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Journal Description

Mathematics

Mathematics is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics )
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 17.1 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the first half of 2024).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Sections: published in 13 topical sections.
Companion journals for Mathematics include: Foundations, Analytics, International Journal of Topology, Geometry and Logics.

Impact Factor: 2.3 (2023); 5-Year Impact Factor: 2.2 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2227-7390

Latest Articles

12 pages, 405 KiB

Open AccessArticle

Diffusion Cascades and Mutually Coupled Diffusion Processes

by Imre Ferenc Barna and L�szl� M�ty�s

Mathematics 2024, 12(20), 3298; https://doi.org/10.3390/math12203298 (registering DOI) - 21 Oct 2024

In this paper, we define and investigate a system of coupled regular diffusion equations in which each concentration acts as a driving term in the next diffusion equation. Such systems can be understood as a kind of cascade process which appear in different [...] Read more.

In this paper, we define and investigate a system of coupled regular diffusion equations in which each concentration acts as a driving term in the next diffusion equation. Such systems can be understood as a kind of cascade process which appear in different fields of physics like diffusion and reaction processes or turbulence. As a solution, we apply the time-dependent self-similar Ansatz method, the obtained solutions can be expressed as the product of a Gaussian and a Kummer’s function. This model physically means that the first diffusion works as a catalyst in the second diffusion system. The coupling of these diffusion systems is only one way. In the second part of the study we investigate mutually coupled diffusion equations which also have the self-similar trial function. The derived solutions show some similarities to the former one. To make our investigation more complete, different kinds of couplings were examined like the linear, the power-law, and the Lorentzian. Finally, a special coupling was investigated which is capable of describing isomerization with temporal decay. Full article

(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)

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18 pages, 2730 KiB

Open AccessArticle

Fast Color Image Encryption Algorithm Based on DNA Coding and Multi-Chaotic Systems

by Shaofang Wang, Jingguo Pan, Yanrong Cui, Zhongju Chen and Wei Zhan

Mathematics 2024, 12(20), 3297; https://doi.org/10.3390/math12203297 (registering DOI) - 21 Oct 2024

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited [...] Read more.

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

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27 pages, 5811 KiB

Open AccessArticle

Advanced Study: Improving the Quality of Cooling Water Towers’ Conductivity Using a Fuzzy PID Control Model

by You-Shyang Chen, Ying-Hsun Hung, Mike Yau-Jung Lee, Jieh-Ren Chang, Chien-Ku Lin and Tai-Wen Wang

Mathematics 2024, 12(20), 3296; https://doi.org/10.3390/math12203296 (registering DOI) - 21 Oct 2024

Cooling water towers are commonly used in industrial and commercial applications. Industrial sites frequently have harsh environments, with certain characteristics such as poor air quality, close proximity to the ocean, large quantities of dust, or water supplies with a high mineral content. In [...] Read more.

Cooling water towers are commonly used in industrial and commercial applications. Industrial sites frequently have harsh environments, with certain characteristics such as poor air quality, close proximity to the ocean, large quantities of dust, or water supplies with a high mineral content. In such environments, the quality of electrical conductivity in the cooling water towers can be significantly negatively affected. Once minerals (e.g., calcium and magnesium) form in the water, conductivity becomes too high, and cooling water towers can become easily clogged in a short time; this leads to a situation in which the cooling water host cannot be cooled, causing it to crash. This is a serious situation because manufacturing processes are then completely shut down, and production yield is thus severely reduced. To solve these problems, in this study, we develop a practical designation for a photovoltaic industry company called Company-L. Three control methods are proposed: the motor control method, the PID control method, and the fuzzy PID control method. These approaches are proposed as solutions for successfully controlling the forced replenishment and drainage of cooling water towers and controlling the opening of proportional control valves for water release; this will further dilute the electrical conductivity and control it, bringing it to 300 µS/cm. In the experimental processes, we first used practical data from Company-L for our case study. Second, from the experimental results of the proposed model for the motor control method, we can see that if electrical conductivity is out of control and the conductivity value exceeds 1000 µS/cm, the communication software LINE v8.5.0 (accessible via smartphone) displays a notification that the water quality of the cooling water towers requires attention. Third, although the PID control method is shown to have errors within an acceptable range, the proportional (P) controller must be precisely controlled; this control method has not yet reached this precise control in the present study. Finally, the fuzzy PID control method was found to have the greatest effect, with the lowest level of errors and the most accurate control. In conclusion, the present study proposes solutions to reduce the risk of ice-water host machines crashing; the solutions use fuzzy logic and can be used to ensure the smooth operation of manufacturing processes in industries. Practically, this study contributes an applicable technical innovation: the use of the fuzzy PID control model to control cooling water towers in industrial applications. Concurrently, we present a three-tier monitoring checkpoint that contributes to the PID control method. Full article

