Symmetry

24 pages, 17380 KiB

Open AccessArticle

Solvatochromic Analysis of Triton X-100 in Binary Mixtures

by Ecaterina Ambrosi, Alexandru Zara, Dana Ortansa Dorohoi and Dan-Gheorghe Dimitriu

Symmetry 2025, 17(2), 199; https://doi.org/10.3390/sym17020199 (registering DOI) - 27 Jan 2025

Abstract

Binary solvent mixtures of the non-ionic surfactant Triton X-100 with water, methanol, ethanol, and 1-propanol, respectively, were investigated by solvatochromic studies. The absorption spectral bands of methyl red dye, used as a solvatochromic probe, were recorded in ternary solutions prepared with different mole [...] Read more.

Binary solvent mixtures of the non-ionic surfactant Triton X-100 with water, methanol, ethanol, and 1-propanol, respectively, were investigated by solvatochromic studies. The absorption spectral bands of methyl red dye, used as a solvatochromic probe, were recorded in ternary solutions prepared with different mole ratios between Triton X-100 and water/alcohols. The Kamlet–Abboud–Taft model was applied to estimate the contribution of each type of intermolecular interaction to the total shift of the electronic absorption band of the solute. The composition of the solute molecule’s first solvation shell was comparatively estimated by using three models: the statistical cell model of ternary solutions, the Suppan model, and the Bosch–Rosés model. The statistical cell model allows the estimation of the difference between the interaction energies in the solute–solvent pairs of molecules. The Bosch–Rosés model provided important information on the 1:1 complex formed between Triton X-100 and water/alcohol molecules, as well as on the symmetry/asymmetry related to the binary mixtures in the cybotactic region of the solute’s molecule. Full article

(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)

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20 pages, 317 KiB

Open AccessArticle

Exploring Fixed-Point Results Using Random Sehgal Contraction in Symmetric Random Cone Metric Spaces with Applications

by Mohsin Nasir, Fahim Ud Din, Umar Ishtiaq, Ljubiša D. R. Kočinac and Ioan-Lucian Popa

Symmetry 2025, 17(2), 198; https://doi.org/10.3390/sym17020198 (registering DOI) - 27 Jan 2025

Abstract

This paper introduces a new concept of random Sehgal contraction in the setting of random cone metric spaces. We explore the modern advancements of traditional fixed-point theorems in a random setting, elaborating on the Sehgal–Guseman fixed-point theorem within the realm of random cone [...] Read more.

This paper introduces a new concept of random Sehgal contraction in the setting of random cone metric spaces. We explore the modern advancements of traditional fixed-point theorems in a random setting, elaborating on the Sehgal–Guseman fixed-point theorem within the realm of random cone metric spaces. A significant aspect of our research is the interplay between symmetry and randomness; while symmetry provides a framework for understanding structural properties, randomness introduces complexity, which can lead to unexpected behaviors. Our research provides a deeper understanding of the classical results and incorporates a detailed example to illustrate our findings. In addition, major random fixed-point results are also established, which could be applied to nonlinear random fractional differential equations (FDEs) and integral equations as well as to random boundary value problems (BVPs) related to homogeneous random transverse bars. Full article

(This article belongs to the Section Mathematics)

15 pages, 4125 KiB

Open AccessArticle

A Novel Slot Spiral Symmetric Array Antenna with a Wide Axial Ratio Beamwidth for Microwave-Induced Thermoacoustic Tomography Applications

by An Yan, Yao Zhang, Chengxiang Gao, Jinghua Ye and Zengpei Zhong

Symmetry 2025, 17(2), 197; https://doi.org/10.3390/sym17020197 (registering DOI) - 27 Jan 2025

Viewed by 147

Abstract

Conventional circularly polarized antennas have been employed to deliver microwave illumination in microwave-induced thermoacoustic tomography (TAT). However, these antennas exhibit several limitations in TAT systems, including low efficiency, poor axial ratio (AR) roundness, and narrow axial ratio beamwidth (ARBW). These issues lead to [...] Read more.

Conventional circularly polarized antennas have been employed to deliver microwave illumination in microwave-induced thermoacoustic tomography (TAT). However, these antennas exhibit several limitations in TAT systems, including low efficiency, poor axial ratio (AR) roundness, and narrow axial ratio beamwidth (ARBW). These issues lead to uniform radiation only within a relatively confined area, thereby restricting their effectiveness in clinical applications such as breast imaging. To address these issues, we propose a novel planar slot array antenna that offers a wide ARBW and improved axial ratio (AR) roundness, enabling homogeneous illumination over a larger field. We validated this approach both theoretically and experimentally. Tissue-mimicking phantoms were imaged, demonstrating that the antenna generated a circularly polarized electric field as well as a uniformly illuminated area. These advantages make the antenna proposed in this paper more suitable for clinical imaging compared to traditional microwave radiating antennas. Full article

(This article belongs to the Special Issue Symmetry Study in Electromagnetism: Topics and Advances)

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24 pages, 21297 KiB

Open AccessArticle

Analysis of Mechanical Behavior of Symmetric Prefabricated Bodies and Metal Connecting Components During Hoisting and Overturning in Assembly Structures

by Kedong Wang, Min Ma, Jiabo Wang, Ran Yang, Liyu Hu and Zhaoxing Luo

Symmetry 2025, 17(2), 196; https://doi.org/10.3390/sym17020196 (registering DOI) - 27 Jan 2025

Viewed by 185

Abstract

Prefabricated assembly structures play a pivotal role in modern building construction and underground transit developments, offering benefits such as ease of installation, rapid construction, and environmental sustainability. These prefabricated assembly structures are always symmetric and particularly prevalent in projects like subway station construction, [...] Read more.

