Crouch gait is one of the most common gait abnormalities; it is usually caused by cerebral palsy. There are few works related to the modeling of crouch gait kinematics, crouch gait analysis, and visualization in both the workspace and joint space. In this work, we present a quaternion-based method to solve the forward kinematics of the position of the lower limbs during walking. For this purpose, we propose a modified eight-DoF human skeletal model. Using this model, we present a geometric method to calculate the gait inverse kinematics. Both methods are applied for gait analysis over normal, mild, and severe crouch gaits, respectively. A metric-based comparison of workspace and joint space for the three gaits for a gait cycle is conducted. In addition, gait visualization is performed using Autodesk Maya for the three anatomical planes. The obtained results allow us to determine the capabilities of the proposed methods to assess the performance of crouch gaits, using a normal pattern as a reference. Both forward and inverse kinematic methods could ultimately be applied in rehabilitation settings for the diagnosis and treatment of diseases derived from crouch gaits or other types of gait abnormalities.

Hypertensive disorders in pregnancy, which include preeclampsia, eclampsia, and chronic hypertension, complicate approximately 10% of all pregnancies in the world, constituting one of the most serious causes of mortality and morbidity in gestation. To help predict the occurrence of hypertensive disorders, a study based on algorithms that help model this health problem using mathematical tools is proposed. This study proposes a fuzzy c-means (FCM) model based on the Takagi–Sugeno (T-S) type of fuzzy rule to predict hypertensive disorders in pregnancy. To test different modeling methodologies, cross-validation comparisons were made between random forest, decision tree, support vector machine, and T-S and FCM methods, which achieved 80.00%, 66.25%, 70.00%, and 90.00%, respectively. The evaluation consisted of calculating the true positive rate (TPR) over the true negative rate (TNR), with equal error rate (EER) curves achieving a percentage of 20%. The learning dataset consisted of a total of 371 pregnant women, of which 13.2% were diagnosed with a condition related to gestational hypertension. The dataset for this study was obtained from the Secretaría de Salud del Estado de Hidalgo (SSEH), México. A random sub-sampling technique was used to adjust the class distribution of the data set, and to eliminate the problem of unbalanced classes. The models were trained using a total of 98 samples. The modeling results indicate that the T-S and FCM method has a higher predictive ability than the other three models in this research.

We report electromagnetic field modes solving the inhomogeneous Maxwell equations for parabolic gradient index fibers in the low refractive index contrast approximation. The first family comprises accelerating fields characterized by an intensity distribution center tracing a circular trajectory transverse to the fiber optical axis. These fields maintain an invariant shape for both their intensity and phase distributions while rotating around their center. The second family comprises breathing fields characterized by an intensity distribution center aligned with the fiber optical axis. These fields exhibit intensity distribution scaling along propagation, while their phase swirls and rotates around the optical axis without changing their intensity distribution shape and topological charge.

This paper presents analytical approximations for the inverse error function, its complementary inverse, and the cumulative distribution function using the Power Series Extender Method (PSEM). The proposed expressions exhibit high accuracy over a wide portion of the domain, particularly in the central region, while maintaining a compact structure based on elementary functions. This formulation ensures practical implementation and computational efficiency without the need for specialized numerical algorithms. The use of strategically selected cancellation points further enhances the accuracy of the approximations, especially in regions of interest. As expected for this class of elementary approximations, a gradual loss of accuracy is observed near the boundaries of the domain due to the asymptotic behavior of the inverse functions. To demonstrate the effectiveness and practical relevance of the proposed expressions, two case studies are presented, involving applications in statistical analysis and engineering contexts.

Quantitative analysis of insect locomotion is important for understanding how environmental variables shape behavioral output and for developing reproducible experimental paradigms in neuroethology and biohybrid research. In this study, locomotor responses of the Madagascar hissing cockroach (Gromphadorhina portentosa) were evaluated across a thermal range from 18 to 38 °C using an integrated low-cost platform combining a spherical treadmill motion-tracking system with synchronized environmental regulation of temperature and illumination. The results suggest a possible non-linear relationship between chamber temperature and locomotor activity. Thermal conditions below the programmed 30 °C chamber temperature were generally associated with higher cumulative activity and elevated peak activity-rate values but not low inactivity proportions. In contrast, higher temperatures were associated with more fragmented locomotor patterns characterized by preserved peak activity but increased inactivity proportions. Complementary repeated-measures illumination assays suggested preliminary UV-associated shifts in locomotor output under the tested treadmill conditions. Together, these findings provide a quantitative framework for studying environmentally modulated locomotion in G. portentosa.

Associative memories are a significant topic in pattern recognition, and therefore, throughout history, numerous memory models have been designed due to their usefulness. One such model is the associative memory minmax, which is highly efficient at learning and recalling patterns as well as being tolerant of high levels of additive and subtractive noise. However, it is not efficient when it comes to mixed noise. To solve this issue in the associative memory minmax, we present the generic model of heteroassociative memory max robust to acquisition noise (mixed noise). This solution is based on understanding the behavior of acquisition noise and mapping the location of noise in binary images and gray-scale through a distance transform. By controlling the location of the noise, the associative memories minmax become highly efficient. Furthermore, our proposed model allows patterns to contain mixed noise while still being able to recall the learned patterns completely. Our results show that the proposed model outperforms a model that has already solved this type of problem and has proven to overcome existing methods that show some solution to mixed noise. Additionally, we demonstrate that our model is applicable to all associative minmax memories with excellent results.