Symmetry

3 pages, 681 KiB

Open AccessEditorial

Recent Progress in Studies of Stability of Numerical Schemes

by Taras I. Lakoba and Sanda Micula

Symmetry 2022, 14(12), 2692; https://doi.org/10.3390/sym14122692 - 19 Dec 2022

Viewed by 1004

Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerical methods for such operator equations is [...] Read more.

Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerical methods for such operator equations is a fundamental property that it is necessary for the method to produce a valid solution. This Special Issue focuses on new theoretical and numerical studies concerning the techniques used for proving stability or instability of numerical schemes, which extend or improve known results. It also includes applications to non-linear physical, chemical, and engineering systems, arising in dynamics of waves, diffusion, or transport problems. Full article

(This article belongs to the Special Issue Recent Progress in Studies of Stability of Numerical Schemes)

14 pages, 1326 KiB

Open AccessArticle

Detecting Compressed Deepfake Images Using Two-Branch Convolutional Networks with Similarity and Classifier

by Ping Chen, Ming Xu and Xiaodong Wang

Symmetry 2022, 14(12), 2691; https://doi.org/10.3390/sym14122691 - 19 Dec 2022

Viewed by 2727

Abstract

As a popular technique for swapping faces with someone else’s in images or videos through deep neural networks, deepfake causes a serious threat to the security of multimedia content today. However, because counterfeit images are usually compressed when propagating over the Internet, and [...] Read more.

As a popular technique for swapping faces with someone else’s in images or videos through deep neural networks, deepfake causes a serious threat to the security of multimedia content today. However, because counterfeit images are usually compressed when propagating over the Internet, and because the compression factor used is unknown, most of the existing deepfake detection models have poor robustness for the detection of compressed images with unknown compression factors. To solve this problem, we notice that an image has a high similarity with its compressed image based on symmetry, and this similarity is not easily affected by the compression factor, so this similarity feature can be used as an important clue for compressed deepfake detection. A TCNSC (Two-branch Convolutional Networks with Similarity and Classifier) method that combines compression factor independence is proposed in this paper. The TCNSC method learns two feature representations from the deepfake image, i.e., similarity of the image and its compressed counterpart and authenticity of the deepfake image. A joint training strategy is then utilized for feature extraction, in which the similarity characteristics are obtained by similarity learning while obtaining authenticity characteristics, so the proposed TCNSC model is trained for robust feature learning. Experimental results on the FaceForensics++ (FF++) dataset show that the proposed method significantly outperforms all competing methods under three compression settings of high-quality (HQ), medium-quality (MQ), and low-quality (LQ). For the LQ, MQ, and HQ settings, TCNSC achieves 91.8%, 93.4%, and 95.3% in accuracy, and outperforms the state-of-art method (Xception-RAW) by 16.9%, 10.1%, and 4.1%, respectively. Full article

(This article belongs to the Special Issue Computer Vision, Pattern Recognition, Machine Learning, and Symmetry)

► Show Figures

Figure 1

14 pages, 5724 KiB

Open AccessArticle

A Method to Design Profiled Cutting Tools for Inner Turning

by Mircea-Viorel Dragoi, Luminita Parv, Adrian Mija and Gheorghe Oancea

Symmetry 2022, 14(12), 2690; https://doi.org/10.3390/sym14122690 - 19 Dec 2022

Viewed by 1472

Abstract

Designing the profile of cutting tools is a specific problem in manufacturing engineering. The profile of the cutting tool has a direct influence on the dimensional and shape precision of the machined parts. When it comes to cutting tools for internal turning, the [...] Read more.