Prefabricated assembly structures play a pivotal role in modern building construction and underground transit developments, offering benefits such as ease of installation, rapid construction, and environmental sustainability. These prefabricated assembly structures are always symmetric and particularly prevalent in projects like subway station construction, where symmetry prefabricated blocks are commonly used. The hoisting and overturning of these blocks are crucial stages in the construction sequence. Given the substantial weight (tens of tons) and size (several meters) of these prefabricated elements, the materials and structural integrity of the metal components, including bolts and steel rods, must meet strict standards during these phases. To ensure stability during overturning and safety throughout hoisting, this paper utilizes a finite element model to analyze the hoisting and overturning of three prefabricated blocks used in subway station assembly. This paper investigates the mechanical behavior of embedded components, such as lifting lugs, steel liners, and hoisting steel rods, during these processes, analyzing their stress and strain. The selection methods of different steel bars (diameter, hollow, solid, etc.) in the hoisting process were obtained, and the operation speed in the hoisting and overturning process was determined, which guided the selection of the hoisting position when the common overturning action was known. The results offer valuable guidelines for the placement and spacing of lifting lugs, as well as the optimal hoisting speed, thereby informing the selection of embedded lifting lugs and the design of operational protocols in actual assembly construction. Full article

(This article belongs to the Section Engineering and Materials)

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19 pages, 4243 KiB

Open AccessArticle

Dual Function Radar and Communication Signal Design with Combined Waveform Selection and Pulse Repetition Interval Agility

by Yu Liu, Xiheng Li, Xing Zou and Zhihang Yang

Symmetry 2025, 17(2), 195; https://doi.org/10.3390/sym17020195 (registering DOI) - 27 Jan 2025

Viewed by 205

Abstract

The traditional probe–pass integration system embeds communication information into a radar waveform, which leads to a high level of waveform autocorrelation sidelobes and a poor false symbol rate at low signal-to-noise ratios. This article proposes a three-dimensional indexed modulation-based design method for probe–pass [...] Read more.

The traditional probe–pass integration system embeds communication information into a radar waveform, which leads to a high level of waveform autocorrelation sidelobes and a poor false symbol rate at low signal-to-noise ratios. This article proposes a three-dimensional indexed modulation-based design method for probe–pass integration waveforms. This method realises communication information modulation and demodulation by simultaneously indexing orthogonal waveform selection, transmitting pulse PRI changes and carrier frequency changes in three dimensions, and applying compressed perception technology to solve the problems of PRI shortcuts and carrier frequency, resulting in a velocity term in the received waveform that cannot be accumulated by phase reference to realise velocity super-resolution. Finally, the radar detection performance and communication performance are simulated and analysed, and the simulation results reveal that the method proposed in this paper can not only satisfy the radar detection performance requirements but also achieve a lower unsigned rate on the basis of an improved communication rate. Full article

(This article belongs to the Section Computer)

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26 pages, 483 KiB

Open AccessReview

Quality of Experience-Oriented Cloud-Edge Dynamic Adaptive Streaming: Recent Advances, Challenges, and Opportunities

by Wei Wang, Xuekai Wei , Wei Tao, Mingliang Zhou and Cheng Ji

Symmetry 2025, 17(2), 194; https://doi.org/10.3390/sym17020194 (registering DOI) - 26 Jan 2025

Viewed by 257

Abstract

The widespread adoption of dynamic adaptive streaming (DAS) has revolutionized the delivery of high-quality internet multimedia content by enabling dynamic streaming quality adjustments based on network conditions and playback capabilities. While numerous reviews have explored DAS technologies, this study differentiates itself by focusing [...] Read more.

The widespread adoption of dynamic adaptive streaming (DAS) has revolutionized the delivery of high-quality internet multimedia content by enabling dynamic streaming quality adjustments based on network conditions and playback capabilities. While numerous reviews have explored DAS technologies, this study differentiates itself by focusing on Quality of Experience (QoE)-oriented optimization in cloud-edge collaborative environments. Traditional DAS optimization often overlooks the asymmetry between cloud and edge nodes, where edge resources are typically constrained. This review emphasizes the importance of dynamic task and traffic allocation between cloud and edge nodes to optimize resource utilization and maintain system efficiency, ultimately improving QoE for end users. This comprehensive analysis explores recent advances in QoE-driven DAS optimization strategies, including streaming models, implementation mechanisms, and the integration of machine learning (ML) techniques. By contrasting ML-based DAS approaches with traditional methods, this study highlights the added value of intelligent algorithms in addressing modern streaming challenges. Furthermore, the review identifies emerging research directions, such as adaptive resource allocation and hybrid cloud-edge solutions, and underscores potential application areas for DAS in evolving multimedia systems. With the aim of serving as a valuable resource for researchers, practitioners, and decision-makers in addressing the challenges of resource-constrained edge environments and the need for QoE-centric solutions, this comprehensive analysis endeavors to promote the development, implementation, and application of DAS optimization. Acknowledging the crucial role of DAS optimization in improving the overall QoE for the end users, we hope to facilitate the continued advancement of video streaming experiences in the cloud-edge collaborated environment. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Embedded Systems)

19 pages, 4393 KiB

Open AccessArticle

Simulation Study on the Navigation Resistance and Shape Optimization of a New Type of Amphibious Vehicle

by Jiawen Fan, Ying Chang, Hui Zhu, Beibei Wan, Jian Ye, Shanhu Zhang and Changwei Jin

Symmetry 2025, 17(2), 193; https://doi.org/10.3390/sym17020193 (registering DOI) - 26 Jan 2025

Viewed by 231

Abstract

Amphibious vehicles are important equipment used by emergency rescue teams to quickly pass through water networks. A numerical model of amphibious vehicle underwater navigation in the lower shell was established in this study using computational fluid dynamics, the Reynolds-averaged Navier–Stokes model, and the [...] Read more.

Amphibious vehicles are important equipment used by emergency rescue teams to quickly pass through water networks. A numerical model of amphibious vehicle underwater navigation in the lower shell was established in this study using computational fluid dynamics, the Reynolds-averaged Navier–Stokes model, and the volume-of-fluid method to investigate the navigation performance of a new all-terrain all-water amphibious emergency rescue vehicle. The navigation resistance was calculated at different speeds. The characteristics of the flow field around the vehicle body were analyzed, and optimization measures for drag reduction by installing a stern flap were proposed. The simulation results show that the existing vehicle body has a relatively high navigation resistance, and the flow field of the amphibious vehicle body is significantly improved after using stern flaps with larger angles and sizes. When the stern flap angle was 38°, the drag-reduction effect was 23%, which effectively improved the navigation performance of the amphibious vehicle. Full article

(This article belongs to the Section Engineering and Materials)

14 pages, 281 KiB

Open AccessArticle

Exploring a Novel Approach to Deferred Nörlund Statistical Convergence

by Ibrahim Sulaiman Ibrahim, Ji-Huan He, Nejmeddine Chorfi, Majeed Ahmad Yousif, Pshtiwan Othman Mohammed and Miguel Vivas-Cortez

Symmetry 2025, 17(2), 192; https://doi.org/10.3390/sym17020192 (registering DOI) - 26 Jan 2025

Viewed by 158

Abstract

This study introduces novel concepts of convergence and summability for numerical sequences, grounded in the newly formulated deferred Nörlund density, and explores their intrinsic connections to symmetry in mathematical structures. By leveraging symmetry principles inherent in sequence behavior and employing two distinct modulus [...] Read more.

