Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Role of enhanced vector transmission of a new West Nile virus strain in an outbreak of equine disease in Australia in 2011

Background In 2011, a variant of West Nile virus Kunjin strain (WNVKUN) caused an unprecedented epidemic of neurological disease in horses in southeast Australia, resulting in almost 1,000 cases and a 9% fatality rate. We investigated whether increased fitness of the virus in the primary vector, Culex annulirostris, and another potential vector, Culex australicus, contributed to the widespread nature of the outbreak. Methods Mosquitoes were exposed to infectious blood meals containing either the virus strain responsible for the outbreak, designated WNVKUN2011, or WNVKUN2009, a strain of low virulence that is typical of historical strains of this virus. WNVKUN infection in mosquito samples was detected using a fixed cell culture enzyme immunoassay and a WNVKUN- specific monoclonal antibody. Probit analysis was used to determine mosquito susceptibility to infection. Infection, dissemination and transmission rates for selected days post-exposure were compared using Fisher’s exact test. Virus titers in bodies and saliva expectorates were compared using t-tests. Results There were few significant differences between the two virus strains in the susceptibility of Cx. annulirostris to infection, the kinetics of virus replication and the ability of this mosquito species to transmit either strain. Both strains were transmitted by Cx. annulirostris for the first time on day 5 post-exposure. The highest transmission rates (proportion of mosquitoes with virus detected in saliva) observed were 68% for WNVKUN2011 on day 12 and 72% for WNVKUN2009 on day 14. On days 12 and 14 post-exposure, significantly more WNVKUN2011 than WNVKUN2009 was expectorated by infected mosquitoes. Infection, dissemination and transmission rates of the two strains were not significantly different in Culex australicus. However, transmission rates and the amount of virus expectorated were significantly lower in Cx. australicus than Cx. annulirostris. Conclusions The higher amount of WNVKUN2011 expectorated by infected mosquitoes may be an indication that this virus strain is transmitted more efficiently by Cx. annulirostris compared to other WNVKUN strains. Combined with other factors, such as a convergence of abundant mosquito and wading bird populations, and mammalian and avian feeding behaviour by Cx. annulirostris, this may have contributed to the scale of the 2011 equine epidemic.

Street-level perceptions of procedural rights for young unemployed people - a comparative study between Sweden and Australia

Two types of welfare states are compared in this article. Differences in procedural rights for young unemployed at the level of service delivery are analyzed. In Australia, rights are regulated through a rigid procedural justice system. The young unemployed within the social assistance system in Sweden encounter staff with high discretionary powers, which makes the legal status weak for the unemployed but, on the other hand, the system is more flexible. Despite the differences, there is striking convergence in how the young unemployed describe how discretionary power among street-level staff affects their procedural rights. This result can be understood as a result of similar professional norms, work customs and occupational cultures of street-level staff, and that there is a basic logic of conditionality in all developed welfare states where procedural rights are tightly coupled with responsibilities.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/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 a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Conceptualising recognition of prior learning processes in the age of open learning

This chapter interrogates what recognition of prior learning (RPL) can and does mean in the higher education sector—a sector in the grip of the widening participation agenda and an open access age. The chapter discusses how open learning is making inroads into recognition processes and examines two studies in open learning recognition. A case study relating to e-portfolio-style RPL for entry into a Graduate Certificate in Policy and Governance at a metropolitan university in Queensland is described. In the first instance, candidates who do not possess a relevant Bachelor degree need to demonstrate skills in governmental policy work in order to be eligible to gain entry to a Graduate Certificate (at Australian Qualifications Framework Level 8) (Australian Qualifications Framework Council, 2013, p. 53). The chapter acknowledges the benefits and limitations of recognition in open learning and those of more traditional RPL, anticipating future developments in both (or their convergence).

Editorial of "Communication Research and Practice, 1(3)"

For the third issue of Communication Research and Practice, we bring together a mix of submitted content and papers presented at events that were hosted under the auspices of the International Communication Association. Dal Yong Jin captures the dynamic and contradictory elements of both convergence and transmedia storytelling, and the ‘Korean Wave’, in his paper on webtoons. Exploring this distinctive online form of transmedia storytelling, Jin considers its evolution from the perspectives of digital content, political economy, convergent media and digital labour, and the tensions that surround its potential expansion into global cultural markets.

