Feature Papers in Mathematical and Computational Applications 2023

Editors

SISSA mathLab, International School for Advanced Studies, Office A-435, Via Bonomea 265, 34136 Trieste, Italy
Interests: numerical analysis and scientific computing; reduced order modelling and methods; efficient reduced-basis methods for parametrized PDEs and a posteriori error estimation; computational fluid dynamics: aero-naval-mechanical engineering; blood flows (haemodynamics); environmental fluid dynamics; multi-physics; software in computational science and engineering
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Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy
Interests: modeling of offshore structures and offshore structural components; structural theories of plates and applied mathematical modeling; mechanics of solids and structures; study of composite laminated structures and advanced composite materials; fracture mechanics and crack propagation and initiation; applied numerical methods such as finite element method and mesh-free element method
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Topical Collection Information

Dear Colleagues,

We are pleased to announce that the journal Mathematical and Computational Applications is presently compiling a collection of papers submitted exclusively by our Editorial Board Members (EBMs) and outstanding scholars in this research field.

The purpose of this collection is to publish a set of papers that typify the most insightful and influential original articles or reviews in which our EBMs discuss key topics in the field. We expect these papers to be widely read and highly influential. All papers in this collection will be collected into a printed book edition that will be extensively promoted.

Prof. Dr. Gianluigi Rozza
Prof. Dr. Oliver Schütze
Dr. Nicholas Fantuzzi
Collection Editors

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Published Papers (14 papers)

