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 18.3 days after submission; acceptance to publication is undertaken in 1.9 days (median values for papers published in this journal in the second 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 17 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

24 pages, 637 KiB

Open AccessReview

Application of Convolutional Neural Networks in Animal Husbandry: A Review

by Rotimi-Williams Bello, Roseline Oluwaseun Ogundokun, Pius A. Owolawi, Etienne A. van Wyk and Chunling Tu

Mathematics 2025, 13(12), 1906; https://doi.org/10.3390/math13121906 - 6 Jun 2025

Abstract

Convolutional neural networks (CNNs) and their application in animal husbandry have in-depth mathematical expressions, which usually revolve around how well they map input data such as images or video frames of animals to meaningful outputs like health status, behavior class, and identification. Likewise, computer vision and deep learning models are driven by CNNs to act intelligently in improving productivity and animal management for sustainable animal husbandry. In animal husbandry, CNNs play a vital role in the management and monitoring of livestock’s health and productivity due to their high-performance accuracy in analyzing images and videos. Monitoring animals’ health is important for their welfare, food abundance, safety, and economic productivity. This paper aims to comprehensively review recent advancements and applications of relevant models that are based on CNNs for livestock health monitoring, covering the detection of their various diseases and classification of their behavior, for overall management gain. We selected relevant articles with various experimental results addressing animal detection, localization, tracking, and behavioral monitoring, validating the high-performance accuracy and efficiency of CNNs. Prominent anchor-based object detection models such as R-CNN (series), YOLO (series) and SSD (series), and anchor-free object detection models such as key-point based and anchor-point based are often used, demonstrating great versatility and robustness across various tasks. From the analysis, it is evident that more significant research contributions to animal husbandry have been made by CNNs. Limited labeled data, variation in data, low-quality or noisy images, complex backgrounds, computational demand, species-specific models, high implementation cost, scalability, modeling complex behaviors, and compatibility with current farm management systems are good examples of several notable challenges when applying CNNs in animal husbandry. By continued research efforts, these challenges can be addressed for the actualization of sustainable animal husbandry. Full article

(This article belongs to the Section E: Applied Mathematics)

3 pages, 124 KiB

Open AccessEditorial

Preface to the Special Issue “Advances in Nonlinear Analysis, Analytic Number Theory, and Mathematical Inequalities”

by Wei-Shih Du, Ravi Prakash Agarwal and Feng Qi

Mathematics 2025, 13(12), 1905; https://doi.org/10.3390/math13121905 - 6 Jun 2025

Abstract

Over the past century, nonlinear analysis has been widely and significantly applied in many areas of mathematics, including nonlinear ordinary and partial differential equations, functional analysis, fixed point theory, nonlinear optimization, variational analysis, convex analysis, dynamical system theory, mathematical economics, signal processing, control [...] Read more.

(This article belongs to the Special Issue Advances in Nonlinear Analysis, Analytic Number Theory, and Mathematical Inequalities)

14 pages, 573 KiB

Open AccessArticle

Special Generation of Random Graphs and Statistical Study of Some of Their Invariants

by Boris Melnikov and Bowen Liu

Mathematics 2025, 13(12), 1904; https://doi.org/10.3390/math13121904 - 6 Jun 2025

Abstract

In this paper, we generate random graphs for a specific area, namely, models of real communication networks. We propose a method that determines the “best” invariant; the corresponding basic algorithm is as follows. For the generated set of graphs, we calculate the numerical values of each of the pre-selected invariants (i.e., indexes of Graovac–Ghorbani, Randic̀, Wiener, global clustering coefficients and the vector of second-order degrees). For all graphs, we arrange these numerical values in descending order, after which, for each of the 10 pairs of invariants, we calculate the rank correlation of these orders; for such calculations, we use 5 different variants of rank correlation algorithms (i.e., usual pair correlation, Spearman’s algorithm, Kendall’s algorithm and its improved version, and the algorithm proposed by the authors). In such a way, we get 10 pairs of rank correlation values, then we arrange them as the values of 10 independent elements of the 5 × 5 table (rows and columns of this table correspond to the 5 invariants under consideration). If the rank correlation values are negative, we record the absolute value of this value in the table. The basic idea is that the “most independent” invariant of the graph gets the minimum sum when summing 4 values of its row, i.e., less than for other invariants (other rows). For our subject area, we obtained the same result for 5 different variants of calculating the rank correlation: the value obtained for the vector of second-order degrees is significantly better than all the others, and among the usual invariants, the global clustering coefficients invariant is significantly better than others ones. This fact corresponds to our previous calculations, in which we ordered the graph invariants according to completely different algorithms. Full article