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Some limit theorems for regenerative queues

We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams

A new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial. These new shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. The natural frequencies predicted by the proposed element are compared with an element with stiff-string, cubic polynomial and quintic polynomial shape functions. It is found that the new element exhibits superior convergence compared to the other basis functions.

Hingeless-rotor aeromechanical stability in axial and forward flight with wake dynamics

A finite-state wake model is used to investigate aeromechanical stability of hingeless-rotor helicopters in the ground-contact, hover and trimmed-night conditions. The investigation covers three items: (1) the convergence of the damping with increasing number of wake harmonics for the lag regressing, and body pitch and roll modes; (2) a parametric study of the damping over a range of thrust level, advance ratio and number of blades; and (3) correlations, primarily with the damping and frequency measurements of these lag and body modes. The convergence and parametric studies are conducted in the hover and trimmed-flight conditions; they include predictions from the widely used dynamic inflow model. The correlations are conducted in the ground-contact conditions and include predictions from the dynamic inflow and vortex models; recently, this vortex model is proposed for the axial-flight conditions and is used to investigate the coupled free vibrations of rotor flapping and body modes. The convergence and parametric studies show that a finite-state wake model that goes well beyond the dynamic inflow model is required for fairly converged damping, Moreover, the correlations from the finite-state wake, dynamic inflow and vortex models are generally satisfactory.

Convergent evolution of marine mammals is associated with distinct substitutions in common genes

Phenotypic convergence is thought to be driven by parallel substitutions coupled with natural selection at the sequence level. Multiple independent evolutionary transitions of mammals to an aquatic environment offer an opportunity to test this thesis. Here, whole genome alignment of coding sequences identified widespread parallel amino acid substitutions in marine mammals; however, the majority of these changes were not unique to these animals. Conversely, we report that candidate aquatic adaptation genes, identified by signatures of likelihood convergence and/or elevated ratio of nonsynonymous to synonymous nucleotide substitution rate, are characterized by very few parallel substitutions and exhibit distinct sequence changes in each group. Moreover, no significant positive correlation was found between likelihood convergence and positive selection in all three marine lineages. These results suggest that convergence in protein coding genes associated with aquatic lifestyle is mainly characterized by independent substitutions and relaxed negative selection.

Reliable estimation via simulation

Let a and s denote the inter arrival times and service times in a GI/GI/1 queue. Let a (n), s (n) be the r.v.s, with distributions as the estimated distributions of a and s from iid samples of a and s of sizes n. Let w be a r.v. with the stationary distribution lr of the waiting times of the queue with input (a, s). We consider the problem of estimating E [w~], tx > 0 and 7r via simulations when (a (n), s (n)) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.

Implicit and multigrid procedures for steady-state computations with upwind algorithms

A computational study for the convergence acceleration of Euler and Navier-Stokes computations with upwind schemes has been conducted in a unified framework. It involves the flux-vector splitting algorithms due to Steger-Warming and Van Leer, the flux-difference splitting algorithms due to Roe and Osher and the hybrid algorithms, AUSM (Advection Upstream Splitting Method) and HUS (Hybrid Upwind Splitting). Implicit time integration with line Gauss-Seidel relaxation and multigrid are among the procedures which have been systematically investigated on an individual as well as cumulative basis. The upwind schemes have been tested in various implicit-explicit operator combinations such that the optimal among them can be determined based on extensive computations for two-dimensional flows in subsonic, transonic, supersonic and hypersonic flow regimes. In this study, the performance of these implicit time-integration procedures has been systematically compared with those corresponding to a multigrid accelerated explicit Runge-Kutta method. It has been demonstrated that a multigrid method employed in conjunction with an implicit time-integration scheme yields distinctly superior convergence as compared to those associated with either of the acceleration procedures provided that effective smoothers, which have been identified in this investigation, are prescribed in the implicit operator.

A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.