Mathematics

21 pages, 3301 KiB

Open AccessArticle

Decoding Colon Cancer Heterogeneity Through Integrated miRNA–Gene Network Analysis

by Qingcai He, Zhilong Mi, Tianyue Liu, Taihang Huang, Mao Li, Binghui Guo and Zhiming Zheng

Mathematics 2025, 13(6), 1020; https://doi.org/10.3390/math13061020 - 20 Mar 2025

Viewed by 220

Abstract

Colon adenocarcinoma (COAD) demonstrates significant clinical heterogeneity across disease stages, gender, and age groups, posing challenges for unified therapeutic strategies. This study establishes a multi-dimensional stratification framework through integrative analysis of miRNA–gene co-expression networks, employing the MRNETB algorithm coupled with Markov flow entropy [...] Read more.

Colon adenocarcinoma (COAD) demonstrates significant clinical heterogeneity across disease stages, gender, and age groups, posing challenges for unified therapeutic strategies. This study establishes a multi-dimensional stratification framework through integrative analysis of miRNA–gene co-expression networks, employing the MRNETB algorithm coupled with Markov flow entropy (MFE) centrality quantification. Analysis of TCGA-COAD cohorts revealed stage-dependent regulatory patterns centered on CDX2-hsa-miR-22-3p-MUC13 interactions, with progressive dysregulation mirroring tumor progression. Gender-specific molecular landscapes have emerged, characterized by predominant SLC26A3 expression in males and GPA33 enrichment in females, suggesting divergent pathogenic mechanisms between genders. Striking age-related disparities were observed, where early-onset cases exhibited molecular signatures distinct from conventional COAD, highlighted by marked XIST expression variations. Drug-target network analysis identified actionable candidates including CEACAM5-directed therapies and differentiation-modulating agents. Our findings underscore the critical need for heterogeneity-aware clinical decision-making, providing a roadmap for stratified intervention paradigms in precision oncology. Full article

(This article belongs to the Special Issue Network Biology and Machine Learning in Bioinformatics)

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24 pages, 2767 KiB

Open AccessFeature PaperArticle

Modeling Non-Normal Distributions with Mixed Third-Order Polynomials of Standard Normal and Logistic Variables

by Mohan D. Pant, Aditya Chakraborty and Ismail El Moudden

Mathematics 2025, 13(6), 1019; https://doi.org/10.3390/math13061019 - 20 Mar 2025

Viewed by 171

Abstract

Continuous data associated with many real-world events often exhibit non-normal characteristics, which contribute to the difficulty of accurately modeling such data with statistical procedures that rely on normality assumptions. Traditional statistical procedures often fail to accurately model non-normal distributions that are often observed [...] Read more.

Continuous data associated with many real-world events often exhibit non-normal characteristics, which contribute to the difficulty of accurately modeling such data with statistical procedures that rely on normality assumptions. Traditional statistical procedures often fail to accurately model non-normal distributions that are often observed in real-world data. This paper introduces a novel modeling approach using mixed third-order polynomials, which significantly enhances accuracy and flexibility in statistical modeling. The main objective of this study is divided into three parts: The first part is to introduce two new non-normal probability distributions by mixing standard normal and logistic variables using a piecewise function of third-order polynomials. The second part is to demonstrate a methodology that can characterize these two distributions through the method of L-moments (MoLMs) and method of moments (MoMs). The third part is to compare the MoLMs- and MoMs-based characterizations of these two distributions in the context of parameter estimation and modeling non-normal real-world data. The simulation results indicate that the MoLMs-based estimates of L-skewness and L-kurtosis are superior to their MoMs-based counterparts of skewness and kurtosis, especially for distributions with large departures from normality. The modeling (or data fitting) results also indicate that the MoLMs-based fits of these distributions to real-world data are superior to their corresponding MoMs-based counterparts. Full article

(This article belongs to the Section D1: Probability and Statistics)

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26 pages, 1567 KiB

Open AccessArticle

A Stochastic Continuous-Time Markov Chain Approach for Modeling the Dynamics of Cholera Transmission: Exploring the Probability of Disease Persistence or Extinction

by Leul Mekonnen Anteneh, Mahouton Norbert Hounkonnou and Romain Glèlè Kakaï

Mathematics 2025, 13(6), 1018; https://doi.org/10.3390/math13061018 - 20 Mar 2025

Viewed by 267

Abstract

In this paper, a stochastic continuous-time Markov chain (CTMC) model is developed and analyzed to explore the dynamics of cholera. The multitype branching process is used to compute a stochastic threshold for the CTMC model. Latin hypercube sampling/partial rank correlation coefficient (LHS/PRCC) sensitivity [...] Read more.

In this paper, a stochastic continuous-time Markov chain (CTMC) model is developed and analyzed to explore the dynamics of cholera. The multitype branching process is used to compute a stochastic threshold for the CTMC model. Latin hypercube sampling/partial rank correlation coefficient (LHS/PRCC) sensitivity analysis methods are implemented to derive sensitivity indices of model parameters. The results show that the natural death rate

(μ_{v})

of a vector is the most sensitive parameter for controlling disease outbreaks. Numerical simulations indicate that the solutions of the CTMC stochastic model are relatively close to the solutions of the deterministic model. Numerical simulations estimate the probability of both disease extinction and outbreak. The probability of cholera extinction is high when it emerges from bacterial concentrations in non-contaminated/safe water in comparison to when it emerges from all infected groups. Thus, any intervention that focuses on reducing the number of infections at the beginning of a cholera outbreak is essential for reducing its transmission. Full article

(This article belongs to the Special Issue Stochastic Models in Mathematical Biology, 2nd Edition)

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13 pages, 15150 KiB

Open AccessArticle

A Validity Index for Clustering Evaluation by Grid Structures

by Jiachen Wang, Zuojing Zhang and Shihong Yue

Mathematics 2025, 13(6), 1017; https://doi.org/10.3390/math13061017 - 20 Mar 2025

Viewed by 191

Abstract

The evaluation of clustering results plays an important role in clustering analysis. Most existing indexes are designed for the evaluation of results from the most-used K-means clustering algorithm; it can identify only spherical clusters rather than arbitrary clusters. However, in recent decades, various [...] Read more.