This study introduces novel concepts of convergence and summability for numerical sequences, grounded in the newly formulated deferred Nörlund density, and explores their intrinsic connections to symmetry in mathematical structures. By leveraging symmetry principles inherent in sequence behavior and employing two distinct modulus functions under varying conditions, profound links between sequence convergence and summability are established. The study further incorporates lacunary refinements, enhancing the understanding of Nörlund statistical convergence and its symmetric properties. Key theorems, properties, and illustrative examples validate the proposed concepts, providing fresh insights into the role of symmetry in shaping broader convergence theories and advancing the understanding of sequence behavior across diverse mathematical frameworks. Full article

(This article belongs to the Section Mathematics)

18 pages, 6203 KiB

Open AccessArticle

Adaptive Terrain Modeling for Side-Slope Surfaces

by Fangxiao Zhou

Symmetry 2025, 17(2), 191; https://doi.org/10.3390/sym17020191 (registering DOI) - 26 Jan 2025

Viewed by 126

Abstract

Three-dimensional site modeling is an important aspect of Building Information Modeling (BIM), especially in mountainous areas. Accurate site modeling is essential for efficient construction planning and resource allocation. A key issue in site modeling is how to accurately calculate the shape of side-slopes. [...] Read more.

Three-dimensional site modeling is an important aspect of Building Information Modeling (BIM), especially in mountainous areas. Accurate site modeling is essential for efficient construction planning and resource allocation. A key issue in site modeling is how to accurately calculate the shape of side-slopes. It involves three sub-problems: geometric representation of side-slopes, determination of fill/cut types, and intersection of side-slopes surface with the terrain surface. To address this, a two-stage method for constructing side-slope models adaptive to terrain is proposed. In the first stage, a marching algorithm along polylines is used to calculate the intersection points of the site boundary polylines with the terrain surface. These intersection points are used to segment the boundary polylines. A rule-based approach is then applied to automatically determine the fill/cut type for each segment. Subsequently, the equations of the side-slopes passing through each segment are derived using geometric principles. In the second stage, a marching algorithm along the plane is used to trace the intersection lines of side-slopes with the terrain. Finally, the side-slopes are rendered with precision by integrating the equations of each segment with the determined intersection lines. The effectiveness of the method is verified through illustrative examples. Algorithm efficiency analysis and 3D modeling illustrations have demonstrated that this method not only boasts accuracy and swift computation but also excels in the level of automation achieved in the modeling process. Full article

(This article belongs to the Section Mathematics)

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17 pages, 875 KiB

Open AccessArticle

Public Opinion Evolution Based on the Two-Dimensional Theory of Emotion and Top2Vec-RoBERTa

by Shaowen Wang, Qingyang Liu, Yanrong Hu and Hongjiu Liu

Symmetry 2025, 17(2), 190; https://doi.org/10.3390/sym17020190 (registering DOI) - 26 Jan 2025

Viewed by 231

Abstract

This paper applies the concept of symmetry to the design of a research methodology for public opinion evolution, emphasizing that both the construction and analysis processes of the method embody symmetrical principles. In today’s information age, dominated by social media, online platforms have [...] Read more.

This paper applies the concept of symmetry to the design of a research methodology for public opinion evolution, emphasizing that both the construction and analysis processes of the method embody symmetrical principles. In today’s information age, dominated by social media, online platforms have become crucial venues for information dissemination. While the free flow of information promotes public participation, it also introduces certain challenges. Therefore, analyzing the evolution of public opinion and extracting public sentiment holds significant practical value for managing online public sentiment. This study takes the Zibo barbecue incident as a case study, utilizing the two-dimensional theory of emotion and Top2Vec for thematic analysis of public opinion comments. By combining sentiment dictionary methods with the RoBERTa model, we conduct a sentiment polarity analysis of public opinion comments. The results show that the RoBERTa model achieved an accuracy of 98.46% on the test set. The proposed method effectively uncovers public sentiment biases and the influencing factors on public emotions during the evolution of public opinion events, providing a more comprehensive understanding of the emotional dynamics throughout the development of public sentiment. This deeper insight aids in addressing issues related to public opinion more effectively. Full article

(This article belongs to the Special Issue Machine Learning and Data Analysis II)

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18 pages, 1212 KiB

Open AccessArticle

Calculation of Stray-Field Loss of TEAM P21 Model Under Complex Excitations Based on the Improved Energetic Hysteresis Model

by Zhigang Zhao and Dehai Li

Symmetry 2025, 17(2), 189; https://doi.org/10.3390/sym17020189 (registering DOI) - 25 Jan 2025

Viewed by 251

Abstract

An efficient numerical calculation method of stray-field loss is investigated for typical magnetic load components (grain-oriented silicon steel sheets (GO), magnetic steel plate, and combined components of both materials) under non-sinusoidal excitations (NSE) containing symmetrical harmonic and DC to avoid the local overheating [...] Read more.

An efficient numerical calculation method of stray-field loss is investigated for typical magnetic load components (grain-oriented silicon steel sheets (GO), magnetic steel plate, and combined components of both materials) under non-sinusoidal excitations (NSE) containing symmetrical harmonic and DC to avoid the local overheating caused by high stray-field loss density. The paper investigates the stray-field loss with different types of load components and working conditions based on the leakage flux complementary-based measurement method, derives an analytical formulation calculating the energetic hysteresis model parameters under different magnetic flux densities to reduce the dependence on measurement data, establishes a loss calculation method considering the influence of non-sinusoidal magnetization on magnetic loss, and discusses the advantages and limitations of existing numerical approaches of additional loss to establish an effective computational strategy of stray-field loss. Finally, the effectiveness of the proposed method is verified by simulations and experiments. Full article

(This article belongs to the Section Engineering and Materials)

14 pages, 3922 KiB

Open AccessArticle

Experimental Study on the Symmetry of the Soil-Arching Effect of a Pile Foundation in a Reinforced High-Fill Area

by Liangdong Zuo, Quanbao Wang and Jia Liu

Symmetry 2025, 17(2), 188; https://doi.org/10.3390/sym17020188 (registering DOI) - 25 Jan 2025

Viewed by 256

Abstract

In addition to the vertical external load and soil settlement load, the pile foundation in reinforced high-fill areas is also affected by the horizontal load caused by the rear stacking load, and pile stress is affected by the soil-arching effect in reinforced areas [...] Read more.

