Logic programming and artificial neural networks in breast cancer detection

About 90% of breast cancers do not cause or are capable of producing death if detected at an early stage and treated properly. Indeed, it is still not known a specific cause for the illness. It may be not only a beginning, but also a set of associations that will determine the onset of the disease. Undeniably, there are some factors that seem to be associated with the boosted risk of the malady. Pondering the present study, different breast cancer risk assessment models where considered. It is our intention to develop a hybrid decision support system under a formal framework based on Logic Programming for knowledge representation and reasoning, complemented with an approach to computing centered on Artificial Neural Networks, to evaluate the risk of developing breast cancer and the respective Degree-of-Confidence that one has on such a happening.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.