Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be mapped to larger regions, containing those regions associated with more specific concepts. However, the power of convexity is rarely leveraged during the actual learning tasks. Here, we introduce BoxLitE, a KB embedding model for DL-Lite that allows for convex optimization. We show that for any satisfiable DL-Lite KB, there is a BoxLitE embedding that is a weakly faithful model. As a proof of concept, we show how to formulate the KB embedding task as a convex optimization problem and how to obtain embeddings with such desirable faithfulness property.

Wireless networking enhanced with multiple transmitting channels has been considered to improve the utilization of the electromagnetic spectrum and to provide ways to accommodation the growing demand for connectivity. In this scenario, the use of a common control channel to coordinate the stations and networking resources is usually employed. This work evaluates the control channel capacity and its impact on the overall system throughput when multiple channels are available. The CSMA/CA mechanism is considered as it is the most used access control mechanism in the wireless local area network. To this end, an analytical model is proposed to evaluate the saturation conditions of the control channel. Empirical results are also provided and compared with the analytical model. The results show that the empirical results are consistent with the analytical model. In particular, it is shown that the ratio of eight data channels per control channel attains the best results.