Symmetry

15 pages, 16677 KiB

Open AccessArticle

Research on the Influence of Symmetrical Installation of Blade on the Sediment Erosion in a Multi-Stage Centrifugal Pump

by Xijie Song, Kuizheng Zhu and Zhengwei Wang

Symmetry 2024, 16(12), 1636; https://doi.org/10.3390/sym16121636 - 11 Dec 2024

Abstract

Double suction pumps are widely used in the Yellow River in the China water intake pump stations, which face serious sediment wear. A prediction model for gap erosion in gas-liquid solid three-phase flow was constructed. A gas core factor has been added to [...] Read more.

Double suction pumps are widely used in the Yellow River in the China water intake pump stations, which face serious sediment wear. A prediction model for gap erosion in gas-liquid solid three-phase flow was constructed. A gas core factor has been added to the gap erosion model to achieve accurate prediction of particle impact velocity and impact angle caused by cavitation air core deformation. The influence mechanism of cavitation flow and sand-laden suction vortex on the sediment erosion. Usually, double suction pumps are one type. This study aims to explore the effects of the symmetrical and asymmetrical installation of double suction pump impellers on the wear and energy dissipation of pumps under sediment conditions in three-stage centrifugal pumps. The research results indicate that under symmetrical installation, the wear of the impeller caused by sediment impact is significantly intensified with a maximum velocity of 27 m/s. In contrast, asymmetric installation significantly improves sediment wear, with a maximum velocity of 24.3 m/s. By optimizing the staggered angle on both sides of the impeller, it was found that when the staggered angle was set to 10.85°, the performance of the pump under sediment conditions reached its optimal level, with a minimal erosion rate of 0.000008 kg·m⁻²·s⁻¹. These results provide an important basis for the design and optimization of three-stage centrifugal pumps in sediment transport and have significant theoretical significance and engineering application value. Full article

(This article belongs to the Special Issue Advances in Multi-phase Flow: Symmetry, Asymmetry, and Applications)

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22 pages, 428 KiB

Open AccessArticle

Estimation of Conditional Covariance Matrices for a Class of High-Dimensional Varying Coefficient Factor-Generalized Autoregressive Conditional Heteroscedasticity Model

by Yujiao Liu, Yuan Li and Xingfa Zhang

Symmetry 2024, 16(12), 1635; https://doi.org/10.3390/sym16121635 - 10 Dec 2024

Abstract

This paper explores a class of High-Dimensional Varying Coefficient Factor-GARCH (Generalized Autoregressive Conditional Heteroscedasticity) model, designed to capture dynamic relationships between variables and account for the heterogeneity of time series data. By exploiting the structure of the model, a mixed approach is proposed [...] Read more.

This paper explores a class of High-Dimensional Varying Coefficient Factor-GARCH (Generalized Autoregressive Conditional Heteroscedasticity) model, designed to capture dynamic relationships between variables and account for the heterogeneity of time series data. By exploiting the structure of the model, a mixed approach is proposed to estimate conditional covariance matrices. Furthermore, asymptotic properties for the estimators are established, providing a theoretical foundation for their consistency and efficiency. A simulation study is conducted to demonstrate the performance of estimators, and a real data example of portfolio allocation is presented to illustrate the practical application of the approach. Full article

(This article belongs to the Section Mathematics)

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21 pages, 7720 KiB

Open AccessArticle

HPDH-MI: A High Payload Data Hiding Technique for Medical Images Based on AMBTC

by Chia-Chen Lin, Mostafa Mirzaei, En-Ting Chu and Chen Chih Cheng

Symmetry 2024, 16(12), 1634; https://doi.org/10.3390/sym16121634 - 10 Dec 2024

Abstract

In the realm of electronic health (eHealth) services powered by the Internet of Things (IoT), vast quantities of medical images and visualized electronic health records collected by IoT devices must be transmitted daily. Given the sensitive nature of medical information, ensuring the security [...] Read more.

