In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

The potential of biological consortia designed for laccase production and dye treatment is discussed in this review. The poor yields in laccase production and low efficiency in dye decolorization of monoculture-based treatments has encouraged the use of designed biological consortia. A consortium is a system where the growth of two or more organisms, chosen to improve a particular bioprocess, is induced in the same medium. Chemical and natural mediators are being replaced by consortia for the production of laccases because, in addition to being less toxic, they induce new enzyme isoforms and lead to high laccase yields. On the other hand, consortia act synergistically in the decolorization of azo dyes through the enzymes they produce, so overall degradation is improved. Designed consortia are an attractive alternative still in development that could provide new biotechnological tools for the treatment of textile effluents.

In this paper we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the possibility of polarization. Particularly, we are interested in dealing with the problem of taking into account the Polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more probably to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.

This review evaluates the trajectory and sustainability of the global and Mexican aquaculture industry. Globally, the sector is experiencing rapid growth, catalyzed by evolving consumption patterns and technological advancements. Notwithstanding the benefits, environmental concerns necessitate an urgent shift towards sustainable practices. The focus then narrows to Mexico's aquaculture, tracing its history from the late 19th century. With an emphasis on species diversification, the country's sector demonstrates resilience and potential, with an impressive yield of 249,613.71 tons in 2021 despite regional consolidation. However, persistent challenges such as technological limitations, funding shortages, and access to quality seeds hinder progress. Risks, including disease outbreaks, negative environmental impact, economic volatility, regulatory compliance, and climate change, further underscore the need for sustainable strategies. With government support and unique geographical and climatic advantages, Mexico shows promise for a significant % growth projection of 25% over the next five years. This review underscores the importance of embracing technological innovation, implementing sustainable practices, and enacting supportive legislation for the long-term success of the aquaculture sector worldwide, with a particular focus on Mexico.