This paper reviews the application of artificial neural network (ANN) models to time series prediction tasks. We begin by briefly introducing some basic concepts and terms related to time series analysis, and by outlining some of the most popular ANN architectures considered in the literature for time series forecasting purposes: feedforward neural networks, radial basis function networks, recurrent neural networks, and self-organizing maps. We analyze the strengths and weaknesses of these architectures in the context of time series modeling. We then summarize some recent time series ANN modeling applications found in the literature, focusing mainly on the previously outlined architectures. In our opinion, these summarized techniques constitute a representative sample of the research and development efforts made in this field. We aim to provide the general reader with a good perspective on how ANNs have been employed for time series modeling and forecasting tasks. Finally, we comment on possible new research directions in this area.

In this work, we consider a generalized form of the classical $(2+1)$-dimensional sine-Gordon system. The mathematical model considers a generalized reaction term, and the two-dimensional Laplacian includes the presence of space-fractional derivatives of the Riesz type with two different differentiation orders in general. The system is equipped with a conserved quantity that resembles the energy functional in the integer-order scenario. We propose a numerical model to approximate the solutions of the fractional sine-Gordon equation. A discretized form of the energy-like quantity is proposed, and we prove that it is conserved throughout the discrete time. Moreover, the analysis of consistency, stability, and convergence is rigorously carried out. The numerical model is implemented computationally, and some computer simulations are presented in this work. As a consequence of our simulations, we show that the discrete energy is approximately conserved throughout time, which coincides with the theoretical results.

In this manuscript, we derive soliton solutions for the (2 + 1)-dimensional nonlinear dissipative Zabolotskaya–Khokhlov equation. This equation addresses nonlinear effects in stratified media and controls the diffraction of sound beam propagation. The dynamical wave solutions are generated by using the bilinear neural network method. These solutions are composed by the specific activation functions of single-layer “3-3-1” model, to obtain the breather wave and lump wave soliton solutions. Meanwhile, a “3-4-1” a model is used to derive the lump wave interaction with the double exponential functions. Moreover, the double-layer model activation function “3-3-4-1” is considered to get the rough wave solitons, while a “3-2-2-1” model is applied to construct the periodic wave. The symbolic computational software Maple is used to verify these solutions and to draw plots for the physical interpretation. The graphical visualization of these solutions is shows in the form of three-dimensional, line and density plots. These results may shed some light in our understanding of the nonlinear dissipative Zabolotskaya–Khokhlov equation.

En este trabajo se presenta un algoritmo de procesamiento de video para mejorar la calidad y facilitar el seguimiento de una rata en un entorno con iluminación roja, optimizado para el software Fiji. El algoritmo emplea técnicas como filtros generales y morfológicos, cambio de dimensiones, resta entre fotogramas y umbralización. Estas técnicas fueron seleccionadas por su efectividad para eliminar ruido y resaltar objetos bajo luz roja. Se proponen además ajustes en el entorno experimental para mejorar el contraste y la precisión del seguimiento.