Several designs of recurrent neural networks have been proposed in the literature involving different clock times. However, the stability and synchronization of this kind of system have not been studied. In this paper, we consider that each neuron or group of neurons of a switched recurrent neural network can have a different sampling period for its activation, which we call switched multi-rate recurrent neural networks, and we propose a dynamical model to describe it. Through Lyapunov methods, sufficient conditions are provided to guarantee the exponential stability of the network. Additionally, these results are extended to the synchronization problem of two identical networks, understanding the synchronization as the agreement of both of them in time. Numerical simulations are presented to validate the theoretical results. The proposed method might help to design more efficient and less computationally demanding neural networks.

In the realm of offline handwritten text recognition, numerous normalization algorithms have been developed over the years to serve as preprocessing steps prior to applying automatic recognition models to handwritten text scanned images. These algorithms have demonstrated effectiveness in enhancing the overall performance of recognition architectures. However, many of these methods rely heavily on heuristic strategies that are not seamlessly integrated with the recognition architecture itself. This paper introduces the use of a Pix2Pix trainable model, a specific type of conditional generative adversarial network, as the method to normalize handwritten text images. Also, this algorithm can be seamlessly integrated as the initial stage of any deep learning architecture designed for handwritten recognition tasks. All of this facilitates training the normalization and recognition components as a unified whole, while still maintaining some interpretability of each module. Our proposed normalization approach learns from a blend of heuristic transformations applied to text images, aiming to mitigate the impact of intra-personal handwriting variability among different writers. As a result, it achieves slope and slant normalizations, alongside other conventional preprocessing objectives, such as normalizing the size of text ascenders and descenders. We will demonstrate that the proposed architecture replicates, and in certain cases surpasses, the results of a widely used heuristic algorithm across two metrics and when integrated as the first step of a deep recognition architecture.

This paper presents a new approach to analyze the teaching assignment plan of a large-sized university department, combining different graph visualizations and complex network metrics. In this study, we propose the usage of a macro-scale analysis solution to offer an overall vision to the department chair and the teaching committee for effective decision making. The proposed method offers several advantages, such as helping the department to identify which faculty categories are overburdened, detect flaws and re-assign courses to faculty members according to their expertise, discover gaps in faculty expertise for future teaching recruitment, among other aspects. The proposed analysis approach is illustrated with a practical use case corresponding to a Spanish Computer Science department of more than 150 teachers and a total of nearly 310 courses taught. The analysis revealed, among other findings, that: there are no distinct subgroups (i.e., clusters) within the department under study; all faculty categories are assigned to at least two types of courses; each course type has at least one primary faculty category that assumes the majority of teaching hours; all faculty categories are interconnected through the course types; and no faculty category systematically avoids any particular course type, although certain course types are noticeably less preferred. All the data and code related to this project can be downloaded from the following GitHub repository: https://github.com/jfvelezserrano/TAP.