Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Quality of work life and turnover intention in primary healthcare organisations : a cross-sectional study of registered nurses in Saudi Arabia

Purpose: The purpose of this study was to improve the retention of primary healthcare (PHC) nurses through exploring and assessing their quality of work life (QWL) and turnover intention. Design and methods: A cross-sectional survey design was used in this study. Data were collected using a questionnaire comprising four sections (Brooks’ survey of Quality of Nursing Work Life [QNWL], Anticipated Turnover Intention, open-ended questions and demographic characteristics). A convenience sample was recruited from 143 PHC centres in Jazan, Saudi Arabia. A response rate of 87% (n = 508/585) was achieved. The SPSS v17 for Windows and NVivo 8 were used for analysis purposes. Procedures and tests used in this study to analyse the quantitative data were descriptive statistics, t-test, ANOVA, General Linear Model (GLM) univariate analysis, standard multiple regression, and hierarchical multiple regression. Qualitative data obtained from responses to the open-ended questions were analysed using the NVivo 8. Findings: Quantitative findings suggested that PHC nurses were dissatisfied with their work life. Respondents’ scores ranged between 45 and 218 (mean = 139.45), which is lower than the average total score on Brooks’ Survey (147). Major influencing factors were classified under four dimensions. First, work life/home life factors: unsuitable working hours, lack of facilities for nurses, inability to balance work with family needs and inadequacy of vacations’ policy. Second, work design factors: high workload, insufficient workforce numbers, lack of autonomy and undertaking many non-nursing tasks. Third, work context factors: management practices, lack of development opportunities, and inappropriate working environment in terms of the level of security, patient care supplies and unavailability of recreation room. Finally, work world factors: negative public image of nursing, and inadequate payment. More positively, nurses were notably satisfied with their co-workers. Conversely, 40.4% (n = 205) of the respondents indicated that they intended to leave their current employment. The relationships between QWL and demographic variables of gender, age, marital status, dependent children, dependent adults, nationality, ethnicity, nursing tenure, organisational tenure, positional tenure, and payment per month were significant (p < .05). The eta squared test for these demographics indicates a small to medium effect size of the variation in QWL scores. Using the GLM univariate analysis, education level was also significantly related to the QWL (p < .05). The relationships between turnover intention and demographic variables including gender, age, marital status, dependent children, education level, nursing tenure, organisational tenure, positional tenure, and payment per month were significant (p < .05). The eta squared test for these demographics indicates a small to moderate effect size of the variation in the turnover intention scores. Using the GLM univariate analysis, the dependent adults’ variable was also significantly related to turnover intention (p < .05). Turnover intention was significantly related to QWL. Using standard multiple regression, 26% of the variance in turnover intention was explained by the QWL F (4,491), 43.71, p < .001, with R² = .263. Further analysis using hierarchical multiple regression found that the total variance explained by the model as a whole (demographics and QWL) was 32.1%, F (17.433) = 12.04, p < .001. QWL explained an additional 19% of the variance in turnover intention, after controlling for demographic variables, R squared change =.19, F change (4, 433) = 30.190, p < .001. The work context variable makes the strongest unique contribution (-.387) to explain the turnover intention, followed by the work design dimension (-.112). The qualitative findings reaffirmed the quantitative findings in terms of QWL and turnover intention. However, the home life/work life and work world dimensions were of great important to both QWL and turnover intention. The qualitative findings revealed a number of new factors that were not included in the survey questionnaire. These included being away from family, lack of family support, social and cultural aspects, accommodation facilities, transportation, building and infrastructure of PHC, nature of work, job instability, privacy at work, patients and community, and distance between home and workplace. Conclusion: Creating and maintaining a healthy work life for PHC nurses is very important to improve their work satisfaction, reduce turnover, enhance productivity and improve nursing care outcomes. Improving these factors could lead to a higher QWL and increase retention rates and therefore reinforcing the stabilisation of the nursing workforce. Significance of the research: Many countries are examining strategies to attract and retain the health care workforce, particularly nurses. This study identified factors that influence the QWL of PHC nurses as well as their turnover intention. It also determined the significant relationship between QWL and turnover intention. In addition, the present study tested Brooks’ survey of QNWL on PHC nurses for the first time. The qualitative findings of this study revealed a number of new variables regarding QWL and turnover intention of PHC nurses. These variables could be used to improve current survey instruments or to develop new research surveys. The study findings could be also used to develop and appropriately implement plans to improve QWL. This may help to enhance the home and work environments of PHC nurses, improve individual and organisational performance, and increase nurses’ commitment. This study contributes to the existing body of research knowledge by presenting new data and findings from a different country and healthcare system. It is the first of its kind in Saudi Arabia, especially in the field of PHC. It has examined the relationship between QWL and turnover intention of PHC nurses for the first time using nursing instruments. The study also offers a fresh explanation (new framework) of the relationship between QWL and turnover intention among PHC nurses, which could be used or tested by researchers in other settings. Implications for further research: Review of the extant literature reveals little in-depth research on the PHC workforce, especially in terms of QWL and organisational turnover in developing countries. Further research is required to develop a QWL tool for PHC nurses, taking into consideration the findings of the current study along with the local culture. Moreover, the revised theoretical framework of the current study could be tested in further research in other regions, countries or healthcare systems in order to identify its ability to predict the level of PHC nurses’ QWL and their intention to leave. There is a need to conduct longitudinal research on PHC organisations to gain an in-depth understanding of the determents of and changes in QWL and turnover intention of PHC nurses at various points of time. An intervention study is required to improve QWL and retention among PHC nurses using the findings of the current study. This would help to assess the impact of such strategies on reducing turnover of PHC nurses. Focusing on the location of the current study, it would be valuable to conduct another study in five years’ time to examine the percentage of actual turnover among PHC nurses compared with the reported turnover intention in the current study. Further in-depth research would also be useful to assess the impact of the local culture on the perception of expatriate nurses towards their QWL and their turnover intention. A comparative study is required between PHC centres and hospitals as well as the public and private health sector agencies in terms of QWL and turnover intention of nursing personnel. Findings may differ from sector to sector according to variations in health systems, working environments and the case mix of patients.

