Relaxed phylogenetics and dating with confidence

In phylogenetics, the unrooted model of phylogeny and the strict molecular clock model are two extremes of a continuum. Despite their dominance in phylogenetic inference, it is evident that both are biologically unrealistic and that the real evolutionary process lies between these two extremes. Fortunately, intermediate models employing relaxed molecular clocks have been described. These models open the gate to a new field of “relaxed phylogenetics.” Here we introduce a new approach to performing relaxed phylogenetic analysis. We describe how it can be used to estimate phylogenies and divergence times in the face of uncertainty in evolutionary rates and calibration times. Our approach also provides a means for measuring the clocklikeness of datasets and comparing this measure between different genes and phylogenies. We find no significant rate autocorrelation among branches in three large datasets, suggesting that autocorrelated models are not necessarily suitable for these data. In addition, we place these datasets on the continuum of clocklikeness between a strict molecular clock and the alternative unrooted extreme. Finally, we present analyses of 102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate alignments. From these we conclude that our method is phylogenetically more accurate and precise than the traditional unrooted model while adding the ability to infer a timescale to evolution.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.

A 2-h diagnostic protocol to assess patients with chest pain symptoms in the Asia-Pacific region (ASPECT): a prospective observational validation study

Background: Patients with chest pain contribute substantially to emergency department attendances, lengthy hospital stay, and inpatient admissions. A reliable, reproducible, and fast process to identify patients presenting with chest pain who have a low short-term risk of a major adverse cardiac event is needed to facilitate early discharge. We aimed to prospectively validate the safety of a predefined 2-h accelerated diagnostic protocol (ADP) to assess patients presenting to the emergency department with chest pain symptoms suggestive of acute coronary syndrome. Methods: This observational study was undertaken in 14 emergency departments in nine countries in the Asia-Pacific region, in patients aged 18 years and older with at least 5 min of chest pain. The ADP included use of a structured pre-test probability scoring method (Thrombolysis in Myocardial Infarction [TIMI] score), electrocardiograph, and point-of-care biomarker panel of troponin, creatine kinase MB, and myoglobin. The primary endpoint was major adverse cardiac events within 30 days after initial presentation (including initial hospital attendance). This trial is registered with the Australia-New Zealand Clinical Trials Registry, number ACTRN12609000283279. Findings: 3582 consecutive patients were recruited and completed 30-day follow-up. 421 (11•8%) patients had a major adverse cardiac event. The ADP classified 352 (9•8%) patients as low risk and potentially suitable for early discharge. A major adverse cardiac event occurred in three (0•9%) of these patients, giving the ADP a sensitivity of 99•3% (95% CI 97•9–99•8), a negative predictive value of 99•1% (97•3–99•8), and a specificity of 11•0% (10•0–12•2). Interpretation: This novel ADP identifies patients at very low risk of a short-term major adverse cardiac event who might be suitable for early discharge. Such an approach could be used to decrease the overall observation periods and admissions for chest pain. The components needed for the implementation of this strategy are widely available. The ADP has the potential to affect health-service delivery worldwide.

Multi-method, multi-theoretical, multi-level research in the learning sciences

We examine methodologies and methods that apply to multi-level research in the learning sciences. In so doing we describe how multiple theoretical frameworks informs the use of different methods that apply to social levels involving space-time relationships that are not accessible consciously as social life is enacted. Most of the methods involve analyses of video and audio files. Within a framework of interpretive research we present a methodology of event-oriented social science, which employs video ethnography, narrative, conversation analysis, prosody analysis, and facial expression analysis. We illustrate multi-method research in an examination of the role of emotions in teaching and learning. Conversation and prosody analyses augment facial expression analysis and ethnography. We conclude with an exploration of ways in which multi-level studies can be complemented with neural level analyses.

Intuitionistic fuzzy Choquet integral operator-based approach for black-start decision-making

Determining the optimal of black-start strategies is very important for speeding the restoration speed of a power system after a global blackout. Most existing black-start decision-making methods are based on the assumption that all indexes are independent of each other, and little attention has been paid to the group decision-making method which is more reliable. Given this background, the intuitionistic fuzzy set and further intuitionistic fuzzy Choquet integral operator are presented, and a black-start decision-making method based on this integral operator is presented. Compared to existing methods, the proposed algorithm cannot only deal with the relevance among the indexes, but also overcome some shortcomings of the existing methods. Finally, an example is used to demonstrate the proposed method. © 2012 The Institution of Engineering and Technology.