In the realm of electronic health (eHealth) services powered by the Internet of Things (IoT), vast quantities of medical images and visualized electronic health records collected by IoT devices must be transmitted daily. Given the sensitive nature of medical information, ensuring the security of transmitted health data is paramount. To address this critical concern, this paper introduces a novel data hiding algorithm tailored for Absolute Moment Block Truncation Coding (AMBTC) in medical images, named HPDH-MI (High Payload Data Hiding for Medical Images). The proposed method embeds secret data into the AMBTC compression code inconspicuously to avoid detection by malicious users. It achieves this by first classifying AMBTC compressed blocks into four categories—flat, smooth, complex I, and complex II—using three predetermined thresholds. A 1-bit indicator, based on the proposed grouping strategy, facilitates efficient and effective block classification. A data embedding strategy is applied to each block type, focusing on block texture and taking into account the symmetric features of the pixels within the block. This approach achieves a balance between data hiding capacity, image quality, and embedding efficiency. Experimental evaluations highlight the superior performance of HPDH-MI. When tested on medical images from the Osirix database, the method achieves an average image quality of 31.22 dB, a payload capacity of 225,911 bits, and an embedding efficiency of 41.78%. These results demonstrate that the HPDH-MI method not only significantly increases the payload for concealing secret data in AMBTC compressed medical images but also maintains high image quality and embedding efficiency. This makes it a promising solution for secure data transmission in telemedicine, addressing the challenges of limited bandwidth while enhancing steganographic capabilities in eHealth applications. Full article

(This article belongs to the Special Issue Security and Privacy Challenges in 5G Networks)

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43 pages, 1877 KiB

Open AccessArticle

Construction of General Types of Fuzzy Implications Produced by Comparing Different t-Conorms: An Application Case Using Meteorological Data

by Athina Daniilidou, Avrilia Konguetsof and Basil Papadopoulos

Symmetry 2024, 16(12), 1633; https://doi.org/10.3390/sym16121633 - 9 Dec 2024

Abstract

The objective of this paper is to compare a fuzzy implication produced by t-conorm probor with three other fuzzy implications constructed by t-conorms max, Einstein, and Lukasiewicz. Firstly, in methodology, six pairs of combinations of five t-conorm comparisons are performed in order to [...] Read more.

The objective of this paper is to compare a fuzzy implication produced by t-conorm probor with three other fuzzy implications constructed by t-conorms max, Einstein, and Lukasiewicz. Firstly, in methodology, six pairs of combinations of five t-conorm comparisons are performed in order to find the ranking order of five fuzzy implications. Moreover, the evaluation and calculation of the four fuzzy implications (probor, max, Einstein, and Lukasiewicz) are made using meteorological data, fuzzifying the crisp values of temperature and humidity, constructing four membership degree functions, and inserting as inputs the membership degrees of meteorological variables into the two variables of the fuzzy implications. Finally, extensive tests are made so as to find which membership degree function and which fuzzy implication receives the best and the worst results. The key findings are that the application of isosceles trapezium to the fuzzy implications of Probor and Einstein gives the best values, while fuzzy implication Lukasiewicz, although it was found to be first in the ranking order, is rejected due to unreliable results. As a result, the crucial role of these implications lies in the fact that they are non-symmetrical, i.e., there is a clear difference between the cause and the causal. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Partial Differential Equations)

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17 pages, 3083 KiB

Open AccessArticle

Dynamic Inverse Control of Uncertain Pure Feedback Systems Based on Extended State Observer

by Yuanqing Wang, Wenyao Ma and Guichen Zhang

Symmetry 2024, 16(12), 1632; https://doi.org/10.3390/sym16121632 - 9 Dec 2024

Abstract

A novel, precise disturbance rejection dynamic inversion control algorithm has been proposed. In the high-order dynamic surface control system, an innovative approach utilizes a monotonically increasing inverse hyperbolic sine function to construct an extended state observer, which estimates the uncertain functions at each [...] Read more.