2023

17 pages, 846 KiB  
Article
Fokker–Planck Analysis of Superresolution Microscopy Images
by Mario Annunziato and Alfio Borzì
Math. Comput. Appl. 2023, 28(6), 113; https://doi.org/10.3390/mca28060113 - 14 Dec 2023
Viewed by 1206
Abstract
A method for the analysis of super-resolution microscopy images is presented. This method is based on the analysis of stochastic trajectories of particles moving on the membrane of a cell with the assumption that this motion is determined by the properties of this [...] Read more.
A method for the analysis of super-resolution microscopy images is presented. This method is based on the analysis of stochastic trajectories of particles moving on the membrane of a cell with the assumption that this motion is determined by the properties of this membrane. Thus, the purpose of this method is to recover the structural properties of the membrane by solving an inverse problem governed by the Fokker–Planck equation related to the stochastic trajectories. Results of numerical experiments demonstrate the ability of the proposed method to reconstruct the potential of a cell membrane by using synthetic data similar those captured by super-resolution microscopy of luminescent activated proteins. Full article
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23 pages, 7673 KiB  
Article
Comparative Study of Metaheuristic Optimization of Convolutional Neural Networks Applied to Face Mask Classification
by Patricia Melin, Daniela Sánchez, Martha Pulido and Oscar Castillo
Math. Comput. Appl. 2023, 28(6), 107; https://doi.org/10.3390/mca28060107 - 01 Nov 2023
Viewed by 1578
Abstract
The preventive measures taken to curb the spread of COVID-19 have emphasized the importance of wearing face masks to prevent potential infection with serious diseases during daily activities or for medical professionals working in hospitals. Due to the mandatory use of face masks, [...] Read more.
The preventive measures taken to curb the spread of COVID-19 have emphasized the importance of wearing face masks to prevent potential infection with serious diseases during daily activities or for medical professionals working in hospitals. Due to the mandatory use of face masks, various methods employing artificial intelligence and deep learning have emerged to detect whether individuals are wearing masks. In this paper, we utilized convolutional neural networks (CNNs) to classify the use of face masks into three categories: no mask, incorrect mask, and proper mask. Establishing the appropriate CNN architecture can be a demanding task. This study compares four swarm intelligent metaheuristics: particle swarm optimization (PSO), grey wolf optimizer (GWO), bat algorithm (BA), and whale optimization algorithm (WOA). The CNN architecture design involves determining the essential hyperparameters of the CNNs. The results indicate the effectiveness of the PSO and BA in achieving an accuracy of 100% when using 10% of the images for testing. Meanwhile, when 90% of the images were used for testing, the results were as follows: PSO 97.15%, WOA 97.14%, BA 97.23%, and GWO 97.18%. These statistically significant differences demonstrate that the BA allows better results than the other metaheuristics analyzed in this study. Full article
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16 pages, 968 KiB  
Article
Modelization of Low-Cost Maneuvers for an Areostationary Preliminary Mission Design
by Marta M. Sánchez-García, Gonzalo Barderas and Pilar Romero
Math. Comput. Appl. 2023, 28(6), 105; https://doi.org/10.3390/mca28060105 - 27 Oct 2023
Viewed by 1065
Abstract
The aim of this paper is to analyze the determination of interplanetary trajectories from Earth to Mars to evaluate the cost of the required impulse magnitudes for an areostationary orbiter mission design. Such analysis is first conducted by solving the Lambert orbital boundary [...] Read more.
The aim of this paper is to analyze the determination of interplanetary trajectories from Earth to Mars to evaluate the cost of the required impulse magnitudes for an areostationary orbiter mission design. Such analysis is first conducted by solving the Lambert orbital boundary value problem and studying the launch and arrival conditions for various date combinations. Then, genetic algorithms are applied to investigate the minimum-energy transfer orbit. Afterwards, an iterative procedure is used to determine the heliocentric elliptic transfer orbit that matches at the entry point of Mars’s sphere of influence with an areocentric hyperbolic orbit imposing specific conditions on inclination and periapsis radius. Finally, the maneuvers needed to obtain an areostationary orbit are numerically computed for different objective condition values at the Mars entry point to evaluate an areostationary preliminary mission cost for further study and characterization. Results show that, for the dates of the minimum-energy Earth–Mars transfer trajectory, a low value for the maneuvers to achieve an areostationary orbit is obtained for an arrival hyperbola with the minimum possible inclination and a capture into an elliptical trajectory with a low periapsis radius and an apoapsis at the stationary orbit. For a 2026 mission with a TOF of 304 for the minimum-energy Earth–Mars transfer trajectory, for a capture with a periapsis of 300 km above the Mars surface the value achieved will be 2.083 km/s. Full article
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18 pages, 2852 KiB  
Article
Observer-Based State Estimation for Recurrent Neural Networks: An Output-Predicting and LPV-Based Approach
by Wanlin Wang, Jinxiong Chen and Zhenkun Huang
Math. Comput. Appl. 2023, 28(6), 104; https://doi.org/10.3390/mca28060104 - 25 Oct 2023
Viewed by 1020
Abstract
