Presentamos una técnica de modulación de señales de tipo senoidal utilizando ideas de la geometría diferencial de superficies y del cálculo fraccionario, en particular de los flujos geodésicos sobre superficies y de la derivada de Caputo de orden fraccionario. El trabajo incia con la introducción de los objetos geométricos denominados embudos que son superficies de revolución con frontera y sobre los cuales se define un flujo geodésico a partir de una señal portadora. Se muestra que si se define la señal modulada punto a punto como la componente normal a la frontera del vector velocidad de una geodésica de dicho flujo, entonces, bajo la derivada usual, tanto señal portadora como señal modulada tienen la misma frecuencia. Sin embargo, se muestra que cuando se utiliza la derivada de Caputo de orden fraccionario variable, donde el orden depende de una señal moduladora, entonces la señal modulada y la señal portadora tienen, en general, parámetros distintos, por lo cual se tiene un método de modulación factible en el cual la señal modulada depende tanto de la señal moduladora como de la geometría del embudo, característica que permite no solo la modulación sino también la encriptación de la información contenida en la señal moduladora.

Path planning and formation control in leader–follower robotic systems are active areas of research, as both are highly relevant to the proper execution of the assigned task. In this work, a dual approach to the A* algorithm is applied to generate consistent trajectories for a multi-agent robotic system with a leader–follower scheme. The conventional A* algorithm aims to minimize the cost of finding the best path by minimizing distances. In this case, a modified A* algorithm is used because, although decision-making also involves choosing among eight options or cells, the goal is not to minimize distance; instead, the focus is on analyzing the direction of acceleration. The proposed algorithm is robust regarding the initial and relative pose of the leader with respect to the followers. The leader is tracked using a digital accelerometer. The algorithm is tested by simulating various patterns and implemented in two experimental test scenarios: the first with differential mobile robots, and the second with an Ackerman-type mobile robot. In both scenarios, the trajectories were achieved with deviations in x and y between the follower’s path and the leader’s path of less than 0.03, and the leader’s pose independence was maintained.

Accurate pharmaceutical demand forecasting is essential to align production with actual market needs, reduce overproduction, prevent stockouts, and improve resource efficiency. This study develops a hybrid bidirectional long short-term memory (BiLSTM)–Transformer model to support sustainable pharmaceutical production through data-driven demand forecasting. We trained the model on real monthly sales and inventory data from a nationwide pharmaceutical company in Mexico, along with epidemiological, climatic, demographic, and economic variables. The study analyzed thirteen sodium naproxen and oseltamivir phosphate pharmaceutical products over forecasting horizons of 3, 6, and 12 months. We evaluated robust scaling and logarithmic transformation during preprocessing and compared the Adam, RMSprop, Nadam, and SGD optimizers. Nadam generally produced the lowest forecasting errors, especially at short- and medium-term horizons. Six of the thirteen evaluated pharmaceutical products achieved cumulative percentage errors below 10% at the three-month forecasting horizon. Compared with the Seasonal Naïve baseline, the proposed model achieved lower cumulative forecasting errors for 11 of 13 products at the 3-month horizon and 9 of 13 products at both the 6- and 12-month horizons, although the baseline performed better for certain products. Performance became more heterogeneous over longer horizons and for products with irregular or highly volatile demand, revealing important limitations for operational use. The findings suggest that hybrid AI-based forecasting may support production planning and inventory management decisions, provided that model selection accounts for product-specific characteristics and forecasting horizons. However, potential benefits related to reduced overproduction, excess inventory, product expiration, and environmental impacts remain prospective applications rather than outcomes directly demonstrated in this study.

This work describes a mathematical model for handwriting devices without a specific reference surface (SRS). The research was carried out on two hypotheses: the first considers possible circular segments that could be made during execution for the reconstruction of the trace, and the second is the combination of lines and circles. The proposed system has no flat reference surface, since the sensor is inside the pencil that describes the trace, not on the surface as in tablets or cell phones. An inertial sensor was used for the measurements, in this case, a commercial Micro-Electro Mechanical sensor of linear acceleration. The tracking device is an IMU sensor and a processing card that allows inertial measurements of the pen during on-the-fly tracing. It is essential to highlight that the system has a non-inertial reference frame. Comparing the two proposed models shows that it is possible to construct shapes from curved lines and that the patterns obtained are similar to what is recognized; this method provides an alternative to quaternion calculus for poorly specified orientation problems.