Symmetry

26 pages, 1875 KiB

Open AccessArticle

Construction Method of Compound Ground Motion Intensity Measure Based on Mutual Information Asymmetry for Engineering Seismic Fragility Analysis

by Zhuo Song, Xiaojun Li, Yushi Wang and Bochang Zhou

Symmetry 2025, 17(5), 699; https://doi.org/10.3390/sym17050699 (registering DOI) - 2 May 2025

Abstract

A significant challenge in probabilistic seismic demand analysis lies in selecting appropriate intensity measures and investigating their relationships with demand parameters to ensure accurate seismic fragility predictions. A single ground motion intensity measure is insufficient to capture the complex characteristics of ground motion, [...] Read more.

A significant challenge in probabilistic seismic demand analysis lies in selecting appropriate intensity measures and investigating their relationships with demand parameters to ensure accurate seismic fragility predictions. A single ground motion intensity measure is insufficient to capture the complex characteristics of ground motion, leading researchers to focus on compound intensity measures. It is essential to investigate the selection of ground motion features and the number of features included in the construction of compound intensity measures, as these measures cannot comprise an unlimited set of ground motion features. This study focused on machine learning feature selection methods to select ground motion features for compound intensity measures, utilizing mutual information for feature selection. Considering the symmetry and asymmetry requirements of this process, optimized features were selected. Based on the selected features, the compound ground motion intensity measure was constructed to evaluate structural seismic fragility. The compound ground motion intensity measure was evaluated against scalar intensity measure in terms of correlation, efficiency, practicality, proficiency, and sufficiency. A comprehensive comparative analysis demonstrates the applicability of the compound intensity measure. The study’s findings support fragility analysis and performance evaluation using compound intensity measures. The corresponding results can be applied in the risk analysis aspect of performance-based earthquake engineering. Full article

(This article belongs to the Section Engineering and Materials)

29 pages, 1161 KiB

Open AccessArticle

Secure and Scalable Device Attestation Protocol with Aggregate Signature

by Hyunsoo Kwon

Symmetry 2025, 17(5), 698; https://doi.org/10.3390/sym17050698 (registering DOI) - 2 May 2025

Abstract

In cloud computing environments, security challenges emerge due to compromised firmware and supply chain attacks that target devices deployed within data centers. The Secure Protocol and Data Model (SPDM) has been widely adopted for device attestation, which verifies device identity and firmware integrity. [...] Read more.

In cloud computing environments, security challenges emerge due to compromised firmware and supply chain attacks that target devices deployed within data centers. The Secure Protocol and Data Model (SPDM) has been widely adopted for device attestation, which verifies device identity and firmware integrity. However, the scalability of the SPDM is challenged by the resource constraints of peripheral devices and the inherent asymmetry of the protocol, where a heavy verification burden on the central requester leads to a potential bottleneck. In order to solve these problems, we propose a secure and scalable device attestation protocol, SPDM-AggSig, that integrates a chainless-certificate-based aggregate signature scheme within the SPDM framework supporting group messaging. Our protocol reduces the communication overhead by replacing the conventional X.509 certificates with lightweight chainless certificates. It also improves the scalability through group-based attestation with constant-size aggregated signatures. The proposed delegation mitigates the asymmetry in the attestation, introducing a tendency toward functional symmetry by distributing the verification burdens from the central requester to group leaders. We also provide a formal security proof demonstrating existential unforgeability under an adaptive chosen message attack (EUF-ACMA). SPDM-AggSig achieves an approximately 84.18% improvement in the computation overhead and a 96.22% decrease in the communication overhead compared to the baseline. Full article

(This article belongs to the Section Computer)

13 pages, 334 KiB

Open AccessArticle

Combinatorial Analysis of k-Oresme and k-Oresme–Lucas Sequences

by Bahar Demirtürk

Symmetry 2025, 17(5), 697; https://doi.org/10.3390/sym17050697 (registering DOI) - 2 May 2025

Abstract

In this study, firstly the definitions and basic algebraic properties of k-Oresme and k-Oresme–Lucas sequences are given. Then, various summation formulae are derived with the help of the first and second derivatives of two polynomials with k-Oresme and k-Oresme–Lucas number coefficients. The main [...] Read more.

