363 research outputs found

    Common Pairs of Graphs

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    A graph HH is said to be common if the number of monochromatic labelled copies of HH in a red/blue edge colouring of a large complete graph is asymptotically minimized by a random colouring with an equal proportion of each colour. We extend this notion to an asymmetric setting. That is, we define a pair (H1,H2)(H_1,H_2) of graphs to be (p,1p)(p,1-p)-common if a particular linear combination of the density of H1H_1 in red and H2H_2 in blue is asymptotically minimized by a random colouring in which each edge is coloured red with probability pp and blue with probability 1p1-p. We extend many of the results on common graphs to this asymmetric setting. In addition, we obtain several novel results for common pairs of graphs with no natural analogue in the symmetric setting. We also obtain new examples of common graphs in the classical sense and propose several open problems.Comment: 50 page

    Off-Diagonal Commonality of Graphs via Entropy

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    A graph HH is common if the limit as nn\to\infty of the minimum density of monochromatic labelled copies of HH in an edge colouring of KnK_n with red and blue is attained by a sequence of quasirandom colourings. We apply an information-theoretic approach to show that certain graphs obtained from odd cycles and paths via gluing operations are common. In fact, for every pair (H1,H2)(H_1,H_2) of such graphs, there exists p(0,1)p\in(0,1) such that an appropriate linear combination of red copies of H1H_1 and blue copies of H2H_2 is minimized by a quasirandom colouring in which p(n2)p\binom{n}{2} edges are red; such a pair (H1,H2)(H_1,H_2) is said to be (p,1p)(p,1-p)-common. Our approach exploits a strengthening of the common graph property for odd cycles that was recently proved using Schur convexity. We also exhibit a (p,1p)(p,1-p)-common pair (H1,H2)(H_1,H_2) such that H2H_2 is uncommon.Comment: 29 pages. Several results and open problems which appear here appeared in early arXiv versions of the paper 'Common Pairs of Graphs' arXiv:2208.02045 which was later split into two papers, of which this is the secon

    Does a powerlifting inspired exercise programme better compliment pain education compared to bodyweight exercise for people with chronic low back pain? A multicentre, single-blind, randomised controlled trial

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    Background Contemporary management of chronic low back pain involves combined exercise and pain education. Currently, there is a gap in the literature for whether any exercise mode better pairs with pain education. The purpose of this study was to compare general callisthenic exercise with a powerlifting style programme, both paired with consistent pain education, for chronic low back pain. We hypothesised powerlifting style training may better compliment the messages of pain education. Methods An 8-week single-blind randomised controlled trial was conducted comparing bodyweight exercise (n  =  32) with powerlifting (n  =  32) paired with the same education, for people with chronic low back pain. Exercise sessions were one-on-one and lasted 60-min, with the last 5–15 min comprising pain education. Pain, disability, fear, catastrophizing, self-efficacy, anxiety, and depression were measured at baseline, 8-weeks, 3-months, and 6-months. Results No significant between-group differences were observed for pain (p≥0.40), or disability (p≥0.45) at any time-point. Within-group differences were significantly improved for pain (p ≤ 0.04) and disability (p ≤ 0.04) at all time-points for both groups, except 6-month disability in the bodyweight group (p  =  0.1). Behavioural measures explained 39–60% of the variance in changes in pain and disability at each time-point, with fear and self-efficacy emerging as significant in these models (p ≤ 0.001) Conclusions Both powerlifting and bodyweight exercise were safe and beneficial when paired with pain education for chronic low back pain, with reductions in pain and disability associated with improved fear and self-efficacy. This study provides opportunity for practitioners to no longer be constrained by systematic approaches to chronic low back pain

    The role of fear-avoidance beliefs on low back pain-related disability in a developing socioeconomic and conservative culture : a cross-sectional study of a Pakistani population

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    Background: The relationship of low back pain, the world’s top disabling condition, with functional disability is often explained by the mediation effect of fear, catastrophizing, and psychological distress. These relationships have not been explored within chronic back pain patients from a low socio-economic, predominantly Muslim country. Thus, it was unclear whether previously established pathways would be consistent in Pakistani pain patients to help guide Pakistani clinicians caring for back pain patients. This cross-sectional study translated English versions of questionnaires within the fear-avoidance model into Urdu, tested the clini-metric properties of the Urdu versions for people with chronic low back pain (CLBP) in Pakistan, and performed mediation analysis to investigate pathways of the fear-avoidance model. Methods: Translation of questionnaires was completed in 4 steps using the forward-backward technique, with subsequent analyses for internal consistency (Cronbach’s α), construct validity (Pearson’s r-value), and test–retest reliability (ICC r-value). Multiple mediation analysis with bootstrapping was performed to analyze pathways within the fear-avoidance model from the Urdu translated questionnaires. Results: A total of 151 people from Pakistan with CLBP completed the questionnaires, with good results for internal consistency (r > 0.85), convergent validity (r > 0.59), and test–retest reliability (ICC r > 0.85). The association of pain with disability was significant (B=2.36, r2 = 0.19, p = 0.19, p<0.001, and the indirect effect of the mediators explained 81% of pain intensity’s total effect on disability. All mediators, apart from physical activity-related fear-avoidance beliefs, were significant mediators of the effect of pain intensity on disability. Conclusion: The Urdu versions of the fear-avoidance questionnaires show good clini-metric properties for use in clinical settings and research in Pakistan. These analyses support existing data for the mediation effect of catastrophizing, psychological distress, and self-efficacy on pain-related disability, and extends these findings to suggest that fear about work may be more important in a relatively lower socioeconomic sample of pain patients