Designing the profile of cutting tools is a specific problem in manufacturing engineering. The profile of the cutting tool has a direct influence on the dimensional and shape precision of the machined parts. When it comes to cutting tools for internal turning, the problem of profile design becomes even more complex, because of the added restrictions the profile and the cutting tool itself are subjected to. Despite its importance and complexity, this problem has been rather poorly considered in the literature. Some side aspects, such as measuring the profile, its wear, and its influence on the part’s geometrical precision have been studied, but not the design process of the profiled shape of cutting edges. This research fills a gap in the literature. It considers profiled cutting tools, in general; and, in particular, investigates tilted cutting edges. The novelty of the present article lies in a method to determine the profile of cutting tools for turning inner-profiled surfaces. The method is CAD-based and provides accurate results. It considers the part’s inner profile, its inner diameter, and the tilting angle of the cutting edge. In addition, possible undercuts are taken into account. The method was validated using two relevant case studies. Despite profiled cutting tools having a certain drawback, which is emphasized in the article, this is balanced by the advantages that their use offers manufacturing. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Industrial Engineering)

► Show Figures

Figure 1

23 pages, 424 KiB

Open AccessFeature PaperArticle

Taking Sides: Asymmetries in the Evolution of Human Brain Development in Better Understanding Autism Spectrum Disorder

by Gerry Leisman, Robert Melillo, Ty Melillo, Calixto Machado, Yanin Machado-Ferrer, Mauricio Chinchilla and Eli Carmeli

Symmetry 2022, 14(12), 2689; https://doi.org/10.3390/sym14122689 - 19 Dec 2022

Cited by 4 | Viewed by 5441

Abstract

Confirmation from structural, functional, and behavioral studies agree and suggest a configuration of atypical lateralization in individuals with autistic spectrum disorders (ASD). It is suggested that patterns of cortical and behavioral atypicality are evident in individuals with ASDs with atypical lateralization being common [...] Read more.

Confirmation from structural, functional, and behavioral studies agree and suggest a configuration of atypical lateralization in individuals with autistic spectrum disorders (ASD). It is suggested that patterns of cortical and behavioral atypicality are evident in individuals with ASDs with atypical lateralization being common in individuals with ASDs. The paper endeavors to better understand the relationship between alterations in typical cortical asymmetries and functional lateralization in ASD in evolutionary terms. We have proposed that both early genetic and/or environmental influences can alter the developmental process of cortical lateralization. There invariably is a “chicken or egg” issue that arises whether atypical cortical anatomy associated with abnormal function, or alternatively whether functional atypicality generates abnormal structure. Full article

(This article belongs to the Special Issue Symmetry and Biology Section: Feature Papers in Neuroscience and Behavior)

13 pages, 5441 KiB

Open AccessFeature PaperArticle

Convective Heat Transfer of a Pseudoplastic Nanosuspension within a Chamber with Two Heated Wall Sections of Various Heat Fluxes

by Darya S. Loenko and Mikhail A. Sheremet

Symmetry 2022, 14(12), 2688; https://doi.org/10.3390/sym14122688 - 19 Dec 2022

Viewed by 1085

Abstract

Cooling of heat-generating elements in different engineering fields is a very important and crucial topic. The present research is devoted to numerical analysis of thermogravitational convection of a pseudoplastic nanosuspension in a chamber with two heated bottom wall sections of various heat fluxes [...] Read more.

Cooling of heat-generating elements in different engineering fields is a very important and crucial topic. The present research is devoted to numerical analysis of thermogravitational convection of a pseudoplastic nanosuspension in a chamber with two heated bottom wall sections of various heat fluxes and isothermally cooling vertical walls. A mathematical model formulated employing the time-dependent Oberbeck–Boussinesq equations with non-primitive variables has been worked out by the finite difference technique. It has been revealed that a mixture of 1% carboxymethylcellulose with water can be the most effective medium to cool the heat-generating elements. At the same time, aluminum oxide nano-sized solid particles have a more essential cooling impact on the heated sections. Full article

(This article belongs to the Special Issue Symmetry: Recent Developments in Engineering Science and Applications)

► Show Figures

Figure 1

19 pages, 2447 KiB

Open AccessArticle

A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application

by Idhia Sriliana, I Nyoman Budiantara and Vita Ratnasari

Symmetry 2022, 14(12), 2687; https://doi.org/10.3390/sym14122687 - 19 Dec 2022

Cited by 3 | Viewed by 1217

Abstract

Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using [...] Read more.

Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using a mixed estimator in nonparametric regression. The objective of this study was to estimate the nonparametric regression curve for longitudinal data using two combined estimators: truncated spline and local linear. The weighted least square method with a two-stage estimation procedure was used to obtain the regression curve estimation of the proposed model. To account for within-subject correlations in the longitudinal data, a symmetric weight matrix was given in the regression curve estimation. The best model was determined by minimizing the generalized cross-validation value. Furthermore, an application to a longitudinal dataset of the poverty gap index in Bengkulu Province, Indonesia, was conducted to illustrate the performance of the proposed mixed estimator. Compared to the single estimator, the truncated spline and local linear mixed estimator had better performance in longitudinal data modeling based on the GCV value. Additionally, the empirical results of the best model indicated that the proposed model could explain the data variation exceptionally well. Full article

► Show Figures

Figure 1

23 pages, 1571 KiB

Open AccessArticle

A Sparsified Densely Connected Network with Separable Convolution for Finger-Vein Recognition

by Qiong Yao, Xiang Xu and Wensheng Li

Symmetry 2022, 14(12), 2686; https://doi.org/10.3390/sym14122686 - 19 Dec 2022

Cited by 2 | Viewed by 1664

Abstract

At present, ResNet and DenseNet have achieved significant performance gains in the field of finger-vein biometric recognition, which is partially attributed to the dominant design of cross-layer skip connection. In this manner, features from multiple layers can be effectively aggregated to provide sufficient [...] Read more.

At present, ResNet and DenseNet have achieved significant performance gains in the field of finger-vein biometric recognition, which is partially attributed to the dominant design of cross-layer skip connection. In this manner, features from multiple layers can be effectively aggregated to provide sufficient discriminant representation. Nevertheless, an over-dense connection pattern may induce channel expansion of feature maps and excessive memory consumption. To address these issues, we proposed a low memory overhead and fairly lightweight network architecture for finger-vein recognition. The core components of the proposed network are a sequence of sparsified densely connected blocks with symmetric structure. In each block, a novel connection cropping strategy is adopted to balance the channel ratio of input/output feature maps. Beyond this, to facilitate smaller model volume and faster convergence, we substitute the standard convolutional kernels with separable convolutional kernels and introduce a robust loss metric that is defined on the geodesic distance of angular space. Our proposed sparsified densely connected network with separable convolution (hereinafter dubbed ‘SC-SDCN’) has been tested on two benchmark finger-vein datasets, including the Multimedia Lab of Chonbuk National University (MMCBNU)and Finger Vein of Universiti Sains Malaysia (FV-USM), and the advantages of our SC-SDCN can be evident from the experimental results. Specifically, an equal error rate (EER) of 0.01% and an accuracy of 99.98% are obtained on the MMCBNU dataset, and an EER of 0.45% and an accuracy of 99.74% are obtained on the FV-USM dataset. Full article

► Show Figures

Figure 1

24 pages, 428 KiB

Open AccessArticle

Soft Expert Symmetric Group and Its Application in MCDM Problem

by Shanmugam Kalaiselvan and Srinivasan Vijayabalaji

Symmetry 2022, 14(12), 2685; https://doi.org/10.3390/sym14122685 - 19 Dec 2022

Cited by 1 | Viewed by 975

Abstract

Researchers are always inspired to broaden their explorations towards uncertainty theories, owing to their great interest and importance. Soft set theory plays a primary role among all recent uncertainty tools. Though this theory sounds good in all aspects, it has its own limitations [...] Read more.

Researchers are always inspired to broaden their explorations towards uncertainty theories, owing to their great interest and importance. Soft set theory plays a primary role among all recent uncertainty tools. Though this theory sounds good in all aspects, it has its own limitations due to a lack of experts. The novel idea of a soft expert set was brought up recently to address this issue. This strategy is innovative and inventive in the sense that it utilizes the expertise of numerous specialists. This novel idea inspired us a lot for the development of the present study. This paper introduces the notion of a soft expert symmetric group as a natural generalization of the symmetric group and soft expert set. Several interesting properties of soft expert symmetric groups are studied. Internal and external products of two soft expert symmetric groups and the homomorphism of soft expert symmetric groups are also presented. The application of a soft expert symmetric group in multi-criteria decision-making situations is also given in a lucid manner. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

26 pages, 9142 KiB

Open AccessReview

Phase Sensitivity Improvement in Correlation-Enhanced Nonlinear Interferometers

by Xinyun Liang, Zhifei Yu, Chun-Hua Yuan, Weiping Zhang and Liqing Chen

Symmetry 2022, 14(12), 2684; https://doi.org/10.3390/sym14122684 - 19 Dec 2022

Cited by 4 | Viewed by 1873

Abstract

Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review [...] Read more.

Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review improvement in phase estimation technologies in correlation-enhanced nonlinear interferometers, including SU(1,1) interferometer and SU(1,1)-SU(2) hybrid interferometer, and so on, and the applications in quantum metrology and quantum sensing networks. Full article

(This article belongs to the Special Issue Quantum Mechanics and Symmetry/Asymmetry: Review Paper on Quantum Nonlinear Interferometers)

► Show Figures

Figure 1

18 pages, 449 KiB

Open AccessArticle

A Simplification and Generalization of Elsayed and Ibrahim’s Two-Dimensional System of Third-Order Difference Equations

by Mensah Folly-Gbetoula and Darlison Nyirenda

Symmetry 2022, 14(12), 2683; https://doi.org/10.3390/sym14122683 - 19 Dec 2022

Viewed by 3250

Abstract

A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give sufficient conditions for the existence of two-periodic and four-periodic solutions in certain cases. Our results generalize [...] Read more.

A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give sufficient conditions for the existence of two-periodic and four-periodic solutions in certain cases. Our results generalize and simplify some work in the literature. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

14 pages, 305 KiB

Open AccessArticle

A Study on the Modified Form of Riemann-Type Fractional Inequalities via Convex Functions and Related Applications

by Muhammad Samraiz, Maria Malik, Kanwal Saeed, Saima Naheed, Sina Etemad, Manuel De la Sen and Shahram Rezapour

Symmetry 2022, 14(12), 2682; https://doi.org/10.3390/sym14122682 - 19 Dec 2022

Cited by 1 | Viewed by 1301

Abstract

In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals of Riemann-type via convex functions. The mean fractional inequalities for functions with convex absolute value derivatives are discovered. Hermite–Hadamard-type fractional inequalities for a symmetric convex [...] Read more.

In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals of Riemann-type via convex functions. The mean fractional inequalities for functions with convex absolute value derivatives are discovered. Hermite–Hadamard-type fractional inequalities for a symmetric convex function are explored. These results are achieved using a fresh and innovative methodology for the modified form of generalized fractional integrals. Some applications for the results explored in the paper are briefly reviewed. Full article

(This article belongs to the Special Issue Mathematical Inequalities, Special Functions and Symmetry)

19 pages, 3480 KiB

Open AccessArticle

Generating Image Captions Using Bahdanau Attention Mechanism and Transfer Learning

by Shahnawaz Ayoub, Yonis Gulzar, Faheem Ahmad Reegu and Sherzod Turaev

Symmetry 2022, 14(12), 2681; https://doi.org/10.3390/sym14122681 - 18 Dec 2022

Cited by 19 | Viewed by 3362

Abstract

Automatic image caption prediction is a challenging task in natural language processing. Most of the researchers have used the convolutional neural network as an encoder and decoder. However, an accurate image caption prediction requires a model to understand the semantic relationship that exists [...] Read more.

Automatic image caption prediction is a challenging task in natural language processing. Most of the researchers have used the convolutional neural network as an encoder and decoder. However, an accurate image caption prediction requires a model to understand the semantic relationship that exists between the various objects present in an image. The attention mechanism performs a linear combination of encoder and decoder states. It emphasizes the semantic information present in the caption with the visual information present in an image. In this paper, we incorporated the Bahdanau attention mechanism with two pre-trained convolutional neural networks—Vector Geometry Group and InceptionV3—to predict the captions of a given image. The two pre-trained models are used as encoders and the Recurrent neural network is used as a decoder. With the help of the attention mechanism, the two encoders are able to provide semantic context information to the decoder and achieve a bilingual evaluation understudy score of 62.5. Our main goal is to compare the performance of the two pre-trained models incorporated with the Bahdanau attention mechanism on the same dataset. Full article