In this study, firstly the definitions and basic algebraic properties of k-Oresme and k-Oresme–Lucas sequences are given. Then, various summation formulae are derived with the help of the first and second derivatives of two polynomials with k-Oresme and k-Oresme–Lucas number coefficients. The main aim of this study is to establish the relations between the generalized Fibonacci and generalized Lucas sequences and the k-Oresme and k-Oresme–Lucas sequences, respectively. These connections allow us to obtain different combinatorial identities of these sequences using the characteristic equation of the k-Oresme and k-Oresme–Lucas sequences. In this way, the discovered combinatorial identities reveal the arithmetic and structural symmetries in the sequences, through the regularities and recurring patterns observed in the algebraic structures of the considered number sequences. The results obtained in this study enable the development of new symmetric approaches in areas such as numerical analysis, cryptography and optimization algorithms, and the algebraic relations derived in this study can contribute to the solution of different problems in disciplines such as mathematical modelling and theoretical physics. Full article

(This article belongs to the Section Mathematics)

14 pages, 2196 KiB

Open AccessArticle

FlexRay Static Segment Message Scheduling Based on Heterogeneous Scheduling Algorithm

by Shuqing Li, Yujing Wu, Yihu Xu, Kaihang Zhang and Yinan Xu

Symmetry 2025, 17(5), 696; https://doi.org/10.3390/sym17050696 (registering DOI) - 2 May 2025

Abstract

With the development of intelligent connected vehicles, higher demands are being placed on the capabilities of in-vehicle bus networks. Compared to traditional in-vehicle bus networks like Local Interconnect Network (LIN) and Controller Area Network (CAN), the FlexRay bus offers advantages such as high [...] Read more.

With the development of intelligent connected vehicles, higher demands are being placed on the capabilities of in-vehicle bus networks. Compared to traditional in-vehicle bus networks like Local Interconnect Network (LIN) and Controller Area Network (CAN), the FlexRay bus offers advantages such as high real-time performance and high transmission rates, making it the core technology of the new generation of in-vehicle bus networks. This study focuses on the phenomenon of bandwidth resource waste in the FlexRay bus and innovatively proposes the FlexRay Static Segment Heterogeneous Scheduling Algorithm (SHSA). The SHSA algorithm optimizes the message transmission performance of the FlexRay bus through heterogeneous allocation of communication channels and message scheduling methods. This study established a simulation experimental platform using the CANoe.FlexRay bus network simulation tool and conducted simulation experiments on the proposed algorithm. Experimental results show that the average bandwidth utilization of the SHSA algorithm is 72.5%, which is 20.91%, 51.14%, and 54% higher than that of the existing Heterogeneous Makespan-minimizing DAG Scheduler (HMDS), Message Packing Scheme, and Jitter-aware Message Scheduling-Simulated Annealing and Greedy Randomized Adaptive Search Procedure (JAMS-SG), respectively. This study provides technical support for message transmission in intelligent connected vehicles and enhances the communication efficiency of the in-vehicle FlexRay bus network. Full article

(This article belongs to the Section Engineering and Materials)

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22 pages, 7628 KiB

Open AccessArticle

Optimization of Actuator Arrangement of Cable–Strut Tension Structures Based on Multi-Population Genetic Algorithm

by Huiting Xiong, Tingmei Zhou, Pei Zhang, Zhibing Shang, Mithun Biswas, Hao Li and Huayang Zhu

Symmetry 2025, 17(5), 695; https://doi.org/10.3390/sym17050695 (registering DOI) - 1 May 2025

Abstract

This study addresses the optimization of actuator arrangements in adaptive cable–strut tension structures to enhance structural controllability and performance. Two novel optimization criteria are proposed: (1) a weighted sensitivity criterion that integrates nodal displacements and internal force increments, and (2) a system strain [...] Read more.

