When communication network planning-design is performed, especially in a short-term case, it is important to utilize existing facilities in the construction of the new network. In this paper, link capacity assignment problem (CA problem) for packet-switched networks is investigated with the consideration of the existing network. To deal with this, per-unit cost of existing link capacity is thought to be less than that of newly installed capacity and a link cost function is modeled by a non-linear, non-differentiable one which is composed of two portions of capacity cost. After formulating the CA problem, two optimum algorithms derived from Lagrange multiplier method are presented and a modified algorithm is used for solving the CA problem in order to reduce the computation time. Some numerical results show that according to the values of link traffic flows, there will be links whose capacities must be set equally to the existing values. Moreover, when link cost difference is introduced in the CA problem, the number of links that the capacities of which have to be changed from existing values is less than that of linear cost function case, i.e., the case without consideration of the cost difference in link capacity.

Mathematical formulae play an important role in many scientific domains. Regardless of the importance of mathematical formula search, conventional keyword-based retrieval methods are not sufficient for searching mathematical formulae, which are structured as trees. The increasing number as well as the structural complexity of mathematical formulae in scientific articles lead to the necessity for large-scale structure-aware formula search techniques. In this paper, we formulate three types of measures that represent distinctive features of semantic similarity of math formulae, and develop efficient hash-based algorithms for the approximate calculation. Our experiments using NTCIR-11 Math-2 Task dataset, a large-scale test collection for math information retrieval with about 60-million formulae, show that the proposed method improves the search precision while also keeps the scalability and runtime efficiency high.

This paper explores the problem of semantic enrichment of mathematical expressions. We formulate this task as the translation of mathematical expressions from presentation markup to content markup. We use MathML, an application of XML, to describe both the structure and content of mathematical notations. We apply a method based on statistical machine translation to extract translation rules automatically. This approach contrasts with previous research, which tends to rely on manually encoded rules. We also introduce segmentation rules used to segment mathematical expressions. Combining segmentation rules and translation rules strengthens the translation system and archives significant improvements over a prior rule-based system.