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A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method. [ABSTRACT FROM AUTHOR]

Ontology, as a useful tool, is widely applied in lots of areas such as social science, computer science, and medical science. Ontology concept similarity calculation is the key part of the algorithms in these applications. A recent approach is to make use of similarity between vertices on ontology graphs. It is, instead of pairwise computations, based on a function that maps the vertex set of an ontology graph to real numbers. In order to obtain this, the ranking learning problem plays an important and essential role, especially k-partite ranking algorithm, which is suitable for solving some ontology problems. A ranking function is usually used to map the vertices of an ontology graph to numbers and assign ranks of the vertices through their scores. Through studying a training sample, such a function can be learned. It contains a subset of vertices of the ontology graph. A good ranking function means small ranking mistakes and good stability. For ranking algorithms, which are in a well-stable state, we study generalization bounds via some concepts of algorithmic stability. We also find that kernel-based ranking algorithms stated as regularization schemes in reproducing kernel Hilbert spaces satisfy stability conditions and have great generalization abilities. [ABSTRACT FROM AUTHOR]