Momentum transferred to a trapped Bose-Einstein condensate by stimulated light scattering

The response of a trapped Bose-Einstein condensed gas to a density perturbation generated by a two-photon Bragg pulse is investigated by solving the time-dependent Gross-Pitaevskii equation. We calculate the total momentum imparted to the condensate as a function of both the time duration of the pulse and the frequency difference of the two laser beams. The role of the dynamic response function in characterizing the time evolution of the system is pointed out, with special emphasis to the phonon regime. Numerical simulations are compared with the predictions of local density approximation. The relevance of our results for the interpretation of current experiments is also discussed.Comment: 7 pages, 3 postscript figure

Limit of vanishing regulator in the functional renormalization group

The nonperturbative functional renormalization group equation depends on the choice of a regulator function, whose main properties are a "coarse-graining scale"k and an overall dimensionless amplitude a. In this paper we shall discuss the limit a→0 with k fixed. This limit is closely related to the pseudoregulator that reproduces the beta functions of the MS¯ scheme that we studied in a previous paper. It is not suitable for precision calculations but it appears to be useful to eliminate the spurious breaking of symmetries by the regulator, both for nonlinear models and within the background field method

Functional renormalization and the MS scheme

Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can be seen as nonperturbative extensions of the MS scheme. We support this claim by recovering all the multicritical models in two dimensions. We discuss a possible generalization to any dimension. Finally, we show that the method also preserves nonlinearly realized symmetries, which is a definite advantage with respect to other regulators

Geometric rescaling algorithms for submodular function minimization

We present a new class of polynomial-time algorithms for submodular function minimization (SFM) as well as a unified framework to obtain strongly polynomial SFM algorithms. Our algorithms are based on simple iterative methods for the minimum-norm problem, such as the conditional gradient and Fujishige–Wolfe algorithms. We exhibit two techniques to turn simple iterative methods into polynomial-time algorithms. First, we adapt the geometric rescaling technique, which has recently gained attention in linear programming, to SFM and obtain a weakly polynomial bound O((n4 · EO + n5)log(nL)). Second, we exhibit a general combinatorial black box approach to turn εL-approximate SFM oracles into strongly polynomial exact SFM algorithms. This framework can be applied to a wide range of combinatorial and continuous algorithms, including pseudo-polynomial ones. In particular, we can obtain strongly polynomial algorithms by a repeated application of the conditional gradient or of the Fujishige–Wolfe algorithm. Combined with the geometric rescaling technique, the black box approach provides an O((n5 · EO + n6)log2n) algorithm. Finally, we show that one of the techniques we develop in the paper can also be combined with the cutting-plane method of Lee et al., yielding a simplified variant of their O(n3log2n · EO + n4logO(1)n) algorithm

Rescaling algorithms for linear conic feasibility

We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix A ∈ R m× n, the kernel problem requires a positive vector in the kernel of A, and the image problem requires a positive vector in the image of A T. Both algorithms iterate between simple first-order steps and rescaling steps. These rescalings improve natural geometric potentials. If Goffin's condition measure ρ A is negative, then the kernel problem is feasible, and the worst-case complexity of the kernel algorithm is O((m 3n + mn 2)log|ρ A| −1); if ρ A > 0, then the image problem is feasible, and the image algorithm runs in time O(m 2n 2 log ρ A −1). We also extend the image algorithm to the oracle setting. We address the degenerate case ρA = 0 by extending our algorithms to find maximum support nonnegative vectors in the kernel of A and in the image of A T. In this case, the running time bounds are expressed in the bit-size model of computation: for an input matrix A with integer entries and total encoding length L, the maximum support kernel algorithm runs in time O((m 3n + mn 2)L), whereas the maximum support image algorithm runs in time O(m 2n 2L). The standard linear programming feasibility problem can be easily reduced to either maximum support problems, yielding polynomial-time algorithms for linear programming

Good Sleep Quality Improves the Relationship Between Pain and Depression Among Individuals With Chronic Pain

Individuals with chronic pain often experience co-existing sleep problems and depression-related states. Chronic pain, sleep problems, and depression interrelate, and have been shown to exacerbate one another, which negatively impacts quality of life. This study explored the relationships between pain severity, pain interference, sleep quality, and depression among individuals with chronic pain. Secondly, we tested whether sleep quality may moderate the relationship between pain and depression. A cross-sectional survey was completed by 1,059 adults with non-malignant chronic pain conditions (Mage 43 years, 88% identified as women) and collected measures related to pain severity, pain interference, sleep quality and depression. Multiple regression analyses found that pain severity, pain interference and sleep quality are all significantly associated with depression. Secondly, moderated regression analyses revealed that sleep quality moderates the relationship between pain interference and depression among individuals with chronic pain such that good sleep quality attenuates the effect of pain interference on depression, and poor sleep quality amplifies the effect of pain interference on depression. These findings suggest that sleep quality may be a relevant therapeutic target for individuals with chronic pain and co-existing depression