In addition to the vertical external load and soil settlement load, the pile foundation in reinforced high-fill areas is also affected by the horizontal load caused by the rear stacking load, and pile stress is affected by the soil-arching effect in reinforced areas that have typical passive pile characteristics. In order to study the symmetry of the soil-arching effect of pile foundations in a reinforced-fill area, indoor model tests were designed and the relevant data for the pile foundation and reinforced soil under surcharge were obtained. Through the analysis, the following conclusions were drawn: the peak bending moment of the pile body is basically consistent with the position of the potential sliding surface of reinforced soil; the maximum shear force of the pile body appears about 150 mm below the embedding point; with an increase in depth, the soil-arching effect becomes obvious. There are two different forms of friction, soil-arching and direct soil-arching between piles and behind piles, and the soil between single-row piles has a symmetrical distribution. In addition to the vertical external load and soil settlement load, the pile foundation in reinforced high-fill areas will also be affected by the horizontal load caused by the rear stacking load, and pile stress will be affected by the soil-arching effect in reinforced areas, which has typical passive pile characteristics. In order to study the symmetry of the soil-arching effect of pile foundations in a reinforced-fill area, indoor model tests were designed, and the relevant data for pile foundation and reinforced soil under surcharge were obtained. Through analysis, the following conclusions were drawn: (1) the peak bending moment of the pile body is basically consistent with the position of the potential sliding surface of reinforced soil; the maximum shear force of the pile body appears about 150 mm below the embedding point; with an increase in depth, the soil-arching effect becomes obvious. There are two different forms of friction, soil-arching and direct soil-arching between piles and behind piles, and the soil between single-row piles has a symmetrical distribution. Full article

(This article belongs to the Section Engineering and Materials)

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24 pages, 6359 KiB

Open AccessArticle

Bezier Curves and Surfaces with the Generalized α-Bernstein Operator

by Davut Canlı and Süleyman Şenyurt

Symmetry 2025, 17(2), 187; https://doi.org/10.3390/sym17020187 (registering DOI) - 25 Jan 2025

Viewed by 143

Abstract

In the field of Computer-Aided Geometric Design (CAGD), a proper model can be achieved depending on certain characteristics of the predefined blending basis functions. The presence of these characteristics ensures the geometric properties necessary for a decent design. The objective of this study, [...] Read more.

In the field of Computer-Aided Geometric Design (CAGD), a proper model can be achieved depending on certain characteristics of the predefined blending basis functions. The presence of these characteristics ensures the geometric properties necessary for a decent design. The objective of this study, therefore, is to examine the generalized

α

-Bernstein operator in the context of its potential classification as a novel blending type basis for the construction of Bézier-like curves and surfaces. First, a recursive definition of this basis is provided, along with its unique representation in terms of that for the classical Bernstein operator. Next, following these representations, the characteristics of the basis are discussed, and one shape parameter for

α

-Bezier curves is defined. In addition, by utilizing the recursive definition of the basis, a de Casteljau-like algorithm is provided such that a subdivision schema can be applied to the construction of the new

α

-Bezier curves. The parametric continuity constraints for

C^{0}

,

C^{1}

, and

C^{2}

are also established to join two

α

-Bezier curves. Finally, a set of cross-sectional engineering surfaces is designed to indicate that the generalized

α

-Bernstein operator, as a basis, is efficient and easy to implement for forming shape-adjustable designs. Full article

(This article belongs to the Section Mathematics)

21 pages, 1936 KiB

Open AccessArticle

Leveraging Quantum Machine Learning to Address Class Imbalance: A Novel Approach for Enhanced Predictive Accuracy

by Seongjun Kwon, Jihye Huh, Sang Ji Kwon, Sang-ho Choi and Ohbyung Kwon

Symmetry 2025, 17(2), 186; https://doi.org/10.3390/sym17020186 (registering DOI) - 25 Jan 2025

Viewed by 237

Abstract

The class imbalance problem presents a critical challenge in real-world applications, particularly in high-stakes domains such as healthcare, finance, disaster management, and fault diagnosis, where accurate anomaly detection is paramount. Class imbalance often disrupts the inherent symmetry of data distributions, resulting in suboptimal [...] Read more.

The class imbalance problem presents a critical challenge in real-world applications, particularly in high-stakes domains such as healthcare, finance, disaster management, and fault diagnosis, where accurate anomaly detection is paramount. Class imbalance often disrupts the inherent symmetry of data distributions, resulting in suboptimal performance of traditional machine learning models. Conventional approaches such as undersampling and oversampling are commonly employed to address this issue; however, these methods can introduce additional asymmetries, including information loss and overfitting, which ultimately compromise model efficacy. This study introduces an innovative approach leveraging quantum machine learning (QML), specifically the Variational Quantum Classifier (VQC), to restore and capitalize on the symmetrical properties of data distributions without relying on resampling techniques. By employing quantum circuits optimized to mitigate the asymmetries inherent in imbalanced datasets, the proposed method demonstrates consistently superior performance across diverse datasets, with notable improvements in Recall for minority classes. These findings underscore the potential of quantum machine learning as a robust alternative to classical methods, offering a symmetry-aware solution to class imbalance and advancing QML-driven technologies in fields where equitable representation and symmetry are of critical importance. Full article

(This article belongs to the Section Computer)

26 pages, 1911 KiB

Open AccessArticle

Machine Learning-Based Stacking Ensemble Model for Prediction of Heart Disease with Explainable AI and K-Fold Cross-Validation: A Symmetric Approach

by Sara Qamar Sultan, Nadeem Javaid, Nabil Alrajeh and Muhammad Aslam

Symmetry 2025, 17(2), 185; https://doi.org/10.3390/sym17020185 (registering DOI) - 25 Jan 2025

Viewed by 257

Abstract

One of the most complex and prevalent diseases is heart disease (HD). It is among the main causes of death around the globe. With changes in lifestyles and the environment, its prevalence is rising rapidly. The prediction of the disease in its early [...] Read more.