This study addresses the optimization of actuator arrangements in adaptive cable–strut tension structures to enhance structural controllability and performance. Two novel optimization criteria are proposed: (1) a weighted sensitivity criterion that integrates nodal displacements and internal force increments, and (2) a system strain energy criterion reflecting overall structural stiffness. Nonlinear optimization models are formulated for these criteria, with actuator positions as design variables, and solved using a robust multi-population genetic algorithm. The weighted sensitivity criterion prioritizes targeted control of specific nodes and members, while the strain energy criterion ensures balanced global response. Numerical validation is conducted on a Geiger cable dome and a four-layer tensegrity structure. Results demonstrate that both criteria yield actuator arrangements satisfying geometric symmetry while achieving high sensitivity in displacement and internal force control. The proposed framework offers practical insights for optimizing adaptive structures under static control requirements, and advances the field by bridging localized and global response optimization, enabling smarter, more resilient tension structures. Full article

(This article belongs to the Section Engineering and Materials)

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19 pages, 3649 KiB

Open AccessArticle

Iterative Learning Control with Forgetting Factor for MIMO Nonlinear Systems with Randomly Varying Iteration Lengths and Disturbances

by Genfeng Liu, Yangyang Wang, Jinhao Li and Qinghe Wang

Symmetry 2025, 17(5), 694; https://doi.org/10.3390/sym17050694 (registering DOI) - 1 May 2025

Abstract

In this paper, a PD-type iterative learning control algorithm with a forgetting factor is developed for MIMO nonlinear systems with randomly varying iteration lengths, initial state shifts and disturbances. Firstly, considering the randomly varying iteration lengths, a modified tracking error is designed. Secondly, [...] Read more.

In this paper, a PD-type iterative learning control algorithm with a forgetting factor is developed for MIMO nonlinear systems with randomly varying iteration lengths, initial state shifts and disturbances. Firstly, considering the randomly varying iteration lengths, a modified tracking error is designed. Secondly, for the initial state shift and disturbances, a PD-type iterative learning control algorithm with a forgetting factor (PDILCFF) method is proposed. A contraction mapping method is exploited to obtain the convergence property of the proposed control scheme, which can guarantee that the tracking error is bounded. Considering the iteration-varying trial lengths, the proposed PDILCFF algorithm is closely related to symmetry. Symmetry can provide prior information about the system’s structure and characteristics for the proposed PDILCFF method, which is helpful for designing more efficient control algorithms. On the other hand, the proposed PDILCFF method exploits system symmetries across different intervals through iterative processes to achieve accurate control and performance optimization of MIMO unknown nonlinear systems. Finally, two simulations are presented, one with a subway train tracking control system and the other with a two-degree-of-freedom robot manipulator system, to verify the effectiveness of the theoretical studies. Full article

(This article belongs to the Section Computer)

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30 pages, 12183 KiB

Open AccessArticle

Improving Hydrodynamics and Energy Efficiency of Bioreactor by Developed Dimpled Turbine Blade Geometry

by Anton Ruzhanskyi, Sergii Kostyk, Igor Korobiichuk and Vladislav Shybetskyi

Symmetry 2025, 17(5), 693; https://doi.org/10.3390/sym17050693 (registering DOI) - 30 Apr 2025

Abstract

The hydrodynamic efficiency of bioreactors is contingent upon the design of the impeller, particularly the blade geometry, which influences flow symmetry. This study evaluates the impact of dimpled surfaces on the blades of a turbine impeller on mixing processes. Investigations were conducted using [...] Read more.

The hydrodynamic efficiency of bioreactors is contingent upon the design of the impeller, particularly the blade geometry, which influences flow symmetry. This study evaluates the impact of dimpled surfaces on the blades of a turbine impeller on mixing processes. Investigations were conducted using simulations in ANSYS (2021R2) with the k-ε turbulence model and experiments measuring vortex funnel depth and power consumption at 247 rpm in an 11-L cylindrical vessel. Results indicate that dimples disrupt the rotational symmetry of the blades, increasing the volume-averaged flow velocity from 0.312 m/s to 0.321 m/s (a 2.9% increase); the maximum shear strain rate from 161 s⁻¹ to 1442 s⁻¹; and the turbulent vortex frequency from 183 s⁻¹ to 290 s⁻¹ (a 58% increase). The volume-averaged shear strain rate rose from 44 s⁻¹ to 63 s⁻¹ (a 43% improvement), and the vortex funnel depth increased from 44 mm to 50 mm (a 14% increase), indicating enhanced homogenization. This facilitates efficient processing of sensitive biological organisms, such as mycoplasmas, and more robust structures, including fungi and mycelium. However, power consumption increased by 4.5% (from 4.9 W to 5.1 W). Thus, disrupting symmetry with dimples intensifies hydrodynamic processes, enhancing mixing efficiency, but requires optimization to reduce energy costs, offering prospects for advancing biotechnological systems. Full article