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

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14 pages, 283 KiB

Open AccessFeature PaperArticle

Non-Isomorphic Cayley Graphs of Metacyclic Groups of Order 8p with the Same Spectrum

by Lang Tang, Weijun Liu and Rongrong Lu

Mathematics 2025, 13(12), 1903; https://doi.org/10.3390/math13121903 - 6 Jun 2025

Abstract

The spectrum of a graph

Γ

, denoted by

S p e c (Γ)

, is the multiset of eigenvalues of its adjacency matrix. A Cayley graph

C a y (G, S)

of a finite group G is [...] Read more.

The spectrum of a graph

Γ

, denoted by

S p e c (Γ)

, is the multiset of eigenvalues of its adjacency matrix. A Cayley graph

C a y (G, S)

of a finite group G is called Cay-DS (Cayley graph determined by its spectrum) if, for any other Cayley graph

C a y (G, T)

S p e c (C a y (G, S)) = S p e c (C a y (G, T))

implies

C a y (G, S) ≅ C a y (G, T)

. A group G is said to be Cay-DS if all Cayley graphs of G are Cay-DS. An interesting open problem in the area of algebraic graph theory involves characterizing finite Cay-DS groups or constructing non-isomorphic Cayley graphs of a non-Cay-DS group that share the same spectrum. The present paper contributes to parts of this problem of metacyclic groups

M_{8 p}

of order

8 p

(with center of order 4), where p is an odd prime, in terms of irreducible characters, which are first presented. Then some new families of pairwise non-isomorphic Cayley graph pairs of

M_{8 p}

(

p \geq 5

) with the same spectrum are found. As a conclusion, this paper concludes that

M_{8 p}

is Cay-DS if and only if

p = 3

. Full article

(This article belongs to the Special Issue Recent Advances in Graph Theory, Applications and Related Topics)

10 pages, 801 KiB

Open AccessArticle

Asymptotic Behavior of the Modulus of the Kernel and Error Bounds of Anti-Gaussian Quadrature Formulas with Jacobi Weights

by Ramon Orive, Ljubica Mihić, Aleksandar Pejčev, Miroslav Pranić and Stefan Spalević

Mathematics 2025, 13(12), 1902; https://doi.org/10.3390/math13121902 - 6 Jun 2025

Abstract

In this paper, the remainder term of anti-Gaussian quadrature rules for analytic integrands with respect to Jacobi weight functions

ω_{a, b} (x) = {(1 - x)}^{a} {(1 + x)}^{b}

, where [...] Read more.

In this paper, the remainder term of anti-Gaussian quadrature rules for analytic integrands with respect to Jacobi weight functions

ω_{a, b} (x) = {(1 - x)}^{a} {(1 + x)}^{b}

, where

a, b > - 1

, is analyzed, and sharp estimates of the error are provided. These kinds of quadrature formulas were introduced by D.P. Laurie and have been recently studied by M.M. Spalević for the case of Jacobi-type weight functions

ω

. Full article

(This article belongs to the Special Issue Numerical Analysis and Scientific Computing for Applied Mathematics)

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22 pages, 1148 KiB

Open AccessArticle

Research on a PTSD Risk Assessment Model Using Multi-Modal Data Fusion

by Youxi Luo, Yucui Shang, Dongfeng Zhu, Tian Zhang and Chaozhu Hu

Mathematics 2025, 13(11), 1901; https://doi.org/10.3390/math13111901 - 5 Jun 2025

