Modularity, balance, and frustration in student social networks: The role of negative relationships in communities.

Signed networks provide information to study the structure and composition of relationships (positive and negative) among individuals in a complex system. Individuals, through different criteria, form groups or organizations called communities. Community structures are one of the important properties of social networks. In this work, we aim to analyze the perturbation of negative relationships in communities. We developed a methodology to obtain and analyze the optimal community partitions in nine school networks in the state of Yucatán, México. We implemented a technique based on the social balance theory in signed networks to complete negative missing links and further applied two methods of community detection: Newman's and Louvain's algorithms. We obtain values close to Dunbar's ratio for both types of relationships, positive and negative. The concepts of balance and frustration were analyzed, and modularity was used to measure the perturbation of negative relationships in communities. We observe differences among communities of different academic degrees. Elementary school communities are unstable, i.e. significantly perturbed by negative relationships, in secondary school communities are semi-stable, and in high school and the university the communities are stable. The analyzes indicate that a greater number of negative links in the networks does not necessarily imply higher instability in the communities, but other social factors are also involved.

Temperature time series analysis at Yucatan using natural and horizontal visibility algorithms.

Several methods to quantify the complexity of a time series have been proposed in the literature, which can be classified into three categories: structure/self-affinity, attractor in the phase space, and randomness. In 2009, Lacasa et al. proposed a new method for characterizing a time series called the natural visibility algorithm, which maps the data into a network. To further investigate the capabilities of this technique, in this work, we analyzed the monthly ambient temperature of 4 cities located in different climatic zones on the Peninsula of Yucatan, Mexico, using detrended fluctuation analysis (structure complexity), approximate entropy (randomness complexity) and the network approach. It was found that by measuring the complexity of the dynamics by structure or randomness, the magnitude was very similar between the cities in different climatic zones; however, by analyzing topological indices such as Laplacian energy and Shannon entropy to characterize networks, we found differences between those cities. With these results, we show that analysis using networks has considerable potential as a fourth way to quantify complexity and that it may be applied to more subtle complex systems such as physiological signals and their high impact on early warnings.

Connectivity in a Karst System Using Electrical Resistivity Tomography and Network Theory.

The Ring of Cenotes (RC) is an alignment of numerous cenotes (sinkholes) in a semicircular form (with a radius of 100 km) located in northwestern Yucatán, México. The formation roughly coincides with a concentric ring that corresponds to a buried structure, which has been identified as the product of a meteor impact, known as the Chicxulub crater. Secondary permeability generated by the fracturing and faulting of the sedimentary sequence in the Chicxulub crater has favored the karstification process and therefore the development of underground rivers that transport water from the mainland to the sea. This study implements the network theory to study the hydrological connectivity between a group of 11 cenotes within the RC. Eight electrical resistivity tomography transects were used as an empirical basis. Each transect was acquired directly in the field using the SuperSting R1/IP equipment with a dipole-dipole configuration. An adapted version of the reliability algorithm for communication networks was used as a theoretical model. We found evidence of the existence of water cavities in the study area. We made a network from the data and assigned connection probabilities among cenotes as a function of the separation length and the number of water cavities, as well as their size.

Friendship Concept and Community Network Structure among Elementary School and University Students.

We use complex network theory to study the differences between the friendship concepts in elementary school and university students. Four friendship networks were identified from surveys. Three of these networks are from elementary schools; two are located in the rural area of Yucatán and the other is in the urban area of Mérida, Yucatán. We analyzed the structure and the communities of these friendship networks and found significant differences among those at the elementary schools compared with those at the university. In elementary schools, the students make friends mainly in the same classroom, but there are also links among different classrooms because of the presence of siblings and relatives in the schools. These kinds of links (sibling-friend or relative-friend) are called, in this work, "mixed links". The classification of the communities is based on their similarity with the classroom composition. If the community is composed principally of students in different classrooms, the community is classified as heterogeneous. These kinds of communities appear in the elementary school friendship networks mainly because of the presence of relatives and siblings. Once the links between siblings and relatives are removed, the communities resembled the classroom composition. On the other hand, the university students are more selective in choosing friends and therefore, even when they have friends in the same classroom, those communities are quite different to the classroom composition. Also, in the university network, we found heterogeneous communities even when the presence of sibling and relatives is negligible. These differences made up a topological structure quite different at different academic levels. We also found differences in the network characteristics. Once these differences are understood, the topological structure of the friendship network and the communities shaped in an elementary school could be predicted if we know the total number of students and the ties between siblings and relatives. However, at the university, we cannot do the same. This discovery implies that friendship is a dynamic concept that produces several changes in the friendship network structure and the way that people make groups of friends; it provides the opportunity to give analytic support to observational studies. Communities were also studied by gender and we found that when the links among relatives and siblings were removed, the number of communities formed by one gender alone increased. At the university, many communities formed by students of the same gender were also found.

Correction: Modeling Social Network Topologies in Elementary Schools.

[This corrects the article on p. e55371 in vol. 8.].

Modeling social network topologies in elementary schools.

Complex networks are used to describe interactions in many real world systems, including economic, biological and social systems. An analysis was done of inter-student friendship, enmity and kinship relationships at three elementary schools by building social networks of these relationships and studying their properties. Friendship network measurements were similar between schools and produced a Poisson topology with a high clustering index. Enmity network measurements were also similar between schools and produced a power law topology. Spatial confinement and the sense of belonging to a social group played vital roles in shaping these networks. Two models were developed which generate complex friendship and enmity networks that reproduce the properties observed at the three studied elementary schools.

Sonoran propolis: chemical composition and antiproliferative activity on cancer cell lines.

In this study, we have analyzed the chemical composition and antiproliferative activity of propolis from three different arid and semiarid regions of Sonora, Mexico. We identified and quantitated the main chemical constituents of propolis by HPLC-MS. The most abundant constituents of propolis were pinocembrin, pinobanksin 3-acetate, and chrysin. Sonoran propolis had a strong antiproliferative activity on both murine and human cancer cell lines in a concentration-dependent manner. The propolis constituents CAPE, galangin, xanthomicrol and chrysin showed significant antiproliferative activity on most of the cancer cells tested. DNA harvested from cancer cell cultures treated with Sonoran propolis exhibited a ladder of internucleosomal DNA cleavage characteristic of apoptosis. In summary, we have identified and quantitated the main constituents of Sonoran propolis. These propolis samples possess a strong antiproliferative activity on cancer cell lines.