(This article belongs to the Special Issue Advances in Fluid Dynamics and Energy Systems: Applications of Symmetry and Asymmetry)

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21 pages, 2108 KiB

Open AccessArticle

A Police Booth Planning Method Based on Wolf Pack Optimization Algorithm Using AAF and DGSS

by Dongxing Wang, Zhishu Sun and Fangbo Wu

Symmetry 2025, 17(5), 692; https://doi.org/10.3390/sym17050692 (registering DOI) - 30 Apr 2025

Abstract

Efficient police booth deployment is vital for optimizing law enforcement and maintaining public safety. This paper tackles two key challenges in current solutions: insufficient coverage and redundant overlaps. First, this article introduces the Simultaneous Optimization for Max Coverage and Min Overlap model (SOOM-MCMO), [...] Read more.

Efficient police booth deployment is vital for optimizing law enforcement and maintaining public safety. This paper tackles two key challenges in current solutions: insufficient coverage and redundant overlaps. First, this article introduces the Simultaneous Optimization for Max Coverage and Min Overlap model (SOOM-MCMO), which formalizes the dual objectives into a unified optimization framework. Second, to address limitations of traditional wolf pack algorithm, this article presents the Adaptive-Approaching Framework with Dynamic-Grid-Siege Wolf Pack Algorithm (AAF-DGS-WPOA). This technique dynamically adjusts searcher populations using spatial symmetry and hybrid optimization strategies, thereby enhancing coverage precision and reducing computational costs. Our proposed method (AAF-DGS-WPOA-based Police Booth Planning Method, PBPM-AAFDGS-WPOA) was evaluated on 20 public datasets as well as SOOM-MCMO. Results showed 15–30% coverage improvement and a 16.65% runtime reduction versus popular benchmarks like PSO, GA, and WDX_WPOA. The improved wolf pack algorithm also outperformed traditional approaches in coverage sufficiency, resource efficiency, and system responsiveness. This work advances practical methods for police booth planning, achieving higher social security outputs with lower resource investment. Full article

(This article belongs to the Section Computer)

17 pages, 13196 KiB

Open AccessArticle

Dual Graph Laplacian RPCA Method for Face Recognition Based on Anchor Points

by Shu-Ting Zhuang, Qing-Wen Wang and Jiang-Feng Chen

Symmetry 2025, 17(5), 691; https://doi.org/10.3390/sym17050691 (registering DOI) - 30 Apr 2025

Abstract

High-dimensional data often contain noise and undancy, which can significantly undermine the performance of machine learning. To address this challenge, we propose an advanced robust principal component analysis (RPCA) model that integrates bidirectional graph Laplacian constraints along with the anchor point technique. This [...] Read more.

High-dimensional data often contain noise and undancy, which can significantly undermine the performance of machine learning. To address this challenge, we propose an advanced robust principal component analysis (RPCA) model that integrates bidirectional graph Laplacian constraints along with the anchor point technique. This approach constructs two graphs from both the sample and feature perspectives for a more comprehensive capture of the underlying data structure. Moreover, the anchor point technique serves to substantially reduce computational complexity, making the model more efficient and scalable. Comprehensive evaluations on both GTdatabase and VGG Face2 dataset confirm that anchor-based methods maintain competitive accuracy with standard graph Laplacian approaches (within 0.5–2.0% difference) while achieving significant computational speedups of 5.7–27.1% and 12.9–14.6% respectively. The consistent performance across datasets, from controlled laboratory conditions to challenging real-world scenarios, demonstrates the robustness and scalability of the proposed anchor technique. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

14 pages, 251 KiB

Open AccessArticle

On the Duality of Codes over Non-Unital Commutative Ring of Order p²

by Tamador Alihia

Symmetry 2025, 17(5), 690; https://doi.org/10.3390/sym17050690 (registering DOI) - 30 Apr 2025

Abstract

This paper establishes an extended theoretical framework centered on the duality of codes constructed over a special class of non-unital, commutative, local rings of order

p^{2}

, where p is a prime satisfying

p \equiv 1 mod 4

or [...] Read more.

