R. Arnau

S. Iserte, P. Carratalà, R. Arnau et al.

The pressure for Water Resource Recovery Facilities (WRRF) operators to efficiently treat wastewater is greater than ever because of the water crisis, produced by the climate change effects and more restrictive regulations. Technicians and researchers need to evaluate WRRF performance to ensure maximum efficiency. For this purpose, numerical techniques, such as CFD, have been widely applied to the wastewater sector to model biological reactors and secondary settling tanks with high spatial and temporal accuracy. However, limitations such as complexity and learning curve, prevent extending CFD usage among wastewater modeling experts. This paper presents HydroSludge, a framework that provides a series of tools that simplify the implementation of the processes and workflows in a WRRF. This work leverages HydroSludge to preprocess existing data, aid the meshing process, and perform CFD simulations. Its intuitive interface proves itself as an effective tool to increase the efficiency of wastewater treatment

S. Sanjuan, D. A. Méndez, R. Arnau et al.

Heat stress is one of the main welfare and productivity problems faced by dairy cattle in Mediterranean climates. In this study, we approach the prediction of the daily shade-seeking count as a non-linear multivariate regression problem and evaluate two soft computing algorithms -- Random Forests and Neural Networks -- trained on high-resolution behavioral and micro-climatic data collected in a commercial farm in Titaguas (Valencia, Spain) during the 2023 summer season. The raw dataset (6907 daytime observations, 5-10 min resolution) includes the number of cows in the shade, ambient temperature and relative humidity. From these we derive three features: current Temperature--Humidity Index (THI), accumulated daytime THI, and mean night-time THI. To evaluate the models' performance a 5-fold cross-validation is also used. Results show that both soft computing models outperform a single Decision Tree baseline. The best Neural Network (3 hidden layers, 16 neurons each, learning rate = 10e-3) reaches an average RMSE of 14.78, while a Random Forest (10 trees, depth = 5) achieves 14.97 and offers best interpretability. Daily error distributions reveal a median RMSE of 13.84 and confirm that predictions deviate less than one hour from observed shade-seeking peaks. These results demonstrate the suitability of soft computing, data-driven approaches embedded in an applied-mathematical feature framework for modeling noisy biological phenomena, demonstrating their value as low-cost, real-time decision-support tools for precision livestock farming under heat-stress conditions.

R. Arnau, A. González Cortés, E. A. Sánchez Pérez et al.

We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and weighted norms. We analyze the main properties of these metric spaces, which provides the foundation for the analysis of weaker forms of instruments to measure relative distances between walks: proximities. We provide some representation formulas for such proximities under different assumptions and provide explicit constructions for these cases. The resulting metric framework allows the use of classical tools from metric modeling, such as the extension of Lipschitz functions from subspaces of walks, which permits extending proximity functions while preserving fundamental properties via the mentioned representations. Potential applications include the estimation of proximities and the development of reinforcement learning strategies based on exploratory walks, offering a robust approach to Lipschitz regression on network structures.