The evaluation of clustering results plays an important role in clustering analysis. Most existing indexes are designed for the evaluation of results from the most-used K-means clustering algorithm; it can identify only spherical clusters rather than arbitrary clusters. However, in recent decades, various algorithms have been proposed to cluster arbitrary clusters that are nonspherical, such as ones with arbitrary shapes, different sizes, distinct densities, and instances where there is overlap among clusters. To effectively solve these issues, in this paper, we propose a new validity index based on a grid-partitioning structure. First, all data points in a dataset are assigned to a group of partitioned grids. Then, each cluster is normalized towards a spherical shape, and the number of empty and intersecting grids in all clusters is computed. The two groups of grids serve as the background of each cluster. Finally, according to various clustering results, the optimal number of clusters is obtained when the number of total grids reaches its minimal value. Experiments are performed on real and synthetic datasets for any algorithms and datasets, revealing the generalization and effectiveness of the new index. Full article

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15 pages, 294 KiB

Open AccessFeature PaperReview

Approximate Solutions of Variational Inequalities and the Ekeland Principle

by Raffaele Chiappinelli and David E. Edmunds

Mathematics 2025, 13(6), 1016; https://doi.org/10.3390/math13061016 - 20 Mar 2025

Viewed by 139

Abstract

Let K be a closed convex subset of a real Banach space X, and let F be a map from X to its dual

X^{*}

. We study the so-called variational inequality problem: given

y \in X^{*,},

does [...] Read more.

Let K be a closed convex subset of a real Banach space X, and let F be a map from X to its dual

X^{*}

. We study the so-called variational inequality problem: given

y \in X^{*,},

does there exist

x_{0} \in K

such that (in standard notation)

⟨F (x_{0}) - y, x - x_{0}⟩ \geq 0

for all

x \in K ?

After a short exposition of work in this area, we establish conditions on F sufficient to ensure a positive answer to the question of whether F is a gradient operator. A novel feature of the proof is the key role played by the well-known Ekeland variational principle. Full article

(This article belongs to the Special Issue Variational Problems and Applications, 3rd Edition)

22 pages, 1463 KiB

Open AccessArticle

Edge Computing-Enabled Train Fusion Positioning: Modeling and Analysis

by Hao Yin, Haifeng Song, Ruichao Wu, Min Zhou, Zixing Deng and Hairong Dong

Mathematics 2025, 13(6), 1015; https://doi.org/10.3390/math13061015 - 20 Mar 2025

Viewed by 196

Abstract

For train control systems, the accuracy of positioning tracking is essential for ensuring the safety and efficiency of operations. Multi-source information fusion techniques can improve positioning accuracy, but the computational limitations of onboard equipment impede the real-time processing capabilities required by advanced information [...] Read more.

For train control systems, the accuracy of positioning tracking is essential for ensuring the safety and efficiency of operations. Multi-source information fusion techniques can improve positioning accuracy, but the computational limitations of onboard equipment impede the real-time processing capabilities required by advanced information fusion algorithms. An innovative approach, which combines multi-sensor information fusion with edge computing, is proposed to reduce the computational load on onboard systems and accelerate data processing. Colored Petri Nets (CPNs) are utilized for the modeling and validation of the algorithm. State-space analysis is used to evaluate the functional safety of the proposed method. Numerical simulations are performed to identify the key factors affecting the train positioning method’s performance. These simulations also determine the minimal tracking interval required for effective operation under edge computing. The results show that the edge computing-based train fusion positioning method reduces data processing delays and improves positioning accuracy. This approach offers a practical solution for real-time and accurate train control systems. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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20 pages, 343 KiB

Open AccessArticle

Mathematical Modeling and Parameter Estimation of Lane-Changing Vehicle Behavior Decisions

by Jianghui Wen, Yebei Xu, Min Dai and Nengchao Lyu

Mathematics 2025, 13(6), 1014; https://doi.org/10.3390/math13061014 - 20 Mar 2025

Viewed by 188

Abstract

Lane changing is a crucial scenario in traffic environments, and accurately recognizing and predicting lane-changing behavior is essential for ensuring the safety of both autonomous vehicles and drivers. Through considering the multi-vehicle information interaction characteristics in lane-changing behavior for vehicles and the impact [...] Read more.

Lane changing is a crucial scenario in traffic environments, and accurately recognizing and predicting lane-changing behavior is essential for ensuring the safety of both autonomous vehicles and drivers. Through considering the multi-vehicle information interaction characteristics in lane-changing behavior for vehicles and the impact of driver experience needs on lane-changing decisions, this paper proposes a lane-changing model for vehicles to achieve safe and comfortable driving. Firstly, a lane-changing intention recognition model incorporating interaction effects was established to obtain the initial lane-changing intention probability of the vehicles. Secondly, by accounting for individual driving styles, a lane-changing behavior decision model was constructed based on a Gaussian mixture hidden Markov model (GMM-HMM) along with a parameter estimation method. The initial lane-changing intention probability serves as the input for the decision model, and the final lane-changing decision is made by comparing the probabilities of lane-changing and non-lane-changing scenarios. Finally, the model was validated using real-world data from the Next Generation Simulation (NGSIM) dataset, with empirical results demonstrating its high accuracy in recognizing and predicting lane-changing behavior. This study provides a robust framework for enhancing lane-changing decision making in complex traffic environments. Full article

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20 pages, 427 KiB

Open AccessFeature PaperArticle

Counting the Number of Squares of Each Colour in Cyclically Coloured Rectangular Grids

by Marcus R. Garvie

Mathematics 2025, 13(6), 1013; https://doi.org/10.3390/math13061013 - 20 Mar 2025

Viewed by 189

Abstract

Modular arithmetic is used to apply generalized C-coloured checkerboard patterns to

m \times n

gridded rectangles, ensuring that colours cycle both horizontally and vertically. This paper yields methods for counting the number of squares of each colour, which is a nontrivial combinatorial [...] Read more.