This paper establishes an extended theoretical framework centered on the duality of codes constructed over a special class of non-unital, commutative, local rings of order

p^{2}

, where p is a prime satisfying

p \equiv 1 mod 4

or

p \equiv 3 mod 4

. The work expands the traditional scope of coding theory by developing and adapting a generalized recursive approach to produce quasi-self-dual and self-dual codes within this algebraic setting. While the method for code generation is rooted in the classical build-up technique, the primary focus is on the duality properties of the resulting codes—especially how these properties manifest under different congruence conditions on p. Computational examples are provided to illustrate the effectiveness of the proposed methods. Full article

(This article belongs to the Section Mathematics)

21 pages, 6959 KiB

Open AccessArticle

Multi-Domain Digital Twin and Real-Time Performance Optimization for Marine Steam Turbines

by Yuhui Liu, Duansen Shangguan, Liping Chen, Xiaoyan Liu, Guihao Yin and Gang Li

Symmetry 2025, 17(5), 689; https://doi.org/10.3390/sym17050689 (registering DOI) - 30 Apr 2025

Abstract

The digital twin model, which serves as a virtual counterpart symmetric to the physical entity, enables high-fidelity simulation and real-time monitoring. However, digital twin implementation for marine steam turbines (MSTs) faces dual multi-domain simulation fidelity and computational efficiency challenges. This study establishes a [...] Read more.

The digital twin model, which serves as a virtual counterpart symmetric to the physical entity, enables high-fidelity simulation and real-time monitoring. However, digital twin implementation for marine steam turbines (MSTs) faces dual multi-domain simulation fidelity and computational efficiency challenges. This study establishes a MST digital twin modeling methodology through two interconnected innovations: (1) a Modelica-based modular architecture enabling cross-domain coupling across mechanical, thermodynamic, and hydrodynamic systems via hierarchical decomposition, ensuring bidirectional symmetry between physical components and their virtual representations; and (2) a hybrid support vector regression-bidirectional long short-term memory (SVR-BiLSTM) surrogate model combining Gaussian radial basis function-supported SVR for steady-state mapping with Bi-LSTM networks for dynamic error compensation. Experimental validation demonstrates: (a) the SVR component achieves <1.57% absolute error under step-load conditions with 85% computational time reduction versus physics-based models; and (b) Bi-LSTM integration improves transient prediction accuracy by 14.85% in maximum absolute error compared to standalone SVR, effectively resolving static–dynamic discrepancies in telemetry simulation. This dual-approach innovation successfully bridges the critical trade-off between real-time computation and predictive accuracy while maintaining symmetric consistency between the physical turbine and its digital counterpart, providing a validated technical foundation for the intelligent operation and maintenance of MSTs. Full article

(This article belongs to the Section Engineering and Materials)

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20 pages, 29506 KiB

Open AccessArticle

On the Robustness of Individual Tree Segmentation to Data Adversarial Attacks from Remote Sensing Point Clouds

by Renhao Shen, Yongwei Miao and Haijian Liu

Symmetry 2025, 17(5), 688; https://doi.org/10.3390/sym17050688 (registering DOI) - 30 Apr 2025

Abstract

Forests play a vital role in maintaining ecological balance, making accurate forest monitoring technologies essential. Remote sensing point cloud data always capture distinctive geometric features of forests, including the cylindrical symmetry of tree trunks and the radial symmetry of canopies. However, the inherent [...] Read more.

Forests play a vital role in maintaining ecological balance, making accurate forest monitoring technologies essential. Remote sensing point cloud data always capture distinctive geometric features of forests, including the cylindrical symmetry of tree trunks and the radial symmetry of canopies. However, the inherent complexity of point cloud data, combined with their vulnerabilities to adversarial attacks, often disrupts these symmetrical patterns, significantly limiting the practical application of deep learning models in forest monitoring. This research presents a novel approach to enhance the robustness of individual tree segmentation networks by combining data augmentation and adversarial training techniques. Our method employs the FGSM algorithm and Gaussian noise attack to generate adversarial samples while utilizing data denoising and controlled noise injection for data augmentation. A dynamic adversarial training framework can adaptively adjust the proportion of adversarial samples during the network training stage to optimize the model. Using remote sensing point cloud datasets from Wisconsin, the experimental results demonstrate the effectiveness of the individual tree segmentation networks, PointNet++ and DBSCAN, in reducing attack success rates whilst improving the stability and accuracy of segmentation results under various adversarial conditions. This study highlights the potential for more robust forest monitoring systems capable of maintaining accuracy even when faced with data perturbations or intentional interference. Full article