A novel, precise disturbance rejection dynamic inversion control algorithm has been proposed. In the high-order dynamic surface control system, an innovative approach utilizes a monotonically increasing inverse hyperbolic sine function to construct an extended state observer, which estimates the uncertain functions at each step. The monotonicity of the inverse hyperbolic sine function simplifies the system stability analysis. Additionally, being a smooth function, it avoids the disturbances caused by piecewise functions at their breakpoints in conventional observer construction, thereby enhancing system stability. The accurate prediction capability of the new observer improves the system’s disturbance rejection performance. To address the inherent differential explosion phenomenon in traditional dynamic inversion control schemes, this paper ingeniously employs a tracking signal observer as a substitute for traditional filters, thus avoiding the differential explosion that may occur with first-order filters. Finally, comparative simulations were conducted to validate the effectiveness of the proposed method. The results show that both the observer and the controller possess high-gain characteristics, and the closed-loop system exhibits a fast convergence rate. Full article

(This article belongs to the Section Engineering and Materials)

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25 pages, 2726 KiB

Open AccessArticle

HybridGNN: A Self-Supervised Graph Neural Network for Efficient Maximum Matching in Bipartite Graphs

by Chun-Hu Pan, Yi Qu, Yao Yao and Mu-Jiang-Shan Wang

Symmetry 2024, 16(12), 1631; https://doi.org/10.3390/sym16121631 - 9 Dec 2024

Abstract

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of [...] Read more.

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of Graph Attention Networks (GATv2), Graph SAGE (SAGEConv), and Graph Isomorphism Networks (GIN) layers to enhance computational efficiency and model performance. Through extensive ablation experiments, we identify that while the SAGEConv layer demonstrates suboptimal performance in terms of accuracy and F₁-score, configurations incorporating GATv2 and GIN layers show significant improvements. Specifically, in six-layer GNN architectures, the combinations of GATv2 and GIN layers with ratios of 4:2 and 5:1 yield superior accuracy and F₁-score. Therefore, we name these GNN configurations HybridGNN₁ and HybridGNN₂. Additionally, techniques such as mixed precision training, gradient accumulation, and Jumping Knowledge networks are integrated to further optimize performance. Evaluations on an email communication dataset reveal that HybridGNNs outperform traditional algorithms such as the Hopcroft–Karp algorithm, the Hungarian algorithm, and the Blossom/Edmonds’ algorithm, particularly for large and complex graphs. These findings highlight HybridGNN’s robust capability to solve maximum matching problems in bipartite graphs, making it a powerful tool for analyzing large-scale and intricate graph data. Furthermore, our study aligns with the goals of the Symmetry and Asymmetry Study in Graph Theory special issue by exploring the role of symmetry in bipartite graph structures. By leveraging GNNs, we address the challenges related to symmetry and asymmetry in graph properties, thereby improving the reliability and fault tolerance of complex networks. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

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15 pages, 10459 KiB

Open AccessArticle

Identification of Structural Constituents in Advanced Multiphase High-Strength Steels Using Electron Back-Scattered Diffraction

by Aleksandra Kozłowska, Krzysztof Radwański and Adam Grajcar

Symmetry 2024, 16(12), 1630; https://doi.org/10.3390/sym16121630 - 9 Dec 2024

Abstract

This study addresses the characterization of the particular microstructural constituents of multiphase transformation-induced plasticity (TRIP)-aided steels belonging to the first and third generations of Advanced High Strength Steels (AHSS) to explore the possibilities of the EBSD method. Complex microstructures composed of ferrite, bainite, [...] Read more.

This study addresses the characterization of the particular microstructural constituents of multiphase transformation-induced plasticity (TRIP)-aided steels belonging to the first and third generations of Advanced High Strength Steels (AHSS) to explore the possibilities of the EBSD method. Complex microstructures composed of ferrite, bainite, retained austenite and martensite were qualitatively and quantitatively assessed. Microstructural constituents with the same crystal structure were distinguished using characteristic EBSD parameters like confidence index (CI), image quality (IQ), kernel average misorientation (KAM) and specific crystallographic orientation relationships. A detailed linear analysis of the IQ parameter and misorientation angles was also performed. These tools are very helpful in linking different symmetric or asymmetric features of metallic alloys with a type of their structure and morphology details. Two types of samples were investigated: thermomechanically processed and subjected to 10% tensile strain to study the microstructural changes caused by plastic deformation. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