Intensity dependent residual amplitude modulation in electro-optic phase modulators

Residual amplitude modulation (RAM) mechanisms in electro-optic phase modulators are detrimental in applications that require high purity phase modulation of the incident laser beam. While the origins of RAMare not fully understood, measurements have revealed that it depends on the beam properties of the laser as well as the properties of the medium. Here we present experimental and theoretical results that demonstrate, for the first time, the dependence of RAM production in electro-optic phase modulators on beam intensity. The results show an order of magnitude increase in the level of RAM, around 10 dB, with a fifteenfold enhancement in the input intensity from 12 to 190 mW/mm 2. We show that this intensity dependent RAM is photorefractive in origin. © 2012 Optical Society of America.

Polarization dependent photorefractive amplitude modulation production in MgO:LiNbO 3 phase modulators

We present experimental and theoretical results of the intensity dependence of residual amplitude modulation (RAM) production in electro-optic phase modulators. By utilizing the anisotropy of the medium, we show that RAM has a photorefractive origin.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Single-subject analysis reveals variation in knee mechanics during step landing

Introduction: Evidence concerning the alteration of knee function during landing suffers from a lack of consensus. This uncertainty can be attributed to methodological flaws, particularly in relation to the statistical analysis of variable human movement data. Aim: The aim of this study was to compare single-subject and group analysis in quantifying alterations in the magnitude and within-participant variability of knee mechanics during a step landing task. Methods: A group of healthy men (N = 12) stepped-down from a knee-high platform for 60 consecutive trials, each trial separated by a 1-minute rest. The magnitude and within-participant variability of sagittal knee stiffness and coordination of the landing leg during the immediate postimpact period were evaluated. Coordination of the knee was quantified in the sagittal plane by calculating the mean absolute relative phase of sagittal shank and thigh motion (MARP1) and between knee rotation and knee flexion (MARP2). Changes across trials were compared between both group and single-subject statistical analyses. Results: The group analysis detected significant reductions in MARP1 magnitude. However, the single-subject analyses detected changes in all dependent variables, which included increases in variability with task repetition. Between-individual variation was also present in the timing, size and direction of alterations to task repetition. Conclusion: The results have important implications for the interpretation of existing information regarding the adaptation of knee mechanics to interventions such as fatigue, footwear or landing height. It is proposed that a familiarisation session be incorporated in future experiments on a single-subject basis prior to an intervention.