We investigate and compare applications of the Zilber–Pink conjecture and dynamical methods to rigidity problems for arithmetic real and complex hyperbolic lattices. Along the way, we obtain new general results about reconstructing a variation of Hodge structure from its typical Hodge locus that may be of independent interest. Applications to Siu’s immersion problem are also discussed, the most general of which only requires the hypothesis that infinitely many closed geodesics map to proper totally geodesic subvarieties under the immersion.

Tiafenacil is a new nonselective protoporphyrinogen IX oxidase (PPO)–inhibiting herbicide with both grass and broadleaf activity labeled for preplant application to corn, cotton, soybean, and wheat. Early-season corn emergence and growth often coincides in the mid-South with preplant herbicide application in cotton and soybean, thereby increasing opportunity for off-target herbicide movement from adjacent fields. Field studies were conducted in 2022 to identify the impacts of reduced rates of tiafenacil (12.5% to 0.4% of the lowest labeled application rate of 24.64 g ai ha–1) applied to two- or four-leaf corn. Corn injury 1 wk after treatment (WAT) for the two- and four-leaf growth stages ranged from 31% to 6% and 37% to 9%, respectively, whereas at 2 WAT these respective ranges were 21.7% to 4% and 22.5% to 7.2%. By 4 WAT, visible injury following the two- and four-leaf exposure timing was no greater than 8% in all instances except the highest tiafenacil rate applied at the four-leaf growth stage (13%). Tiafenacil had no negative season-long impact, as the early-season injury observed was not manifested in a reduction in corn height 2 WAT or yield. Application of tiafenacil directly adjacent to corn in early vegetative stages of growth should be avoided. In cases where off-target movement does occur, however, affected corn should be expected to fully recover with no impact on growth and yield, assuming adequate growing conditions and agronomic/pest management practices are provided.

Migrants and refugees face elevated risks for mental health problems but have limited access to services. This study compared two strategies for training and supervising nonspecialists to deliver a scalable psychological intervention, Group Problem Management Plus (gPM+), in northern Colombia. Adult women who reported elevated psychological distress and functional impairment were randomized to receive gPM+ delivered by nonspecialists who received training and supervision by: 1) a psychologist (specialized technical support); or 2) a nonspecialist who had been trained as a trainer/supervisor (nonspecialized technical support). We examined effectiveness and implementation outcomes using a mixed-methods approach. Thirteen nonspecialists were trained as gPM+ facilitators and three were trained-as-trainers. We enrolled 128 women to participate in gPM+ across the two conditions. Intervention attendance was higher in the specialized technical support condition. The nonspecialized technical support condition demonstrated higher fidelity to gPM+ and lower cost of implementation. Other indicators of effectiveness, adoption and implementation were comparable between the two implementation strategies. These results suggest it is feasible to implement mental health interventions, like gPM+, using lower-resource, community-embedded task sharing models, while maintaining safety and fidelity. Further evidence from fully powered trials is needed to make definitive conclusions about the relative cost of these implementation strategies.