Modular arithmetic is used to apply generalized C-coloured checkerboard patterns to

m \times n

gridded rectangles, ensuring that colours cycle both horizontally and vertically. This paper yields methods for counting the number of squares of each colour, which is a nontrivial combinatorial problem in discrete geometry. The main theorem provides a closed-form expression for a sum of floor functions, representing the count of squares for each colour. Two proofs are presented: a heuristic, constructive approach dividing the problem into sub-cases, and a purely mathematical derivation that transforms the floor sum into a closed-form solution, computable in

O (1)

operations, independent of

m, n

and C. Numerical counts are validated using a brute-force procedure in MATLAB (Version 9.14, R2023a). Full article

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13 pages, 1159 KiB

Open AccessArticle

Ricci Semi-Symmetric Robertson–Walker Spacetime in f(R)-Gravity

by H. Aruna Kumara, Abdul Haseeb, V. Venkatesha and Mohd Bilal

Mathematics 2025, 13(6), 1012; https://doi.org/10.3390/math13061012 - 20 Mar 2025

Viewed by 190

Abstract

We investigated the properties of Ricci semi-symmetric Robertson–Walker spacetimes within the framework of

f (R)

-gravity theory. Initially, we established that Ricci semi-symmetric Robertson–Walker spacetimes are locally isometric to either Minkowski or de Sitter spacetimes. We then focused on the 4-dimensional [...] Read more.

We investigated the properties of Ricci semi-symmetric Robertson–Walker spacetimes within the framework of

f (R)

-gravity theory. Initially, we established that Ricci semi-symmetric Robertson–Walker spacetimes are locally isometric to either Minkowski or de Sitter spacetimes. We then focused on the 4-dimensional formulation of these spacetimes in

f (R)

-gravity, deriving expressions for the isotropic pressure p and energy density

σ

. To further develop our understanding, we explored various energy conditions to constrain the functional form of

f (R)

. We analyzed several models, namely

f (R) = R - α (1 - e^{- \frac{R}{α}})

,

f (R) = R - β tanh R

, and

f (R) = R - log (m R)

, where

α

,

β

, and m are constants. Our findings suggest that the equations of state parameters for these models are compatible with the universe’s accelerating expansion, indicating an equation of state parameter

ω = - 1

. Moreover, while these models satisfy the null, weak, and dominant energy conditions reflective of the observed accelerated expansion, our analysis reveals that they violate the strong energy condition. Full article

(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications)

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16 pages, 2628 KiB

Open AccessArticle

Improving Recommender Systems for Fake News Detection in Social Networks with Knowledge Graphs and Graph Attention Networks

by Aleksei Golovin, Nataly Zhukova, Radhakrishnan Delhibabu and Alexey Subbotin

Mathematics 2025, 13(6), 1011; https://doi.org/10.3390/math13061011 - 20 Mar 2025

Viewed by 334

Abstract

This paper addresses the pervasive problem of fake news propagation in social networks. Traditional text-based detection models often suffer from performance degradation over time due to their reliance on evolving textual features. To overcome this limitation, we propose a novel recommender system that [...] Read more.

This paper addresses the pervasive problem of fake news propagation in social networks. Traditional text-based detection models often suffer from performance degradation over time due to their reliance on evolving textual features. To overcome this limitation, we propose a novel recommender system that leverages the power of knowledge graphs and graph attention networks (GATs). This approach captures both the semantic relationships within the news content and the underlying social network structure, enabling more accurate and robust fake news detection. The GAT model, by assigning different weights to neighboring nodes, effectively captures the importance of various users in disseminating information. We conducted a comprehensive evaluation of our system using the FakeNewsNet dataset, comparing its performance against classical machine learning models and the DistilBERT language model. Our results demonstrate that the proposed graph-based system achieves state-of-the-art performance, with an F1-score of 95%, significantly outperforming other models. Moreover, it maintains its effectiveness over time, unlike text-based approaches that are susceptible to concept drift. This research underscores the potential of knowledge graphs and GATs in combating fake news and provides a robust framework for building more resilient and accurate detection systems. Full article

(This article belongs to the Special Issue Advances in Recommender Systems and Intelligent Agents)

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18 pages, 610 KiB

Open AccessFeature PaperArticle

Analysis of Dynamic Transaction Fee Blockchain Using Queueing Theory

by Koki Inami and Tuan Phung-Duc

Mathematics 2025, 13(6), 1010; https://doi.org/10.3390/math13061010 - 20 Mar 2025

Viewed by 268

Abstract

In recent years, blockchains have been attracting attention because they are decentralized networks with transparency and trustworthiness. Generally, transactions on blockchain networks with higher transaction fees are processed preferentially compared to others. The processing fee varies significantly depending on other transactions; it is [...] Read more.

In recent years, blockchains have been attracting attention because they are decentralized networks with transparency and trustworthiness. Generally, transactions on blockchain networks with higher transaction fees are processed preferentially compared to others. The processing fee varies significantly depending on other transactions; it is difficult to predict the fee, and it may be significantly high. These are major barriers to blockchain utilization. Although several consensus algorithms have been proposed to solve these problems, their performance has not been fully evaluated. In this study, we model a blockchain system with a base fee, such as in Ethereum, via a priority queueing model. To assess the model’s performance, we derive the stability condition, stationary probability, average number of customers, and average waiting time for each type of customer. In deriving the stability conditions, we propose a method that uses the theoretical values of the partial models. These theoretical values match well with those obtained from Monte Carlo simulations, confirming the validity of the analysis. Full article

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

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21 pages, 413 KiB

Open AccessArticle

Construction of a Hybrid Class of Special Polynomials: Fubini–Bell-Based Appell Polynomials and Their Properties

by Yasir A. Madani, Abdulghani Muhyi, Khaled Aldwoah, Amel Touati, Khidir Shaib Mohamed and Ria H. Egami

Mathematics 2025, 13(6), 1009; https://doi.org/10.3390/math13061009 - 20 Mar 2025

Viewed by 178

Abstract

This paper aims to establish a new hybrid class of special polynomials, namely, the Fubini–Bell-based Appell polynomials. The monomiality principle is used to derive the generating function for these polynomials. Several related identities and properties, including symmetry identities, are explored. The determinant representation [...] Read more.

