Mathematical Modeling

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 9915

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Enginieering Division of the Campus Irapuato-Salamanca, University of Guanajuato, Salamanca 36885, Mexico
Interests: computer vision; pattern recognition; optimization methods; automatic control; machine and deep learning
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Special Issue Information

Dear Colleagues,

The numerical and mathematical analysis of complex systems requires formal modeling and accurate signal interpretation in order to make the right decisions or systems improvements in vast application areas, such as energy, medicine, and automation. Many modern solutions using whether classical (gradient-based) or metaheuristic optimization methods for modern controllers’ design in renewable energies, tumors detection in biomedical images, and fault diagnosing in industrial applications are welcome. In addition, this Special Issue covers the new recognition and classification applications based on machine learning methods that are prioritized when modest or small databases are available, as well as cutting-edge methodologies based on deep learning technics using formal mathematical analysis.

Dr. Juan Gabriel Avina-Cervantes
Guest Editor

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Keywords

  • Mateheuristics optimization
  • Machine Learning
  • Deep Learning
  • Renewable energies
  • Biomedical imaging

Published Papers (4 papers)

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Research

20 pages, 4999 KiB  
Article
EEG-Based Person Identification and Authentication Using Deep Convolutional Neural Network
by Walaa Alsumari, Muhammad Hussain, Laila Alshehri and Hatim A. Aboalsamh
Axioms 2023, 12(1), 74; https://doi.org/10.3390/axioms12010074 - 11 Jan 2023
Cited by 4 | Viewed by 3468
Abstract
Using biometric modalities for person recognition is crucial to guard against impostor attacks. Commonly used biometric modalities, such as fingerprint scanners and facial recognition, are effective but can easily be tampered with and deceived. These drawbacks have recently motivated the use of electroencephalography [...] Read more.
Using biometric modalities for person recognition is crucial to guard against impostor attacks. Commonly used biometric modalities, such as fingerprint scanners and facial recognition, are effective but can easily be tampered with and deceived. These drawbacks have recently motivated the use of electroencephalography (EEG) as a biometric modality for developing a recognition system with a high level of security. The majority of existing EEG-based recognition methods leverage EEG signals measured either from many channels or over a long temporal window. Both set limits on their usability as part of real-life security systems. Moreover, nearly all available methods use hand-engineered techniques and do not generalize well to unknown data. The few EEG-based recognition methods based on deep learning suffer from an overfitting problem, and a large number of model parameters must be learned from only a small amount of available EEG data. Leveraging recent developments in deep learning, this study addresses these issues and introduces a lightweight convolutional neural network (CNN) model consisting of a small number of learnable parameters that enable the training and evaluation of the CNN model on a small amount of available EEG data. We present a robust and efficient EEG-based recognition system using this CNN model. The system was validated on a public domain benchmark dataset and achieved a rank-1 identification result of 99% and an equal error rate of authentication performance of 0.187%. The system requires only two EEG channels and a signal measured over a short temporal window of 5 s. Consequently, this method can be used in real-life settings to identify or authenticate biometric security systems. Full article
(This article belongs to the Special Issue Mathematical Modeling)
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24 pages, 1831 KiB  
Article
Patron–Prophet Artificial Bee Colony Approach for Solving Numerical Continuous Optimization Problems
by Kalaipriyan Thirugnanasambandam, Rajakumar Ramalingam, Divya Mohan, Mamoon Rashid, Kapil Juneja and Sultan S. Alshamrani
Axioms 2022, 11(10), 523; https://doi.org/10.3390/axioms11100523 - 01 Oct 2022
Cited by 5 | Viewed by 1417
Abstract
The swarm-based Artificial Bee Colony (ABC) algorithm has a significant range of applications and is competent, compared to other algorithms, regarding many optimization problems. However, the ABC’s performance in higher-dimension situations towards global optima is not on par with other models due to [...] Read more.
The swarm-based Artificial Bee Colony (ABC) algorithm has a significant range of applications and is competent, compared to other algorithms, regarding many optimization problems. However, the ABC’s performance in higher-dimension situations towards global optima is not on par with other models due to its deficiency in balancing intensification and diversification. In this research, two different strategies are applied for the improvement of the search capability of the ABC in a multimodal search space. In the ABC, the first strategy, Patron–Prophet, is assessed in the scout bee phase to incorporate a cooperative nature. This strategy works based on the donor–acceptor concept. In addition, a self-adaptability approach is included to balance intensification and diversification. This balancing helps the ABC to search for optimal solutions without premature convergence. The first strategy explores unexplored regions with better insight, and more profound intensification occurs in the discovered areas. The second strategy controls the trap of being in local optima and diversification without the pulse of intensification. The proposed model, named the PP-ABC, was evaluated with mathematical benchmark functions to prove its efficiency in comparison with other existing models. Additionally, the standard and statistical analyses show a better outcome of the proposed algorithm over the compared techniques. The proposed model was applied to a three-bar truss engineering design problem to validate the model’s efficacy, and the results were recorded. Full article