Abstract

Post-traumatic stress disorder (PTSD) is a complex psychological disorder caused by multiple factors, which are not only related to individual psychological states but also closely linked to physiological responses, social environments, and personal experiences. Therefore, traditional single data source assessment methods are difficult to fully understand and evaluate the complexity of PTSD. To overcome this challenge, the focus of this study is on developing a PTSD risk assessment model based on multi-modal data fusion. The importance of multi-modal data fusion lies in its ability to integrate data from different dimensions and provide a more comprehensive PTSD risk assessment. For multi-modal data fusion, two sets of solutions are proposed: the first is to extract EEG features using B-spline basis functions, combined with questionnaire data, to construct a multi-modal Zero-Inflated Poisson regression model; the second is to build a multi-modal deep neural network fusion prediction model to automatically extract and fuse multi-modal data features. The results show that the multi-modal data model is more accurate than the single data model, with significantly improved prediction ability. Zero-inflated Poisson models are prone to over-fitting when data is limited, while deep neural network models show superior performance in both training and prediction sets, especially the Hybrid LSTM-FCNN model, which not only has high accuracy but also strong generalization ability. This study proves the potential of multi-modal data fusion in PTSD prediction, and the Hybrid LSTM-FCNN model stands out for its high accuracy and good generalization ability, providing scientific evidence for early warning of PTSD in rescue personnel. Future research can further explore model optimization and clinical applications to promote the mental health maintenance of rescue personnel. Full article

(This article belongs to the Section D: Statistics and Operational Research)

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15 pages, 296 KiB

Open AccessArticle

On the Product of Zeta-Functions

by Nianliang Wang, Kalyan Chakraborty and Takako Kuzumaki

Mathematics 2025, 13(11), 1900; https://doi.org/10.3390/math13111900 - 5 Jun 2025

Abstract

In this paper, we study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference

α

, an integer with the Voronoĭ function weight

V_{k}

. In the case of [...] Read more.

In this paper, we study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference

α

, an integer with the Voronoĭ function weight

V_{k}

. In the case of

V_{1} (x) = e^{- x}

, the results reduce to Bochner modular relations, which include the Ramanujan formula, Wigert–Bellman approximate functional equation, and the Ewald expansion. The results abridge analytic number theory and the theory of modular forms in terms of the sum-of-divisor function. We pursue the problem of (approximate) automorphy of the associated Lambert series. The

α = 0

case is the divisor function, while the

α = 1

case would lead to a proof of automorphy of the Dedekind eta-function à la Ramanujan. Full article

(This article belongs to the Special Issue Analytic Methods in Number Theory and Allied Fields)

16 pages, 339 KiB

Open AccessArticle

An Efficient Numerical Method for the Fractional Bagley–Torvik Equation of Variable Coefficients with Robin Boundary Conditions

by S. Joe Christin Mary, Sekar Elango, Muath Awadalla and Rabab Alzahrani

Mathematics 2025, 13(11), 1899; https://doi.org/10.3390/math13111899 - 5 Jun 2025

Abstract

In this paper, we propose a numerical method for the fractional Bagley–Torvik equation of variable coefficients with Robin boundary conditions. The problem is approximated using a finite difference scheme on a uniform mesh that combines the L1 scheme with central differences. We prove that this numerical method is almost first-order convergent. The error bounds for the numerical approximation are derived. The numerical calculations carried out for the given examples validate the theoretical results. Full article

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23 pages, 1723 KiB

Open AccessFeature PaperArticle

A Comprehensive Study on the Different Approaches of the Symmetric Difference in Nilpotent Fuzzy Systems

by Luca Sára Pusztaházi, György Eigner and Orsolya Csiszár

Mathematics 2025, 13(11), 1898; https://doi.org/10.3390/math13111898 - 5 Jun 2025

Abstract

This paper comprehensively examines symmetric difference operators within logical systems generated by nilpotent t-norms and t-conorms, specifically addressing their behavior and applicability in bounded and Łukasiewicz fuzzy logic systems. We identify two distinct symmetric difference operators and analyze their fundamental properties, revealing their inherent non-associativity. Recognizing the limitations posed by non-associative behavior in practical multi-step logical operations, we introduce a novel aggregated symmetric difference operator constructed through the arithmetic mean of the previously defined operators. The primary theoretical contribution of our research is establishing the associativity of this new aggregated operator, significantly enhancing its effectiveness for consistent multi-stage computations. Moreover, this operator retains critical properties including symmetry, neutrality, antitonicity, and invariance under negation, thus making it particularly valuable for various computational and applied domains such as image processing, pattern recognition, fuzzy neural networks, cryptographic schemes, and medical data analysis. The demonstrated theoretical robustness and practical versatility of our associative operator provide a clear improvement over existing methodologies, laying a solid foundation for future research in fuzzy logic and interdisciplinary applications. Our broader aim is to derive and study symmetric difference operators in both bounded and Łukasiewicz systems, as this represents a new direction of research. Full article

(This article belongs to the Special Issue New Approaches to Data Analysis and Data Analytics)

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35 pages, 432 KiB

Open AccessFeature PaperArticle

Correctness of Fuzzy Inference Systems Based on f-Inclusion

by Carolina Díaz-Montarroso, Nicolás Madrid and Eloísa Ramírez-Poussa

Mathematics 2025, 13(11), 1897; https://doi.org/10.3390/math13111897 - 5 Jun 2025

Abstract

Recent work has shown that the f-index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to [...] Read more.