(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering, 3rd Edition)

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29 pages, 3060 KiB

Open AccessFeature PaperArticle

Applying Multi-Task Deep Learning Methods in Electricity Load Forecasting Using Meteorological Factors

by Kai-Bin Huang, Tian-Shyug Lee, Jonathan Lee, Jy-Ping Wu, Leemen Lee and Hsiu-Mei Lee

Mathematics 2024, 12(20), 3295; https://doi.org/10.3390/math12203295 (registering DOI) - 21 Oct 2024

The steady rise in carbon emissions has significantly exacerbated the global climate crisis, posing a severe threat to ecosystems due to the greenhouse gas effect. As one of the most pressing challenges of our time, the need for an immediate transition to renewable [...] Read more.

The steady rise in carbon emissions has significantly exacerbated the global climate crisis, posing a severe threat to ecosystems due to the greenhouse gas effect. As one of the most pressing challenges of our time, the need for an immediate transition to renewable energy is imperative to meet the carbon reduction targets set by the Paris Agreement. Buildings, as major contributors to global energy consumption, play a pivotal role in climate change. This study diverges from previous research by employing multi-task deep learning techniques to develop a predictive model for electricity load in commercial buildings, incorporating auxiliary tasks such as temperature and cloud coverage. Using real data from a commercial building in Taiwan, this study explores the effects of varying batch sizes (100, 125, 150, and 200) on the model’s performance. The findings reveal that the multi-task deep learning model consistently surpasses single-task models in predicting electricity load, demonstrating superior accuracy and stability. These insights are crucial for companies aiming to enhance energy efficiency and formulate effective renewable energy procurement strategies, contributing to broader sustainability efforts and aligning with global climate action goals. Full article

(This article belongs to the Special Issue Applied Statistics in Management Sciences)

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20 pages, 2344 KiB

Open AccessArticle

An Efficient Fusion Network for Fake News Classification

by Muhammad Swaileh A. Alzaidi, Alya Alshammari, Abdulkhaleq Q. A. Hassan, Samia Nawaz Yousafzai, Adel Thaljaoui, Norma Latif Fitriyani, Changgyun Kim and Muhammad Syafrudin

Mathematics 2024, 12(20), 3294; https://doi.org/10.3390/math12203294 (registering DOI) - 20 Oct 2024

Nowadays, it is very tough to differentiate between real news and fake news due to fast-growing social networks and technological progress. Manipulative news is defined as calculated misinformation with the aim of creating false beliefs. This kind of fake news is highly detrimental [...] Read more.

Nowadays, it is very tough to differentiate between real news and fake news due to fast-growing social networks and technological progress. Manipulative news is defined as calculated misinformation with the aim of creating false beliefs. This kind of fake news is highly detrimental to society since it deepens political division and weakens trust in authorities and institutions. Therefore, the identification of fake news has emerged as a major field of research that seeks to validate content. The proposed model operates in two stages: First, TF-IDF is applied to an entire document to obtain its global features, and its spatial and temporal features are simultaneously obtained by employing Bidirectional Encoder Representations from Transformers and Bidirectional Long Short-Term Memory with a Gated Recurrent Unit. The Fast Learning Network efficiently classifies the extracted features. Comparative experiments were conducted on three easily and publicly obtainable large-scale datasets for the purposes of analyzing the efficiency of the approach proposed. The results also show how well the model performs compared with past methods of classification. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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25 pages, 1310 KiB

Open AccessArticle

Performance Optimization with LPV Synthesis for Disturbance Attenuation in Planar Motors

by Khac Huan Su, Keunhoon Park, Young Seop Son and Youngwoo Lee

Mathematics 2024, 12(20), 3293; https://doi.org/10.3390/math12203293 (registering DOI) - 20 Oct 2024

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method [...] Read more.

