Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

Neural interface systems : a new legal frontier?

In an age where digital innovation knows no boundaries, research in the area of brain-computer interface and other neural interface devices go where none have gone before. The possibilities are endless and as dreams become reality, the implications of these amazing developments should be considered. Some of these new devices have been created to correct or minimise the effects of disease or injury so the paper discusses some of the current research and development in the area, including neuroprosthetics. To assist researchers and academics in identifying some of the legal and ethical issues that might arise as a result of research and development of neural interface devices, using both non-invasive techniques and invasive procedures, the paper discusses a number of recent observations of authors in the field. The issue of enhancing human attributes by incorporating these new devices is also considered. Such enhancement may be regarded as freeing the mind from the constraints of the body, but there are legal and moral issues that researchers and academics would be well advised to contemplate as these new devices are developed and used. While different fact situation surround each of these new devices, and those that are yet to come, consideration of the legal and ethical landscape may assist researchers and academics in dealing effectively with matters that arise in these times of transition. Lawyers could seek to facilitate the resolution of the legal disputes that arise in this area of research and development within the existing judicial and legislative frameworks. Whether these frameworks will suffice, or will need to change in order to enable effective resolution, is a broader question to be explored.

A highway for research in science education that no longer leads to the frontier

A review of "Progressing science education: constructing the scientific research programme into the contingent nature of learning science", by Keith S. Taber, Dordrecht, Springer, 2009.

Renegades on the frontier of innovation: The shanzhai grassroots communities of Shenzhen in China's creative economy

Two Australian researchers specializing in China's creative industries examine recent developments in southern China commonly associated with the shanzhai phenomenon (e.g., production and sale of cheap local facsimiles of globally branded goods). While shanzhai is often condemned as the embodiment of China's "knock-off" industries, the authors argue that it might be more appropriately viewed as an instance of China's emerging creative economy and an example of rapid prototyping. The paper traces the evolution of shanzhai mobile phones and the materialization of the shanzhai ethos in popular culture. In arguing that shanzhai provides inputs into creative industries, the paper describes the fuzzy boundary between formal and informal culture and notes the interaction between three spheres of activity: official culture, the market, and grassroots culture.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

Modelling passenger flow at airport terminals : individual agent decision model for stochastic passenger behaviour

Airport system is complex. Passenger dynamics within it appear to be complicate as well. Passenger behaviours outside standard processes are regarded more significant in terms of public hazard and service rate issues. In this paper, we devised an individual agent decision model to simulate stochastic passenger behaviour in airport departure terminal. Bayesian networks are implemented into the decision making model to infer the probabilities that passengers choose to use any in-airport facilities. We aim to understand dynamics of the discretionary activities of passengers.

Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

Crime talk, FIFO workers and cultural conflict on the mining boom frontier

Australia is experiencing an unprecedented expansion in mining due to intense demand from Asian economies thirsty for Australia’s non-renewable resources, with over $260 billion worth of capital investment currently in the pipeline (BREE 10). The scale of the present boom coupled with the longer term intensification of competitiveness in the global resources sector is changing the very nature of mining operations in Australia. Of particular note is the increasingly heavy reliance on a non-resident workforce, currently sourced from within Australia but with some recent proposals for projects to draw on overseas guest workers. This is no longer confined, as it once was, to remote, short term projects or to exploration and construction phases of operations, but is emerging as the preferred industry norm. Depending upon project location, workers may either fly-in, fly-out (FIFO) or drive-in, drive-out (DIDO), the critical point being that these operations are frequently undertaken in or near established communities. Drawing primarily on original fieldwork in one of Australia’s mining regions at the forefront of the boom, this paper explores some of the local impacts of new mining regimes, in particular their tendency to undermine collective solidarities, promote social division and fan cultural conflict.

Factors affecting technical efficiency of rice farmers in village reservoir irrigation systems of Sri Lanka

Given the importance of water for rice production, this study examines the factors affecting the technical efficiency (TE) of irrigated rice farmers in village irrigation systems (VIS) in Sri Lanka. Primary data were collected from 460 rice farmers in the Kurunagala District, Sri Lanka, to estimate a stochastic translog production frontier for rice production. The mean TE of rice farming in village irrigation was found to be 0.72, although 63% of rice farmers exceeded this average. The most influential factors of TE are membership of Farmer Organisations (FOs) and the participatory rate in collective actions organised by FOs. The results suggest that enhancement of co-operative arrangements of farmers by strengthening the membership of FOs is considered important for increasing TE in rice farming in VIS.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type.