LU

enriched with fuzzy modifiers (also known as fuzzy hedges). This logic background provides to the approach a strength absent in most fuzzy inference systems in the literature, which allows us to formally prove a series of results that culminate in a final correctness theorem for the proposed fuzzy inference system. This paper also presents a running example aimed at showing the potential applicability of the proposal. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

23 pages, 2180 KiB

Open AccessArticle

Leveraging Advanced Mathematical Methods in Artificial Intelligence to Explore Heterogeneity and Asymmetry in Cross-Border Travel Satisfaction

by Yan Xu, Huajie Yang, Zibin Ye, Xiaobo Ma, Lei Tong and Xinyi Yu

Mathematics 2025, 13(11), 1896; https://doi.org/10.3390/math13111896 - 5 Jun 2025

Abstract

The cross-border port serves as a crucial cross-border travel connecting mainland China with Hong Kong and Macau, directly impacting the overall satisfaction of cross-border travel. While previous studies on neighborhoods, communities, and other areas have thoroughly examined the heterogeneity and asymmetry in satisfaction, research on the satisfaction of cross-border travel at ports remains notably limited. This paper explores the heterogeneity and asymmetry of cross-border travel satisfaction using gradient boosted decision trees (GBDT) and k-means cluster analysis under the framework of three-factor theory, aiming to demonstrate the latest scientific research results on the fundamental theories and applications of artificial intelligence. The results show prevalent asymmetric relationships between factors and cross-border travel satisfaction, with the factor structure exhibiting heterogeneity across different groups. High-income individuals were more likely to prioritize the reliability of cross-border travel, whereas low-income individuals tended to emphasize the convenience of travel. Finally, this paper proposes improvement priorities for different types of passengers, reflecting the practical application of advanced mathematical methods in artificial intelligence to drive intelligent decision-making. Full article

(This article belongs to the Special Issue Artificial Intelligence Applications with Advanced Mathematical Methods)

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30 pages, 4366 KiB

Open AccessArticle

Carbon Dioxide Emission Forecasting Using BiLSTM Network Based on Variational Mode Decomposition and Improved Black-Winged Kite Algorithm

by Yueqiao Yang, Shichuang Li, Haijun Liu and Jidong Guo

Mathematics 2025, 13(11), 1895; https://doi.org/10.3390/math13111895 - 5 Jun 2025

Abstract

With the growing severity of global climate change, forecasting and managing carbon dioxide (CO₂) emissions has become one of the critical tasks in addressing climate change. To improve the accuracy of CO₂ emission forecasting, an innovative framework based on variational mode decomposition (VMD), improved black-winged kite algorithm (IBKA), and BiLSTM networks is proposed. This framework aims to address the challenges associated with predicting non-stationary data and optimizing model hyperparameters. Initially, experiments were conducted on 29 benchmark functions using the IBKA algorithm, demonstrating its superior performance in highly nonlinear and complex environments. Subsequently, the BiLSTM model optimized by IBKA was employed to predict CO₂ emission trends across four major industries in China, confirming its enhanced prediction accuracy. Finally, a comparative analysis with other mainstream machine learning and deep learning models revealed that the BiLSTM model consistently achieved the best predictive performance across all industries. This research proposes an efficient and practical technical pathway for intelligent carbon emission prediction under the “dual-carbon” strategic goals, offering scientific support for policy formulation and the low-carbon transition. Full article

34 pages, 418 KiB

Open AccessFeature PaperReview

Queues with Working Vacations: A Survey

by Dieter Fiems

Mathematics 2025, 13(11), 1894; https://doi.org/10.3390/math13111894 - 5 Jun 2025

Abstract

In this paper, we present an extensive literature review on queueing systems with working vacations. The concept of a working vacation generalises the concept of server vacations, which are time periods during which the server is absent and cannot serve waiting customers. During a working vacation, the server remains active, albeit at a reduced service rate. Our literature survey mainly highlights the structural properties of the Markov chains that underlie working vacation queueing models, as well as various methodological approaches to assessing the performance of queues with working vacations. Moreover, queueing games with working vacations and applications of queues with working vacations are discussed. Full article