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H_∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H_∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation. Full article

13 pages, 288 KiB

Open AccessFeature PaperArticle

Some Symmetry and Duality Theorems on Multiple Zeta(-Star) Values

by Kwang-Wu Chen, Minking Eie and Yao Lin Ong

Mathematics 2024, 12(20), 3292; https://doi.org/10.3390/math12203292 (registering DOI) - 20 Oct 2024

In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. We find that the summation [...] Read more.

In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. We find that the summation

\sum_{a + b = r - 1} {(- 1)}^{a} ζ^{★} (a + 2, {2}^{p - 1}) ζ^{★} ({1}^{b + 1}, {2}^{q})

equals

ζ^{★} ({2}^{p}, {1}^{r}, {2}^{q}) + {(- 1)}^{r + 1} ζ^{★} ({2}^{q}, r + 2, {2}^{p - 1})

. With the help of this equation and Zagier’s

ζ^{★} ({2}^{p}, 3, {2}^{q})

formula, we can easily determine

ζ^{★} ({2}^{p}, 1, {2}^{q})

and several interesting expressions. Full article

(This article belongs to the Special Issue Polynomials: Theory and Applications, 2nd Edition)

19 pages, 3727 KiB

Open AccessArticle

Dynamic Programming-Based Approach to Model Antigen-Driven Immune Repertoire Synthesis

by Alexander S. Bratus, Gennady Bocharov and Dmitry Grebennikov

Mathematics 2024, 12(20), 3291; https://doi.org/10.3390/math12203291 (registering DOI) - 20 Oct 2024

This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the [...] Read more.

This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the antigen-driven immune repertoire synthesis. The processes of formation of new receptor specificity of lymphocytes (the growth of their affinity during maturation) are described by an ordinary differential equation (ODE) with a piecewise-constant right-hand side. Optimal control synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation implementing the dynamic programming approach for controlling Gaussian random processes generated by a stochastic differential equation (SDE) with the noise in the form of the Wiener process. The proposed description of the clonal repertoire of the immune system allows us to introduce an integral characteristic of the immune repertoire completeness or the integrative fitness of the whole immune system. The quantitative index for characterizing the immune system fitness is analytically derived using the Feynman–Kac–Kolmogorov equation. Full article

(This article belongs to the Special Issue Applied Mathematics in Disease Control and Dynamics)

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24 pages, 342 KiB

Open AccessFeature PaperArticle

On the Generalized (p,q)-ϕ-Calculus with Respect to Another Function

by Sina Etemad, Ivanka Stamova, Sotiris K. Ntouyas and Jessada Tariboon

Mathematics 2024, 12(20), 3290; https://doi.org/10.3390/math12203290 (registering DOI) - 20 Oct 2024

In the present paper, we generalized some of the operators defined in

(p, q)

-calculus with respect to another function. More precisely, the generalized

(p, q)

-

ϕ

-derivatives and

(p, q)

-

ϕ

[...] Read more.