One of the most complex and prevalent diseases is heart disease (HD). It is among the main causes of death around the globe. With changes in lifestyles and the environment, its prevalence is rising rapidly. The prediction of the disease in its early stages is crucial, as delays in diagnosis can cause serious complications and even death. Machine learning (ML) can be effective in this regard. Many researchers have used different techniques for the efficient detection of the disease and to overcome the drawbacks of existing models. Several ensemble models have also been applied. We proposed a stacking ensemble model named NCDG, which uses Naive Bayes, Categorical Boosting, and Decision Tree as base learners, with Gradient Boosting serving as the meta-learner classifier. We performed preprocessing using a factorization method to convert string columns into integers. We employ the Synthetic Minority Oversampling TEchnique (SMOTE) and BorderLineSMOTE balancing techniques to address the issue of data class imbalance. Additionally, we implemented hard and soft voting using voting classifier and compared the results with the proposed stacking model. For the Artificial Intelligence-based eXplainability of our proposed NCDG model, we use the SHapley Additive exPlanations (SHAP) technique. The outcomes show that our suggested stacking model, NCDG, performs better than the benchmark existing techniques. The experimental results of our proposed stacking model achieved the highest accuracy, F1-Score, precision and recall of 0.91, 0.91, 0.91 and 0.91, respectively, and an execution time of 653 s. Moreover, we have also utilized K-Fold Cross-Validation method to validate our predicted results. It is worth mentioning that our prediction results and their validation strongly coincide with each other which proves our approach to be symmetric. Full article

(This article belongs to the Section Computer)

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15 pages, 289 KiB

Open AccessArticle

Solvability of Boundary Value Problems for Differential Equations Combining Ordinary and Fractional Derivatives of Non-Autonomous Variable Order

by Mohammed Said Souid, Amar Benkerrouche, Souad Guedim, Sandra Pinelas and Abdelkader Amara

Symmetry 2025, 17(2), 184; https://doi.org/10.3390/sym17020184 (registering DOI) - 25 Jan 2025

Viewed by 259

Abstract

This study introduces a novel approach for investigating the solvability of boundary value problems for differential equations that incorporate both ordinary and fractional derivatives, specifically within the context of non-autonomous variable order. Unlike traditional methods in the literature, which often rely on generalized [...] Read more.

This study introduces a novel approach for investigating the solvability of boundary value problems for differential equations that incorporate both ordinary and fractional derivatives, specifically within the context of non-autonomous variable order. Unlike traditional methods in the literature, which often rely on generalized intervals and piecewise constant functions, we propose a new fractional operator better suited for this problem. We analyze the existence and uniqueness of solutions, establishing the conditions necessary for these properties to hold using the Krasnoselskii fixed-point theorem and Banach’s contraction principle. Our study also addresses the Ulam–Hyers stability of the proposed problems, examining how variations in boundary conditions influence the solution dynamics. To support our theoretical framework, we provide numerical examples that not only validate our findings but also demonstrate the practical applicability of these mixed derivative equations across various scientific domains. Additionally, concepts such as symmetry may offer further insights into the behavior of solutions. This research contributes to a deeper understanding of complex differential equations and their implications in real-world scenarios. Full article

(This article belongs to the Section Mathematics)

17 pages, 440 KiB

Open AccessArticle

Frobenius Norm-Based Global Stability Analysis of Delayed Bidirectional Associative Memory Neural Networks

by N. Mohamed Thoiyab, Saravanan Shanmugam, Rajarathinam Vadivel and Nallappan Gunasekaran

Symmetry 2025, 17(2), 183; https://doi.org/10.3390/sym17020183 (registering DOI) - 24 Jan 2025

Viewed by 510

Abstract

The present research investigates the global asymptotic stability of bidirectional associative memory (BAM) neural networks using distinct sufficient conditions. The primary objective of this study is to establish new generalized criteria for the global asymptotic robust stability of time-delayed BAM neural networks at [...] Read more.

The present research investigates the global asymptotic stability of bidirectional associative memory (BAM) neural networks using distinct sufficient conditions. The primary objective of this study is to establish new generalized criteria for the global asymptotic robust stability of time-delayed BAM neural networks at the equilibrium point, utilizing the Frobenius norm and the positive symmetrical approach. The new sufficient conditions are derived with the help of the Lyapunov–Krasovskii functional and the Frobenius norm, which are important in deep learning for a variety of reasons. The derived conditions are not influenced by the system parameter delays of the BAM neural network. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed conclusions regarding network parameters. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Systems)

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24 pages, 4029 KiB

Open AccessArticle

Multi-Label Learning with Distribution Matching Ensemble: An Adaptive and Just-In-Time Weighted Ensemble Learning Algorithm for Classifying a Nonstationary Online Multi-Label Data Stream

by Chao Shen, Bingyu Liu, Changbin Shao, Xibei Yang, Sen Xu, Changming Zhu and Hualong Yu

Symmetry 2025, 17(2), 182; https://doi.org/10.3390/sym17020182 - 24 Jan 2025

Viewed by 363

Abstract

Learning from a nonstationary data stream is challenging, as a data stream is generally considered to be endless, and the learning model is required to be constantly amended for adapting the shifting data distributions. When it meets multi-label data, the challenge would be [...] Read more.

Learning from a nonstationary data stream is challenging, as a data stream is generally considered to be endless, and the learning model is required to be constantly amended for adapting the shifting data distributions. When it meets multi-label data, the challenge would be further intensified. In this study, an adaptive online weighted multi-label ensemble learning algorithm called MLDME (multi-label learning with distribution matching ensemble) is proposed. It simultaneously calculates both the feature matching level and label matching level between any one reserved data block and the new received data block, further providing an adaptive decision weight assignment for ensemble classifiers based on their distribution similarities. Specifically, MLDME abandons the most commonly used but not totally correct underlying hypothesis that in a data stream, each data block always has the most approximate distribution with that emerging after it; thus, MLDME could provide a just-in-time decision for the new received data block. In addition, to avoid an infinite extension of ensemble classifiers, we use a fixed-size buffer to store them and design three different dynamic classifier updating rules. Experimental results for nine synthetic and three real-world multi-label nonstationary data streams indicate that the proposed MLDME algorithm is superior to some popular and state-of-the-art online learning paradigms and algorithms, including two specifically designed ones for classifying a nonstationary multi-label data stream. Full article

(This article belongs to the Section Computer)

19 pages, 710 KiB

Open AccessArticle

Identifying Patients with Temporomandibular Joint Disorders Based on Patterns of Electromyographic Activity of the Masseter and Temporalis Muscles

by Aleksandra Radecka, Waldemar Pluta, Krzysztof Antczak, Michał Lubkowski and Anna Lubkowska

Symmetry 2025, 17(2), 181; https://doi.org/10.3390/sym17020181 - 24 Jan 2025

Viewed by 339

Abstract

Background: Temporomandibular disorder (TMD) is a collective term covering acute or chronic musculoskeletal and neuromuscular pain associated with the masticatory muscles, temporomandibular joint, and the associated structures. The surface electromyography (sEMG) test represents clinical potential as an additional diagnostic tool. The purpose of [...] Read more.