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15 pages, 756 KiB

Open AccessArticle

Relational Extraction from Biomedical Texts with Capsule Network and Hybrid Knowledge Graph Embeddings

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

Symmetry 2024, 16(12), 1629; https://doi.org/10.3390/sym16121629 - 9 Dec 2024

Abstract

In the expanding landscape of biomedical literature, numerous latent associations outlined in scholarly papers await discovery and integration into biomedical databases. Biomedical Natural Language Processing (NLP) research focuses on automating knowledge extraction and mining from this literature, particularly emphasizing the essential task of [...] Read more.

In the expanding landscape of biomedical literature, numerous latent associations outlined in scholarly papers await discovery and integration into biomedical databases. Biomedical Natural Language Processing (NLP) research focuses on automating knowledge extraction and mining from this literature, particularly emphasizing the essential task of Relation Extraction (RE). However, existing models have limitations, mainly in their applicability to partial datasets for RE tasks. Moreover, conventional models often treat RE as a binary classification challenge, which proves suboptimal given the diverse relationships, including intricate ones like similarity and hierarchy, present in the RE dataset. These limitations are exacerbated by the models’ inability to capture word-level positional nuances and sentence-level language features. In response to these challenges, we present a novel RE model called BicapBert. This model integrates neural networks and capsule networks, enhancing them with hybrid knowledge graph embeddings to extract relevant features. BicapBert utilizes PubMedBERT and capsule networks to extract word-level positional and sentence-level language features. It further captures knowledge features from a biomedical knowledge graph, integrating them with the aforementioned linguistic features. The amalgamated information is then input into a multi-layer perceptron, culminating in results derived through a softmax classifier. Experimental evaluations on three extensive RE task datasets showcase the state-of-the-art performance of our proposed model. Additionally, we validate the model’s efficacy on three randomly selected biomedical datasets for various tasks, further affirming its superiority. Full article

(This article belongs to the Section Computer)

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14 pages, 2537 KiB

Open AccessArticle

The Role of Radiation in Mixed Convection Heat Transfer from a Rectangular Fin Heat Sink: Experimental Investigation

by Mahmoud Rasti, Mohammad Hossein Kashefi, Amirreza Shahsavari, Mirae Kim, Wonseop Chung, Kyung Chun Kim and Se Chul Oh

Symmetry 2024, 16(12), 1628; https://doi.org/10.3390/sym16121628 - 8 Dec 2024

Abstract

Nowadays, effective thermal management is essential to prevent overheating in high-power devices. The utilization of high-emissivity materials plays a crucial role in enhancing heat transfer efficiency in both natural and mixed convection systems. This study presents an experimental investigation of a rectangular fin [...] Read more.

Nowadays, effective thermal management is essential to prevent overheating in high-power devices. The utilization of high-emissivity materials plays a crucial role in enhancing heat transfer efficiency in both natural and mixed convection systems. This study presents an experimental investigation of a rectangular fin heat sink’s thermal performance, exploring the effect of mixed convection and radiation heat transfer on two symmetrical fins with an aspect ratio of

S^{*} =

0.4 and 0.8. The experiment was carried out in a laboratory-scale wind tunnel, where the inlet fluid velocity was maintained at a constant value of u = 0.3 m/s across a range of Richardson number (0.6–5) and Rayleigh number (1.09–9.15

\times 10^{5}

), corresponding to the variation of heat loads 18–100 W. High-emissivity paint (ε = 0.85) was applied to the heat sink fins and compared to a low-emissivity paint (ε = 0.05) to assess the effect of performance. The results reveal that the high emissivity fin dissipated heat more effectively, with radiation and convection contributing approximately 25% and 75%, respectively, at the highest Rayleigh number. The study also revealed that increased fin spacing enhanced the view factor, although radiation heat transfer was higher for lower fin spacing due to a greater number of fins. Additionally, fin effectiveness was influenced more by fin spacing compared to surface emissivity, with effectiveness decreasing at higher Rayleigh numbers across all conditions. Infrared (IR) imaging confirmed that the high-emissivity coating allowed the heat sink to dissipate up to 30 °C from the heated surface, underscoring the substantial impact of high-emissivity materials in thermal management applications. Full article

