Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

We employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent structure ansatz to the Gross-Pitaevskii equation to obtain a parametrically forced Duffing equation describing the spatial dynamics of the condensate. For shallow-well, intermediate-well, and deep-well potentials, we find KAM tori and Aubry-Mather sets to prove that one obtains mostly quasiperiodic dynamics for condensate wave functions of sufficiently large amplitude, where the minimal amplitude depends on the experimentally adjustable BEC parameters. We show that this threshold scales with the square root of the inverse of the two-body scattering length, whereas the rotation number of tori above this threshold is proportional to the amplitude. As a consequence, one obtains the same dynamical picture for lattices of all depths, as an increase in depth essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.Comment: 29 pages, 6 figures (several with multiple parts; higher-quality versions of some of them available at http://www.its.caltech.edu/~mason/papers), to appear very soon in Journal of Nonlinear Scienc

The effect of shoulder stability training on upper limb function and quality of life in patients with hemiplegia

A dissertation submitted to the Faculty of Health Sciences, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Physiotherapy Johannesburg, 2016INTRODUCTION Stroke is a major cause of mortality and long-term adult disability and has a significant physical and psychosocial impact on individuals and their Health-Related Quality of Life (HRQoL). The loss of upper limb function post-stroke directly impacts on shoulder girdle stability of the affected side. Shoulder girdle stability is essential for optimal functioning of the upper limb; good shoulder function is a prerequisite for effective hand function and the execution of the expected tasks with regard to activities of daily living (ADL). It is well known that the rehabilitation of the upper limb post-stroke remains challenging. AIM The aim of the study was to determine the effect of shoulder stability training using the Biodex Balance System (BBS) on shoulder girdle stability, upper-limb function, pain control and HRQoL in patients with hemiplegia post-stroke. METHODS The study utilised a quantitative longitudinal randomised control trial design with single blinding. Participants who met the inclusion criteria and who gave informed consent were assigned to one of two groups, the experimental or the control group, using computer-generated random numbers with concealed allocation. Participants were included in the study if they met the following criteria: were either male or female patients, who had a stroke, resulting in hemiplegia and/or shoulder instability, and were between the ages of 18 and 85 years. In addition to usual care, shoulder girdle stability training using the BBS was given to the participants in the experimental group. Assessments were done at baseline and one, three and six month’s post-baseline. All the participants were assessed by the research assistant using the following: pain measured by the Wong-Baker FACES Pain Rating Scale, the functionality of the upper limb measured by the Fugl-Meyer Assessment Upper Extremity, the shoulder girdle stability measured by the Postural Stability Test on the BBS and HRQoL measured by the SF-36v2 Health Survey. RESULTS AND DISCUSSION A total of 17 participants were included in the main study after screening and, 53% were males. The median age of the study sample was 53 years. The control group comprised more female (n=5) than male (n=2) participants, while the experimental group comprised more male (n=7) than female (n=3) participants. All the participants in the control group were right-handed implying that more of them had their dominant hand affected than those in the experimental group. At baseline the two groups were comparable with regard to shoulder girdle stability, upper limb function and the HRQoL, but were not comparable regarding pain, as the control group experienced significantly more pain than the experimental group. There were no statistically significant differences between the two groups with regard to shoulder girdle stability on any of the three BBS stability levels neither at the baseline (p=0.69) nor at one-month follow-up post-baseline (p=0.77). There was no significant difference in upper limb function (baseline p=0.5, one month follow-up post-baseline p=0.93) between the control and the experimental groups for the entire study period. The severity of the impairment of upper limb function for both the control and the experimental group was comparable at baseline and improved from moderate (56-79) to mild (>79) during the duration of the study. At baseline the participants in the control group already expierienced more pain than the experimental group (p=0.05). Participants in the control group experienced significantly more shoulder pain than the experimental group at the one-month followup (p=0.02), but no differences were found at the three- (p=0.17) and sixmonths( p=0.12) follow-up post-baseline. At baseline a statistically significant difference was found regarding the impact of emotional problems on role limitation (p = 0.03) and pain (p = 0.05) between the two groups, with the control group indicating lower scores than the experimental group. At one month a statistically significant difference was found between the two groups regarding the extent of impaired social functioning (p = 0.05). The participants in the experimental group reported improvement in their health over time (baseline = 67.5 and six-month follow-up post baseline = 86.11). None of the factors investigated in this study impacted on HRQoL outcomes over time. CONCLUSION Shoulder girdle stability training using the BBS did not result in significant improvements in shoulder girdle stability, upper limb function, pain relief and HRQoL post-stroke in this cohort. The findings in this study could have been influenced by the small sample size (the power calculation was done only for the shoulder girdle stability) and also by participants in the control and experimental group continuing with their standard care, which included an intensive rehabilitation programme. This could have been a confounding factor impacting on the outcome. Further research in this field is required.MT201

On the Benefit of Forward Error Correction at IEEE 802.11 Link Layer Level

This study examines the error distribution of aggregated MPDUs in 802.11n networks and whether or not forward error correction like raptor coding at the link layer would be useful in these networks. Several experiments with Qualcomm 4x4 802.11n hardware were performed. Two devices were used in a data link, while a third device sniffed all transmitted packets. The collected data was analyzed and used to calculate the packet error rate which would be obtained if FEC was used in order to determine whether FEC is useful at the link layer. It is shown that the error distribution of A-MPDUs does not follow the binomial distribution. Because of this, the performance of FEC in real networks is worse than for theoretical cases where a binomial distribution is assumed. Therefore, other ways to decrease the packet error rate have more impact than forward error correction

