The methodology presented in this paper is based on concept mapping, which is a technique for representing knowledge in graphs. Its applications are broader and cover, in addition to presentation of knowledge, the complex organization of systems such as web sites. The paper presents a method for reaching consensus from several organizations of data/web site independently produced by different people. A class of methods was initiated, considering a number of parameters that can be chosen in order to match closely any specific real-life application. Although the methodology can be fully automated in terms of a suitable computer program, it is meant to be mainly a useful tool for experts in web site organization.
COBISS.SI-ID: 51728482
In the paper we show that the bibliographic data can be transformed into a collection of compatible networks. Using network multiplication different interesting derived networks can be obtained. In defining them an appropriate normalization should be considered. The proposed approach can be applied also to other collections of compatible networks. The networks obtained from the bibliographic data bases can be large (hundreds of thousands of vertices). Fortunately they are sparse and can be still processed relatively fast. We answer the question when the multiplication of sparse networks preserves sparseness. The proposed approaches are illustrated with analyses of collection of networks on the topic "social network" obtained from the Web of Science. The works with large number of co-authors add large complete subgraphs to standard collaboration network thus bluring the collaboration structure. We show that using an appropriate normalization their effect can be neutralized. Among other, we propose a measure of collaborativness of authors with respect to a given bibliography and show how to compute the network of citations between authors and identify citation communities.
COBISS.SI-ID: 16739929
In this paper, a particular shape preserving parametric polynomial approximation of conic sections is studied. The approach is based upon the parametric approximation of implicitly defined planar curves. Polynomial approximants derived are given in a closed form and provide the highest possible approximation order.
COBISS.SI-ID: 16716121
Summation is closely related to solving linear recurrence equations, since an indefinite sum satisfies a first-order linear recurrence with constant coefficients, and a definite proper-hypergeometric sum satisfies a linear recurrence with polynomial coefficients. Conversely, d'Alembertian solutions of linear recurrences can be expressed as nested indefinite sums with hypergeometric summands. We sketch the simplest algorithms for finding polynomial, rational, hypergeometric, d'Alembertian, and Liouvillian solutionsof linear recurrences with polynomial coefficients, and refer to the relevant literature for state-of-the-art algorithms for these tasks. We outline an algorithm for finding the minimal annihilator of a given P-recursive sequence, prove the salient closure properties of d'Alembertian sequences, and present an alternative proof of a recent result of Reutenauer'sthat Liouvillian sequences are precisely the interlacings of d'Alembertian ones.
COBISS.SI-ID: 16779353
Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs. We extend this result to two one-variable deformations of Cayley polytopes (which we call $t$-Cayley and $t$-Gayley polytopes), and to the most general two-variable deformations, which we call Tutte polytopes. The volume of the latter is given via an evaluation of the Tutte polynomial of the complete graph. Our approach is based on an explicit triangulation of the Cayley and Tutte polytopes. We prove that simplices in the triangulations correspond to labeled trees. The heart of the proof is a direct bijection based on the neighbors-first search graph traversal algorithm.
COBISS.SI-ID: 16706905