(This article belongs to the Section Mathematics)

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18 pages, 975 KiB

Open AccessArticle

Gain-Scheduled Energy-to-Peak Approach for Vehicle Sideslip Angle Filtering

by Taha Zoulagh, Hicham El Aiss, Fernando Tadeo, Badreddine El Haiek, Karina A. Barbosa and Abdelaziz Hmamed

Symmetry 2024, 16(12), 1627; https://doi.org/10.3390/sym16121627 - 8 Dec 2024

Abstract

The ongoing development of gain-scheduled filters is motivated by the estimation of the sideslip angle of ground vehicles. The present work proposes an approach based on finite-frequency specifications and an energy-to-peak (E2P) index for designing linear parameter-varying (LPV) filters. After reporting a new [...] Read more.

The ongoing development of gain-scheduled filters is motivated by the estimation of the sideslip angle of ground vehicles. The present work proposes an approach based on finite-frequency specifications and an energy-to-peak (E2P) index for designing linear parameter-varying (LPV) filters. After reporting a new theoretical result, analysis and synthesis conditions are proposed for gain-scheduled and robust filters. Their properties are tested and illustrated using a simulated ground vehicle system via a comparative study, highlighting the advantages of the proposed approach. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

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15 pages, 4201 KiB

Open AccessArticle

Precise Authentication Watermarking Algorithm Based on Multiple Sorting Mechanisms for Vector Geographic Data

by Qifei Zhou, Na Ren and Changqing Zhu

Symmetry 2024, 16(12), 1626; https://doi.org/10.3390/sym16121626 - 7 Dec 2024

Abstract

Symmetry-breaking in security mechanisms can create vulnerabilities which attackers may exploit to gain unauthorized access or cause data leakage, ultimately compromising the integrity and security of vector geographic data. How to achieve tamper localization remains a challenging task in the field of data [...] Read more.

Symmetry-breaking in security mechanisms can create vulnerabilities which attackers may exploit to gain unauthorized access or cause data leakage, ultimately compromising the integrity and security of vector geographic data. How to achieve tamper localization remains a challenging task in the field of data authentication research. We propose a precise authentication watermarking algorithm for vector geographic data based on multiple sorting mechanisms. During the watermark embedding process, a sequence of points is initially extracted from the original data, followed by embedding watermarks into each coordinate point. The embedded watermark information consists of the self-identification and ordering information of each coordinate point. Ordering information is crucial for establishing relationships among points and enhancing tamper localization. During the authentication phase, the extracted watermark information is compared with the newly generated watermark information. Self-identification information is used to authenticate addition attacks, while ordering information is used to authenticate deletion attacks. Experimental results demonstrate that the proposed algorithm achieves high precision in detecting and localizing both addition and deletion attacks, significantly outperforming the comparison method. Full article

(This article belongs to the Section Computer)

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31 pages, 7994 KiB

Open AccessArticle

Robustness of the Proxy-SU(3) Symmetry in Atomic Nuclei and the Role of the Next-Highest-Weight Irreducible Representation

by Dennis Bonatsos, Andriana Martinou, Spyridon K. Peroulis, Dimitrios Petrellis, Polytimos Vasileiou, Theodoros J. Mertzimekis and Nikolay Minkov

Symmetry 2024, 16(12), 1625; https://doi.org/10.3390/sym16121625 - 7 Dec 2024

Abstract

The proxy-SU(3) symmetry predicts, in a parameter-free way, the collective deformation variables

β

and

γ

in even–even atomic nuclei away from closed shells based on the highest weight irreducible representations (irreps) of SU(3) in the relevant proton and neutron shells, which are the [...] Read more.