(This article belongs to the Special Issue Mathematical Modeling)
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21 pages, 2360 KiB  
Article
Identifying Stock Prices Using an Advanced Hybrid ARIMA-Based Model: A Case of Games Catalogs
by You-Shyang Chen, Chih-Lung (Jerome) Chou, Yau-Jung (Mike) Lee, Su-Fen Chen and Wen-Ju Hsiao
Axioms 2022, 11(10), 499; https://doi.org/10.3390/axioms11100499 - 24 Sep 2022
Viewed by 1534
Abstract
At the beginning of 2020, the COVID-19 pandemic struck the world, affecting the pace of life and the economic behavioral patterns of people around the world, with an impact exceeding that of the 2008 financial crisis, causing a global stock market crash and [...] Read more.
At the beginning of 2020, the COVID-19 pandemic struck the world, affecting the pace of life and the economic behavioral patterns of people around the world, with an impact exceeding that of the 2008 financial crisis, causing a global stock market crash and even the first recorded negative oil prices. Under the impact of this pandemic, due to the global large-scale quarantine and lockdown measures, game stocks belonging to the stay-at-home economy have become the focus of investors from all over the world. Therefore, under such incentives, this study aims to construct a set of effective prediction models for the price of game stocks, which could help relevant stakeholders—especially investors—to make efficient predictions so as to achieve a profitable investment niche. Moreover, because stock prices have the characteristics of a time series, and based on the relevant discussion in the literature, we know that ARIMA (the autoregressive integrated moving average) prediction models have excellent prediction performance. In conclusion, this study aims to establish an advanced hybrid model based on ARIMA as an excellent prediction technology for the price of game stocks, and to construct four groups of different investment strategies to determine which technical models of investment strategies are suitable for different game stocks. There are six important directions, experimental results, and research findings in the construction of advanced models: (1) In terms of the experiment, the data are collected from the daily closing prices of game-related stocks on the Taiwan Stock Exchange, and the sample range is from 2014 to 2020. (2) In terms of the performance verification, the return on investment is used as the evaluation standard to verify the availability of the ARIMA prediction model. (3) In terms of the research results, the accuracy of the model in predicting the prices of listed stocks can reach the 95% confidence interval predicted by the model 14 days after the closing price, and the OTC stocks fall within the 95% confidence interval for 3 days. (4) In terms of the empirical study of the rate of return, the investors can obtain a better rate of return than the benchmark strategy by trading the game stocks based on the indices set by the ARIMA model in this study. (5) In terms of the research findings, this study further compares the rate of return of trading strategies with reference to the ARIMA index and the rate of return of trading strategies with reference to the monitoring indicator, finding no significant difference between the two. (6) Different game stocks apply for different technical models of investment strategies. Full article
(This article belongs to the Special Issue Mathematical Modeling)
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20 pages, 971 KiB  
Article
PTG-PLM: Predicting Post-Translational Glycosylation and Glycation Sites Using Protein Language Models and Deep Learning
by Alhasan Alkuhlani, Walaa Gad, Mohamed Roushdy, Michael Gr. Voskoglou and Abdel-badeeh M. Salem
Axioms 2022, 11(9), 469; https://doi.org/10.3390/axioms11090469 - 14 Sep 2022
Cited by 4 | Viewed by 2859
Abstract
Post-translational glycosylation and glycation are common types of protein post-translational modifications (PTMs) in which glycan binds to protein enzymatically or nonenzymatically, respectively. They are associated with various diseases such as coronavirus, Alzheimer’s, cancer, and diabetes diseases. Identifying glycosylation and glycation sites is significant [...] Read more.
Post-translational glycosylation and glycation are common types of protein post-translational modifications (PTMs) in which glycan binds to protein enzymatically or nonenzymatically, respectively. They are associated with various diseases such as coronavirus, Alzheimer’s, cancer, and diabetes diseases. Identifying glycosylation and glycation sites is significant to understanding their biological mechanisms. However, utilizing experimental laboratory tools to identify PTM sites is time-consuming and costly. In contrast, computational methods based on machine learning are becoming increasingly essential for PTM site prediction due to their higher performance and lower cost. In recent years, advances in Transformer-based Language Models based on deep learning have been transferred from Natural Language Processing (NLP) into the proteomics field by developing language models for protein sequence representation known as Protein Language Models (PLMs). In this work, we proposed a novel method, PTG-PLM, for improving the performance of PTM glycosylation and glycation site prediction. PTG-PLM is based on convolutional neural networks (CNNs) and embedding extracted from six recent PLMs including ProtBert-BFD, ProtBert, ProtAlbert, ProtXlnet, ESM-1b, and TAPE. The model is trained and evaluated on two public datasets for glycosylation and glycation site prediction. The results show that PTG-PLM based on ESM-1b and ProtBert-BFD has better performance than PTG-PLM based on the other PLMs. Comparison results with the existing tools and representative supervised learning methods show that PTG-PLM surpasses the other models for glycosylation and glycation site prediction. The outstanding performance results of PTG-PLM indicate that it can be used to predict the sites of the other types of PTMs. Full article
(This article belongs to the Special Issue Mathematical Modeling)
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