Shape-Constrained Symbolic Regression-Improving Extrapolation with Prior Knowledge.

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce, for example, monotonicity of the function over selected inputs. The aim is to find models which conform to expected behavior and which have improved extrapolation capabilities. We demonstrate the feasibility of the idea and propose and compare two evolutionary algorithms for shape-constrained symbolic regression: (i) an extension of tree-based genetic programming which discards infeasible solutions in the selection step, and (ii) a two-population evolutionary algorithm that separates the feasible from the infeasible solutions. In both algorithms we use interval arithmetic to approximate bounds for models and their partial derivatives. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Both algorithms are able to identify models which conform to shape constraints which is not the case for the unmodified symbolic regression algorithms. However, the predictive accuracy of models with constraints is worse on the training set and the test set. Shape-constrained polynomial regression produces the best results for the test set but also significantly larger models.

[Long-term follow-up of traumatic hip fracture in childhood]. / Langzeitverlauf nach traumatischer Hüftluxation im Kindesalter.

Traumatic hip dislocation is a rare emergency situation in childhood. Long-term follow-up (10 1/12 years [10/12-20 years]) of 9 patients treated at our institution between 1971 and 1992 revealed no late sequelae. There was no case of necrosis of the femoral head. One patient had a recurrent dislocation of the hip 17 and 18 years after the first dislocation. For post-reduction treatment we propose bedrest until pain relief and mobilisation with crutches for 4 weeks. Regular clinical and radiographic controls, including bone scan and/or MRI, are mandatory during the first 2 years.

Screening of patients with Turner syndrome for "hidden" Y-mosaicism.

The presence of Y-chromosomal sequences in the cells of patients with Turner-Syndrome (TS) is a risk factor for the development of gonadal tumors. Therefore and since demonstration of Y-material usually results in prophylactic gonadectomy optimal sensitivity and specificity of the diagnosis have to be attempted. We wanted to evaluate the diagnostic potential of cytogenetic investigations as routinely employed in TS. In the most comprehensive study published so far we screened 208 TS patients for the presence of Y-chromosomal sequences by polymerase chain reaction (PCR) specific for eight different loci along the Y-chromosome. Six patients (3%) without cytogenetic evidence of Y-chromosome were found to be Y-positive. Among 12 cases with marker chromosomes two more Y-chromosomal fragments were identified. Thus, PCR-screening for Y-specific sequences was shown to be a valuable tool in the clinical management of Turner patients.