The proxy-SU(3) symmetry predicts, in a parameter-free way, the collective deformation variables

β

and

γ

in even–even atomic nuclei away from closed shells based on the highest weight irreducible representations (irreps) of SU(3) in the relevant proton and neutron shells, which are the most symmetric irreps allowed by the Pauli principle and the short-range nature of the nucleon–nucleon interactions. The special cases in which the use of the next-highest-weight irrep of SU(3) becomes necessary are pointed out, and numerical results are given for several regions of the nuclear chart, which can be used as input for irrep-mixing calculations. Full article

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

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15 pages, 1819 KiB

Open AccessArticle

Kernel Adaptive Filtering Algorithm Based on Hyperbolic Tangent Mixed Error Function

by Yongbing Hu, Chenchong Bi and Yong Chen

Symmetry 2024, 16(12), 1624; https://doi.org/10.3390/sym16121624 - 7 Dec 2024

Abstract

This paper proposes an adaptive filtering algorithm based on the symmetry Kernel Hyperbolic Tangent Mixed Error Criterion (KHTMC), aimed at addressing the identification of nonlinear systems under non-Gaussian noise environments. The algorithm optimizes signal processing by constructing a mixed cost function that combines [...] Read more.

This paper proposes an adaptive filtering algorithm based on the symmetry Kernel Hyperbolic Tangent Mixed Error Criterion (KHTMC), aimed at addressing the identification of nonlinear systems under non-Gaussian noise environments. The algorithm optimizes signal processing by constructing a mixed cost function that combines the symmetry logarithmic square error and the hyperbolic tangent function and integrates it with the kernel adaptive filtering method. Simulation results show that, compared to existing kernel adaptive filtering algorithms, the KHTMC algorithm exhibits significant advantages in terms of convergence speed and steady-state mean square error. It demonstrates strong robustness and tracking performance, especially when dealing with mixed non-Gaussian noise. Therefore, this algorithm shows great potential in signal processing applications under complex noise conditions, offering a more reliable and efficient solution. Full article

(This article belongs to the Section Computer)

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21 pages, 1358 KiB

Open AccessArticle

Differences in the Lateralization of Theta and Alpha Power During n-Back Task Performance Between Older and Young Adults in the Context of the Hemispheric Asymmetry Reduction in Older Adults (HAROLD) Model

by Ludmiła Zając-Lamparska, Emilia Zabielska-Mendyk, Dariusz Zapała and Paweł Augustynowicz

Symmetry 2024, 16(12), 1623; https://doi.org/10.3390/sym16121623 - 7 Dec 2024

Abstract

Hemispheric Asymmetry Reduction in Old Adults (HAROLD) is one of the most well-known models of compensatory brain involvement in older adults. Most evidence supports its occurrence from the perspective of PET and fMRI studies, with a deficiency in electroencephalographic research in this domain. [...] Read more.

Hemispheric Asymmetry Reduction in Old Adults (HAROLD) is one of the most well-known models of compensatory brain involvement in older adults. Most evidence supports its occurrence from the perspective of PET and fMRI studies, with a deficiency in electroencephalographic research in this domain. Therefore, we aimed to investigate the possibility of identifying the HAROLD pattern in older adults’ power of theta and alpha. The study sample comprised 50 older adults and 60 young adults performing n-back tasks while recording EEG signals. The level of cognitive performance and the theta and alpha power for pairs of symmetrical electrodes in the prefrontal, frontal, and parietal areas were analyzed. Older adults exhibited inferior cognitive performance compared to young adults and heightened theta power in the right hemisphere within the prefrontal and parietal areas. However, they also demonstrated increased alpha power in the right frontal pole, which contradicts the compensatory effects of theta power. Moreover, the two indicated phenomena of lateralization of theta and alpha power in older adults were unrelated to individual cognitive performance. The results make it challenging to discern whether the revealed age-related differences in theta and alpha power lateralization denote compensation, dedifferentiation, or nonselective recruitment as neutral features of brain activity in old adults. Full article

(This article belongs to the Special Issue Asymmetry and Symmetry in Cognitive and Clinical Neuropsychology)

