Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

El audiovisual como herramienta de cambio social de jóvenes en situación de exclusión en Guatemala (2004-2014)

The audiovisual as a tool for social change among youth in social exclusion situations in Guatemala (2004-2014)” is the title of this research paper which aims to study the organizations and projects that have worked with video tools and participatory methodology with young people in marginalized social sectors in order to improve their opportunities and social inclusion. The purpose of this study also includes the analysis of the finish video products as well as the impact of the projects on the youth participants. Guatemala is a country with deep rooted and historical social inequality. This situation is currently reflected by the high violence rates, the extreme poverty and the exclusion of populations, including youth. As social participants, young people have much to say about the construction of a future plan for the country, but they are not heard. That’s why it is so important to facilitate a youth voice and research the tools that can help reach that goal. The participatory methodologies are based on the popular education theories developed by the Latinamerican School with authors such as Paulo Freire, Juan Díaz Bordenave, Jesús Martín Barbero and Mario Kaplún, among others. These methodologies have proved to be a lateral way to face the educational process by promoting dialogue, analysis, consensus search and consciousness-raising. In addition, these methodologies provide a more democratic way to format educational processes that provide students tools to promote an active attitude towards social questions. They can develop their own role of responsibility in the improvement of their own lives and contribute to the progress of their community. This research is based on observation, an extensive bibliographical review, analysis protocols for the study of video materials and projects and closed structured interviews with facilitators and project coordinators. It includes open qualitative interviews with some selected participants and with other specialists in order to complete the necessary information to structure the historical, social and political context of Guatemala...

A Diagnostic Calculator for Detecting Glaucoma on the Basis of Retinal Nerve Fiber Layer, Optic Disc, and Retinal Ganglion Cell Analysis by Optical Coherence Tomography

Purpose: The purpose of this study was to develop and validate a multivariate predictive model to detect glaucoma by using a combination of retinal nerve fiber layer (RNFL), retinal ganglion cell-inner plexiform (GCIPL), and optic disc parameters measured using spectral-domain optical coherence tomography (OCT). Methods: Five hundred eyes from 500 participants and 187 eyes of another 187 participants were included in the study and validation groups, respectively. Patients with glaucoma were classified in five groups based on visual field damage. Sensitivity and specificity of all glaucoma OCT parameters were analyzed. Receiver operating characteristic curves (ROC) and areas under the ROC (AUC) were compared. Three predictive multivariate models (quantitative, qualitative, and combined) that used a combination of the best OCT parameters were constructed. A diagnostic calculator was created using the combined multivariate model. Results: The best AUC parameters were: inferior RNFL, average RNFL, vertical cup/disc ratio, minimal GCIPL, and inferior-temporal GCIPL. Comparisons among the parameters did not show that the GCIPL parameters were better than those of the RNFL in early and advanced glaucoma. The highest AUC was in the combined predictive model (0.937; 95% confidence interval, 0.911–0.957) and was significantly (P = 0.0001) higher than the other isolated parameters considered in early and advanced glaucoma. The validation group displayed similar results to those of the study group. Conclusions: Best GCIPL, RNFL, and optic disc parameters showed a similar ability to detect glaucoma. The combined predictive formula improved the glaucoma detection compared to the best isolated parameters evaluated. The diagnostic calculator obtained good classification from participants in both the study and validation groups.