In the present paper, we generalized some of the operators defined in

(p, q)

-calculus with respect to another function. More precisely, the generalized

(p, q)

-

ϕ

-derivatives and

(p, q)

-

ϕ

-integrals were introduced with respect to the strictly increasing function

ϕ

with the help of different orders of the q-shifting, p-shifting, and

(q / p)

-shifting operators. Then, after proving some related properties, and as an application, we considered a generalized

(p, q)

-

ϕ

-difference problem and studied the existence property for its unique solutions with the help of the Banach contraction mapping principle. Full article

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)

16 pages, 37586 KiB

Open AccessArticle

Driver Distraction Detection Based on Fusion Enhancement and Global Saliency Optimization

by Xueda Huang, Shuangshuang Gu, Yuanyuan Li, Guanqiu Qi, Zhiqin Zhu and Yiyao An

Mathematics 2024, 12(20), 3289; https://doi.org/10.3390/math12203289 (registering DOI) - 20 Oct 2024

Driver distraction detection not only effectively prevents traffic accidents but also promotes the development of intelligent transportation systems. In recent years, thanks to the powerful feature learning capabilities of deep learning algorithms, driver distraction detection methods based on deep learning have increased significantly. [...] Read more.

Driver distraction detection not only effectively prevents traffic accidents but also promotes the development of intelligent transportation systems. In recent years, thanks to the powerful feature learning capabilities of deep learning algorithms, driver distraction detection methods based on deep learning have increased significantly. However, for resource-constrained onboard devices, real-time lightweight models are crucial. Most existing methods tend to focus solely on lightweight model design, neglecting the loss in detection performance for small targets. To achieve a balance between detection accuracy and network lightweighting, this paper proposes a driver distraction detection method that combines enhancement and global saliency optimization. The method mainly consists of three modules: context fusion enhancement module (CFEM), channel optimization feedback module (COFM), and channel saliency distillation module (CSDM). In the CFEM module, one-dimensional convolution is used to capture information between distant pixels, and an injection mechanism is adopted to further integrate high-level semantic information with low-level detail information, enhancing feature fusion capabilities. The COFM module incorporates a feedback mechanism to consider the impact of inter-layer and intra-layer channel relationships on model compression performance, achieving joint pruning of global channels. The CSDM module guides the student network to learn the salient feature information from the teacher network, effectively balancing the model’s real-time performance and accuracy. Experimental results show that this method outperforms the state-of-the-art methods in driver distraction detection tasks, demonstrating good performance and potential application prospects. Full article

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16 pages, 599 KiB

Open AccessArticle

Variational Autoencoding with Conditional Iterative Sampling for Missing Data Imputation

by Shenfen Kuang, Jie Song, Shangjiu Wang and Huafeng Zhu

Mathematics 2024, 12(20), 3288; https://doi.org/10.3390/math12203288 (registering DOI) - 20 Oct 2024

Variational autoencoders (VAEs) are popular for their robust nonlinear representation capabilities and have recently achieved notable advancements in the problem of missing data imputation. However, existing imputation methods often exhibit instability due to the inherent randomness in the sampling process, leading to either [...] Read more.

Variational autoencoders (VAEs) are popular for their robust nonlinear representation capabilities and have recently achieved notable advancements in the problem of missing data imputation. However, existing imputation methods often exhibit instability due to the inherent randomness in the sampling process, leading to either underestimation or overfitting, particularly when handling complex missing data types such as images. To address this challenge, we introduce a conditional iterative sampling imputation method. Initially, we employ an importance-weighted beta variational autoencoder to learn the conditional distribution from the observed data. Subsequently, leveraging the importance-weighted resampling strategy, samples are drawn iteratively from the conditional distribution to compute the conditional expectation of the missing data. The proposed method has been experimentally evaluated using classical generative datasets and compared with various well-known imputation methods to validate its effectiveness. Full article

(This article belongs to the Special Issue Applied Mathematics in Data Science and High-Performance Computing)

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15 pages, 1315 KiB

Open AccessArticle

Leveraging Universal Adversarial Perturbation and Frequency Band Filters Against Face Recognition

by Limengnan Zhou, Bufan He, Xi Jin and Guangling Sun

Mathematics 2024, 12(20), 3287; https://doi.org/10.3390/math12203287 (registering DOI) - 20 Oct 2024

Universal adversarial perturbation (UAP) exhibits universality as it is independent of specific images. Although previous investigations have shown that the classification of natural images is susceptible to universal adversarial attacks, the impact of UAP on face recognition has not been fully investigated. Thus, [...] Read more.