This paper aims to establish a new hybrid class of special polynomials, namely, the Fubini–Bell-based Appell polynomials. The monomiality principle is used to derive the generating function for these polynomials. Several related identities and properties, including symmetry identities, are explored. The determinant representation of the Fubini–Bell-based Appell polynomials is also established. Furthermore, some special members of the Fubini–Bell-based Appell family—such as the Fubini–Bell-based Bernoulli polynomials and the Fubini–Bell-based Euler polynomials—are derived, with analogous results presented for each. Finally, computational results and graphical representations of the zero distributions of these members are investigated. Full article

(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)

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10 pages, 1196 KiB

Open AccessArticle

A Study of Winning Percentage in the MLB Using Fuzzy Markov Regression

by Seung Hoe Choi and Seo-Kyung Ji

Mathematics 2025, 13(6), 1008; https://doi.org/10.3390/math13061008 - 20 Mar 2025

Viewed by 174

Abstract

In this study, we analyze the winning percentage of 16 teams that have participated in Major League Baseball since 1901. First, 69 variables for each team are classified into pitching, batting, and fielding using factor analysis, and then the effect of the newly [...] Read more.

In this study, we analyze the winning percentage of 16 teams that have participated in Major League Baseball since 1901. First, 69 variables for each team are classified into pitching, batting, and fielding using factor analysis, and then the effect of the newly classified variables on the winning percentage is analyzed. In addition, after expressing each team’s winning rate as a fuzzy number using a fuzzy partition, the linear relationship between the previous year and the next year using the fuzzy probability is investigated, and we estimate the fuzzy regression model and Markov regression model using the Double Least Absolute Deviation (DLAD) method. The proposed fuzzy model describes variables that affect the winning percentage of the next year according to the winning rate of the previous year. The estimated fuzzy regression model showed that the on-base percentage allowed by the pitcher and the on-base percentage of the batter had the greatest effect on the winning percentage. Full article

(This article belongs to the Special Issue Research Progress of Probability Statistics)

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19 pages, 452 KiB

Open AccessArticle

A Surrogate-Assisted Gray Prediction Evolution Algorithm for High-Dimensional Expensive Optimization Problems

by Xiaoliang Huang, Hongbing Liu, Quan Zhou and Qinghua Su

Mathematics 2025, 13(6), 1007; https://doi.org/10.3390/math13061007 - 20 Mar 2025

Viewed by 253

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs), which combine the search capabilities of evolutionary algorithms (EAs) with the predictive capabilities of surrogate models, are effective methods for solving expensive optimization problems (EOPs). However, the over-reliance on the accuracy of the surrogate model causes the optimization performance [...] Read more.

Surrogate-assisted evolutionary algorithms (SAEAs), which combine the search capabilities of evolutionary algorithms (EAs) with the predictive capabilities of surrogate models, are effective methods for solving expensive optimization problems (EOPs). However, the over-reliance on the accuracy of the surrogate model causes the optimization performance of most SAEAs to decrease drastically with the increase in dimensionality. To tackle this challenge, this paper proposes a surrogate-assisted gray prediction evolution (SAGPE) algorithm based on gray prediction evolution (GPE). In SAGPE, both the global and local surrogate model are constructed to assist the GPE search alternately. The proposed algorithm improves optimization efficiency by combining the macro-predictive ability of the even gray model in GPE for population update trends and the predictive ability of surrogate models to synergistically guide population searches in promising directions. In addition, an inferior offspring learning strategy is proposed to improve the utilization of population information. The performance of SAGPE is tested on eight common benchmark functions and a speed reducer design problem. The optimization results are compared with existing algorithms and show that SAGPE has significant performance advantages in terms of convergence speed and solution accuracy. Full article

(This article belongs to the Special Issue Advances in Intelligent Computing, Machine Learning and Pattern Recognition)

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23 pages, 4342 KiB

Open AccessArticle

A Mathematical Model for Determining Coordinates of Points in a Desired Trimetric Projection of a Three-Dimensional Object

by Nebojša Nikolić, Dragi Radomirović, Pavel Benka and Boris Stojić

Mathematics 2025, 13(6), 1006; https://doi.org/10.3390/math13061006 - 20 Mar 2025

Viewed by 173

Abstract

The aim of this paper is to develop a mathematical model for determining coordinates of points in a desired trimetric projection of a three-dimensional object. The desired trimetric projection is quantitatively specified according to the observer’s preference to emphasize one face of the [...] Read more.

The aim of this paper is to develop a mathematical model for determining coordinates of points in a desired trimetric projection of a three-dimensional object. The desired trimetric projection is quantitatively specified according to the observer’s preference to emphasize one face of the object more than another. Within the mathematical model, equations defining the interdependencies of trimetric parameters are derived first. It is then demonstrated how the projection of an arbitrary point of the observed object can be determined based on these trimetric parameters. Subsequently, equations are derived that enable the calculation of the necessary trimetric parameters to achieve a desired projection. By employing the developed model, one can accurately determine the coordinates of points in the desired trimetric projection, provided that the corresponding spatial coordinates are known, as demonstrated through several examples. Full article

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

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14 pages, 452 KiB

Open AccessArticle

A Comprehensive Comparative Study of Quick Invariant Signature (QIS), Dynamic Time Warping (DTW), and Hybrid QIS + DTW for Time Series Analysis

by Hamid Reza Shahbazkia, Hamid Reza Khosravani, Alisher Pulatov, Elmira Hajimani and Mahsa Kiazadeh

Mathematics 2025, 13(6), 999; https://doi.org/10.3390/math13060999 - 19 Mar 2025

Viewed by 1858

Abstract

This study presents a comprehensive evaluation of the quick invariant signature (QIS), dynamic time warping (DTW), and a novel hybrid QIS + DTW approach for time series analysis. QIS, a translation and rotation invariant shape descriptor, and DTW, a widely used alignment technique, [...] Read more.

