Heat stress is one of the main welfare and productivity problems faced by dairy cattle in Mediterranean climates. The main objective of this work is to predict heat stress in livestock from shade-seeking behavior captured by computer vision, combined with some climatic features, in a completely non-invasive way. To this end, we evaluate two soft computing algorithms—Random Forests and Neural Networks—clarifying the trade-off between accuracy and interpretability for real-world farm deployment. Data were gathered at a commercial dairy farm in Titaguas (Valencia, Spain) using overhead cameras that counted cows in the shade every 5–10 min during summer 2023. Each record contains the shaded-cow count, ambient temperature, relative humidity, and an exact timestamp. From here, three thermal indices were derived: the current THI, the previous-night mean THI, and the day-time accumulated THI. The resulting dataset covers 75 days and 6907 day-time observations. To evaluate the models’ performance a 5-fold cross-validation is also used. The 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 $={10}^{-3}$) reaches an average RMSE of $14.78$, while a Random Forest (10 trees, depth $=5$) achieves $14.97$ and offers the 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. Although the dataset came from a single farm, the results generalized well within the observed range. However, the models could not accurately predict the exact number of cows in the shade. This suggests the influence of other variables not included in the analysis (such as solar radiation or wind data), which opens the door for future research.

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. 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. It has the distinct characteristic that, when calculated along the same path, it may result in a shorter distance between far-apart vertices than between adjacent ones. This property can be particularly useful for modeling scenarios where the connections between vertices are obscured by numerous intermediate vertices, such as in cases of financial fraud. For example, to hide dirty money from financial authorities, fraudsters often use multiple institutions, banks, and intermediaries between the source of the money and its final recipient. Our distance would serve to make such situations explicit. 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, since the calculation formula contains a weight that explicitly depends on the number of intermediate vertices. This fact totally conditions the algorithm, because longer paths could provide shorter distances—contrary to the classical algorithms mentioned above. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples.

After reviewing various notions of symmetry in graph theory, which are typically defined by the connections between vertices, we demonstrate that traditional concepts of symmetry, such as vertex transitivity, can be too restrictive for certain applications. For instance, in some areas of graph analysis, symmetry based on metric properties (such as average distances between vertices) may be more appropriate, particularly in social network analysis or economic fraud detection. This paper focuses on developing metric-based symmetry concepts by introducing mathematical analysis tools, all related to the central idea of the distance distribution function, to group vertices according to their distance-related properties within the graph. In particular, we prove several results that show, under certain compactness properties for the set of distribution functions of all the vertices in an infinite graph, that it is always possible to group these vertices into a finite number of classes with the desired accuracy based on distances.

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.

Este trabajo presenta una sesión tipo taller dirigida a estudiantes universitarios, cuyo objetivo es introducir los fundamentos de la simulación de datos sintéticos a través de una aplicación práctica en ciencia animal. Usando como ejemplo el comportamiento de cabras registradas mediante sensores de acelerometría triaxial, se explican dos métodos matemáticos clave de simulación: el método de Montecarlo, aplicado tanto a distribuciones discretas no paramétricas —para simular la secuencia de actividades— como a distribuciones continuas paramétricas —para modelar su duración—, y los modelos VAR —para generar señales de aceleración realistas—. La propuesta permite comprender cómo la simulación puede suplir la escasez de datos reales y apoyar el desarrollo de modelos predictivos.