(This article belongs to the Special Issue Queue and Stochastic Models for Operations Research, 3rd Edition)

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15 pages, 467 KiB

Open AccessFeature PaperArticle

Linear Trend, HP Trend, and bHP Trend

by Hiroshi Yamada

Mathematics 2025, 13(11), 1893; https://doi.org/10.3390/math13111893 - 5 Jun 2025

Abstract

The modelling of the trend component of economic time series has a long history, and the most primitive and popular model displays the trend as a linear function of time. However, the residuals of such a linear trend frequently exhibit long-period fluctuations. The Hodrick–Prescott (HP) filter is able to capture such long-period fluctuations well, resulting in a very realistic trend-cycle decomposition. It may be queried whether the HP trend residuals no longer contain useful long-period fluctuations. If such long-period fluctuations are present, then taking them into consideration could improve the HP trend. In a recent article, a new approach to address this issue, the boosted HP (bHP) filter, was proposed. The three trends mentioned above, i.e., the linear trend, the HP trend, and the bHP trend, can be treated in a unified manner. In this paper, we demonstrate the relationship in detail. We show how the bHP trend is constructed from the linear/HP trend, and long-period fluctuations remained in their trend residuals. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis)

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23 pages, 2098 KiB

Open AccessArticle

Modeling Time Series with SARIMAX and Skew-Normal and Zero-Inflated Skew-Normal Errors

by M. Alejandro Dinamarca, Fernando Rojas, Claudia Ibacache-Quiroga and Karoll González-Pizarro

Mathematics 2025, 13(11), 1892; https://doi.org/10.3390/math13111892 - 5 Jun 2025

Abstract

This study proposes an extension of Seasonal Autoregressive Integrated Moving Average models with exogenous regressors (SARIMAX) by incorporating skew-normal and zero-inflated skew-normal error structures to better accommodate asymmetry and excess zeros in time series data. The proposed framework demonstrates improved flexibility and robustness compared to traditional Gaussian-based models. Simulation experiments reveal that the skewness parameter significantly affect forecasting accuracy, with reductions in mean absolute error (MAE) and root mean square error (RMSE) observed across both positively and negatively skewed scenarios. Notably, in negative-skew contexts, the model achieved an MAE of 0.40 and RMSE of 0.49, outperforming its symmetric-error counterparts. The inclusion of zero-inflation probabilities further enhances model performance in sparse datasets, yielding superior values in goodness-of-fit criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). To illustrate the practical value of the methodology, a real-world case study is presented involving the modeling of optical density (OD₆₀₀) data from Escherichia coli during stationary-phase growth. A SARIMAX(1,1,1) model with skew-normal errors was fitted to 200 time-stamped absorbance measurements, revealing significant positive skewness in the residuals. Bootstrap-derived confidence intervals confirmed the significance of the estimated skewness parameter (

α = 14.033

with 95% CI [12.07, 15.99]). The model outperformed the classical ARIMA benchmark in capturing the asymmetry of the stochastic structure, underscoring its relevance for biological, environmental, and industrial applications in which non-Gaussian features are prevalent. Full article

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

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25 pages, 510 KiB

Open AccessArticle

An Adaptive Evolutionary Causal Dynamic Factor Model

by Qian Wei and Heng-Guo Zhang

Mathematics 2025, 13(11), 1891; https://doi.org/10.3390/math13111891 - 5 Jun 2025

Abstract

Background: With COVID-19 having a significant impact on economic activity, it has become difficult for the existing dynamic factor models (nowcasting models) to forecast macroeconomics with high accuracy. The real-time monitoring of macroeconomics has become an important research problem faced by banks, governments, and corporations. Subjects and Methods: This paper proposes an adaptive evolutionary causal dynamic factor model (AcNowcasting) for macroeconomic forecasting. Unlike the classical nowcasting models, the AcNowcasting algorithm has the ability to perform feature selection. The criteria for feature selection are based on causality strength rather than being based on the quality of the prediction results. In addition, the factors in the AcNowcasting algorithm have the capacity for adaptive differential evolution, which can generate the best factors. These two abilities are not possessed by classical nowcasting models. Results: The experimental results show that the AcNowcasting algorithm can extract common factors that reflect macroeconomic fluctuations better, and the prediction accuracy of the AcNowcasting algorithm is more accurate than that of traditional nowcasting models. Contributions: The AcNowcasting algorithm provides a new prediction theory and a means for the real-time monitoring of macroeconomics, which has good theoretical and practical value. Full article