A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEs

This is the published version, also available here: http://dx.doi.org/10.1137/0915058.The authors show that for dynamical systems that possess a type of piecewise hyperbolicity in which there is no decrease in the number of stable modes, the global error in a numerical approximation may be obtained as a reasonable magnification of the local error. In particular, under certain conditions the authors prove the existence of a trajectory on an infinite time interval of the given ordinary differential equation uniformly close to a given numerically computed orbit of the same differential equation by allowing for different initial conditions. For finite time intervals a general result is proved for obtaining a posteriori bounds on the global error based on computable quantities and on finding and bounding the norm of a right inverse of a particular matrix. Two methods for finding and bounding/estimating the norm of a right inverse are considered. One method is based upon the choice of the pseudo or generalized inverse. The other method is based upon solving multipoint boundary value problems (BVPs) with the choice of boundary conditions motivated by the piecewise hyperbolicity concept. Numerical results are presented for the logistic equation, the forced pendulum equation, and the space discretized Chafee–Infante equation

Fast cross-validation for multi-penalty ridge regression

High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of many more complex models and learners, and that allows inclusion of data type specific penalties. The largest challenge for multi-penalty ridge is to optimize these penalties efficiently in a cross-validation (CV) setting, in particular for GLM and Cox ridge regression, which require an additional estimation loop by iterative weighted least squares (IWLS). Our main contribution is a computationally very efficient formula for the multi-penalty, sample-weighted hat-matrix, as used in the IWLS algorithm. As a result, nearly all computations are in low-dimensional space, rendering a speed-up of several orders of magnitude. We developed a flexible framework that facilitates multiple types of response, unpenalized covariates, several performance criteria and repeated CV. Extensions to paired and preferential data types are included and illustrated on several cancer genomics survival prediction problems. Moreover, we present similar computational shortcuts for maximum marginal likelihood and Bayesian probit regression. The corresponding R-package, multiridge, serves as a versatile standalone tool, but also as a fast benchmark for other more complex models and multi-view learners

Short communication: a hierarchy of items within Eysenck’s EPI

Based on the recent finding of a hierarchical scale for Neuroticism in the NEO-Five Factor Inventory, two further personality inventories: the Eysenck Personality Inventory and Goldberg’s International Personality Item Pool were analysed using the Mokken Scaling Procedure for hierarchical scales. Items from two dimensions of the Eysenck Personality Inventory: Neuroticism and Extraversion produced hierarchical scales of 12 and five items, respectively. The Neuroticism items ran from items expressing mild to more extreme worry and the Extraversion items ran from mild sociability to more extreme ‘showing off’. The utility of hierarchical scales in personality measurement is discussed in terms of furthering theoretical understanding of personality and also practical application. In addition, the reasons why only one of these scales should produce hierarchical sets of items is discussed

Fast marginal likelihood estimation of penalties for group-adaptive elastic net

Nowadays, clinical research routinely uses omics data, such as gene expression, for predicting clinical outcomes or selecting markers. Additionally, so-called co-data are often available, providing complementary information on the covariates, like p-values from previously published studies or groups of genes corresponding to pathways. Elastic net penalisation is widely used for prediction and covariate selection. Group-adaptive elastic net penalisation learns from co-data to improve the prediction and covariate selection, by penalising important groups of covariates less than other groups. Existing methods are, however, computationally expensive. Here we present a fast method for marginal likelihood estimation of group-adaptive elastic net penalties for generalised linear models. We first derive a low-dimensional representation of the Taylor approximation of the marginal likelihood and its first derivative for group-adaptive ridge penalties, to efficiently estimate these penalties. Then we show by using asymptotic normality of the linear predictors that the marginal likelihood for elastic net models may be approximated well by the marginal likelihood for ridge models. The ridge group penalties are then transformed to elastic net group penalties by using the variance function. The method allows for overlapping groups and unpenalised variables. We demonstrate the method in a model-based simulation study and an application to cancer genomics. The method substantially decreases computation time and outperforms or matches other methods by learning from co-data.Comment: 16 pages, 6 figures, 1 tabl

Assessing the deterrent effect of symbolic guardianship through neighbourhood watch signs and police signs: a virtual reality study

This study examines the deterrent effects of neighbourhood watch signs and police signs as measures of symbolic guardianship on burglars versus non-offenders. In a virtual reality experiment, 181 burglars and 172 non-offenders scouted a virtual neighbourhood and were exposed to neighbourhood watch signs and/or signs suggesting police surveillance in the area. With neighbourhood watch signs present, both burglars and non-offenders perceived the neighbourhood residents as more likely to intervene. Burglars were also more likely to select a target closer to the exit than non-offenders when neighbourhood watch signs were present. The presence of police signs reduced the time spent scouting and the distance travelled for both burglars and non-offenders. Furthermore, as compared to non-offenders burglars selected houses with easier access, travelled less distance, and reported higher anticipation of neighbourhood resident intervention. Symbolic guardianship through neighbourhood watch or police sign seems to elicit only small effects in deterring burglars. They should not immediately be discounted as preventive measures, however, as small-effect interventions may be valuable as additions to well-established interventions