(This article belongs to the Section Computer)

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13 pages, 856 KiB

Open AccessArticle

Shape Transition and Coexistence in ⁶⁶Se Studied with Phenomenological and Microscopic Models

by Petricǎ Buganu, Sara Chafik, Alaaeddine Lahbas and Mustapha Oulne

Symmetry 2025, 17(5), 687; https://doi.org/10.3390/sym17050687 (registering DOI) - 30 Apr 2025

Abstract

A comprehensive theoretical investigation of shape coexistence and transition phenomena in the neutron-deficient nucleus

{}^{66}{Se}

, using complementary microscopic and phenomenological approaches, is presented. The analysis employs the Covariant Density Functional Theory with the Density-Dependent Meson Exchange Model interaction to map the [...] Read more.

A comprehensive theoretical investigation of shape coexistence and transition phenomena in the neutron-deficient nucleus

{}^{66}{Se}

, using complementary microscopic and phenomenological approaches, is presented. The analysis employs the Covariant Density Functional Theory with the Density-Dependent Meson Exchange Model interaction to map the potential energy surface. This microscopic foundation is complemented by calculations using the Bohr–Mottelson Hamiltonian with a sextic oscillator potential, specifically adapted to explore shape coexistence between spherical and

γ

-unstable configurations. The latter model successfully reproduces the experimental energy spectrum, including the critical low-lying

0_{2}^{+}

state at 1226 keV—a key signature of shape coexistence. An analysis of probability density distributions indicates a distinctive manifestation of shape coexistence wherein different shapes exist without significant mixing in the states. These findings provide crucial insights into the structural dynamics of

{}^{66}{Se}

and establish it as an important case study for understanding shape evolution in neutron-deficient nuclei beyond the

N = Z

line. Full article

(This article belongs to the Special Issue Advances in Nuclear Physics and Symmetry)

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20 pages, 2822 KiB

Open AccessArticle

Multivariate Time-Series Missing Data Imputation with Convolutional Transformer Model

by Yanxia Wang, He Ding and Hongdun Li

Symmetry 2025, 17(5), 686; https://doi.org/10.3390/sym17050686 (registering DOI) - 30 Apr 2025

Abstract

The rapid progress in artificial intelligence technologies has significantly impacted the global economy, driving transformative changes in manufacturing and giving rise to intelligent manufacturing. In this context, multivariable time-series data have become an essential resource for modern industries. This paper introduces the Point [...] Read more.

The rapid progress in artificial intelligence technologies has significantly impacted the global economy, driving transformative changes in manufacturing and giving rise to intelligent manufacturing. In this context, multivariable time-series data have become an essential resource for modern industries. This paper introduces the Point Energy Technology, an advanced system for energy monitoring and data acquisition developed by our team. The system has been successfully deployed with several industrial partners, including a combined heat and power system in a local industrial park. Despite its capabilities, data loss remains a persistent issue, which is often caused by measurement or transmission errors during the data collection and transfer stages. These errors result in the loss of vital data samples for effective process monitoring and control. To tackle this issue, we present a convolutional transformer imputation model that is based on self-attention to generate missing data samples. This model effectively captures both historical and future sequence information through an enhanced masking mechanism while also incorporating local dependency information through the symmetrically balanced use of convolution and self-attention. To evaluate the performance of the proposed model against classical models, the energy-related data from a local industrial park were used in this experiment. Considering the real-world conditions, the missing data were categorized into two types: continuous missing and random missing. The experimental results demonstrate that our model produced high-quality data samples, effectively compensating for gaps in the multivariable time-series data. Full article

(This article belongs to the Section Engineering and Materials)

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18 pages, 25119 KiB

Open AccessArticle

Dynamics, Circuit Simulation and Fixed-Time Projection Synchronization in a Memristor-Based Hyperchaotic System

by Yan Zhou, Ruimei Li and Zhuang Cui

Symmetry 2025, 17(5), 685; https://doi.org/10.3390/sym17050685 (registering DOI) - 29 Apr 2025

Abstract

Introducing a memristor into chaotic systems facilitates the construction of high-dimensional hyperchaotic systems. The hyperchaotic signals generated by these systems have important applications in the field of information security. A five-dimensional hyperchaotic system is constructed by introducing a memristor. Its hyperchaotic nature is [...] Read more.

