A variant-dependent molecular clock with anomalous diffusion models SARS-CoV-2 evolution in humans.

The evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in humans has been monitored at an unprecedented level due to the public health crisis, yet the stochastic dynamics underlying such a process is dubious. Here, considering the number of acquired mutations as the displacement of the viral particle from the origin, we performed biostatistical analyses from numerous whole genome sequences on the basis of a time-dependent probabilistic mathematical model. We showed that a model with a constant variant-dependent evolution rate and nonlinear mutational variance with time (i.e., anomalous diffusion) explained the SARS-CoV-2 evolutionary motion in humans during the first 120 wk of the pandemic in the United Kingdom. In particular, we found subdiffusion patterns for the Primal, Alpha, and Omicron variants but a weak superdiffusion pattern for the Delta variant. Our findings indicate that non-Brownian evolutionary motions occur in nature, thereby providing insight for viral phylodynamics.

Gramian angular fields for leveraging pretrained computer vision models with anomalous diffusion trajectories.

Anomalous diffusion is present at all scales, from atomic to large ones. Some exemplary systems are ultracold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, arthropods' free movement, and birds' migration patterns. The characterization of the diffusion gives critical information about the dynamics of these systems and provides an interdisciplinary framework with which to study diffusive transport. Thus, the problem of identifying underlying diffusive regimes and inferring the anomalous diffusion exponent α with high confidence is critical to physics, chemistry, biology, and ecology. Classification and analysis of raw trajectories combining machine learning techniques with statistics extracted from them have widely been studied in the Anomalous Diffusion Challenge [Muñoz-Gil et al., Nat. Commun. 12, 6253 (2021)2041-172310.1038/s41467-021-26320-w]. Here we present a new data-driven method for working with diffusive trajectories. This method utilizes Gramian angular fields (GAF) to encode one-dimensional trajectories as images (Gramian matrices), while preserving their spatiotemporal structure for input to computer-vision models. This allows us to leverage two well-established pretrained computer-vision models, ResNet and MobileNet, to characterize the underlying diffusive regime and infer the anomalous diffusion exponent α. Short raw trajectories of lengths between 10 and 50 are commonly encountered in single-particle tracking experiments and are the most difficult ones to characterize. We show that GAF images can outperform the current state-of-the-art while increasing accessibility to machine learning methods in an applied setting.

Predicting COVID-19 pandemic waves including vaccination data with deep learning.

Introduction: During the recent COVID-19 pandemics, many models were developed to predict the number of new infections. After almost a year, models had also the challenge to include information about the waning effect of vaccines and by infection, and also how this effect start to disappear. Methods: We present a deep learning-based approach to predict the number of daily COVID-19 cases in 30 countries, considering the non-pharmaceutical interventions (NPIs) applied in those countries and including vaccination data of the most used vaccines. Results: We empirically validate the proposed approach for 4 months between January and April 2021, once vaccination was available and applied to the population and the COVID-19 variants were closer to the one considered for developing the vaccines. With the predictions of new cases, we can prescribe NPIs plans that present the best trade-off between the expected number of COVID-19 cases and the social and economic cost of applying such interventions. Discussion: Whereas, mathematical models which include the effect of vaccines in the spread of the SARS-COV-2 pandemic are available, to the best of our knowledge we are the first to propose a data driven method based on recurrent neural networks that considers the waning effect of the immunization acquired either by vaccine administration or by recovering from the illness. This work contributes with an accurate, scalable, data-driven approach to modeling the pandemic curves of cases when vaccination data is available.

Objective comparison of methods to decode anomalous diffusion.

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.