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18 pages, 7765 KiB

Open AccessArticle

Secure Parallel Image Cryptographic Hash Function Using a Novel 2D High-Randomness Hyperchaotic Map

by Mingrui Qi and Dongdong Wang

Mathematics 2025, 13(11), 1890; https://doi.org/10.3390/math13111890 - 5 Jun 2025

Abstract

For image data, the processing of each pixel using a cryptographic hash function is linear, and the existing cryptographic hash function lacks parallel processing of image width and height. In order to improve the computational efficiency and ensure the security of the hash function in image cryptography, we design a 2D hyperchaotic map, whose good chaotic dynamics and randomness fully meet the needs of the hash function. Based on the proposed mapping, we propose an image-specific chaotic hash function for confusion diffusion and extraction in both width and height dimensions in parallel. The designed hash function of image cryptography can set some common hash lengths and also support the setting of key. For image data, the proposed method has higher computational efficiency than other common hash functions and has good encryption security and anti-collision characteristics. Full article

(This article belongs to the Special Issue Complex System Dynamics and Image Processing)

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26 pages, 1610 KiB

Open AccessArticle

Forecasting Stock Market Volatility Using CNN-BiLSTM-Attention Model with Mixed-Frequency Data

by Yufeng Zhang, Tonghui Zhang and Jingyi Hu

Mathematics 2025, 13(11), 1889; https://doi.org/10.3390/math13111889 - 5 Jun 2025

Abstract

Existing stock volatility forecasting models predominantly rely on same-frequency market data while neglecting mixed-frequency integration and face particular challenges in incorporating low-frequency macroeconomic variables that exhibit temporal mismatches with financial market dynamics. To address this limitation, this study develops a novel hybrid approach for stock market volatility forecasting, which synergistically combines a deep learning model (CNN-BiLSTM-Attention) with the GARCH-MIDAS model. The GARCH-MIDAS model can fully exploit mixed-frequency information, including daily returns, monthly macroeconomic variables, and EPU. The deep learning model can effectively capture both spatial and temporal patterns of multivariate time-series data, thus effectively improving prediction accuracy and generalization ability in stock market volatility forecasting. The results indicate that the CNN-BiLSTM-Attention model yields the most accurate forecasts compared to the benchmark models. Furthermore, incorporating additional predictors, such as macroeconomic indicators and the Economic Policy Uncertainty Index, also provides valuable information for stock market volatility prediction, notably enhancing the model’s forecasting effect. Full article

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3 pages, 142 KiB

Open AccessEditorial

Preface to the Special Issue “Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research”

by Marcio Pereira Basilio, Valdecy Pereira and Marcos dos Santos

Mathematics 2025, 13(11), 1888; https://doi.org/10.3390/math13111888 - 5 Jun 2025

Abstract

Decision-making is a consistent part of the daily activities of individuals and organizations [...] Full article

16 pages, 503 KiB

Open AccessArticle

Overcoming Class Imbalance in Incremental Learning Using an Elastic Weight Consolidation-Assisted Common Encoder Approach

by Engin Baysal and Cüneyt Bayılmış

Mathematics 2025, 13(11), 1887; https://doi.org/10.3390/math13111887 - 4 Jun 2025

Abstract

Incremental learning empowers models to continuously acquire knowledge of new classes while retaining previously learned information. However, catastrophic forgetting and class imbalance often impede this process, especially when new classes are introduced sequentially. We propose a hybrid method that integrates Elastic Weight Consolidation (EWC) with a shared encoder architecture to overcome these obstacles. This approach provides robust feature extraction, while EWC safeguards vital parameters and preserves prior knowledge. Moreover, task-specific output layers enable flexible adaptation to new classes. We evaluated our method using the CICIoT2023 dataset, a class-incremental IoT anomaly detection benchmark. Our results demonstrated a 15.3% improvement in the macro F1-score and a 1.28% increase in overall accuracy compared to a baseline model that did not incorporate EWC, with particular advantages for underrepresented classes. These findings underscore the effectiveness of the EWC-assisted shared encoder framework for class-imbalanced incremental learning in streaming environments. Full article

(This article belongs to the Special Issue New Insights in Machine Learning (ML) and Deep Neural Networks)

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