Mathematics Research Center

Cognitive Computing (CC), as a promising technological paradigm, brings computational systems closer to human reasoning in order to solve complex problems across sectors that demand efficiency, reliability, and innovation. This article presents an analysis of CC modeling processes applied to the industrial sector, through a Systematic Review (SR) of studies published between 2019 and 2024. The results, organized around three guiding questions, enabled the comparison of six selected studies, highlighting their practical applications, advantages, and limitations. The conclusions demonstrate the potential of CC in industrial applications and its integration with emerging technologies. The study also identifies challenges and research gaps, and provides recommendations for future practices and investigations.

This study presented a novel application of the VQE to approximate the solution of the one-dimensional Helmholtz equation, a fundamental problem in seismic modeling. By reformulating the problem as an eigenvalue problem and implementing it within a hybrid quantum-classical framework, we demonstrated the feasibility of using quantum computing tools, specifically the VQE algorithm with the EfficientSU2 ansatz, for Helmholtz-based modeling. The results obtained for systems with 2 to 4 qubits showed good agreement with the analytical solution, indicating that quantum algorithms can capture the essential behavior of physical systems. Importantly, this work also highlights some of the limitations of the current generation of quantum algorithms, such as increased errors for larger qubit counts and sensitivity to the choice of ansatz and optimizer.

The scalar Helmholtz equation, governing wave propagation in the frequency domain for media with variable velocity and constant density, can be reformulated as a Lippmann-Schwinger integral equation. The resulting discretized linear system is large and computationally expensive to solve directly, making iterative methods more practical. The Traditional Born Series (TBS) offers a low-cost approximation but converges only for weak scattering potentials. To overcome this, modified scattering series with enhanced convergence, such as the Convergent Born Series (CBS), use preconditioners based on the scattering potential or generalized over-relaxation. This work introduces a Modified Born Series (MBS) within a reconditioned Richardson iteration, equivalent to CBS and convergent in strongly scattering media. Numerical tests compare MBS seismograms with time-domain extrapolation results, showing MBS as an effective alternative.

Marchenko multiple elimination (MME) is a data-driven scheme capable of attenuating internal multiples of all orders, provided that the seismic data amplitudes are correctly normalized using an optimal global scale factor (SF). MME tends to be inefficient when the optimal SF is unknown, highlighting its dependence on a SF. This work combines the MME scheme with an adaptive filter based on a U-Net neural network to reduce this dependence. The results prove that the proposed approach effectively removes internal multiples even when the optimal SF is unavailable.

This paper presents a systematic literature review of the application of retrieval-augmented generation (RAG) systems in educational settings, with a focus on teaching software engineering and related computing disciplines. Drawing on case studies, academic experiments, and surveys of teachers and students, it provides an overview of the current landscape, highlighting perceptions, reported effectiveness, and the technology’s impact in academia. Based on an analysis of 71 selected scientific papers, the review synthesises evidence on the extent to which RAG systems mitigate hallucinations and improve human–AI interaction. In addition, it suggests that many approaches discussed across studies could be strategically aligned with the integration of DevOps practices and RAG, enhancing their use through automation, continuous improvement, and the agile adoption of technologies within educational processes.

Nowadays, the teaching of mathematics has been modified as electronic instruments advance. Throughout history, teaching has evolved in an impressive way. Today, education is not immune to all these changes, and therefore, it relies on current technology. One of the most important branches of this evolution in mathematics education is virtual reality. In Mexico, there are several lines of research to develop mathematical skills. This is why this work conducts an investigation into the implementation of virtual reality applied to mathematics education with a pedagogical focus and supported by a multidisciplinary group. This is achieved through an ecosystem model that helps create, implement, and provide feedback on current technology. This work proposes a case study, its implementation, and the acquisition of implementation results, which are subsequently analysed.

Convolutional neural networks (CNNs) are widely used for image classification; however, setting the appropriate hyperparameters before training is subjective and time consuming, and the search space is not properly explored. This paper presents a novel method for the automatic neural architecture search based on an estimation of distribution algorithm (EDA) for binary classification problems. The hyperparameters were coded in binary form due to the nature of the metaheuristics used in the automatic search stage of CNN architectures which was performed using the Boltzmann Univariate Marginal Distribution algorithm (BUMDA) chosen by statistical comparison between four metaheuristics to explore the search space, whose computational complexity is O(229). Moreover, the proposed method is compared with multiple state-of-the-art methods on five databases, testing its efficiency in terms of accuracy and F1-score. In the experimental results, the proposed method achieved an F1-score of 97.2%, 98.73%, 97.23%, 98.36%, and 98.7% in its best evaluation, better results than the literature. Finally, the computational time of the proposed method for the test set was ≈0.6 s, 1 s, 0.7 s, 0.5 s, and 0.1 s, respectively.