Universal adversarial perturbation (UAP) exhibits universality as it is independent of specific images. Although previous investigations have shown that the classification of natural images is susceptible to universal adversarial attacks, the impact of UAP on face recognition has not been fully investigated. Thus, in this paper we assess the vulnerability of face recognition for UAP. We propose FaUAP-FBF, which exploits the frequency domain by learning high, middle, and low band filters as an additional dimension of refining facial UAP. The facial UAP and filters are alternately and repeatedly learned from a training set. Furthermore, we convert non-target attacks to target attacks by customizing a target example, which is an out-of-distribution sample for a training set. Accordingly, non-target and target attacks form a uniform target attack. Finally, the variance of cosine similarity is incorporated into the adversarial loss, thereby enhancing the attacking capability. Extensive experiments on LFW and CASIA-WebFace datasets show that FaUAP-FBF has a higher fooling rate and better objective stealthiness metrics across the evaluated network structures compared to existing universal adversarial attacks, which confirms the effectiveness of the proposed FaUAP-FBF. Our results also imply that UAP poses a real threat for face recognition systems and should be taken seriously when face recognition systems are being designed. Full article

(This article belongs to the Special Issue New Solutions for Multimedia and Artificial Intelligence Security)

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21 pages, 3768 KiB

Open AccessArticle

A Lightweight GCT-EEGNet for EEG-Based Individual Recognition Under Diverse Brain Conditions

by Laila Alshehri and Muhammad Hussain

Mathematics 2024, 12(20), 3286; https://doi.org/10.3390/math12203286 (registering DOI) - 20 Oct 2024

A robust biometric system is essential to mitigate various security threats. Electroencephalography (EEG) brain signals present a promising alternative to other biometric traits due to their sensitivity, non-duplicability, resistance to theft, and individual-specific dynamics. However, existing EEG-based biometric systems employ deep neural networks, [...] Read more.

A robust biometric system is essential to mitigate various security threats. Electroencephalography (EEG) brain signals present a promising alternative to other biometric traits due to their sensitivity, non-duplicability, resistance to theft, and individual-specific dynamics. However, existing EEG-based biometric systems employ deep neural networks, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), which face challenges such as high parameter complexity, limiting their practical application. Additionally, their ability to generalize across a large number of subjects remains unclear. Moreover, they have been validated on datasets collected in controlled environments, which do not accurately reflect real-world scenarios involving diverse brain conditions. To overcome these challenges, we propose a lightweight neural network model, GCT–EEGNet, which is based on the design ideas of a CNN model and incorporates an attention mechanism to pay attention to the appropriate frequency bands for extracting discriminative features relevant to the identity of a subject despite diverse brain conditions. First, a raw EEG signal is decomposed into frequency bands and then passed to GCT–EEGNet for feature extraction, which utilizes a gated channel transformation (GCT) layer to selectively emphasize informative features from the relevant frequency bands. The extracted features were used for subject recognition through a cosine similarity metric that measured the similarity between feature vectors of different EEG trials to identify individuals. The proposed method was evaluated on a large dataset comprising 263 subjects. The experimental results demonstrated that the method achieved a correct recognition rate (CRR) of 99.23% and an equal error rate (EER) of 0.0014, corroborating its robustness against different brain conditions. The proposed model maintains low parameter complexity while keeping the expressiveness of representations, even with unseen subjects. Full article

(This article belongs to the Special Issue Computational Intelligence and Human–Computer Interaction: Modern Methods and Applications, 2nd Edition)

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30 pages, 10109 KiB

Open AccessArticle

AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

by Kostadin Yotov, Emil Hadzhikolev, Stanka Hadzhikoleva and Mariyan Milev

Mathematics 2024, 12(20), 3285; https://doi.org/10.3390/math12203285 (registering DOI) - 19 Oct 2024

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training [...] Read more.