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22 pages, 2765 KiB

Open AccessArticle

New Combined Metric for Full-Reference Image Quality Assessment

by Mariusz Frackiewicz, Łukasz Machalica and Henryk Palus

Symmetry 2024, 16(12), 1622; https://doi.org/10.3390/sym16121622 - 7 Dec 2024

Abstract

In recent years, many new metrics highly correlated with the Mean Opinion Score (MOS) have been proposed for assessing image quality through Full-Reference Image Quality Assessment (FR-IQA) methods, such as MDSI, HPSI, and GMSD. Eight of these selected metrics, which compare reference and [...] Read more.

In recent years, many new metrics highly correlated with the Mean Opinion Score (MOS) have been proposed for assessing image quality through Full-Reference Image Quality Assessment (FR-IQA) methods, such as MDSI, HPSI, and GMSD. Eight of these selected metrics, which compare reference and distorted images in a symmetrical manner, are briefly described in this article, and their performance is evaluated using correlation criteria (PLCC, SROCC, and KROCC), as well as RMSE. The aim of this paper is to develop a new, efficient quality index based on a combination of several high-performance metrics already utilized in the field of Image Quality Assessment (IQA). The study was conducted on four benchmark image databases (TID2008, TID2013, KADID-10k, and PIPAL) and identified the three best-performing metrics for each database. The paper introduces a New Combined Metric (NCM), which is a weighted sum of three component metrics, and demonstrates its superiority over each of its component metrics across all the examined databases. An optimization method for determining the weights of the NCM is also presented. Additionally, an alternative version of the combined metric, based on the fastest metrics and employing symmetric calculations for pairs of compared images, is discussed. This version also demonstrates strong performance. Full article

(This article belongs to the Section Computer)

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11 pages, 262 KiB

Open AccessArticle

The Exact Traveling Wave Solutions of a KPP Equation

by Eugene Kogan

Symmetry 2024, 16(12), 1621; https://doi.org/10.3390/sym16121621 - 6 Dec 2024

Abstract

We obtain the exact analytical traveling wave solutions of the Kolmogorov–Petrovskii–Piskunov equation, with the reaction term belonging to the class of functions, which includes that of the (generalized) Fisher equation, for the particular values of the wave’s speed. Additionally we obtain the exact [...] Read more.

We obtain the exact analytical traveling wave solutions of the Kolmogorov–Petrovskii–Piskunov equation, with the reaction term belonging to the class of functions, which includes that of the (generalized) Fisher equation, for the particular values of the wave’s speed. Additionally we obtain the exact analytical traveling wave solutions of the generalized Burgers–Huxley equation. Full article

(This article belongs to the Special Issue Nonlinear Science and Numerical Simulation with Symmetry)

17 pages, 5291 KiB

Open AccessArticle

Dynamic-Aware Network for Moving Object Detection

by Hongrui Zhang, Luxia Yang and Xiaona Du

Symmetry 2024, 16(12), 1620; https://doi.org/10.3390/sym16121620 - 6 Dec 2024

Abstract

Moving object detection (MOD) plays an important role in many applications that aim to identify regions of interest in videos. However, most existing MOD methods ignore the variability brought by time-varying information. Additionally, many network frameworks primarily focus on low-level feature learning, neglecting [...] Read more.

Moving object detection (MOD) plays an important role in many applications that aim to identify regions of interest in videos. However, most existing MOD methods ignore the variability brought by time-varying information. Additionally, many network frameworks primarily focus on low-level feature learning, neglecting the higher-level contextual understanding required for accurate detection. To solve the above issues, we propose a symmetric Dynamic-Aware Network (DAN) for MOD. DAN explores the interactions between different types of information via structural design and feature optimization. To locate the object position quickly, we build a Siamese convolutional network to emphasize changes in the scene. Subsequently, a Change-Aware Module (CAM) is designed, which can maximize the perception of object change cues by exploiting complementary depth-varying features and different levels of disparity information, thereby enhancing the feature discrimination capability of the network. Moreover, to reinforce the effective transfer between features, we devise a Motion-Attentive Selection Module (MASM) to construct an autonomous decoder for augmenting detail representation. Experimental results on benchmark datasets indicate the rationality and validity of the proposed approach. Full article