An innovative cascade predictor is presented in this study to forecast the state of recurrent neural networks (RNNs) with delayed output. This cascade predictor is a chain-structured observer, as opposed to the conventional single observer, and is made up of several sub-observers that [...] Read more.
An innovative cascade predictor is presented in this study to forecast the state of recurrent neural networks (RNNs) with delayed output. This cascade predictor is a chain-structured observer, as opposed to the conventional single observer, and is made up of several sub-observers that individually estimate the state of the neurons at various periods. This new cascade predictor is more useful than the conventional single observer in predicting neural network states when the output delay is arbitrarily large but known. In contrast to examining the stability of error systems solely employing the Lyapunov–Krasovskii functional (LKF), several new global asymptotic stability standards are obtained by combining the application of the Linear Parameter Varying (LPV) approach, LKF and convex principle. Finally, a series of numerical simulations verify the efficacy of the obtained results. Full article
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31 pages, 1242 KiB  
Article
On Generalized Dominance Structures for Multi-Objective Optimization
by Kalyanmoy Deb and Matthias Ehrgott
Math. Comput. Appl. 2023, 28(5), 100; https://doi.org/10.3390/mca28050100 - 07 Oct 2023
Viewed by 1582
Abstract
Various dominance structures have been proposed in the multi-objective optimization literature. However, a systematic procedure to understand their effect in determining the resulting optimal set for generic domination principles, besides the standard Pareto-dominance principle, is lacking. In this paper, we analyze and lay [...] Read more.
Various dominance structures have been proposed in the multi-objective optimization literature. However, a systematic procedure to understand their effect in determining the resulting optimal set for generic domination principles, besides the standard Pareto-dominance principle, is lacking. In this paper, we analyze and lay out properties of generalized dominance structures which help provide insights for resulting optimal solutions. We introduce the concept of the anti-dominance structure, derived from the chosen dominance structure, to explain how the resulting non-dominated or optimal set can be identified easily compared to using the dominance structure directly. The concept allows a unified explanation of optimal solutions for both single- and multi-objective optimization problems. The anti-dominance structure is applied to analyze respective optimal solutions for most popularly used static and spatially changing dominance structures. The theoretical and deductive results of this study can be utilized to create more meaningful dominance structures for practical problems, understand and identify resulting optimal solutions, and help develop better test problems and algorithms for multi-objective optimization. Full article
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19 pages, 2887 KiB  
Article
Predictive Modeling and Control Strategies for the Transmission of Middle East Respiratory Syndrome Coronavirus
by Bibi Fatima, Mehmet Yavuz, Mati ur Rahman, Ali Althobaiti and Saad Althobaiti
Math. Comput. Appl. 2023, 28(5), 98; https://doi.org/10.3390/mca28050098 - 30 Sep 2023
Cited by 6 | Viewed by 1241
Abstract
The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical [...] Read more.
The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system’s equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health. Full article
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29 pages, 1311 KiB  
Article
Preconditioning Technique for an Image Deblurring Problem with the Total Fractional-Order Variation Model
by Adel M. Al-Mahdi
Math. Comput. Appl. 2023, 28(5), 97; https://doi.org/10.3390/mca28050097 - 22 Sep 2023
Viewed by 1127
Abstract
Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagrange equations associated with the TFOV model generates a saddle point [...] Read more.
Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagrange equations associated with the TFOV model generates a saddle point system of equations where the coefficient matrix of this system is dense and ill conditioned (it has a huge condition number). The ill-conditioned property leads to slowing of the convergence of any iterative method, such as Krylov subspace methods. One treatment for the slowness property is to apply the preconditioning technique. In this paper, we propose a block triangular preconditioner because we know that using the exact triangular preconditioner leads to a preconditioned matrix with exactly two distinct eigenvalues. This means that we need at most two iterations to converge to the exact solution. However, we cannot use the exact preconditioner because the Shur complement of our system is of the form S=K*K+λLα which is a huge and dense matrix. The first matrix, K*K, comes from the blurred operator, while the second one is from the TFOV regularization model. To overcome this difficulty, we propose two preconditioners based on the circulant and standard TV matrices. In our algorithm, we use the flexible preconditioned GMRES method for the outer iterations, the preconditioned conjugate gradient (PCG) method for the inner iterations, and the fixed point iteration (FPI) method to handle the nonlinearity. Fast convergence was found in the numerical results by using the proposed preconditioners. Full article
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16 pages, 4977 KiB  
Article
New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation
by Guilmer Ferdinand González Flores and Pablo Barrera Sánchez
