Construction of a Mean Square Error Adaptive Euler--Maruyama Method with Applications in Multilevel Monte Carlo

A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise a posteriori adaptive time stepping Euler--Maruyama method for numerical solutions of SDE, and the resulting method is incorporated into a multilevel Monte Carlo (MLMC) method for weak approximations of SDE. This gives an efficient MSE adaptive MLMC method for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC method is shown to outperform the uniform time stepping MLMC method by orders of magnitude, producing output whose error with high probability is bounded by TOL>0 at the near-optimal MLMC cost rate O(TOL^{-2}log(TOL)^4).Comment: 43 pages, 12 figure

A brand within a brand: an integrated understanding of internal brand management and brand architecture in the public sector

Branding in the public sector is emerging as an interesting area of research, as diverse organisations find themselves using branding principles to promote a consistent, clear brand. However, very little is known how public organisations could, or should, manage their brands. The purpose of this research, therefore, is to explore brand management processes in the public sector, and its implication for brand architecture, from an employee perspective. With a qualitative approach, the study argues that branding is important not only for the organisation, but also for individual departments. Further, unlike branding in the private sector, public organisations may be more concerned with supporting a positive perception and organisational attractiveness rather than a unique and differentiated brand. This may have implications for brand architecture. By allowing individual departments to manage their brand with support from organisational structures that provide alignment and focus, organisations can form a brand architecture that supports a strong organisational brand and employee brand commitment

Analysis of LIDAR data fused with co-registered bands

Staphylococcus aureus and Streptococcus pyogenes, two important human pathogens, target host fibronectin (Fn) in their adhesion to and invasion of host cells1, 2. Fibronectin-binding proteins (FnBPs), anchored in the bacterial cell wall, have multiple Fn-binding repeats3 in an unfolded4, 5 region of the protein. The bacterium-binding site in the amino-terminal domain (1–5F1) of Fn contains five sequential Fn type 1 (F1) modules. Here we show the structure of a streptococcal (S. dysgalactiae) FnBP peptide (B3)6, 7 in complex with the module pair 1F12F1. This identifies 1F1- and 2F1-binding motifs in B3 that form additional antiparallel -strands on sequential F1 modules—the first example of a tandem -zipper. Sequence analyses of larger regions of FnBPs from S. pyogenes and S. aureus reveal a repeating pattern of F1-binding motifs that match the pattern of F1 modules in 1–5F1 of Fn. In the process of Fn-mediated invasion of host cells, therefore, the bacterial proteins seem to exploit the modular structure of Fn by forming extended tandem -zippers. This work is a vital step forward in explaining the full mechanism of the integrin-dependent2, 8 FnBP-mediated invasion of host cells

Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift

This paper proposes an adaptive timestep construction for an Euler–Maruyama approximation of SDEs with nonglobally Lipschitz drift. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Furthermore, the order of strong convergence is the same as usual, that is, order 12 for SDEs with a nonuniform globally Lipschitz volatility, and order 1 for Langevin SDEs with unit volatility and a drift with sufficient smoothness. For a class of ergodic SDEs, we also show that the bound for the moments and the strong error of the numerical solution are uniform in T, which allow us to introduce the adaptive multilevel Monte Carlo method to compute the expectations with respect to the invariant distribution. The analysis is supported by numerical experiments

A distributed task allocation algorithm for a multi-robot system in healthcare facilities

Various ambient assisted living (AAL) technologies have been proposed for improving the living conditions of elderly people. One of them is to introduce robots to reduce dependency on support staff. The tasks commonly encountered in a healthcare facility such as a care home for elderly people are heterogeneous and are of different priorities. A care home environment is also dynamic and new emergency priority tasks, which if not attended shortly may result in fatal situations, may randomly appear. Therefore, it is better to use a multi-robot system (MRS) consisting of heterogeneous robots than designing a single robot capable of doing all tasks. An efficient task allocation algorithm capable of handling the dynamic nature of the environment, the heterogeneity of robots and tasks, and the prioritisation of tasks is required to reap the benefits of introducing an MRS. This paper proposes Consensus Based Parallel Auction and Execution (CBPAE), a distributed algorithm for task allocation in a system of multiple heterogeneous autonomous robots deployed in a healthcare facility, based on auction and consensus principles. Unlike many of the existing market based task allocation algorithms, which use a time extended allocation of tasks before the actual execution is initialised, the proposed algorithm uses a parallel auction and execution framework, and is thus suitable for highly dynamic real world environments. The robots continuously resolve any conflicts in the bids on tasks using inter-robot communication and a consensus process in each robot before a task is assigned to a robot. We demonstrate the effectiveness of the CBPAE by comparing its simulation results with those of an existing market based distributed multi-robot task allocation algorithm and through experiments on real robots

A higher-order numerical framework for stochastic simulation of chemical reaction systems

<p>Abstract</p> <p>Background</p> <p>In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and <it>θ</it>-trapezoidal <it>τ</it>-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system.</p> <p>Results</p> <p>By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint <it>τ</it>-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and <it>θ</it>-trapezoidal <it>τ</it>-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations.</p> <p>Conclusions</p> <p>Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.</p