Introducing a memristor into chaotic systems facilitates the construction of high-dimensional hyperchaotic systems. The hyperchaotic signals generated by these systems have important applications in the field of information security. A five-dimensional hyperchaotic system is constructed by introducing a memristor. Its hyperchaotic nature is discussed using phase diagrams and Lyapunov exponential diagrams. The effects of the parameters on the dynamical behavior are examined by bifurcation diagrams and Lyapunov exponential diagrams. To validate the theoretical model, an electronic circuit was designed for circuit simulation. The electronic simulation of the circuit was carried out using the Multisim simulation platform. Finally, the fixed-time projection synchronization of the system was taken into consideration. Three sets of synchronization schemes were considered and simulated. The synchronization scheme has the features of fast synchronization speed and robustness. It is potentially valuable for applications in the fields of chaotic communication and chaotic encryption. Full article

(This article belongs to the Special Issue Symmetry in Complex System and Network Science)

13 pages, 309 KiB

Open AccessArticle

Factorizations and Accurate Computations with Min and Max Matrices

by Yasmina Khiar, Esmeralda Mainar and Eduardo Royo-Amondarain

Symmetry 2025, 17(5), 684; https://doi.org/10.3390/sym17050684 (registering DOI) - 29 Apr 2025

Abstract

Min and max matrices are structured matrices that appear in diverse mathematical and computational applications. Their inherent structures facilitate highly accurate numerical solutions to algebraic problems. In this research, the total positivity of generalized Min and Max matrices is characterized, and their bidiagonal [...] Read more.

Min and max matrices are structured matrices that appear in diverse mathematical and computational applications. Their inherent structures facilitate highly accurate numerical solutions to algebraic problems. In this research, the total positivity of generalized Min and Max matrices is characterized, and their bidiagonal factorizations are derived. It is also demonstrated that these decompositions can be computed with high relative accuracy (HRA), enabling the precise computations of eigenvalues and singular values and the solution of linear systems. Notably, the discussed approach achieves relative errors on the order of the unit roundoff, even for large and ill-conditioned matrices. To illustrate the exceptional accuracy of this method, numerical experiments on quantum extensions of Min and L-Hilbert matrices are presented, showcasing their superior precisions compared to those of standard computational techniques. Full article

(This article belongs to the Section Mathematics)

19 pages, 4317 KiB

Open AccessArticle

Stochastic Programming-Based Annual Peak-Regulation Potential Assessing Method for Virtual Power Plants

by Yayun Qu, Chang Liu, Xiangrui Tong and Yiheng Xie

Symmetry 2025, 17(5), 683; https://doi.org/10.3390/sym17050683 (registering DOI) - 29 Apr 2025

Abstract

The intervention of distributed loads, propelled by the swift advancement of distributed energy sources and the escalating demand for diverse load types encompassing electricity and cooling within virtual power plants (VPPs), has exerted an influence on the symmetry of the grid. Consequently, a [...] Read more.

The intervention of distributed loads, propelled by the swift advancement of distributed energy sources and the escalating demand for diverse load types encompassing electricity and cooling within virtual power plants (VPPs), has exerted an influence on the symmetry of the grid. Consequently, a quantitative assessment of the annual peak-shaving capability of a VPP is instrumental in mitigating the peak-to-valley difference in the grid, enhancing the operational safety of the grid, and reducing grid asymmetry. This paper presents a peak-shaving optimization method for VPPs, which takes into account renewable energy uncertainty and flexible load demand response. Firstly, wind power (WP), photovoltaic (PV) generation, and demand-side response (DR) are integrated into the VPP framework. Uncertainties related to WP and PV generation are incorporated through the scenario method within deterministic constraints. Secondly, a stochastic programming (SP) model is established for the VPP, with the objective of maximizing the peak-regulation effect and minimizing electricity loss for demand-side users. The case study results indicate that the proposed model effectively tackles peak-regulation optimization across diverse new energy output scenarios and accurately assesses the peak-regulation potential of the power system. Specifically, the proportion of load decrease during peak hours is 18.61%, while the proportion of load increase during off-peak hours is 17.92%. The electricity loss degrees for users are merely 0.209 in summer and 0.167 in winter, respectively. Full article

