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The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks. [ABSTRACT FROM AUTHOR]

Summary: This paper compares two Monte Carlo sequential data assimilation methods based on the Kalman filter, for estimating the effect of measurements on simulations of state error variance made by a one-dimensional hydrodynamic model. The first method used an ensemble Kalman filter (EnKF) to update state estimates, which were then used as initial conditions for further simulations. The second method used an ensemble transform Kalman filter (ETKF) to quickly estimate the effect of measurement error covariance on forecast error covariance without the need to re-run the simulation model. The ETKF gave an unbiased estimate of EnKF analysed error variance, although differences in the treatment of measurement errors meant the results were not identical. Estimates of forecast error variance could also be made, but their accuracy deteriorated as the time from measurements increased due in part to model non-linearity and the decreasing signal variance. The motivation behind the study was to assess the ability of the ETKF to target possible measurements, as part of an adaptive sampling framework, before they are assimilated by an EnKF-based forecasting model on the River Crouch, Essex, UK. The ETKF was found to be a useful tool for quickly estimating the error covariance expected after assimilating measurements into the hydrodynamic model. It, thus, provided a means of quantifying the ‘usefulness’ (in terms of error variance) of possible sampling schemes. [Copyright &y& Elsevier]