    Transverse susceptibility study of the effect of varying dipolar interactions on anisotropy peaks in a three-dimensional assembly of soft ferrite nanoparticles

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    Collective magnetization dynamics in nanoparticle assemblies is of current interest as it forms the basis of high density storage media. It is important to understand how interparticle interactions in a three-dimensional (3D) arrangement of superparamagnetic nanoparticles would affect the overall effective magnetic anisotropy of the system. We have studied the influence of varying strengths of dipolar interaction on the static and dynamic magnetic properties of surfactant-coated monodispersed manganese zinc ferrite nanoparticles using reversible transverse susceptibility. We track the evolution of the anisotropy peaks with varying magnetic field, temperature, and interaction strength. The blocking temperature shows an increase from 28 to 32 K and the coercive field (at 10 K) shows an increase from 144 to 192 Oe as the system changes from the case of weakly interacting to strongly interacting 3D assembly of the particles

    Improved bounds for cross-Sperner systems

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    A collection of families (F1,F2,⋯,Fk)∈P([n])k is cross-Sperner if there is no pair i≠j for which some Fi∈Fi is comparable to some Fj∈Fj. Two natural measures of the 'size' of such a family are the sum ∑ki=1|Fi| and the product ∏ki=1|Fi|. We prove new upper and lower bounds on both of these measures for general n and k≥2 which improve considerably on the previous best bounds. In particular, we construct a rich family of counterexamples to a conjecture of Gerbner, Lemons, Palmer, Patkós, and Szécsi from 2011

    Reductions in movement-associated fear are dependent upon graded exposure in chronic low back pain : an exploratory analysis of a modified 3-item fear hierarchy

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    Objective: To explore the effectiveness of a modified fear hierarchy on measuring improvements in movement-associated fear in chronic low back pain. Methods: A modified 3-item fear hierarchy was created and implemented based on principles of graded exposure. This study was an exploratory analysis of the modified 3-item fear hierarchy from a larger clinical trial data set. Both groups received pain education and exercise, either bodyweight or strength training. Both groups performed item one on the hierarchy, the squat. Only the strength training group performed item 2, the deadlift. Neither group performed item 3, the overhead press. Analysis of Covariance and stepwise linear regression were used to explore results. Results: Improvement in movement-associated fear was conditional upon graded exposure. Both groups improved in the squat movement (p ≤ 0.05), which both performed. Only the strength training group improved in the deadlift (p ≤ 0.01), and neither improved in the overhead press (p ≥ 0.05). Conclusion: Reductions in movement-associated fear are conditional upon graded exposure, based on the use of a novel modified 3-item fear hierarchy. Further research is needed to understand the utility of this tool in a patient-led approach to co-designing a graded exposure-based intervention

    Comparing usage of a web and app stress management intervention : an observational study

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    Choices in the design and delivery of digital health behaviour interventions may have a direct influence on subsequent usage and engagement. Few studies have been able to make direct, detailed comparisons of differences in usage between interventions that are delivered via web or app. This study compared the usage of two versions of a digital stress management intervention, one delivered via a website (Healthy Paths) and the other delivered via an app (Healthy Mind). Design modifications were introduced within Healthy Mind to take account of reported differences in how individuals engage with websites compared to apps and mobile phones. Data were collected as part of an observational study nested within a broader exploratory trial of Healthy Mind. Objective usage of Healthy Paths and Healthy Mind were automatically recorded, including frequency and duration of logins, access to specific components within the intervention and order of page/screen visits. Usage was compared for a two week period following initial registration. In total, 381 participants completed the registration process for Healthy Paths (web) and 162 participants completed the registration process for Healthy Mind (app). App users logged in twice as often (Mdn = 2.00) as web users (Mdn = 1.00), U = 13,059.50, p ≤ 0.001, but spent half as much time (Mdn = 5.23 min) on the intervention compared to web users (Mdn = 10.52 min), U = 19,740.00, p ≤ 0.001. Visual exploration of usage patterns over time revealed that a significantly higher proportion of app users (n = 126, 82.35%) accessed both types of support available within the intervention (i.e. awareness and change-focused tools) compared to web users (n = 92, 40.17%), χ2(1, n = 382) = 66.60, p < 0.001. This study suggests that the digital platform used to deliver an intervention (i.e. web versus app) and specific design choices (e.g. navigation, length and volume of content) may be associated with differences in how the intervention content is used. Broad summative usage data (e.g. total time spent on the intervention) may mask important differences in how an intervention is used by different user groups if it is not complemented by more fine-grained analyses of usage patterns over time. Trial registration number: ISRCTN67177737
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