(This article belongs to the Section Computer)

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20 pages, 1332 KiB

Open AccessArticle

Differential Transform Method (DTM) and Physics-Informed Neural Networks (PINNs) in Solving Integral–Algebraic Equation Systems

by Rafał Brociek and Mariusz Pleszczyński

Symmetry 2024, 16(12), 1619; https://doi.org/10.3390/sym16121619 - 6 Dec 2024

Abstract

Integral–algebraic equations and their systems are a common description of many technical and engineering problems. Often, such models also describe certain dependencies occurring in nature (e.g., ecosystem behaviors). The integral equations occurring in this problem may have two types of domains—symmetric or asymmetric. [...] Read more.

Integral–algebraic equations and their systems are a common description of many technical and engineering problems. Often, such models also describe certain dependencies occurring in nature (e.g., ecosystem behaviors). The integral equations occurring in this problem may have two types of domains—symmetric or asymmetric. Depending on whether such symmetry exists in the system describing a given problem, we must choose the appropriate method to solve this system. In this task, the absence of symmetry is more advantageous, but the presented examples demonstrate how one can approach cases where symmetry is present. In this paper, we present the application of two methods for solving such tasks: the analytical Differential Transform Method (DTM) and Physics-informed Neural Networks (PINNs). We consider a wide class of these types of equation systems, including Volterra and Fredholm integrals (which are also in a single model). We demonstrate that despite the complex nature of the problem, both methods are capable of handling such tasks, and thus, they can be successfully applied to the issues discussed in this article. Full article

(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)

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20 pages, 1327 KiB

Open AccessArticle

Generalization Process of the Integrated Mathematical Model Created for the Development of the Production Geometry of Complicated Surfaces

by Zsuzsa Balajti

Symmetry 2024, 16(12), 1618; https://doi.org/10.3390/sym16121618 - 6 Dec 2024

Abstract

Computer modelling of technical constructions is increasingly carried out using software that includes more detailed knowledge, which requires an increase in the level as well as an expansion of the scope of the geometric knowledge. A significant part of motion transmission mechanisms are [...] Read more.

Computer modelling of technical constructions is increasingly carried out using software that includes more detailed knowledge, which requires an increase in the level as well as an expansion of the scope of the geometric knowledge. A significant part of motion transmission mechanisms are worm drive pairs, for which the separation of the parts dealing with the theoretical and practical problems found in the literature can be experienced in numerous instances. Due to the different technical features, in many cases the helical surfaces are not designed and manufactured in a geometrically correct way, or the best solution is not the compulsory chosen. The geometric model describing the production process of the worm surfaces provides the basis for examining the deviation between the surface mathematically determined by the designer and the surface produced. An integrated mathematical kinematic model was developed for the production geometrical analysis of the elements of cylindrical and conical worm gear drive pairs for machining with a traditional thread grinding machine, which causes a serious pitch fluctuating error among several other problems in the case of machining the conical worm. Modelling of the production process of surfaces and the simultaneous study of the manufacturing errors is basically performed with the toolbox of descriptive geometry, including the use of the projective invariants. Knowing the inheritance of the invariants of projective geometry, the aim was the mathematical generalization of the integrated model and the creation of a projective relationship between the reference surfaces of conical and cylindrical spiral surfaces. As a result, the improved constructive geometric model was created, in which the method of analytically creating the projective geometric relationship between the reference surfaces of conical and cylindrical helicoid surfaces has been described for the first time in this article. This procedure is considered the most important result of the present article. Another significance of the further development presented is that during production of the conical helicoid surface, the thread pitch fluctuation has been eliminated. The results obtained, consisting of an improved geometric model, lead to a new geometry of the technological environment regarding the relative position of the cutting tool and the workpiece as well as the relative motion between them. Full article

(This article belongs to the Section Mathematics)

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