No abstract

Linked Open Data has been recognized as a valuable source for background information in many data mining and information retrieval tasks. However, most of the existing tools require features in propositional form, i.e., a vector of nominal or numerical features associated with an instance, while Linked Open Data sources are graphs by nature. In this paper, we present RDF2Vec, an approach that uses language modeling approaches for unsupervised feature extraction from sequences of words, and adapts them to RDF graphs. We generate sequences by leveraging local information from graph sub-structures, harvested by Weisfeiler-Lehman Subtree RDF Graph Kernels and graph walks, and learn latent numerical representations of entities in RDF graphs. We evaluate our approach on three different tasks: (i) standard machine learning tasks, (ii) entity and document modeling, and (iii) content-based recommender systems. The evaluation shows that the proposed entity embeddings outperform existing techniques, and that pre-computed feature vector representations of general knowledge graphs such as DBpedia and Wikidata can be easily reused for different tasks.

The concepts of infinity and infinitesimal in mathematics date back to anciens Greek and have always attracted great attention. Very recently, a new methodology has been proposed by Sergeyev [10] for performing calculations with infinite and infinitesimal quantities, by introducing an infinite unit of measure expressed by the numeral ① (grossone). An important characteristic of this novel approach is its attention to numerical aspects. In this paper we will present some possible applications and use of ① in Operations Research and Mathematical Programming. In particular, we will show how the use of ① can be beneficial in anti-cycling procedure for the well-known simplex method for solving Linear Programming Problems and in defining exact differentiable Penalty Functions in Nonlinear Programming.

Reversible aggregation processes were simulated for systems of freely diffusing sticky particles. Reversibility was introduced by allowing that all bonds in the system may break with a given probability per time interval. In order to describe the kinetics of such aggregation-fragmentation processes, a fragmentation kernel was developed and then used together with the Brownian aggregation kernel for solving the corresponding kinetic master equation. The deduced fragmentation kernel considers a single characteristic lifetime for all bonds and accounts for the cluster morphology by averaging over all possible configurations for clusters of a given size. It became evident that the simulated cluster-size distributions could be described only when an additional fragmentation effectiveness was considered. Doing so, the stochastic solutions were in good agreement with the simulated data.