This study presents a comprehensive evaluation of the quick invariant signature (QIS), dynamic time warping (DTW), and a novel hybrid QIS + DTW approach for time series analysis. QIS, a translation and rotation invariant shape descriptor, and DTW, a widely used alignment technique, were tested individually and in combination across various datasets, including ECG5000, seismic data, and synthetic signals. Our hybrid method was designed to embed the structural representation of the QIS with the temporal alignment capabilities of DTW. This hybrid method achieved a performance of up to 93% classification accuracy on ECG5000, outperforming DTW alone (86%) and a standard MLP classifier in noisy or low-data conditions. These findings confirm that integrating structural invariance (QIS) with temporal alignment (DTW) yields superior robustness to noise and time compression artifacts. We recommend adopting hybrid QIS + DTW, particularly for applications in biomedical signal monitoring and earthquake detection, where real-time analysis and minimal labeled data are critical. The proposed hybrid approach does not require extensive training, making it suitable for resource-constrained scenarios. Full article

(This article belongs to the Special Issue Mathematical Modeling and Optimization in Signal Processing)

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19 pages, 326 KiB

Open AccessArticle

Multi-View Contrastive Fusion POI Recommendation Based on Hypergraph Neural Network

by Luyao Hu, Guangpu Han, Shichang Liu, Yuqing Ren, Xu Wang, Ya Liu, Junhao Wen and Zhengyi Yang

Mathematics 2025, 13(6), 998; https://doi.org/10.3390/math13060998 - 19 Mar 2025

Viewed by 230

Abstract

In the era of information overload, location-based social software has gained widespread popularity, and the demand for personalized POI (Point of Interest) recommendation services is growing rapidly. Recommending the next POI is crucial in recommendation systems, aiming to suggest appropriate next-visit locations based [...] Read more.

In the era of information overload, location-based social software has gained widespread popularity, and the demand for personalized POI (Point of Interest) recommendation services is growing rapidly. Recommending the next POI is crucial in recommendation systems, aiming to suggest appropriate next-visit locations based on users’ historical trajectories and check-in data. However, the existing research often neglects user preferences’ diversity and dynamic nature and the need for the deep modeling of key collaborative relationships across various dimensions. As a result, the recommendation performance is limited. To address these challenges, this paper introduces an innovative Multi-View Contrastive Fusion Hypergraph Learning Model (MVHGAT). The model first constructs three distinct hypergraphs, representing interaction, trajectory, and geographical location, capturing the complex relationships and high-order dependencies between users and POIs from different perspectives. Subsequently, a targeted hypergraph convolutional network is designed for aggregation and propagation, learning the latent factors within each view. Through multi-view weighted contrastive learning, the model uncovers key collaborative effects between views, enhancing both user and POI representations’ consistency and discriminative power. The experimental results demonstrate that MVHGAT significantly outperforms several state-of-the-art methods across three public datasets, effectively addressing issues such as data sparsity and oversmoothing. This model provides new insights and solutions for the next POI recommendation task. Full article

(This article belongs to the Special Issue Advances in Recommender Systems and Intelligent Agents)

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10 pages, 274 KiB

Open AccessArticle

Redundant Trees in Bipartite Graphs

by Yanmei Hong, Yihong Wu and Qinghai Liu

Mathematics 2025, 13(6), 1005; https://doi.org/10.3390/math13061005 - 19 Mar 2025

Viewed by 173

Abstract

It has been conjectured that for each positive integer k and each tree T with bipartite

(Z_{1}, Z_{2})

, every k-connected bipartite graph G with [...] Read more.

It has been conjectured that for each positive integer k and each tree T with bipartite

(Z_{1}, Z_{2})

, every k-connected bipartite graph G with

δ (G) \geq k + max {| Z_{1} |, | Z_{2} |}

admits a subgraph

T^{'} ≅ T

such that

G - V (T^{'})

is still k-connected. In this paper, we generalize the ear decompositions of 2-connected graphs into a

(k, a_{k})

-extensible system for a general k-connected graph. As a result, we confirm the conjecture for

k \leq 3

by proving a slightly stronger version of it. Full article

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

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20 pages, 6070 KiB

Open AccessFeature PaperArticle

Distributed Collaborative Learning with Representative Knowledge Sharing

by Joseph Casey, Qianjiao Chen, Mengchen Fan, Baocheng Geng, Roman Shterenberg, Zhong Chen and Keren Li

Mathematics 2025, 13(6), 1004; https://doi.org/10.3390/math13061004 - 19 Mar 2025

Viewed by 199

Abstract

Distributed Collaborative Learning (DCL) addresses critical challenges in privacy-aware machine learning by enabling indirect knowledge transfer across nodes with heterogeneous feature distributions. Unlike conventional federated learning approaches, DCL assumes non-IID data and prediction task distributions that span beyond local training data, requiring selective [...] Read more.

Distributed Collaborative Learning (DCL) addresses critical challenges in privacy-aware machine learning by enabling indirect knowledge transfer across nodes with heterogeneous feature distributions. Unlike conventional federated learning approaches, DCL assumes non-IID data and prediction task distributions that span beyond local training data, requiring selective collaboration to achieve generalization. In this work, we propose a novel collaborative transfer learning (CTL) framework that utilizes representative datasets and adaptive distillation weights to facilitate efficient and privacy-preserving collaboration. By leveraging Energy Coefficients to quantify node similarity, CTL dynamically selects optimal collaborators and refines local models through knowledge distillation on shared representative datasets. Simulations demonstrate the efficacy of CTL in improving prediction accuracy across diverse tasks while balancing trade-offs between local and global performance. Furthermore, we explore the impact of data spread and dispersion on collaboration, highlighting the importance of tailored node alignment. This framework provides a scalable foundation for cross-domain generalization in distributed machine learning. Full article

(This article belongs to the Special Issue Advances in Mathematical Methods for Distributed Learning and High-Dimensional Data Analysis)

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32 pages, 920 KiB

Open AccessArticle

Scalar Field Static Spherically Symmetric Solutions in Teleparallel F(T) Gravity

by Alexandre Landry

Mathematics 2025, 13(6), 1003; https://doi.org/10.3390/math13061003 - 19 Mar 2025

Viewed by 290

Abstract

We investigate in this paper the static radial coordinate-dependent spherically symmetric spacetime in teleparallel

F (T)

gravity for a scalar field source. We begin by setting the static field equations (FEs) to be solved and solve the conservation laws for scalar [...] Read more.