(This article belongs to the Special Issue Symmetry in Digitalisation of Distribution Power System)

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21 pages, 3055 KiB

Open AccessArticle

Integrated Scheduling Algorithm Based on the Improved Floyd Algorithm

by Yingxin Wei, Wei Zhou, Zhiqiang Xie, Ming Sun, Zhenjiang Tan and Wangcheng Cao

Symmetry 2025, 17(5), 682; https://doi.org/10.3390/sym17050682 - 29 Apr 2025

Abstract

In the research and practice of integrated scheduling problems, the tree structure of complex products usually presents an asymmetric and complex form. This asymmetry is mainly reflected in the hierarchical relationship between the various components of the product, the degree of dependence, and [...] Read more.

In the research and practice of integrated scheduling problems, the tree structure of complex products usually presents an asymmetric and complex form. This asymmetry is mainly reflected in the hierarchical relationship between the various components of the product, the degree of dependence, and the sequence of production processes. Existing studies often neglect that leaf nodes with the lowest layer priority can be scheduled at any moment, leading to underutilization of parallelism potential under symmetric structures and exacerbation of critical path delays under asymmetric structures. Aiming at solving this kind of problem, an integrated scheduling algorithm based on the improved Floyd algorithm (ISA-IFA) is proposed. According to the improved Floyd algorithm, the algorithm proposed a path-weighted strategy, which constructs the vertical path value according to the processing time of the process itself. Combined with the proposed process scheduling advantage strategy, the leaf node process is especially emphasized as the priority scheduling object, which makes the connection between the processes more closely, and then significantly reduces the idle time of the equipment. The empirical results show that the ISA-IFA algorithm shortens the completion time of complex products and simultaneously improves the equipment utilization rate to 55.9%, verifying its effectiveness in dynamic scheduling and resource co-optimization. Full article

(This article belongs to the Section Mathematics)

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46 pages, 1618 KiB

Open AccessReview

Electroweak Form Factors of Baryons in Dense Nuclear Matter

by G. Ramalho, K. Tsushima and Myung-Ki Cheoun

Symmetry 2025, 17(5), 681; https://doi.org/10.3390/sym17050681 - 29 Apr 2025

Abstract

There is evidence that the properties of hadrons are modified in a nuclear medium. Information about the medium modifications of the internal structure of hadrons is fundamental for the study of dense nuclear matter and high-energy processes, including heavy-ion and nucleus–nucleus collisions. At [...] Read more.

There is evidence that the properties of hadrons are modified in a nuclear medium. Information about the medium modifications of the internal structure of hadrons is fundamental for the study of dense nuclear matter and high-energy processes, including heavy-ion and nucleus–nucleus collisions. At the moment, however, empirical information about medium modifications of hadrons is limited; therefore, theoretical studies are essential for progress in the field. In the present work, we review theoretical studies of the electromagnetic and axial form factors of octet baryons in symmetric nuclear matter. The calculations are based on a model that takes into account the degrees of freedom revealed in experimental studies of low and intermediate square transfer momentum

q^{2} = - Q^{2}

: valence quarks and meson cloud excitations of baryon cores. The formalism combines a covariant constituent quark model, developed for a free space (vacuum) with the quark–meson coupling model for extension to the nuclear medium. We conclude that the nuclear medium modifies the baryon properties differently according to the flavor content of the baryons and the medium density. The effects of the medium increase with density and are stronger (quenched or enhanced) for light baryons than for heavy baryons. In particular, the in-medium neutrino–nucleon and antineutrino–nucleon cross-sections are reduced compared to the values in free space. The proposed formalism can be extended to densities above the normal nuclear density and applied to neutrino–hyperon and antineutrino–hyperon scattering in dense nuclear matter. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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