Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

On measuring quality of a probabilistic commodity forecast for a system that incorporates seasonal climate forecasts

Regional commodity forecasts are being used increasingly in agricultural industries to enhance their risk management and decision-making processes. These commodity forecasts are probabilistic in nature and are often integrated with a seasonal climate forecast system. The climate forecast system is based on a subset of analogue years drawn from the full climatological distribution. In this study we sought to measure forecast quality for such an integrated system. We investigated the quality of a commodity (i.e. wheat and sugar) forecast based on a subset of analogue years in relation to a standard reference forecast based on the full climatological set. We derived three key dimensions of forecast quality for such probabilistic forecasts: reliability, distribution shift, and change in dispersion. A measure of reliability was required to ensure no bias in the forecast distribution. This was assessed via the slope of the reliability plot, which was derived from examination of probability levels of forecasts and associated frequencies of realizations. The other two dimensions related to changes in features of the forecast distribution relative to the reference distribution. The relationship of 13 published accuracy/skill measures to these dimensions of forecast quality was assessed using principal component analysis in case studies of commodity forecasting using seasonal climate forecasting for the wheat and sugar industries in Australia. There were two orthogonal dimensions of forecast quality: one associated with distribution shift relative to the reference distribution and the other associated with relative distribution dispersion. Although the conventional quality measures aligned with these dimensions, none measured both adequately. We conclude that a multi-dimensional approach to assessment of forecast quality is required and that simple measures of reliability, distribution shift, and change in dispersion provide a means for such assessment. The analysis presented was also relevant to measuring quality of probabilistic seasonal climate forecasting systems. The importance of retaining a focus on the probabilistic nature of the forecast and avoiding simplifying, but erroneous, distortions was discussed in relation to applying this new forecast quality assessment paradigm to seasonal climate forecasts. Copyright (K) 2003 Royal Meteorological Society.