We investigate in this paper the static radial coordinate-dependent spherically symmetric spacetime in teleparallel

F (T)

gravity for a scalar field source. We begin by setting the static field equations (FEs) to be solved and solve the conservation laws for scalar field potential solutions. We simplify the FEs and then find a general formula for computing the new teleparallel

F (T)

solutions applicable for any scalar field potential

V (T)

and coframe ansatz. We compute new non-trivial teleparallel

F (T)

solutions by using a power-law coframe ansatz for each scalar potential case arising from the conservation laws. We apply this formula to find new exact teleparallel

F (T)

solutions for several cases of coframe ansatz parameter. The new

F (T)

solution classes will be relevant for studying the models close to Born–Infeld and/or scalarized Black Hole (BH) solutions inside the dark energy (DE) described by a fundamental scalar field such as quintessence, phantom energy or quintom system, to name only those types. Full article

(This article belongs to the Special Issue Geometry and Symmetry in Mathematical Physics)

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24 pages, 3282 KiB

Open AccessArticle

Research on the Pricing Model of B2B Data Transactions and Its Nature for a Single Industrial Chain

by Weiqing Zhuang, Hanyu Yu and Morgan C. Wang

Mathematics 2025, 13(6), 1002; https://doi.org/10.3390/math13061002 - 19 Mar 2025

Viewed by 198

Abstract

With the advancement of global digital transformation, data trading has become a pivotal element in value circulation and innovation among enterprises. In particular, pricing strategies in the industrial chain’s data trading process critically influence the cooperation and market competitiveness of upstream and downstream [...] Read more.

With the advancement of global digital transformation, data trading has become a pivotal element in value circulation and innovation among enterprises. In particular, pricing strategies in the industrial chain’s data trading process critically influence the cooperation and market competitiveness of upstream and downstream enterprises. To address this issue, this study develops a Business-to-Business data transaction pricing model tailored to a single industry chain. The model incorporates factors such as data scarcity, encryption protection efforts, and market demand dynamics. By employing a Stackelberg dynamic model, the study systematically examines the pricing strategies of upstream and downstream enterprises under various incentive mechanisms and evaluates the impacts of encryption protection efforts and incentive mechanism coefficients on the profitability of the industry chain. The experimental results reveal that introducing incentive mechanisms for downstream enterprises modestly increases the profits of both upstream and downstream entities. Meanwhile, incentivizing upstream enterprises yields a multiplier effect, significantly boosting their profits while causing a slight decline in the profitability of downstream enterprises. Full article

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49 pages, 4018 KiB

Open AccessArticle

Structural Equation Modeling Approaches to Estimating Score Dependability Within Generalizability Theory-Based Univariate, Multivariate, and Bifactor Designs

by Walter P. Vispoel, Hyeryung Lee and Tingting Chen

Mathematics 2025, 13(6), 1001; https://doi.org/10.3390/math13061001 - 19 Mar 2025

Viewed by 167

Abstract

Generalizability theory (GT) provides an all-encompassing framework for estimating accuracy of scores and effects of multiple sources of measurement error when using measures intended for either norm- or criterion-referencing purposes. Structural equation models (SEMs) can replicate results from GT-based ANOVA procedures while extending [...] Read more.

Generalizability theory (GT) provides an all-encompassing framework for estimating accuracy of scores and effects of multiple sources of measurement error when using measures intended for either norm- or criterion-referencing purposes. Structural equation models (SEMs) can replicate results from GT-based ANOVA procedures while extending those analyses to account for scale coarseness, generate Monte Carlo-based confidence intervals for key parameters, partition universe score variance into general and group factor effects, and assess subscale score viability. We apply these techniques in R to univariate, multivariate, and bifactor designs using a novel indicator-mean approach to estimate absolute error. When representing responses to items from the shortened form of the Music Self-Perception Inventory (MUSPI-S) using 2-, 4-, and 8-point response metrics over two occasions, SEMs reproduced results from the ANOVA-based mGENOVA package for univariate and multivariate designs with score accuracy and subscale viability indices within bifactor designs comparable to those from corresponding multivariate designs. Adjusting for scale coarseness improved the accuracy of scores across all response metrics, with dichotomous observed scores least approximating truly continuous scales. Although general-factor effects were dominant, subscale viability was supported in all cases, with transient measurement error leading to the greatest reductions in score accuracy. Key implications are discussed. Full article

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

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25 pages, 2086 KiB

Open AccessArticle

Evaluation Model for Indoor Comprehensive Environmental Comfort Based on the Utility Function Method

by Xiaona Fan and Yiyun Zhu

Mathematics 2025, 13(6), 1000; https://doi.org/10.3390/math13061000 - 19 Mar 2025

Viewed by 138

Abstract

Indoor environmental comfort is closely related to human health and well-being. This study aimed to establish a quantitative evaluation model for indoor comprehensive environmental comfort based on multiple physical environmental parameters. Firstly, based on the subjective evaluation characteristics of indoor environmental comfort and [...] Read more.

