Emilio Vilches

Copper mine tailings are hazardous environments characterized by high metal bioavailability, acidic pH, and long-term risks to surrounding ecosystems. Although in-situ phytomanagement is increasingly documented, the way contrasting plant ecological strategies shape rhizosphere microbial assembly and translate structural shifts into realized metabolic functions remains poorly resolved. To address this structure-to-function gap, we compared two phylogenetically divergent pioneer trees that spontaneously co-colonized the Cauquenes Cu tailings (Chile): a deciduous angiosperm (willow) and an evergreen gymnosperm (pine). We evaluated their associations with soluble metal pools, plant metal partitioning, and the taxonomic, network, assembly, and functional attributes of soil bacterial communities. Vegetated soils showed a pH increase from ~4 to ~7 and a >300-fold reduction in soluble Cu relative to unvegetated tailings. The two tree strategies were associated with contrasting metal-partitioning pathways: willow favored Cu retention in roots, whereas pine showed stronger Cu and Zn translocation to shoots. Vegetation also restructured bacterial communities, increasing Proteobacteria dominance, enriching Actinobacteria under willow, and promoting more modular, positively associated networks governed by deterministic assembly (βNTI < -2), in contrast to the stochastic patterns of unvegetated soils. This ecological restructuring was coupled to enhanced functional capacity: PICRUSt2 predictions and EcoPlate assays consistently indicated broader substrate use and higher C/N metabolic potential in vegetated soils, particularly under pine. Together, these findings show that, within the same extreme Cu-tailings substrate, contrasting pioneer tree strategies are associated with coordinated divergence in geochemical hazard attenuation, microbial assembly, network topology, and realized community-level metabolism. This integrative signal provides an ecological framework for tracking revegetation-associated recovery trajectories in extreme mine tailings.

In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly proxregular values and varies continuously with respect to the Hausdorff distance, without smoothness assumptions. We propose a minimal geometric framework for such moving sets, make precise the logical implications between several standard hypotheses in the literature, and provide practical sufficient conditions that apply in particular to constraints defined as finite intersections of sublevel sets. Within this setting, we establish existence of weak and strong solutions and prove pathwise uniqueness for the associated stochastic differential equations reflected in time-dependent domains.

In this paper, we develop an inexact version of the catching-up algorithm for sweeping processes. We define a new notion of approximate projection, which is compatible with any numerical method for approximating exact projections, as this new notion is not restricted to remain strictly within the set. We provide several properties of the new approximate projections, which enable us to prove the convergence of the inexact catching-up algorithm in three general frameworks: prox-regular moving sets, subsmooth moving sets, and merely closed sets. Additionally, we apply our numerical results to address complementarity dynamical systems, particularly electrical circuits with ideal diodes. In this context, we implement the inexact catching-up algorithm using a primal-dual optimization method, which typically does not necessarily guarantee a feasible point. Our results are illustrated through an electrical circuit with ideal diodes. Our results recover classical existence results in the literature and provide new insights into the numerical simulation of sweeping processes.