A Model for Ant Trail Formation and its Convergence Properties (Extended Abstract)

We introduce a model for ant trail formation, building upon previous work on biologically feasible local algorithms that plausibly describe how ants maintain trail networks. The model is a variant of a reinforced random walk on a directed graph, where ants lay pheromone on edges as they traverse them and the next edge to traverse is chosen based on the level of pheromone; this pheromone decays with time. There is a bidirectional flow of ants in the network: the forward flow proceeds along forward edges from source (e.g. the nest) to sink (e.g. a food source), and the backward flow in the opposite direction. Some fraction of ants are lost as they pass through each node (modeling the loss of ants due to exploration observed in the field). We initiate a theoretical study of this model. We note that ant navigation has inspired the field of ant colony optimization, heuristics that have been applied to several combinatorial optimization problems; however the algorithms developed there are considerably more complex and not constrained to being biologically feasible. We first consider the linear decision rule, where the flow divides itself among the next set of edges in proportion to their pheromone level. Here, we show that the process converges to the path with minimum leakage when the forward and backward flows do not change over time. On the other hand, when the forward and backward flows increase over time (caused by positive reinforcement from the discovery of a food source, for example), we show that the process converges to the shortest path. These results are for graphs consisting of two parallel paths (a case that has been investigated before in experiments). Through simulations, we show that these results hold for more general graphs drawn from various random graph models; proving this convergence in the general case is an interesting open problem. Further, to understand the behaviour of other decision rules beyond the linear rule, we consider a general family of decision rules. For this family, we show that there is no advantage of using a non-linear decision rule, if the goal is to find the shortest or the minimum leakage path. We also show that bidirectional flow is necessary for convergence to such paths. Our results provide a plausible explanation for field observations, and open up new avenues for further theoretical and experimental investigation

Arboreal Ants Suggest Surprising Algorithms for the Shortest Path Problem and its Variants

The arboreal turtle ant creates trail networks linking nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants lay a volatile pheromone on edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a field study, Chandrasekhar et al. (2021) observed that trail networks approximately minimize the number of vertices, solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of reinforced random walk on a graph, that explains this observation, and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics of our model converges to the path with the minimum number of vertices, explaining the field observations. The dynamics converges to the shortest path when the rate of flow increases with time, showing that an ant colony can solve the shortest path problem just by varying the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules.Comment: New simulation results and significant changes in presentation compared to the previous versio

Influence of Biostimulants on Yield and Quality of Dendrobium Orchid (Dendrobium Nobile Lindl.) var. Sonia-17 under Protected Cultivation

An experiment was carried out at farmer’s field, Chapparamane during 2017-19 to know the efficacy of biostimulants on yield and quality of dendrobium orchid var. Sonia-17. Eight biostimulants in two combinations were taken for the study in comparision with Recommended dose of Fertilizers (30:10:10 at vegetative stage and 10:20:20 at flowering stage) as control. The results revealed that among the biostimulant treatments, the plants receiving Biovita (Brown seaweed extract) @ 1.5 per cent produced maximum number of spikes per plant, spikes per square meter and spike yield per 560 square meter (3.93, 55.67 and 31,170 numbers, respectively) with maximum number of florets per spike (9.74), spike length (45.89 cm) spike girth (4.10 mm), spike weight (30.06 g),  diameter of floret (9.14 cm) and enhanced vase life of 32.75 days compared to all other treatments and control

Heat-stable carbetocin versus oxytocin to prevent hemorrhage after vaginal birth

10.1056/NEJMoa1805489New England Journal of Medicine3798743-75