Indoor environmental comfort is closely related to human health and well-being. This study aimed to establish a quantitative evaluation model for indoor comprehensive environmental comfort based on multiple physical environmental parameters. Firstly, based on the subjective evaluation characteristics of indoor environmental comfort and the principles of a multi-factor comprehensive evaluation, a comprehensive environmental comfort evaluation method utilizing the utility function approach was proposed. Secondly, subjective questionnaires and objective measurements were conducted in the indoor physical environment of rural dwellings in the Guanzhong Plain. The Kano model was employed to quantitatively analyze the influence of individual environmental comfort factors on the comprehensive environmental comfort based on the survey results. The findings revealed that thermal, lighting, and acoustic environments were the key influencing factors, while air quality was considered a non-key factor. Furthermore, quantitative relationships between environmental comfort and individual parameters were established, and the weights of individual environmental factors were determined using the analytic hierarchy process and the entropy weight method, based on the perspective of categorizing functional rooms and usage time periods. Finally, a quantitative evaluation model for indoor comprehensive environmental comfort was proposed that considered the one-vote veto characteristics and differentiated demands. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)

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25 pages, 1451 KiB

Open AccessFeature PaperArticle

A Graph Neural Network-Based Context-Aware Framework for Sentiment Analysis Classification in Chinese Microblogs

by Zhesheng Jin and Yunhua Zhang

Mathematics 2025, 13(6), 997; https://doi.org/10.3390/math13060997 - 18 Mar 2025

Viewed by 341

Abstract

Sentiment analysis in Chinese microblogs is challenged by complex syntactic structures and fine-grained sentiment shifts. To address these challenges, a Contextually Enriched Graph Neural Network (CE-GNN) is proposed, integrating self-supervised learning, context-aware sentiment embeddings, and Graph Neural Networks (GNNs) to enhance sentiment classification. [...] Read more.

Sentiment analysis in Chinese microblogs is challenged by complex syntactic structures and fine-grained sentiment shifts. To address these challenges, a Contextually Enriched Graph Neural Network (CE-GNN) is proposed, integrating self-supervised learning, context-aware sentiment embeddings, and Graph Neural Networks (GNNs) to enhance sentiment classification. First, CE-GNN is pre-trained on a large corpus of unlabeled text through self-supervised learning, where Masked Language Modeling (MLM) and Next Sentence Prediction (NSP) are leveraged to obtain contextualized embeddings. These embeddings are then refined through a context-aware sentiment embedding layer, which is dynamically adjusted based on the surrounding text to improve sentiment sensitivity. Next, syntactic dependencies are captured by Graph Neural Networks (GNNs), where words are represented as nodes and syntactic relationships are denoted as edges. Through this graph-based structure, complex sentence structures, particularly in Chinese, can be interpreted more effectively. Finally, the model is fine-tuned on a labeled dataset, achieving state-of-the-art performance in sentiment classification. Experimental results demonstrate that CE-GNN achieves superior accuracy, with a Macro F-measure of 80.21% and a Micro F-measure of 82.93%. Ablation studies further confirm that each module contributes significantly to the overall performance. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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29 pages, 391 KiB

Open AccessReview

Mathematical Methods in Feature Selection: A Review

by Firuz Kamalov, Hana Sulieman, Ayman Alzaatreh, Maher Emarly, Hasna Chamlal and Murodbek Safaraliev

Mathematics 2025, 13(6), 996; https://doi.org/10.3390/math13060996 - 18 Mar 2025

Viewed by 419

Abstract

Feature selection is essential in machine learning and data science. Recently, there has been a growing effort to apply various mathematical methods to construct novel feature selection algorithms. In this study, we present a comprehensive state-of-the-art review of such techniques. We propose a [...] Read more.

Feature selection is essential in machine learning and data science. Recently, there has been a growing effort to apply various mathematical methods to construct novel feature selection algorithms. In this study, we present a comprehensive state-of-the-art review of such techniques. We propose a new mathematical framework-based taxonomy to group the existing literature and provide an analysis of the research in each category from a mathematical perspective. The key frameworks discussed include variance-based methods, regularization methods, and Bayesian methods. By analyzing the strengths and limitations of each technique, we provide insights into their applicability across various domains. The review concludes with emerging trends and future research directions for mathematical methods in feature selection. Full article

(This article belongs to the Special Issue Mathematical Methods in Machine Learning and Data Science)

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34 pages, 414 KiB

Open AccessArticle

Existence Results and Gap Functions for Nonsmooth Weak Vector Variational-Hemivariational Inequality Problems on Hadamard Manifolds

by Balendu Bhooshan Upadhyay, Shivani Sain, Priyanka Mishra and Ioan Stancu-Minasian

Mathematics 2025, 13(6), 995; https://doi.org/10.3390/math13060995 - 18 Mar 2025

Viewed by 197

Abstract

In this paper, we consider a class of nonsmooth weak vector variational-hemivariational inequality problems (abbreviated as, WVVHVIP) in the framework of Hadamard manifolds. By employing an analogous to the KKM lemma, we establish the existence of the solutions for WVVHVIP without utilizing any [...] Read more.

In this paper, we consider a class of nonsmooth weak vector variational-hemivariational inequality problems (abbreviated as, WVVHVIP) in the framework of Hadamard manifolds. By employing an analogous to the KKM lemma, we establish the existence of the solutions for WVVHVIP without utilizing any monotonicity assumptions. Moreover, a uniqueness result for the solutions of WVVHVIP is established by using generalized geodesic strong monotonicity assumptions. We formulate Auslender, regularized, and Moreau-Yosida regularized type gap functions for WVVHVIP to establish necessary and sufficient conditions for the existence of the solutions to WVVHVIP. In addition to this, by employing the Auslender, regularized, and Moreau-Yosida regularized type gap functions, we derive the global error bounds for the solution of WVVHVIP under the generalized geodesic strong monotonicity assumptions. Several non-trivial examples are furnished in the Hadamard manifold setting to illustrate the significance of the established results. To the best of our knowledge, this is the first time that the existence results, gap functions, and global error bounds for WVVHVIP have been investigated in the framework of Hadamard manifolds via Clarke subdifferentials. Full article

14 pages, 495 KiB

Open AccessArticle

A Fast Projected Gradient Algorithm for Quaternion Hermitian Eigenvalue Problems

by Shan-Qi Duan and Qing-Wen Wang

Mathematics 2025, 13(6), 994; https://doi.org/10.3390/math13060994 - 18 Mar 2025

Viewed by 225

Abstract

In this paper, based on the novel generalized Hamilton-real (GHR) calculus, we propose for the first time a quaternion Nesterov accelerated projected gradient algorithm for computing the dominant eigenvalue and eigenvector of quaternion Hermitian matrices. By introducing momentum terms and look-ahead updates, the [...] Read more.

