Matchings on infinite graphs

Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We overcome this lack of correlation decay by introducing a perturbative parameter (temperature), which we let progressively go to zero. This allows us to uniquely identify the correct solution. In the important case where the graph limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation that can be solved explicitly, leading to a new asymptotic formula that considerably extends the well-known one by Karp and Sipser for Erd\"os-R\'enyi random graphs.Comment: 23 page

Chloroplast morphology and pyrenoid ultrastructural analyses reappraise the diversity of the lichen phycobiont genus Trebouxia (Chlorophyta)

Trebouxiophyceae is a wide class of green algae comprising coccoid and elliptic unicells, filaments, blades and colony-forming species that occur in diverse terrestrial and aquatic environments. Within this class, the genus Trebouxia Puymaly is among the most widespread lichen phycobionts worldwide. However, the 29 formally described species based on the combination of morphological traits and genetic diversity woefully underrepresented the overall species-level diversity recognized in the genus. In Trebouxia, reliable differentiation and characterization of the species-level lineages can be achieved by studying the diversity of key diagnostic features of pyrenoid ultrastructure and chloroplast morphology of axenically grown algal cultures. Here, we used transmission electron microscopy (TEM) coupled with confocal laser scanning microscopy (CLSM) to analyze the pyrenoid and the chloroplast of 20 Trebouxia species-level lineages grown directly on solid agar medium and on cellulose-acetate discs laid over the agar medium. With the new, detailed morphoanatomical characterization of these species-level lineages, we reappraise Trebouxia taxonomy in light of the most recent phylogenetic delimitation provided by Muggia et al. (2020)

Lotus Spp.: A foreigner that came to stay forever: Economic and environmental changes caused by its naturalization in the Salado River Basin (Argentina)

The Flooding Pampas in Buenos Aires Province is Argentina’s is one of cattle-raising areas. Climatic, topographic and edaphic conditions limit its potential in this area for growing crops such as soybean and wheat. The introduction of L. tenuis in the Flooding Pampas area triggered research based on its ability to tolerate the abiotic stresses that characterize the region and on its role in the improvement of the quality of forage resources. Along with research on abiotic stress tolerance, productive strategies have been developed to enhance the establishment of L. tenuis grassland and beef production. Research on Lotus spp. in the Flooding Pampas has therefore studied not only the biotechnological development and evaluation of new plant resources, but also the accompanying plant diversity, soil microorganisms and symbionts and their impact on environmental dynamics and sustainability. Based on this research, productive strategies have been designed, including continuous evaluation of the impact of cattle production on vulnerable ecosystems. In addition, basic and applied research on grasslands have been combined in order to respond to the environmental impact of the introduction and use of Lotus in these particular ecosystems.Fil: Nieva, Amira Susana del Valle. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Biotecnológicas. Instituto de Investigaciones Biotecnológicas "Dr. Raúl Alfonsín" (sede Chascomús). Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas. Instituto de Investigaciones Biotecnológicas "Dr. Raúl Alfonsín" (sede Chascomús); Argentina. Institut Max Planck fur Molekulare Physiologie; AlemaniaFil: Ruiz, Oscar Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Biotecnológicas. Instituto de Investigaciones Biotecnológicas "Dr. Raúl Alfonsín" (sede Chascomús). Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas. Instituto de Investigaciones Biotecnológicas "Dr. Raúl Alfonsín" (sede Chascomús); Argentin