Background: Temporomandibular disorder (TMD) is a collective term covering acute or chronic musculoskeletal and neuromuscular pain associated with the masticatory muscles, temporomandibular joint, and the associated structures. The surface electromyography (sEMG) test represents clinical potential as an additional diagnostic tool. The purpose of this study was to evaluate differences in masseter and temporalis muscle activity (in sEMG) in subjects with TMD compared to a control group. Methods: The TMD group included 45 people qualified according to the diagnostic criteria for temporomandibular disorder (DC/TMD). In the control group, there were 30 subjects. All participants underwent detailed examinations including sEMG diagnosis of the masseter and temporalis muscles. The sEMG was measured both at rest and during maximal voluntary contraction (MVC). Amplitude root mean square (A_RMS) values for the analysis were determined. Results: No differences were shown in the value of the results between TMD and control group in RS A_RMS transformed data values (p = 0.086) and in the MVC A_RMStransformed data values (p = 0.536). The presence of TMD has no significant effect on the symmetry index value for the temporalis (p = 0.42) and masseter muscles (p = 0.379). Conclusions: Analysis of both raw and normalized sEMG signals is insufficient to differentiate TMD patients from healthy individuals. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Life Sciences: Feature Papers 2024)

25 pages, 372 KiB

Open AccessArticle

Existence and Uniqueness Results for Fuzzy Bipolar Metric Spaces

by Umar Ishtiaq, Fahad Jahangeer, Mubariz Garayev and Ioan-Lucian Popa

Symmetry 2025, 17(2), 180; https://doi.org/10.3390/sym17020180 - 24 Jan 2025

Viewed by 201

Abstract

In this paper, we present the concept of (Υ,Ω)-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring consistency and uniformity in measurement [...] Read more.

In this paper, we present the concept of (Υ,Ω)-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring consistency and uniformity in measurement regardless of the order in which the elements are considered. Furthermore, we prove several best proximity point results by utilizing (Υ,Ω)-fuzzy bipolar proximal contraction, (Υ,Ω)-Reich–Rus–Ciric type proximal contraction, (Υ,Ω)-Kannan type proximal contraction and (Υ,Ω)-Hardy–Rogers type contraction. Furthermore, we provide some non-trivial examples to show the comparison with the existing results in the literature. At the end, we present an application to find the existence and uniqueness of a solution of an integral equation by applying the main result. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry II)

13 pages, 536 KiB

Open AccessArticle

Symmetric Point Sets with Few Intersection Numbers in PG(r,q)

by Stefano Innamorati

Symmetry 2025, 17(2), 179; https://doi.org/10.3390/sym17020179 (registering DOI) - 24 Jan 2025

Viewed by 254

Abstract

In 1965, H. Retkin and E. Stein defined a symmetric point set as a set of points with the same intersection numbers. In this paper, we perform a detailed analysis of symmetric point sets of the finite projective space which shows that the [...] Read more.

In 1965, H. Retkin and E. Stein defined a symmetric point set as a set of points with the same intersection numbers. In this paper, we perform a detailed analysis of symmetric point sets of the finite projective space which shows that the class of symmetric sets is very broad including caps, two-character sets and transitive sets. We derive necessary conditions for the existence of such sets. Since the most studied sets are caps and two-character sets and not much seems to be known in the general case of sets, which are different from caps, with more than two intersection numbers, by using incidence-preserving group actions, symmetric point sets with few intersection numbers are provided. The results indicate that any finite projective space contains symmetric sets with few intersection numbers. Full article

(This article belongs to the Special Issue Symmetry in Combinatorics and Discrete Mathematics)

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67 pages, 1129 KiB

Open AccessSystematic Review

Systematic Literature Review of Optimization Algorithms for P||C_max Problem

by Dragutin Ostojić, Dušan Ramljak, Andrija Urošević, Marija Jolović, Radovan Drašković, Jainil Kakka, Tatjana Jakšić Krüger and Tatjana Davidović

Symmetry 2025, 17(2), 178; https://doi.org/10.3390/sym17020178 (registering DOI) - 24 Jan 2025

Viewed by 255

Abstract

In the era of open data and open science, it is important that, before announcing their new results, authors consider all previous studies and ensure that they have competitive material worth publishing. To save time, it is popular to replace the exhaustive search [...] Read more.

In the era of open data and open science, it is important that, before announcing their new results, authors consider all previous studies and ensure that they have competitive material worth publishing. To save time, it is popular to replace the exhaustive search of online databases with the utilization of generative Artificial Intelligence (AI). However, especially for problems in niche domains, generative AI results may not be precise enough and sometimes can even be misleading. A typical example is

P | | C_{m a x}

, an important scheduling problem studied mainly in a wider context of parallel machine scheduling. As there is an uncovered symmetry between

P | | C_{m a x}

and other similar optimization problems, it is not easy for generative AI tools to include all relevant results into search. Therefore, to provide the necessary background data to support researchers and generative AI learning, we critically discuss comparisons between algorithms for

P | | C_{m a x}

that have been presented in the literature. Thus, we summarize and categorize the “state-of-the-art” methods, benchmark test instances, and compare methodologies, all over a long time period. We aim to establish a framework for fair performance evaluation of algorithms for

P | | C_{m a x}

, and according to the presented systematic literature review, we uncovered that it does not exist. We believe that this framework could be of wider importance, as the identified principles apply to a plethora of combinatorial optimization problems. Full article

(This article belongs to the Section Computer)

24 pages, 1331 KiB

Open AccessArticle

Acid-Base Equilibria for Tautomeric Heterocycles in the Gas-Phase: A Case of Uracil

by Ewa Daniela Raczyńska

Symmetry 2025, 17(2), 177; https://doi.org/10.3390/sym17020177 - 24 Jan 2025

Viewed by 345

Abstract

Prototropic conversion (prototropy) for heterocyclic nucleobases was already signaled by Watson and Crick about seventy years ago as one of the reasons for nucleic acids mutations. This isomeric phenomenon has been investigated for neutral derivatives by means of both experimental and theoretical procedures, [...] Read more.