In this paper, based on the novel generalized Hamilton-real (GHR) calculus, we propose for the first time a quaternion Nesterov accelerated projected gradient algorithm for computing the dominant eigenvalue and eigenvector of quaternion Hermitian matrices. By introducing momentum terms and look-ahead updates, the algorithm achieves a faster convergence rate. We theoretically prove the convergence of the quaternion Nesterov accelerated projected gradient algorithm. Numerical experiments show that the proposed method outperforms the quaternion projected gradient ascent method and the traditional algebraic methods in terms of computational accuracy and runtime efficiency. Full article

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20 pages, 993 KiB

Open AccessArticle

Calculus of Long Rectangular Plates Embedded in Long Borders with Uniform Vertical Load on a Line Parallel to the Long Borders

by Daniel Opruţa, Mihai-Sorin Tripa, Luminiţa Codrea, Cristian Boldor, Dan Dumea, Robert Gyorbiro, Cosmin Brisc, Iulia Bărăian, Petre Opriţoiu, Aurel Chereches and Mihaela Suciu

Mathematics 2025, 13(6), 993; https://doi.org/10.3390/math13060993 - 18 Mar 2025

Viewed by 172

Abstract

This article presents the Transfer Matrix Method as a mathematical approach for the calculus of different structures that can be discretized into elements using an iterative calculus for future applications in the vehicle industry. Plate calculus is important in construction, medicine, orthodontics, and [...] Read more.

This article presents the Transfer Matrix Method as a mathematical approach for the calculus of different structures that can be discretized into elements using an iterative calculus for future applications in the vehicle industry. Plate calculus is important in construction, medicine, orthodontics, and many other fields. This work is original due to the mathematical apparatus used in the calculus of long rectangular plates embedded in both long borders and required by a uniformly distributed force on a line parallel to the long borders. The plate is discretized along its length in unitary beams, which have the width of the rectangular plate. The unitary beam can also be discretized into parts. As applications, the long rectangular plates embedded on the two long borders and charged with a vertical uniform load that acts on a line parallel to the long borders are studied. A state vector is associated with each side. For each of the four cases studied, a matrix relationship was written for each side, based on a transfer matrix, the state vector corresponding to the origin side, and the vector due to the action of external forces acting on the considered side. After, it is possible to calculate all the state vectors for all sides of the unity beam. Now, the efforts, deformations, and stress can be calculated in any section of the beam, respectively, for the long rectangular plate. This calculus will serve as a calculus of resistance for different pieces of the components of vehicles. Full article

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

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15 pages, 2016 KiB

Open AccessArticle

Distributionally Robust Energy Optimization with Renewable Resource Uncertainty

by Zhangyi Wang, Rui Cao, Dan Tang, Chunsheng Wang, Xiaoyu Liu and Weiguang Hu

Mathematics 2025, 13(6), 992; https://doi.org/10.3390/math13060992 - 18 Mar 2025

Viewed by 295

Abstract

With the increasing prevalence of intermittent power generation, the volatility, intermittency, and randomness of renewable energy pose significant challenges to the planning and operation of distribution networks. In this study, a data-driven distributionally robust optimization model is introduced. This model takes into account [...] Read more.

With the increasing prevalence of intermittent power generation, the volatility, intermittency, and randomness of renewable energy pose significant challenges to the planning and operation of distribution networks. In this study, a data-driven distributionally robust optimization model is introduced. This model takes into account the forecasting errors of wind power generation, as well as the operational constraints and coordinated control of energy storage, demand-side loads, and conventional generating units. The model can obtain the scheduling scheme with the lowest cost in scenarios with uncertain wind power. Unlike traditional stochastic methods, this model uses the Wasserstein metric to construct the uncertainty set from wind power big data without the need to pre-determine the probability distribution or distribution interval of errors. This is achieved through a Wasserstein ball centered on empirical distribution. As the amount of historical data grows, the model adjusts the radius of the Wasserstein ball, thus reducing the conservatism of the results. Compared with traditional robust optimization methods, this system can achieve lower operating costs. Compared with traditional stochastic programming methods, this system has higher reliability. Finally, the superiority of the proposed model over traditional models is verified through simulation analysis. Full article

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

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22 pages, 11281 KiB

Open AccessArticle

Splitting and Merging for Active Contours: Plug-and-Play

by Mojtaba Lashgari, Abhirup Banerjee and Hossein Rabbani

Mathematics 2025, 13(6), 991; https://doi.org/10.3390/math13060991 - 18 Mar 2025

Viewed by 180

Abstract

This study tackles the challenge of splitting and merging in parametric active contours or snakes. The proposed method comprises three stages: (1) fully 4-connected interpolation, (2) snake splitting, and (3) snakes merging. For this purpose, first, the coordinates of snake points are separated [...] Read more.

This study tackles the challenge of splitting and merging in parametric active contours or snakes. The proposed method comprises three stages: (1) fully 4-connected interpolation, (2) snake splitting, and (3) snakes merging. For this purpose, first, the coordinates of snake points are separated into two corrupted 1D signals, with missing X/Y samples in the signals representing missing snakes’ coordinates. These missing X/Y samples are estimated using a constrained Tikhonov regularisation model, ensuring fully 4-connected snakes. Next, crossing points are identified by plotting snake points onto a raster matrix, detecting overlaps where multiple snake points occupy the same raster cell. Finally, snakes are split or merged by extracting snake points between crossing snake points that form a loop using a heuristic approach. Experimental results on the boundary detection of enamel in Micro-CT images and coronary arteries’ lumen in CT images demonstrate the proposed method’s ability to handle contour splitting and merging effectively. Full article

(This article belongs to the Special Issue Bioinformatics, Computational Theory and Intelligent Algorithms)

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Mathematics, Volume 13, Issue 6 (March-2 2025) – 128 articles

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