Carlo Manzo

Gabriel Fernández-Fernández, Carlo Manzo, Maciej Lewenstein et al.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $β$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

Jesús Pineda, Sergi Masó-Orriols, Joan Bertran et al.

Single-molecule localization microscopy generates point clouds corresponding to fluorophore localizations. Spatial cluster identification and analysis of these point clouds are crucial for extracting insights about molecular organization. However, this task becomes challenging in the presence of localization noise, high point density, or complex biological structures. Here, we introduce MIRO (Multimodal Integration through Relational Optimization), an algorithm that uses recurrent graph neural networks to transform the point clouds in order to improve clustering efficiency when applying conventional clustering techniques. We show that MIRO supports simultaneous processing of clusters of different shapes and at multiple scales, demonstrating improved performance across varied datasets. Our comprehensive evaluation demonstrates MIRO's transformative potential for single-molecule localization applications, showcasing its capability to revolutionize cluster analysis and provide accurate, reliable details of molecular architecture. In addition, MIRO's robust clustering capabilities hold promise for applications in various fields such as neuroscience, for the analysis of neural connectivity patterns, and environmental science, for studying spatial distributions of ecological data.

Mirja Granfors, Jesús Pineda, Blanca Zufiria Gerbolés et al.

Graphs provide a powerful framework for modeling complex systems, but their structural variability poses significant challenges for analysis and classification. To address these challenges, we introduce GAUDI (Graph Autoencoder Uncovering Descriptive Information), a novel unsupervised geometric deep learning framework designed to capture both local details and global structure. GAUDI employs an innovative hourglass architecture with hierarchical pooling and upsampling layers linked through skip connections, which preserve essential connectivity information throughout the encoding-decoding process. Even though identical or highly similar underlying parameters describing a system's state can lead to significant variability in graph realizations, GAUDI consistently maps them into nearby regions of a structured and continuous latent space, effectively disentangling invariant process-level features from stochastic noise. We demonstrate GAUDI's versatility across multiple applications, including small-world networks modeling, characterization of protein assemblies from super-resolution microscopy, analysis of collective motion in the Vicsek model, and identification of age-related changes in brain connectivity. Comparison with related approaches highlights GAUDI's superior performance in analyzing complex graphs, providing new insights into emergent phenomena across diverse scientific domains.

Carlo Manzo

The study of the dynamics of natural and artificial systems has provided several examples of deviations from Brownian behavior, generally defined as anomalous diffusion. The investigation of these dynamics can provide a better understanding of diffusing objects and their surrounding media, but a quantitative characterization from individual trajectories is often challenging. Efforts devoted to improving anomalous diffusion detection using classical statistics and machine learning have produced several new methods. Recently, the anomalous diffusion challenge (AnDi, www.andi-challenge.org) was launched to objectively assess these approaches on a common dataset, focusing on three aspects of anomalous diffusion: the inference of the anomalous diffusion exponent; the classification of the diffusion model; and the segmentation of trajectories. In this article, I describe a simple approach to tackle the tasks of the AnDi challenge by combining extreme learning machine and feature engineering (AnDi-ELM). The method reaches satisfactory performance while offering a straightforward implementation and fast training time with limited computing resources, making it a suitable tool for fast preliminary screening of anomalous diffusion.

Gorka Muñoz-Gil, Miguel Angel Garcia-March, Carlo Manzo et al.

In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion, and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate even very short trajectories to the underlying diffusion mechanism with a high accuracy. In addition, the method is able to classify the motion according to normal or anomalous diffusion, and determine its anomalous exponent with a small error. The method provides highly accurate outputs even when working with very short trajectories and in the presence of experimental noise. We further demonstrate the application of transfer learning to experimental and simulated data not included in the training/testing dataset. This allows for a full, high-accuracy characterization of experimental trajectories without the need of any prior information.