also age, cadence, walking variability measures and their interactions were included were significant determinants of 6MWD (total variance in 6MWD explained: 88%). CONCLUSIONS/SIGNIFICANCE: COPD patients have an altered walking pattern during 6MWT compared to healthy subjects. These differences in walking pattern partially explain the lower 6MWD in patients with COPD

Study protocol: differential effects of diet and physical activity based interventions in pregnancy on maternal and fetal outcomes--individual patient data (IPD) meta-analysis and health economic evaluation.

© 2014 Ruifrok et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.BACKGROUND: Pregnant women who gain excess weight are at risk of complications during pregnancy and in the long term. Interventions based on diet and physical activity minimise gestational weight gain with varied effect on clinical outcomes. The effect of interventions on varied groups of women based on body mass index, age, ethnicity, socioeconomic status, parity, and underlying medical conditions is not clear. Our individual patient data (IPD) meta-analysis of randomised trials will assess the differential effect of diet- and physical activity-based interventions on maternal weight gain and pregnancy outcomes in clinically relevant subgroups of women. METHODS/DESIGN: Randomised trials on diet and physical activity in pregnancy will be identified by searching the following databases: MEDLINE, EMBASE, BIOSIS, LILACS, Pascal, Science Citation Index, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, and Health Technology Assessment Database. Primary researchers of the identified trials are invited to join the International Weight Management in Pregnancy Collaborative Network and share their individual patient data. We will reanalyse each study separately and confirm the findings with the original authors. Then, for each intervention type and outcome, we will perform as appropriate either a one-step or a two-step IPD meta-analysis to obtain summary estimates of effects and 95% confidence intervals, for all women combined and for each subgroup of interest. The primary outcomes are gestational weight gain and composite adverse maternal and fetal outcomes. The difference in effects between subgroups will be estimated and between-study heterogeneity suitably quantified and explored. The potential for publication bias and availability bias in the IPD obtained will be investigated. We will conduct a model-based economic evaluation to assess the cost effectiveness of the interventions to manage weight gain in pregnancy and undertake a value of information analysis to inform future research. SYSTEMATIC REVIEW REGISTRATION: PROSPERO 2013: CRD42013003804.This study was funded by the National Institute for Health Research (NIHR) HTA (Health Technology Assessment) UK programme 12/01