A note on the Balanced method

Recently the Balanced method was introduced as a class of quasi-implicit methods for solving stiff stochastic differential equations. We examine asymptotic and mean-square stability for several implementations of the Balanced method and give a generalized result for the mean-square stability region of any Balanced method. We also investigate the optimal implementation of the Balanced method with respect to strong convergence.

What determines the finance-growth nexus? Empirical evidence for threshold models

This paper elaborates the notion of balanced'' financial development that is contingent on a country's general level of development. We develop an empirical framework to address this point, referring to threshold regressions and a bootstrap test for structural shift in a growth equation. We find that countries gain less from financial activity, if the latter fails to keep up with or exceeds what would follow from a balanced expansion path. These analyses contribute to the finance and growth literature in providing empirical support for the balanced'' financial development hypothesis.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed 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. (C) 2004 Elsevier B.V. All rights reserved.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

SARS coronavirus nucleocapsid immunodominant T-cell epitope cluster is common to both exogenous recombinant and endogenous DNA-encoded immunogens

Correspondence between the T-cell epitope responses of vaccine immunogens and those of pathogen antigens is critical to vaccine efficacy. In the present study, we analyzed the spectrum of immune responses of mice to three different forms of the SARS coronavirus nucleocapsid (N): (1) exogenous recombinant protein (N-GST) with Freund's adjuvant; (2) DNA encoding unmodified N as an endogenous cytoplasmic protein (pN); and (3) DNA encoding N as a LAMP-I chimera targeted to the lysosomal MHC II compartment (p-LAMP-N). Lysosomal trafficking of the LAMP/N chimera in transfected cells was documented by both confocal and immunoelectron microscopy. The responses of the immunized mice differed markedly. The strongest T-cell IFN-gamma and CTL responses were to the LAMP-N chimera followed by the pN immunogen. In contrast, N-GST elicited strong T cell IL-4 but minimal IFN-gamma responses and a much greater antibody response. Despite these differences, however, the immunodominant T-cell ELISpot responses to each of the three immunogens were elicited by the same N peptides, with the greatest responses being generated by a cluster of five overlapping peptides, N76-114, each of which contained nonameric H2(d) binding domains with high binding scores for both class I and, except for N76-93, class II alleles. These results demonstrate that processing and presentation of N, whether exogenously or endogenously derived, resulted in common immunodominant epitopes, supporting the usefulness of modified antigen delivery and trafficking forms and, in particular, LAMP chimeras as vaccine candidates. Nevertheless, the profiles of T-cell responses were distinctly different. The pronounced Th-2 and humoral response to N protein plus adjuvant are in contrast to the balanced IFN-gamma and IL-4 responses and strong memory CTL responses to the LAMP-N chimera. (C) 2005 Elsevier Inc. All rights reserved.

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

On the construction of nearest neighbour balanced row-column designs

Nearest–neighbour balance is considered a desirable property for an experiment to possess in situations where experimental units are influenced by their neighbours. This paper introduces a measure of the degree of nearest–neighbour balance of a design. The measure is used in an algorithm which generates nearest–neighbour balanced designs and is readily modified to obtain designs with various types of nearest–neighbour balance. Nearest–neighbour balanced designs are produced for a wide class of parameter settings, and in particular for those settings for which such designs cannot be found by existing direct combinatorial methods. In addition, designs with unequal row and column sizes, and designs with border plots are constructed using the approach presented here.

The line structure of balanced ternary designs with block size three, index three and rho(2) = 1, 2

In this paper necessary and sufficient conditions for a vector to be the fine structure of a balanced ternary design with block size 3, index 3 and rho(2) = 1 and 2 are determined with one unresolved case.

Review of Beginning Reading: A balanced approach to teaching literacy during the first three years at school by Yola Centre

Beginning Reading: A Balanced Approach to Literacy Instruction during the First Three Years at School by Yola Center is intended for those involved in teaching and supporting literacy practices in regular classrooms and addresses literacy practices for learners with disabilities and those experiencing difficulties in literacy learning.

A review of the use of the basic cation saturation ratio and the "ideal" soil

The use of 'balanced' Ca, Mg, and K ratios, as prescribed by the basic cation saturation ratio (BCSR) concept, is still used by some private soil-testing laboratories for the interpretation of soil analytical data. This review aims to examine the suitability of the BCSR concept as a method for the interpretation of soil analytical data. According to the BCSR concept, maximum plant growth will be achieved only when the soil’s exchangeable Ca, Mg, and K concentrations are approximately 65 % Ca, 10 % Mg, and 5 % K (termed the ‘ideal soil’). This ‘ideal soil’ was originally proposed by Firman Bear and co-workers in New Jersey (USA) during the 1940s as a method of reducing luxury K uptake by alfalfa (Medicago sativa L.). At about the same time, William Albrecht, working in Missouri (USA), concluded through his own investigations that plants require a soil with a high Ca saturation for optimal growth. Whilst it now appears that several of Albrecht’s experiments were fundamentally flawed, the BCSR (‘balanced soil’) concept has been widely promoted, suggesting that the prescribed cationic ratios provide optimum chemical, physical, and biological soil properties. Our examination of data from numerous studies (particularly those of Albrecht and Bear, themselves) would suggest that, within the ranges commonly found in soils, the chemical, physical, and biological fertility of a soil is generally not influenced by the ratios of Ca, Mg, and K. The data do not support the claims of the BCSR, and continued promotion of the BCSR will result in the inefficient use of resources in agriculture and horticulture.