We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave, which emanates from a set of known nodes at an initial time, to all other unknown nodes at later times with an ordering determined by the arrival time of the information wave front. A second class of models is based on the notion of a travel time along paths between nodes. The time of information propagation from an initial known set of nodes to a node is defined as the minimum of a generalised travel time over subsets of all admissible paths. A final class is given by imposing a local equation of an eikonal form at each unknown node, with boundary conditions at the known nodes. The solution value of the local equation at a node is coupled to those of neighbouring nodes with lower values. We provide precise formulations of the model classes and prove equivalences between them. Finally, we apply the front propagation models on graphs to semi-supervised learning via label propagation and information propagation on trust networks.

People with psychosis in Malawi have very limited access to timely assessment and evidence-based care, leading to a long duration of untreated psychosis and persistent disability. Most people with psychosis in the country consult traditional or religious healers. Stigmatising attitudes are common and services have limited capacity, particularly in rural areas. This paper, focusing on pathways to care for psychosis in Malawi, is based on the Wellcome Trust Psychosis Flagship Report on the Landscape of Mental Health Services for Psychosis in Malawi. Its purpose is to inform Psychosis Recovery Orientation in Malawi by Improving Services and Engagement (PROMISE), a longitudinal study that aims to build on existing services to develop sustainable psychosis detection systems and management pathways to promote recovery.

Glyphosate-tolerant and glyphosate-resistant weeds are becoming increasingly problematic in cotton fields in Australia, necessitating a return from a glyphosate dominated system to a more integrated approach to weed management. The development of an integrated weed management system can be facilitated by identifying the critical period for weed control (CPWC), a model that enables cotton growers to optimize the timing of their weed control inputs. Using data from field studies conducted from 2003 to 2015, CPWC models using extended functions, including weed biomass in the relationships, were developed for the mimic weeds, common sunflower and Japanese millet, in high-yielding, fully irrigated cotton. A multispecies CPWC model was developed after combining these data sets with data for mungbean in irrigated cotton, using weed height and weed biomass as descriptors in the models. Comparison of observed and predicted relative cotton-lint yields from the multispecies CPWC model demonstrated that the model reasonably described the competition from these three very different mimic weeds, opening the possibility for cotton growers to use a multispecies CPWC model in their production systems.

Research using the critical period for weed control (CPWC) has shown that high-yielding cotton crops are very sensitive to competition from grasses and large broadleaf weeds, but the CPWC has not been defined for smaller broadleaf weeds in Australian cotton. Field studies were conducted over five seasons from 2003 to 2015 to determine the CPWC for smaller broadleaf weeds, using mungbean as a mimic weed. Mungbean was planted at densities of 1, 3, 6, 15, 30, and 60 plants m−2 with or after cotton emergence and added and removed at approximately 0, 150, 300, 450, 600, 750, and 900 degree days of crop growth (GDD). Mungbean competed strongly with cotton, with season-long interference; 60 mungbean plants m−2 resulted in an 84% reduction in cotton yield. A dynamic CPWC function was developed for densities of 1 to 60 mungbean plants m−2 using extended Gompertz and exponential curves including weed density as a covariate. Using a 1% yield-loss threshold, the CPWC defined by these curves extended for the full growing season of the crop at all weed densities. The minimum yield loss from a single weed control input was 35% at the highest weed density of 60 mungbean plants m−2. The relationship for the critical time of weed removal was further improved by substituting weed biomass for weed density in the relationship.

Field studies were conducted over five seasons from 2004 to 2015 to determine the critical period for weed control (CPWC) in high-yielding, irrigated cotton using a competitive mimic grass weed, Japanese millet. Japanese millet was planted with or after cotton emergence at densities of 10, 20, 50, 100, and 200 plants m−2. Japanese millet was added and removed at approximately 0, 150, 300, 450, 600, 750, and 900 degree days of crop growth (GDD). Data were combined over years. Japanese millet competed strongly with cotton, with season-long interference resulting in an 84% reduction in cotton yield with 200 Japanese millet plants m−2. The data were fit to extended Gompertz and logistic curves including weed density as a covariate, allowing a dynamic CPWC to be estimated for densities of 10 to 200 Japanese millet plants m−2. Using a 1% yield-loss threshold, the CPWC commenced at 65 GDD, corresponding to 0 to 7 d after crop emergence (DAE), and ended at 803 GDD, 76 to 98 DAE with 10 Japanese millet plants m−2, and 975 GDD, 90 to 115 DAE with 200 Japanese millet plants m−2. These results highlight the high level of weed control required throughout the cropping season in high-yielding cotton to ensure crop losses do not exceed the cost of weed control.

Field studies were conducted over six seasons to determine the critical period for weed control (CPWC) in high-yielding cotton, using common sunflower as a mimic weed. Common sunflower was planted with or after cotton emergence at densities of 1, 2, 5, 10, 20, and 50 plants m−2. Common sunflower was added and removed at approximately 0, 150, 300, 450, 600, 750, and 900 growing degree days (GDD) after planting. Season-long interference resulted in no harvestable cotton at densities of five or more common sunflower plants m−2. High levels of intraspecific and interspecific competition occurred at the highest weed densities, with increases in weed biomass and reductions in crop yield not proportional to the changes in weed density. Using a 5% yield-loss threshold, the CPWC extended from 43 to 615 GDD, and 20 to 1,512 GDD for one and 50 common sunflower plants m−2, respectively. These results highlight the high level of weed control required in high-yielding cotton to ensure crop losses do not exceed the cost of control.

Crop plants have been used as mimic weeds to substitute for real weeds in competition studies. These mimic weeds have the advantages of availability of seed, uniform germination and growth, and the potential to confer better experimental controllability and repeatability. However, the underlying assumption that the competitive effects of mimic weeds are similar to real weeds has not been tested. We compared a range of morphological traits (plant height, node and leaf number, leaf area, leaf size, and dry weight) between the mimic weeds and real weeds: Japanese millet vs. junglerice, mungbean vs. bladder ketmia, and common sunflower vs. fierce thornapple. The impact of these mimic and real weeds on cotton was also assessed. There were similarities and differences between the mimic and real weeds, but impact on cotton lint yield was most closely associated with weed height and dry weight at mid-season. Mimic weeds may be satisfactorily substituted for real weeds in competition experiments where seasonal and environmental conditions are not limiting, such as with fully irrigated cotton, provided the plants have similar dry weight and height at mid-season. Alternatively, one can account for the differences in dry weight and height. We define here a generalized relationship estimating the yield loss of high-yielding, irrigated cotton from weed competition over a range of weed dry weights and heights, allowing extrapolation from the results with mimic weeds to the competitive effects of a range of weeds.

Extended abstract of a paper presented at Microscopy and Microanalysis 2004 in Savannah, Georgia, USA, August 1–5, 2004.