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks. Full article

(This article belongs to the Special Issue Machine Learning and Evolutionary Algorithms: Theory and Applications)

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23 pages, 358 KiB

Open AccessArticle

Adaptive Bi-Level Variable Selection for Quantile Regression Models with a Diverging Number of Covariates

by Xianwen Ding and Zhihuang Yang

Mathematics 2024, 12(20), 3284; https://doi.org/10.3390/math12203284 (registering DOI) - 19 Oct 2024

The paper develops an innovatively adaptive bi-level variable selection methodology for quantile regression models with a diverging number of covariates. Traditional variable selection techniques in quantile regression, such as the lasso and group lasso techniques, offer solutions predominantly for either individual variable selection [...] Read more.

The paper develops an innovatively adaptive bi-level variable selection methodology for quantile regression models with a diverging number of covariates. Traditional variable selection techniques in quantile regression, such as the lasso and group lasso techniques, offer solutions predominantly for either individual variable selection or group-level selection, but not for both simultaneously. To address this limitation, we introduce an adaptive group bridge approach for quantile regression, to simultaneously select variables at both the group and within-group variable levels. The proposed method offers several notable advantages. Firstly, it adeptly handles the heterogeneous and/or skewed data inherent to quantile regression. Secondly, it is capable of handling quantile regression models where the number of parameters grows with the sample size. Thirdly, via employing an ingeniously designed penalty function, our method surpasses traditional group bridge estimation techniques in identifying important within-group variables with high precision. Fourthly, it exhibits the oracle group selection property, implying that the relevant variables at both the group and within-group levels can be identified with a probability converging to one. Several numerical studies corroborated our theoretical results. Full article

(This article belongs to the Section Probability and Statistics)

21 pages, 3846 KiB

Open AccessArticle

A New Method Based on Belief Rule Base with Balanced Accuracy and Interpretability for Student Achievement Prediction

by Zongjun Zhang, Qian Deng, Wei He and Cuiping Yang

Mathematics 2024, 12(20), 3283; https://doi.org/10.3390/math12203283 (registering DOI) - 19 Oct 2024

In the field of education, the accurate prediction of students’ future performance is essential for personalized instruction and efficient allocation of resources. Such predictions not only help education professionals develop targeted educational strategies but also identify students’ learning needs at an early stage [...] Read more.

In the field of education, the accurate prediction of students’ future performance is essential for personalized instruction and efficient allocation of resources. Such predictions not only help education professionals develop targeted educational strategies but also identify students’ learning needs at an early stage so that timely interventions and support can be provided. To gain the trust of educational experts and ensure the practical application value of the prediction results, the prediction methods used must be highly interpretable. However, there are two problems with the current belief rule base (BRB) applied to student performance prediction. First, there is a current lack of effective strategies for enhancing the interpretability of the optimization process. Second, BRB models that overemphasize accuracy tend to exhibit characteristics of black-box models. To overcome these challenges, this paper proposes a new method based on BRB with balanced accuracy and interpretability (BRB-Bai) for student achievement prediction. First, an attribute selection method is proposed to filter out important features associated with student performance. Then, expert knowledge credibility is calculated, and four interpretability strategies are proposed to ensure the interpretability of the model and to achieve a balance between interpretability and accuracy on the basis of expert knowledge credibility. The effectiveness of the proposed model is demonstrated by conducting experiments on the student achievement dataset. Full article

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12 pages, 949 KiB

Open AccessArticle

Topological Interactions Between Homotopy and Dehn Twist Varieties

by Susmit Bagchi

Mathematics 2024, 12(20), 3282; https://doi.org/10.3390/math12203282 (registering DOI) - 19 Oct 2024

The topological Dehn twists have several applications in mathematical sciences as well as in physical sciences. The interplay between homotopy theory and Dehn twists exposes a rich set of properties. This paper generalizes the Dehn twists by proposing the notion of pre-twisted space, [...] Read more.

