arXiv subjects

R. Arnau

Publications and source records attributed to R. Arnau.

6 recordsLinked to original sources

arXiv2026

Modeling of Wastewater Treatment Processes with HydroSludge

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

cs.CE↗

arXiv2025

Metric spaces of walks and Lipschitz duality on graphs

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.

cs.LG↗

arXiv2025

Soft Computing Approaches for Predicting Shade-Seeking Behaviour in Dairy Cattle under Heat Stress: A Comparative Study of Random Forests and Neural Networks

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.

cs.LG↗

arXiv2024

Eccentric $p-$summing Lipschitz operators and integral inequalities on metric spaces and graphs

The extension of the concept of $p-$summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space $M$ afforded by the associated Arens-Eells space, along with the duality between $M$ and the metric dual space $M^\#$ defined by the real-valued Lipschitz functions on $M.$ However, alternative approaches to measuring distances between sequences of elements of metric spaces (essentially involved in the definition of $p-$summability) exist. One approach involves considering specific subsets of the unit ball of $M^\#$ for computing the distances between sequences, such as the real Lipschitz functions derived from evaluating the difference of the values of the metric from two points to a fixed point. We introduce new notions of summability for Lipschitz operators involving such functions, which are characterized by integral dominations for those operators. To show the applicability of our results, we use in the last part of the paper the theoretical tools obtained in the first part to the analysis of metric graphs. In particular, we show new results on the behavior of numerical indices defined on these graphs satisfying certain conditions of summability and symmetry.

math.FA↗

arXiv2024

A Bellman-Ford algorithm for the path-length-weighted distance in graphs

Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. Thus, although our algorithm is based on arguments similar to those at work for the Bellman-Ford and Dijkstra methods, it is in fact essentially different. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples.

cs.DS↗

arXiv2024

Moduli of Continuity in Metric Models and Extension of Liveability Indices

Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function $ϕ$. The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modelling of livability indices in North American cities.

stat.ME↗