On finding exact solutions of linear programs in the oracle model

We consider linear programming in the oracle model: mincT x s.t. x ∊ P, where the polyhedron P = {x ∊ ℝn: Ax ≤ b} is given by a separation oracle that returns violated inequalities from the system Ax ≤ b. We present an algorithm that finds exact primal and dual solutions using O(n2 log(n/δ)) oracle calls and O(n4 log(n/δ) + n6 log log(1/δ)) arithmetic operations, where δ is a geometric condition number associated with the system (A, b). These bounds do not depend on the cost vector c. The algorithm works in a black box manner, requiring a subroutine for approximate primal and dual solutions; the above running times are achieved when using the cutting plane method of Jiang, Lee, Song, and Wong (STOC 2020) for this subroutine. Whereas approximate solvers may return primal solutions only, we develop a general framework for extracting dual certificates based on the work of Burrell and Todd (Math. Oper. Res. 1985). Our algorithm works in the real model of computation, and extends results by Grötschel, Lovász, and Schrijver (Prog. Comb. Opt. 1984), and by Frank and Tardos (Combinatorica 1987) on solving LPs in the bit-complexity model. We show that under a natural assumption, simultaneous Diophantine approximation in these results can be avoided

Acute impact of a national lockdown during the COVID-19 pandemic on wellbeing outcomes among individuals with chronic pain

Changes to wellbeing in a community- based sample of 638 adults with non-malignant chronic pain were assessed during a period of mandated lockdown measures in the UK to control the COVID-19 outbreak. Participants completed an online survey pre-lockdown and were followed up during lockdown. Multivariate analysis demonstrate that decreased ability to self-manage, restricted access to healthcare and increased dependence on others were associated with negative wellbeing outcomes related to sleep, anxiety and depression. Essential but nonurgent services are required during periods of lockdown to maintain independence and self-management in order to preserve wellbeing in this population

Residual hip dysplasia in children: osseous and cartilaginous acetabular angles to guide further treatment-a pilot study.

In case of residual hip dysplasia (RHD) in children, pelvic radiographs are sometimes insufficient to precisely evaluate the entire coverage of the femoral head, when trying to decide on the need for further reconstructive procedures. This study retrospectively compares the bony and the cartilaginous acetabular angle of Hilgenreiner (HTE) of 60 paediatric hips on pelvic MRI separated in two groups. Group 1 included 31 hips with RHD defined by a bony HTE > 20°. Group 2 included 27 hips with a HTE < 20°. They were compared by introducing a new ratio calculated from the square of cartilaginous HTE above the bony HTE on frontal MRI. The normal upper limit for this acetabular angle ratio was extrapolated from the published normal values of cartilaginous HTE and bony HTE in children. The acetabular angle ratio was statistically significantly increased in the hips with RHD with a mean value of 7.1 ± 4.7 compared to the hips in the control group presenting a mean value of 2.1 ± 1.9 (p < 0.00001). This newly introduced ratio seems to be a helpful tool to orientate the further treatment in children presenting borderline RHD

The Impact of the COVID-19 Pandemic on Students’ Mental Health and Sleep in Saudi Arabia

BACKGROUND: Mental health problems are prevalent among university students in Saudi Arabia. This study aimed to investigate the impact of the COVID-19 pandemic on university students’ mental health and sleep in Saudi Arabia. Method: A total of 582 undergraduate students from Saudi Arabia aged between 18 and 45 years old (M = 20.91, SD = 3.17) completed a cross-sectional online questionnaire measuring depression, anxiety, stress, resilience, and insomnia during the COVID-19 pandemic (2020). Analysis included an independent samples t-test, one-way ANOVA, and Hierarchical regression analysis. RESULTS: Undergraduate students reported high levels of depression, anxiety, and perceived stress and low levels of resilience (p < 0.001) during the pandemic. In addition, students reported experiencing insomnia. A hierarchical regression analysis indicated that lower resilience, high levels of insomnia, having a pre-existing mental health condition, and learning difficulties (such as dyslexia, dyspraxia, or dyscalculia) were significantly associated with high levels of depression and stress. In addition, lower resilience, a high level of insomnia, and pre-existing mental health conditions were significantly associated with high levels of anxiety. Finally, a lower level of psychological resilience and a high level of insomnia were significantly associated with increased levels of depression, anxiety and stress within university students. CONCLUSION: This study has provided evidence that a lower level of psychological resilience and insomnia were associated with mental health problems among undergraduate students in Saudi Arabia, thus enhancing psychological resilience and interventions to support sleep and mental health are vital to support student well-being outcomes throughout the pandemic