Prototropic conversion (prototropy) for heterocyclic nucleobases was already signaled by Watson and Crick about seventy years ago as one of the reasons for nucleic acids mutations. This isomeric phenomenon has been investigated for neutral derivatives by means of both experimental and theoretical procedures, and their favored tautomers discussed in numerous articles published in the last fifty years. Protonation/deprotonation reactions in the gas phase have also been studied using both quantum-chemical calculations and experimental techniques. Some thermochemical parameters of these processes have been documented. However, prototropy has not always been taken into account in protonation/deprotonation reactions. Most frequently, tautomeric heterocycles have been treated as simple polyfunctional compounds without possible intramolecular protontransfers. Taking into account the lack of data for the complete tautomeric mixtures, quantum-chemical investigations have been undertaken by us about twenty-five years ago for prototropic heterosystems. In this work, the pyrimidine base uracil (U) was chosen. It possesses two identical exo groups (=O/OH) at the 2- and 4-positions, two labile (tautomeric) protons, and five conjugated sites (N1, N3, C5, O7, and O8). Different types of isomerism, prototropy and OH-rotation, were considered for the neutral, protonated, and deprotonated forms. Using quantum-chemical methods, thermochemical stabilities of all possible tautomers-rotamers were examined in vacuo and the potential isomers selected. The selected isomeric mixtures for the neutral and ionic forms were applied for the determination of the thermochemical parameters in the four-step acid/base equilibria: B²⁻ BH⁻ BH₂ BH₃⁺ BH₄²⁺, where BH₂ indicates U. For each step, the microscopic (kinetic) and macroscopic (thermodynamic) acid/base parameters were estimated, and sites of the proton gain and proton loss examined. The similarities and differences between the acid/base equilibria for uracil and other pyrimidine nucleobases were discussed. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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19 pages, 4986 KiB

Open AccessArticle

Bayesian-Based Standard Values of Effective Friction Angle for Clayey Strata

by Ningfeng Chen, Kai Fang, Nianwu Liu and Yanru Wang

Symmetry 2025, 17(2), 176; https://doi.org/10.3390/sym17020176 - 24 Jan 2025

Viewed by 298

Abstract

In this study, a methodology using probabilistic distribution techniques to determine the parameters of the soil’s effective internal friction angle (

φ ’

) was proposed. The method was grounded in quantitative survey information extracted from geotechnical reports. Extensive equivalent samples were estimated [...] Read more.

In this study, a methodology using probabilistic distribution techniques to determine the parameters of the soil’s effective internal friction angle (

φ ’

) was proposed. The method was grounded in quantitative survey information extracted from geotechnical reports. Extensive equivalent samples were estimated using Markov chain Monte Carlo (MCMC) simulations and probability density functions (

P D F s

). The effective internal friction angle (

φ ’

) of silty clay layers was probabilistically characterized using the plasticity index (

P_{I}

), in situ static cone penetration test (

q_{c}

), and standard penetration test (

N_{S P T}

). A systematic quantitative analysis integrated prior information from different sources was systematically integrated with sampling data. By establishing a Bayesian framework that incorporated the regression relationship and uncertainties associated with the effective internal friction angle (

φ ’

), the model ensured balance and symmetry in the treatment of prior information and observed data. The model was then transformed into equivalent sample values based on three models, reflecting the symmetrical consideration of different data sources. Further considerations involved correcting the three different analysis methods. A comparison of equivalent sample values with the mean values of the sampling data, along with the parameter optimization updates, was performed by combining the three models. Using three sets of sampling data, a linear relationship model for the new soil parameters was derived. The analysis results demonstrated that the proposed method could obtain equivalent samples for the effective internal friction angle. Full article

(This article belongs to the Section Engineering and Materials)

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19 pages, 9572 KiB

Open AccessArticle

Logarithmic Separable Solutions of Force-Free Magnetic Fields in Plane-Parallel and Axial Symmetry

by Konstantinos N. Gourgouliatos

Symmetry 2025, 17(2), 175; https://doi.org/10.3390/sym17020175 - 24 Jan 2025

Viewed by 244

Abstract

This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the transformation of the non-linear partial differential equation, corresponding to force-free magnetic fields, [...] Read more.

This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the transformation of the non-linear partial differential equation, corresponding to force-free magnetic fields, to a system of decoupled ordinary differential equations, which nevertheless, are in general non-linear. It is then shown that such solutions are feasible for configurations where the electric current has a logarithmic dependence to the magnetic field flux. The properties of the magnetic fields are studied for a variety of physical parameters, through solution of the systems of the ordinary differential equations for various values of the parameters. It is demonstrated that this new logarithmic family of solutions has properties that are highly distinct from the known linear and non-linear equations, as it allows for bounded solutions of magnetic fields, for periodic solutions and for solutions that extend to infinity. Possible applications to astrophysical fields and plasmas are discussed as well as their use in numerical studies, and the overall enrichment of our understanding of force-free configurations. Full article

(This article belongs to the Section Physics)

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16 pages, 19985 KiB

Open AccessArticle

A Chaotic Jerk Oscillator with Complete Control via Fractional Exponentiation and Its Experimental Analog Circuit Realization

by Menghui Shen, Chunbiao Li, Xiaoliang Cen, Manyu Zhao, Yuanxiao Xu and Ludovico Minati

Symmetry 2025, 17(2), 174; https://doi.org/10.3390/sym17020174 - 24 Jan 2025

Viewed by 287

Abstract

By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also [...] Read more.

By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also features two-dimensional offset boosting, where a single parameter can realize direct offset boosting while another provides interlocked cross-dimensional offset boosting. Furthermore, this jerk system has a parameter-dominated symmetric attractor, which means that symmetric attractors appear successively as the parameter changes from positive to negative. Circuit experiments confirm the feasibility of analog fractional exponentiation using the 444 circuit and the complete control, including amplitude control and offset boosting, of the resulting system. The proposed circuit may facilitate applications of chaotic signal generators where signal versatility is important and exemplifies the generative potential of analog fractional exponentiation. Full article

(This article belongs to the Section Engineering and Materials)

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16 pages, 627 KiB

Open AccessArticle

Integrating Transformer Architecture and Householder Transformations for Enhanced Temporal Knowledge Graph Embedding in DuaTHP

by Yutong Chen, Xia Li, Yang Liu and Tiangui Hu

Symmetry 2025, 17(2), 173; https://doi.org/10.3390/sym17020173 - 24 Jan 2025

Viewed by 256

Abstract

The rapid advancement of knowledge graph (KG) technology has led to the emergence of temporal knowledge graphs (TKGs), which represent dynamic relationships over time. Temporal knowledge graph embedding (TKGE) techniques are commonly employed for link prediction and knowledge graph completion, among other tasks. [...] Read more.