Math. Comput. Appl. 2023, 28(5), 95; https://doi.org/10.3390/mca28050095 - 09 Sep 2023
Viewed by 849
Abstract
In this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the [...] Read more.
In this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the grid. We also define new discrete functionals, which are implemented as objective functions in an optimization-based method for quadrilateral grid generation and improvement. These functionals are linearly combined with a discrete functional whose domain has an infinite barrier at the boundary of the set of unfolded grids to preserve convex grid cells in each step of the optimization process. Full article
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35 pages, 5613 KiB  
Article
Exploring the Potential of Mixed Fourier Series in Signal Processing Applications Using One-Dimensional Smooth Closed-Form Functions with Compact Support: A Comprehensive Tutorial
by Carlos-Iván Páez-Rueda, Arturo Fajardo, Manuel Pérez, German Yamhure and Gabriel Perilla
Math. Comput. Appl. 2023, 28(5), 93; https://doi.org/10.3390/mca28050093 - 01 Sep 2023
Viewed by 1169
Abstract
This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and [...] Read more.
This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its application in signal processing, especially because it allows us to control the decreasing rate of Fourier coefficients and avoids the Gibbs phenomenon. Therefore, this method improves the signal processing performance in a wide range of scenarios, such as function approximation, interpolation, increased convergence with quasi-spectral accuracy using the time domain or the frequency domain, numerical integration, and solutions of inverse problems such as ordinary differential equations. Moreover, the paper provides comprehensive examples of one-dimensional problems to showcase the advantages of this approach. Full article
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11 pages, 269 KiB  
Article
Conservation Laws and Symmetry Reductions of the Hunter–Saxton Equation via the Double Reduction Method
by Molahlehi Charles Kakuli, Winter Sinkala and Phetogo Masemola
Math. Comput. Appl. 2023, 28(5), 92; https://doi.org/10.3390/mca28050092 - 22 Aug 2023
Viewed by 956
Abstract
This study investigates via Lie symmetry analysis the Hunter–Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation that arise from first-order multipliers. Conservation laws of the equation, [...] Read more.
This study investigates via Lie symmetry analysis the Hunter–Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation that arise from first-order multipliers. Conservation laws of the equation, combined with the admitted Lie point symmetries, enable us to perform symmetry reductions by employing the double reduction method. The method exploits the relationship between symmetries and conservation laws to reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter–Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation. While the double reduction method may be more complex to implement than the classical method, since it involves finding Lie point symmetries and deriving conservation laws, it has some advantages over the classical method of reducing PDEs. Firstly, it is more efficient in that it can reduce the number of variables and order of the equation in a single step. Secondly, by incorporating conservation laws, physically meaningful solutions that satisfy important physical constraints can be obtained. Full article
37 pages, 7671 KiB  
Article
FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation
by Hamidreza Eivazi, Jendrik-Alexander Tröger, Stefan Wittek, Stefan Hartmann and Andreas Rausch
Math. Comput. Appl. 2023, 28(4), 91; https://doi.org/10.3390/mca28040091 - 16 Aug 2023
Cited by 1 | Viewed by 1453
Abstract
Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are [...] Read more.
Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE2 simulations with special focus on the errors compared to conventional FE2 simulations, and the implementation aspect to gain considerable speed-up. As it is known, the Sobolev training and automatic differentiation increase data efficiency, prediction accuracy and speed-up in comparison to using two different neural networks for stress and tangent matrix prediction. To gain a significant speed-up of the FE2 computations, an efficient implementation of the trained neural network in a finite element code is provided. This is achieved by drawing on state-of-the-art high-performance computing libraries and just-in-time compilation yielding a maximum speed-up of a factor of more than 5000 compared to a reference FE2 computation. Moreover, the deep neural network surrogate model is able to overcome load-step size limitations of the RVE computations in step-size controlled computations. Full article
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20 pages, 5359 KiB  
Article
Vehicle Make and Model Recognition as an Open-Set Recognition Problem and New Class Discovery
by Diana-Itzel Vázquez-Santiago, Héctor-Gabriel Acosta-Mesa and Efrén Mezura-Montes
Math. Comput. Appl. 2023, 28(4), 80; https://doi.org/10.3390/mca28040080 - 03 Jul 2023
Cited by 1 | Viewed by 934
Abstract
One of the main limitations of traditional neural-network-based classifiers is the assumption that all query data are well represented within their training set. Unfortunately, in real-life scenarios, this is often not the case, and unknown class data may appear during testing, which drastically [...] Read more.
