Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

The results of the Anomalous Diffusion Challenge (AnDi Challenge) (Muñoz-Gil et al, 2021) have shown that machine learning methods can outperform classical statistical methodology at the characterizing of anomalous diffusion in both the inference of the anomalous diffusion exponent $\alpha$ associated with each trajectory (Task 1), and the determination of the underlying diffusive regime which produced such trajectories (Task 2). Furthermore, of the five teams that finished in the top three across both tasks of the AnDi challenge, three of those teams used \textit{recurrent neural networks} (RNNs). While RNNs, like the \textit{long short-term memory} (LSTM) network, are effective at learning long-term dependencies in sequential data, their key disadvantage is that they must be trained sequentially. In order to facilitate training with larger data sets, by training in parallel, we propose a new \textit{transformer} based neural network architecture for the characterization of anomalous diffusion. Our new architecture, the \textit{Convolutional Transformer} (ConvTransformer) uses a bi-layered convolutional neural network to extract features from our diffusive trajectories that can be thought of as being words in a sentence. These features are then fed to two transformer encoding blocks that perform either regression (Task 1) or classification (Task 2). To our knowledge, this is the first time transformers have been used for characterizing anomalous diffusion. Moreover, this may be the first time that a transformer encoding block has been used with a convolutional neural network and without the need for a transformer decoding block or positional encoding. Apart from being able to train in parallel, we show that the ConvTransformer is able to outperform the previous state-of-the-art at determining the underlying diffusive regime (Task2) in short trajectories (length 10-50 steps), which are the most important for experimental researchers.

Integrated pest management (IPM) programs for the spotted-wing drosophila Drosophila suzukii (Diptera: Drosophilidae) rely on insecticide applications to reduce adult populations and prevent fruit infestation. Although monitoring traps are used for early D. suzukii adult detection to time the start of insecticide applications, it remains unclear whether trap counts can be used to determine the efficacy of these programs and predict the risk of fruit infestation. To address this, a 2-yr study (2016–2017) was conducted in highbush blueberries in New Jersey (USA) to interpret D. suzukii trap count variation in relation to the frequency of insecticide applications and proximity to forest habitats. We also correlated trap counts with fruit infestation and used traps to determine the maximum dispersive distance traveled by D. suzukii adults within blueberry fields by using mark-release-capture studies. Using a trapping network across nine farms, we demonstrated that insecticide applications reduce D. suzukii trap counts, but this varied according to seasonality, and that traps placed closer to forest habitats within farms had higher fly counts than those placed in farm interiors. Moreover, blueberry fields that had zero fruit infestation also had predictably lower trap counts than fields with infested fruit, and the maximum dispersive distance for D. suzukii within blueberry fields was 90 m. In summary, while D. suzukii trap counts in blueberry farms could predict the frequency of insecticide applications and fruit infestation, the predictive power of our trap data was too variable across the blueberry harvest period to make it a reliable tool.

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This 2-year study (2013–2014) assessed the efficacy of an odor-baited “trap bush” approach to aggregate plum curculio, Conotrachelus nenuphar, adult injury, i.e., number of oviposition-scared fruit, in four commercial highbush blueberry farms in New Jersey (USA). In each farm, we compared fruit injury in bushes baited with grandisoic acid and benzaldehyde along the perimeter of trap-bush plots versus unbaited bushes in control plots. We also measured the amount of fruit injury in neighboring bushes (i.e., spillover effect) and in the plots’ interior. In both years, the amount of fruit injury by C. nenuphar adults was greater on and near odor-baited bushes in trap-bush plots compared with those on and near unbaited bushes in control plots, indicative of aggregation. Injury in unbaited bushes neighboring trap bushes was often greater than unbaited bushes in control plots, providing some evidence for a spillover effect. However, no difference in fruit injury was found between interior trap-bush and control plots. Therefore, odor-baited trap bushes can be used in blueberries to manipulate C. nenuphar foraging behavior, i.e., aggregate adults, without compromising injury in field interiors. Under this approach, insecticides could then be targeted at only a few (perimeter-row) bushes within fields rather than entire fields.