The rapid advancement of knowledge graph (KG) technology has led to the emergence of temporal knowledge graphs (TKGs), which represent dynamic relationships over time. Temporal knowledge graph embedding (TKGE) techniques are commonly employed for link prediction and knowledge graph completion, among other tasks. However, existing TKGE models mainly rely on basic arithmetic operations, such as addition, subtraction, and multiplication, which limits their capacity to capture complex, non-linear relationships between entities. Moreover, many neural network-based TKGE models focus on static entities and relationships, overlooking the temporal dynamics of entity neighborhoods and their potential for encoding relational patterns, which can result in significant semantic loss. To address these limitations, we propose DuaTHP, a novel model that integrates Transformer blocks with Householder projections in the dual quaternion space. DuaTHP utilizes Householder projections to map head-to-tail entity relations, effectively capturing key relational patterns. The model incorporates two Transformer blocks: the entity Transformer, which models entity–relationship interactions, and the context Transformer, which aggregates relational and temporal information. Additionally, we introduce a time-restricted neighbor selector, which focuses on neighbors interacting within a specific time frame to enhance domain-specific analysis. Experimental results demonstrate that DuaTHP significantly outperforms existing methods in link prediction and knowledge graph completion, effectively addressing both semantic loss and time-related issues in TKGs. Full article

(This article belongs to the Section Computer)

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24 pages, 1608 KiB

Open AccessArticle

Symmetry in Genetic Distance Metrics: Quantifying Variability in Neurological Disorders for Personalized Treatment of Alzheimer’s and Dementia

by Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Marco Antonio Márquez-Vera, Ricardo A. Barrera-Cámara, Alejandro Fuentes-Penna, Eric Simancas-Acevedo, Miguel A. Ruiz-Jaimes, Juan M. Xicoténcatl-Pérez and Julio Cesar Ramos-Fernández

Symmetry 2025, 17(2), 172; https://doi.org/10.3390/sym17020172 - 23 Jan 2025

Viewed by 389

Abstract

This paper aims to adapt and apply genetic distance metrics in biomedical signal processing to improve the classification and monitoring of neurological disorders, specifically Alzheimer’s disease and frontotemporal dementia. The primary objectives are: (1) to quantify the variability in EEG signal patterns among [...] Read more.

This paper aims to adapt and apply genetic distance metrics in biomedical signal processing to improve the classification and monitoring of neurological disorders, specifically Alzheimer’s disease and frontotemporal dementia. The primary objectives are: (1) to quantify the variability in EEG signal patterns among the distinct subtypes of neurodegenerative disorders and healthy individuals, and (2) to explore the potential of a novel genetic similarity metric in establishing correlations between brain signal dynamics and clinical progression. Using a dataset of resting-state EEG recordings (eyes closed) from 88 subjects (36 with Alzheimer’s disease, 23 with frontotemporal dementia, and 29 healthy individuals), a comparative analysis of brain activity patterns was conducted. Symmetry plays a critical role in the proposed genetic similarity metric, as it captures the balanced relationships between intra- and inter-group EEG signal patterns. Our findings demonstrate that this approach significantly improves disease subtype identification and highlights the potential of the genetic similarity metric to optimize the predictive models. Furthermore, this methodology supports the development of personalized therapeutic interventions tailored to individual patient profiles, making a novel contribution to the field of neurological signal analysis and advancing the application of EEG in personalized medicine. Full article

(This article belongs to the Special Issue Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data)

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15 pages, 532 KiB

Open AccessArticle

What Is Inside the Double–Double Structure of the Radio Galaxy J0028+0035?

by Sándor Frey, Andrzej Marecki, Krisztina Éva Gabányi and Marek Jamrozy

Symmetry 2025, 17(2), 171; https://doi.org/10.3390/sym17020171 - 23 Jan 2025

Viewed by 355

Abstract

The radio source J0028+0035 is a recently discovered double–double radio galaxy at redshift

z = 0.398

. Its relic outer lobes are separated by about

3^{'}

in the sky, corresponding to ∼1 Mpc projected linear size. Inside this large-scale structure, the inner [...] Read more.

The radio source J0028+0035 is a recently discovered double–double radio galaxy at redshift

z = 0.398

. Its relic outer lobes are separated by about

3^{'}

in the sky, corresponding to ∼1 Mpc projected linear size. Inside this large-scale structure, the inner pair of collinear lobes span about 100 kpc. In the arcsec-resolution radio images of J0028+0035, there is a central radio feature that offers the intriguing possibility of being resolved into a pc-scale, third pair of innermost lobes. This would make this radio galaxy a rare triple–double source where traces of three distinct episodes of radio activity could be observed. To reveal the compact radio structure of the central component, we conducted observation with the European Very Long Baseline Interferometer Network and the enhanced Multi Element Remotely Linked Interferometer Network. Our

1.66

GHz image with high (∼5 milliarcsec) resolution shows a compact central radio core with no indication of a third, innermost double feature. The observation performed in multi-phase-centre mode also revealed that the physically unrelated but in projection closely separated background source 5BZU J0028+0035 has a single weak, somewhat resolved radio feature, at odds with its blazar classification. Full article

(This article belongs to the Section Physics)

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24 pages, 651 KiB

Open AccessArticle

Triply Heavy Tetraquark States in a Mass-Splitting Model

by Shi-Yuan Li, Yan-Rui Liu, Zi-Long Man, Cheng-Rui Shu, Zong-Guo Si and Jing Wu

Symmetry 2025, 17(2), 170; https://doi.org/10.3390/sym17020170 - 23 Jan 2025

Viewed by 229

Abstract

In a modified chromomagnetic interaction model, assuming

X (4140)

to be the lowest

1^{+ +}

c s \bar{c} \bar{s}

tetraquark and treating it as the reference state, we systematically investigated the masses of the triply heavy tetraquark states [...] Read more.

In a modified chromomagnetic interaction model, assuming

X (4140)

to be the lowest

1^{+ +}

c s \bar{c} \bar{s}

tetraquark and treating it as the reference state, we systematically investigated the masses of the triply heavy tetraquark states

Q Q \bar{Q} \bar{q}

(

Q = c, b; q = u, d, s

). Because of their higher masses, no stable tetraquarks were found. Using a simple scheme, we also estimated the partial widths of the rearrangement decay channels and relevant ratios. A compact triply heavy tetraquark candidate would be favored if its observed mass and partial width ratios were comparable with our predictions. We hope that the present work will be helpful for further studies. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

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