One of the main limitations of traditional neural-network-based classifiers is the assumption that all query data are well represented within their training set. Unfortunately, in real-life scenarios, this is often not the case, and unknown class data may appear during testing, which drastically weakens the robustness of the algorithms. For this type of problem, open-set recognition (OSR) proposes a new approach where it is assumed that the world knowledge of algorithms is incomplete, so they must be prepared to detect and reject objects of unknown classes. However, the goal of this approach does not include the detection of new classes hidden within the rejected instances, which would be beneficial to increase the model’s knowledge and classification capability, even after training. This paper proposes an OSR strategy with an extension for new class discovery aimed at vehicle make and model recognition. We use a neuroevolution technique and the contrastive loss function to design a domain-specific CNN that generates a consistent distribution of feature vectors belonging to the same class within the embedded space in terms of cosine similarity, maintaining this behavior in unknown classes, which serves as the main guide for a probabilistic model and a clustering algorithm to simultaneously detect objects of new classes and discover their classes. The results show that the presented strategy works effectively to address the VMMR problem as an OSR problem and furthermore is able to simultaneously recognize the new classes hidden within the rejected objects. OSR is focused on demonstrating its effectiveness with benchmark databases that are not domain-specific. VMMR is focused on improving its classification accuracy; however, since it is a real-world recognition problem, it should have strategies to deal with unknown data, which has not been extensively addressed and, to the best of our knowledge, has never been considered from an OSR perspective, so this work also contributes as a benchmark for future domain-specific OSR. Full article
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13 pages, 530 KiB  
Article
Evolutionary Selection of a Set of Association Rules Considering Biological Constraints Describing the Prevalent Elements in Bacterial Vaginosis
by María Concepción Salvador-González, Juana Canul-Reich, Rafael Rivera-López, Efrén Mezura-Montes and Erick de la Cruz-Hernandez
Math. Comput. Appl. 2023, 28(3), 75; https://doi.org/10.3390/mca28030075 - 14 Jun 2023
Viewed by 995
Abstract
Bacterial Vaginosis is a common disease and recurring public health problem. Additionally, this infection can trigger other sexually transmitted diseases. In the medical field, not all possible combinations among the pathogens of a possible case of Bacterial Vaginosis are known to allow a [...] Read more.
Bacterial Vaginosis is a common disease and recurring public health problem. Additionally, this infection can trigger other sexually transmitted diseases. In the medical field, not all possible combinations among the pathogens of a possible case of Bacterial Vaginosis are known to allow a diagnosis at the onset of the disease. It is important to contribute to this line of research, so this study uses a dataset with information from sexually active women between 18 and 50 years old, including 17 numerical attributes of microorganisms and bacteria with positive and negative results for BV. These values were semantically categorized for the Apriori algorithm to create the association rules, using support, confidence, and lift as statistical metrics to evaluate the quality of the rules, and incorporate those results in the objective function of the DE algorithm. To guide the evolutionary process we also incorporated the knowledge of a human expert represented as a set of biologically meaningful constraints. Thus, we were able to compare the performance of the rand/1/bin and best/1/bin versions from Differential Evolution to analyze the results of 30 independent executions. Therefore the experimental results allowed a reduced subset of biologically meaningful association rules by their executions, dimension, and DE version to be selected. Full article
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11 pages, 1084 KiB  
Article
Neuroevolution of Convolutional Neural Networks for Breast Cancer Diagnosis Using Western Blot Strips
by José-Luis Llaguno-Roque, Rocio-Erandi Barrientos-Martínez, Héctor-Gabriel Acosta-Mesa, Tania Romo-González and Efrén Mezura-Montes
Math. Comput. Appl. 2023, 28(3), 72; https://doi.org/10.3390/mca28030072 - 24 May 2023
Viewed by 1406
Abstract
Breast cancer has become a global health problem, ranking first in incidences and fifth in mortality in women around the world. In Mexico, the first cause of death in women is breast cancer. This work uses deep learning techniques to discriminate between healthy [...] Read more.
Breast cancer has become a global health problem, ranking first in incidences and fifth in mortality in women around the world. In Mexico, the first cause of death in women is breast cancer. This work uses deep learning techniques to discriminate between healthy and breast cancer patients, based on the banding patterns obtained from the Western Blot strip images of the autoantibody response to antigens of the T47D tumor line. The reaction of antibodies to tumor antigens occurs early in the process of tumorigenesis, years before clinical symptoms. One of the main challenges in deep learning is the design of the architecture of the convolutional neural network. Neuroevolution has been used to support this and has produced highly competitive results. It is proposed that neuroevolve convolutional neural networks (CNN) find an optimal architecture to achieve competitive ranking, taking Western Blot images as input. The CNN obtained reached 90.67% accuracy, 90.71% recall, 95.34% specificity, and 90.69% precision in classifying three different classes (healthy, benign breast pathology, and breast cancer). Full article
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