This is a completely revised and updated translation of the Russian original work Numerical Metho(Js for Solving lll-Posed Problems, Nauka, Moscow © 1990 Translation by R.A.M. Hoksbergen All Rights Reserved

The Electroencephalogram (EEG) measures electrical potentials at the surface of the head. Localizing the sources of the electrical activity inside the brain is an important question in neurology and psychiatry and has received considerable attention. The so called forward solution of this problem constructs the scalp potentials based on the electrical sources and a transfer matrix reflecting the conductivity of the head and the brain. The inverse solution tries to reconstruct the sources based on the scalp potentials and the transfer matrix. Unfortunately this is an inherently ill-posed problem, i.e. an infinite number of different source combinations may produce exactly the same scalp potentials. As a result a simple least squares solution is not feasible and a regularization of the inverse solution is required. A common approach is based on Tikhonov regularization (Tikhonov and Arsenin, 1977). This approach combines the fit of the data and a function which measures the smoothness of the solution. A frequently used method is LORETA (Pascual-Marqui et al, 1994) which applies the constraint that neighboring voxels have similar activity. This inverse solution may be classified using a mixture model approach using disease mapping methods Schlattmann et al., 2002. Besides Tikhonov regularization also Bayesian approaches may be used for the regularization of the inverse problem (Louis, 1989). Typically likelihood and prior are assumed to follow a multivariate normal distribution which is equivalent to Tikhonov regularization. In this paper a semiparametric mixture model is proposed as prior distribution. This has the advantage that simultaneously regularization and spatial localization of individual voxels within the same model can be achieved. Estimation of the model parameters and the sources is based on the EM-algorithm. The procedure will be presented using a spherical head model and simulated data. During the last decades up to present times only very few studies addressed this isssue fundamental to tropical oncology. In the sixties and the seventies of the last century circumstantial geographical evidence was put forward first for Burkitt's lymphoma (BL) and later on for other entities of malignant lymphomas (ML). The observations were reported from East Africa, but an early comparative study from Uganda noted concomitant distributions only for BL and not for the other groups of ML. In Uganda, a little country under the Equator with very marked variations in geography and thus in malarial endemicity, a cancer registry was in operation for the whole of the country during the years 1964-1975 when medical services were of high standard. In a review of this archival biopsy material on the basis of the Kiel-classification more than ten years ago ML of high grade malignancy other than BL would also relate to malarial endemicity. A similar analysis in neighbouring almost malaria-free Rwanda confirmed a low frequency of high grade ML. Abundancy of cancer cases kept in the no longer functioning registry would allow to l...

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