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Finite difference methods, such as the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial differential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in… (More)

SUMMARY For the approximate solution of ill-posed inverse problems, the formulation of a regularization functional involves two separate decisions: the choice of the residual minimizer and the choice of the regularizor. In this paper, the Kullback–Leibler functional is used for both. The resulting regularization method can solve problems for which the… (More)

When deriving rates of convergence for the approximations generated by the application of Tikhonov regularization to ill–posed operator equations , assumptions must be made about the nature of the stabilization (i.e., the choice of the seminorm in the Tikhonov regularization) and the regularity of the least squares solutions which one looks for. In fact, it… (More)

- M Hegland, R S Anderssen
- 1996

1. Introduction Various authors have explored the role of molliication in the solution of improperly posed problems such as numerical diierentiation and the numerical solution of rst kind integral equations. For example, Murio 13], exploiting earlier suggestions of Manselli and Miller 11] as well as Vasin 16], has shown how molliied numerical diierentiators… (More)

Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis… (More)

- Weiwei Deng, Jenni Clausen, Scott Boden, Sandra N. Oliver, M. Cristina Casao, Brett Ford +3 others
- PloS one
- 2015

The plant circadian clock is an internal timekeeper that coordinates biological processes with daily changes in the external environment. The transcript levels of clock genes, which oscillate to control circadian outputs, were examined during early seedling development in barley (Hordeum vulgare), a model for temperate cereal crops. Oscillations of clock… (More)

In the modelling of genetic signalling, communication and switching (GSCS), there is a need to identify the various mechanistic models, which nature has discovered, in terms of simple positional information rules (Wolpert (1969a)). The discovery of such simple rules, however, is a highly non-trivial process; in part, because of the complexity of the… (More)