The topological Dehn twists have several applications in mathematical sciences as well as in physical sciences. The interplay between homotopy theory and Dehn twists exposes a rich set of properties. This paper generalizes the Dehn twists by proposing the notion of pre-twisted space, orientations of twists and the formation of pointed based space under a homeomorphic continuous function. It is shown that the Dehn twisted homotopy under non-retraction admits a left lifting property (LLP) through the local homeomorphism. The LLP extends the principles of Hurewicz fibration by avoiding pullback. Moreover, this paper illustrates that the Dehn twisted homotopy up to a base point in a based space can be formed by considering retraction. As a result, two disjoint continuous functions become point-wise continuous at the base point under retracted homotopy twists. Interestingly, the oriented Dehn twists of a pre-twisted space under homotopy retraction mutually commute in a contractible space. Full article

(This article belongs to the Special Issue Geometry and Topology with Applications)

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20 pages, 6400 KiB

Open AccessArticle

Transfer Learning-Based Physics-Informed Convolutional Neural Network for Simulating Flow in Porous Media with Time-Varying Controls

by Jungang Chen, Eduardo Gildin and John E. Killough

Mathematics 2024, 12(20), 3281; https://doi.org/10.3390/math12203281 (registering DOI) - 19 Oct 2024

A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network parameterizes the solutions with time-varying controls to establish a control-to-state [...] Read more.

A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network parameterizes the solutions with time-varying controls to establish a control-to-state regression. Firstly, a finite volume scheme is adopted to discretize flow equations and formulate a loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states (e.g., oil pressure and water saturation). To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state-space equations. We train the network progressively for every time step, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for a subsequent time step. The proposed model is used to simulate oil–water porous flow scenarios with varying reservoir model dimensionality, and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The comparison with numerical methods demonstrates that a PICNN is highly efficient yet preserves decent accuracy. Full article

(This article belongs to the Special Issue Modeling of Multiphase Flow Phenomena)

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19 pages, 336 KiB

Open AccessArticle

Soft Weakly Quasi-Continuous Functions Between Soft Topological Spaces

by Samer Al-Ghour, Dina Abuzaid and Monia Naghi

Mathematics 2024, 12(20), 3280; https://doi.org/10.3390/math12203280 (registering DOI) - 19 Oct 2024

As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we prove that soft weak quasi-continuity [...] Read more.

As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we prove that soft weak quasi-continuity is strictly weaker than both soft semi-continuity and soft weak continuity. We introduce many characterizations of soft weak quasi-continuity. Moreover, we study the relationship between soft quasi-continuity and weak quasi-continuity with their analogous notions in general topology. Furthermore, we show that soft regularity of the co-domain of a soft function is a sufficient condition for equivalence between soft semi-continuity and soft weakly quasi-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and soft graph theorems in terms of soft weak quasi-continuity. Full article

17 pages, 5181 KiB

Open AccessArticle

Shift-Invariance Robustness of Convolutional Neural Networks in Side-Channel Analysis

by Marina Krček, Lichao Wu, Guilherme Perin and Stjepan Picek

Mathematics 2024, 12(20), 3279; https://doi.org/10.3390/math12203279 (registering DOI) - 18 Oct 2024

Convolutional neural networks (CNNs) offer unrivaled performance in profiling side-channel analysis. This claim is corroborated by numerous results where CNNs break targets protected with masking and hiding countermeasures. One hiding countermeasure commonly investigated in related works is desynchronization (misalignment). The conclusions usually state [...] Read more.

Convolutional neural networks (CNNs) offer unrivaled performance in profiling side-channel analysis. This claim is corroborated by numerous results where CNNs break targets protected with masking and hiding countermeasures. One hiding countermeasure commonly investigated in related works is desynchronization (misalignment). The conclusions usually state that CNNs can break desynchronization as they are shift-invariant. This paper investigates that claim in more detail and reveals that the situation is more complex. While CNNs have certain shift-invariance, it is insufficient for commonly encountered scenarios in deep learning-based side-channel analysis. We investigate data augmentation to improve the shift-invariance and, in a more powerful version, ensembles of data augmentation. Our results show that the proposed techniques work very well and improve the attack significantly, even for an order of magnitude. Full article

(This article belongs to the Special Issue Applications of Artificial Intelligence to Cryptography)

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