Non-invasive method for detecting changes in soil moisture using wireless sensor networks

There are several popular soil moisture measurement methods today such as time domain reflectometry, electromagnetic (EM) wave, electrical and acoustic methods. Significant studies have been dedicated in developing method of measurements using those concepts, especially to achieve the characteristics of noninvasiveness. EM wave method provides an advantage because it is non-invasive to the soil and does not need to utilise probes to penetrate or bury in the soil. But some EM methods are also too complex, expensive, and not portable for the application of Wireless Sensor Networks; for example satellites or UAV (Unmanned Aerial Vehicle) based sensors. This research proposes a method in detecting changes in soil moisture using soil-reflected electromagnetic (SREM) wave from Wireless Sensor Networks (WSNs). Studies have shown that different levels of soil moisture will affects soil’s dielectric properties, such as relative permittivity and conductivity, and in turns change its reflection coefficients. The SREM wave method uses a transmitter adjacent to a WSNs node with purpose exclusively to transmit wireless signals that will be reflected by the soil. The strength from the reflected signal that is determined by the soil’s reflection coefficients is used to differentiate the level of soil moisture. The novel nature of this method comes from using WSNs communication signals to perform soil moisture estimation without the need of external sensors or invasive equipment. This innovative method is non-invasive, low cost and simple to set up. There are three locations at Brisbane, Australia chosen as the experiment’s location. The soil type in these locations contains 10–20% clay according to the Australian Soil Resource Information System. Six approximate levels of soil moisture (8, 10, 13, 15, 18 and 20%) are measured at each location; with each measurement consisting of 200 data. In total 3600 measurements are completed in this research, which is sufficient to achieve the research objective, assessing and proving the concept of SREM wave method. These results are compared with reference data from similar soil type to prove the concept. A fourth degree polynomial analysis is used to generate an equation to estimate soil moisture from received signal strength as recorded by using the SREM wave method.

Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.

RCA method for fault diagnosis in digital substations of power systems

The authors present a Cause-Effect fault diagnosis model, which utilises the Root Cause Analysis approach and takes into account the technical features of a digital substation. The Dempster/Shafer evidence theory is used to integrate different types of fault information in the diagnosis model so as to implement a hierarchical, systematic and comprehensive diagnosis based on the logic relationship between the parent and child nodes such as transformer/circuit-breaker/transmission-line, and between the root and child causes. A real fault scenario is investigated in the case study to demonstrate the developed approach in diagnosing malfunction of protective relays and/or circuit breakers, miss or false alarms, and other commonly encountered faults at a modern digital substation.

Investigating the potential value of individual parameters of histological grading systems in a sheep model of cartilage damage : the modified Mankin method

A total histological grade does not necessarily distinguish between different manifestations of cartilage damage or degeneration. An accurate and reliable histological assessment method is required to separate normal and pathological tissue within a joint during treatment of degenerative joint conditions and to sub-classify the latter in meaningful ways. The Modified Mankin method may be adaptable for this purpose. We investigated how much detail may be lost by assigning one composite score/grade to represent different degenerative components of the osteoarthritic condition. We used four ovine injury models (sham surgery, anterior cruciate ligament/medial collateral ligament instability, simulated anatomic anterior cruciate ligament reconstruction and meniscal removal) to induce different degrees and potentially 'types' (mechanisms) of osteoarthritis. Articular cartilage was systematically harvested, prepared for histological examination and graded in a blinded fashion using a Modified Mankin grading method. Results showed that the possible permutations of cartilage damage were significant and far more varied than the current intended use that histological grading systems allow. Of 1352 cartilage specimens graded, 234 different manifestations of potential histological damage were observed across 23 potential individual grades of the Modified Mankin grading method. The results presented here show that current composite histological grading may contain additional information that could potentially discern different stages or mechanisms of cartilage damage and degeneration in a sheep model. This approach may be applicable to other grading systems.

Evolutionary design of bone scaffolds with reference to material selection

The favourable scaffold for bone tissue engineering should have desired characteristic features, such as adequate mechanical strength and three-dimensional open porosity, which guarantee a suitable environment for tissue regeneration. In fact, the design of such complex structures like bone scaffolds is a challenge for investigators. One of the aims is to achieve the best possible mechanical strength-degradation rate ratio. In this paper we attempt to use numerical modelling to evaluate material properties for designing bone tissue engineering scaffold fabricated via the fused deposition modelling technique. For our studies the standard genetic algorithm was used, which is an efficient method of discrete optimization. For the fused deposition modelling scaffold, each individual strut is scrutinized for its role in the architecture and structural support it provides for the scaffold, and its contribution to the overall scaffold was studied. The goal of the study was to create a numerical tool that could help to acquire the desired behaviour of tissue engineered scaffolds and our results showed that this could be achieved efficiently by using different materials for individual struts. To represent a great number of ways in which scaffold mechanical function loss could proceed, the exemplary set of different desirable scaffold stiffness loss function was chosen. © 2012 John Wiley & Sons, Ltd.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.