No abstract

No abstract

Collatz conjecture states that iterating the map that takes even natural number n to {n \over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.

In social network analysis, for determining the relevance or significance of a node in the network, several node centrality measures are often used such as degree centrality, betwenness centrality, closeness centrality, eigenvector, subgraph and page rank centrality. In this paper we apply a principal components analysis over the traditional centrality measures for obtaining an overall single metric that combines the best attributes of the traditional centrality measures and permits to detect relevant nodes in the network. Concretely, a detailed study of the Spanish stocks market will be used for demonstrating the advantages of this approach.