The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Considerations in the design of a mixed-method cluster evaluation of a community programme for 'at-risk' young people

This article discusses the design of a comprehensive evaluation of a community development programme for young people 'at-risk' of self-harming behaviour. It outlines considerations in the design of the evaluation and focuses on the complexities and difficulties associated with the evaluation of a community development programme. The challenge was to fulfil the needs of the funding body for a broad, outcome-focused evaluation while remaining close enough to the programme to accurately represent its activities and potential effects at a community level. Specifically, the strengths and limitations of a mixed-method evaluation plan are discussed with recommendations for future evaluation practice.

Ionic strontium fluorescence as a method for flow tagging velocimetry

A flow tagging technique based upon ionic fluorescence in strontium is investigated for applications to velocity measurements in gas flows. The method is based upon a combination of two laser based spectroscopic techniques, i.e. resonantly-enhanced ionisation and laser-induced ionic fluorescence. Strontium is first ionised and then planar laser-induced fluorescence is utilised to give 2D 'bright images' of the ionised region of the flow at a given time delay. The results show that this method can be used for velocity measurements. The velocities were measured in two types of air-acetylene flames - a slot burner and a circular burner yielding velocities of 5.1 +/- 0.1 m/s and 9.3 +/- 0.2 m/s, respectively. The feasibility of the method for the determination of velocities in faster flows than those investigated here is discussed.

Patient based method of assessing adverse events in clinical trials in rheumatology: the revised Stanford Toxicity Index

We describe the progress towards developing a patient rated toxicity index that meets all of the patient-important attributes defined by the OMERACT Drug Safety Working Party, These attributes are frequency, severity. importance to patient, importance to the clinician, impact on economics, impact on activities, and integration of adverse effects with benefits. The Stanford Toxicity Index (STI) has been revised to collect all attributes with the exception of impact on activities. However, since the STI is a part of the Health Assessment Questionnaire (HAQ). impact on activities is collected by the HAQ. In particular, a new question asks patients to rate overall satisfaction, taking into consideration both benefits and adverse effects. The nest step in the development of this tool is to ensure that the STI meets the OMERACT filter of truth, discrimination, and feasibility. Although truth and feasibility have been confirmed by comparisons within the ARAMIS database, discrimination needs to be assessed in clinical trials.

A novel method for solid-phase synthesis of oligosaccharides using the N-1-(4,4-dimethyl-2,6-dioxocyclohexylidene)ethyl (Dde) linker

The application of the N-1-(4,4-dimethyl-2,6-dioxocyclohexylidene)ethyl (Dde) linker for the solid-phase synthesis of oligosaccharides is described. The oligosaccharide products can be cleaved from the resin by hydrazine, ammonia or primary amines, but the linker is stable under the conditions of oligosaccharide synthesis. The first sugar can be attached to the resin linker via a vinylogous amide bond, or by ether linkage using a p-aminobenzyl alcohol converter. (C) 2001 Elsevier Science Ltd. All rights reserved.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

An extended interval dosing method for gentamicin in neonates

Traditional gentamicin dosing every 8–24 h depending on age and weight in neonates does not provide the ideal concentration–time profile to both optimize the concentration-dependent killing by aminoglycosides and minimize toxicity. Fifty-three neonates were audited prospectively while receiving gentamicin 2.5 mg/kg every 8–24 h, aiming for peak concentrations (Cmax) of 6–10 mg/L and trough concentrations (Cmin) 10 mg/L after the first dose. The mean area under the concentration versus time curve AUC0–24 was 93 mg•h/L (target = 100 mg•h/L). The extended interval dosing achieved higher Cmax values while ensuring that overall exposure per 24 h was acceptable. Prospective testing of the method demonstrated good predictive ability.

The reliability of immunohistochemistry as a prescreening method for the diagnosis of hereditary nonpolyposis colorectal cancer (HNPCC) - Results of an international collaborative study

Hereditary nonpolyposis colorectal cancer syndrome (HNPCC) is an autosomal dominant condition accounting for 2–5% of all colorectal carcinomas as well as a small subset of endometrial, upper urinary tract and other gastrointestinal cancers. An assay to detect the underlying defect in HNPCC, inactivation of a DNA mismatch repair enzyme, would be useful in identifying HNPCC probands. Monoclonal antibodies against hMLH1 and hMSH2, two DNA mismatch repair proteins which account for most HNPCC cancers, are commercially available. This study sought to investigate the potential utility of these antibodies in determining the expression status of these proteins in paraffin-embedded formalin-fixed tissue and to identify key technical protocol components associated with successful staining. A set of 20 colorectal carcinoma cases of known hMLH1 and hMSH2 mutation and expression status underwent immunoperoxidase staining at multiple institutions, each of which used their own technical protocol. Staining for hMSH2 was successful in most laboratories while staining for hMLH1 proved problematic in multiple labs. However, a significant minority of laboratories demonstrated excellent results including high discriminatory power with both monoclonal antibodies. These laboratories appropriately identified hMLH1 or hMSH2 inactivation with high sensitivity and specificity. The key protocol point associated with successful staining was an antigen retrieval step involving heat treatment and either EDTA or citrate buffer. This study demonstrates the potential utility of immunohistochemistry in detecting HNPCC probands and identifies key technical components for successful staining.

Contradictions and institutional convergences: Genre as method

My purpose here is to put forward a conception of genre as a way to conduct Futures Studies. To demonstrate the method, I present some examples of contemporary political and corporate discourses and contextualise them in broader institutional and historical settings. I elaborate the method further by giving examples of ‘genre chaining’ and ‘genre hybridity’ (Fairclough 1992 2000) to show how past, present, and future change can be viewed through the lens of genre.