► Show Figures

Figure 1

30 pages, 1054 KiB

Open AccessFeature PaperArticle

Overview of Seniority Isomers

by Bhoomika Maheshwari and Kosuke Nomura

Symmetry 2022, 14(12), 2680; https://doi.org/10.3390/sym14122680 - 18 Dec 2022

Cited by 4 | Viewed by 1516

Abstract

Nuclear isomers are the metastable excited states of nuclei. The isomers can be categorized into a few classes including spin, seniority, K, shape and fission isomers depending upon the hindrance mechanisms. In this paper, we aim to present an overview of seniority [...] Read more.

Nuclear isomers are the metastable excited states of nuclei. The isomers can be categorized into a few classes including spin, seniority, K, shape and fission isomers depending upon the hindrance mechanisms. In this paper, we aim to present an overview of seniority isomers, which is a category related to the seniority quantum number. The discussion is mainly based on the concepts of seniority and generalized seniority. Various aspects of seniority isomers and their whereabouts have been covered along with the situations where seniority mixing prevents the isomerism. Full article

(This article belongs to the Special Issue Selected Papers from Shapes and Symmetries in Nuclei: From Experiment to Theory (SSNET’21 Conference))

► Show Figures

Figure 1

19 pages, 20756 KiB

Open AccessArticle

A Recognition Method of Ancient Architectures Based on the Improved Inception V3 Model

by Xinyang Wang, Jiaxun Li, Jin Tao, Ling Wu, Chao Mou, Weihua Bai, Xiaotian Zheng, Zirui Zhu and Zhuohong Deng

Symmetry 2022, 14(12), 2679; https://doi.org/10.3390/sym14122679 - 18 Dec 2022

Cited by 4 | Viewed by 2441

Abstract

Traditional ancient architecture is a symbolic product of cultural development and inheritance, with high social and cultural value. An automatic recognition model of ancient building types is one possible application of asymmetric systems, and it will be of great significance to be able [...] Read more.

Traditional ancient architecture is a symbolic product of cultural development and inheritance, with high social and cultural value. An automatic recognition model of ancient building types is one possible application of asymmetric systems, and it will be of great significance to be able to identify ancient building types via machine vision. In the context of Chinese traditional ancient buildings, this paper proposes a recognition method of ancient buildings, based on the improved asymmetric Inception V3 model. Firstly, the improved Inception V3 model adds a dropout layer between the global average pooling layer and the SoftMax classification layer to solve the overfitting problem caused by the small sample size of the ancient building data set. Secondly, migration learning and the ImageNet dataset are integrated into model training, which improves the speed of network training while solving the problems of the small scale of the ancient building dataset and insufficient model training. Thirdly, through ablation experiments, the effects of different data preprocessing methods and different dropout rates on the accuracy of model recognition were compared, to obtain the optimized model parameters. To verify the effectiveness of the model, this paper takes the ancient building dataset that was independently constructed by the South China University of Technology team as the experimental data and compares the recognition effect of the improved Inception V3 model proposed in this paper with several classical models. The experimental results show that when the data preprocessing method is based on filling and the dropout rate is 0.3, the recognition accuracy of the model is the highest; the accuracy rate of identifying ancient buildings using our proposed improved Inception V3 model can reach up to 98.64%. Compared with other classical models, the model accuracy rate has increased by 17.32%, and the average training time has accelerated by 2.29 times, reflecting the advantages of the model proposed in this paper. Finally, the improved Inception V3 model was loaded into the ancient building identification system to prove the practical application value of this research. Full article

(This article belongs to the Special Issue Computer Vision, Pattern Recognition, Machine Learning, and Symmetry)

► Show Figures

Figure 1

13 pages, 3622 KiB

Open AccessFeature PaperArticle

Effect of Thermal Treatment of Symmetric TiO₂ Nanotube Arrays in Argon on Photocatalytic CO₂ Conversion

by Timofey Savchuk, Ilya Gavrilin, Andrey Savitskiy, Alexey Dronov, Daria Dronova, Svetlana Pereverzeva, Andrey Tarhanov, Tomasz Maniecki, Sergey Gavrilov and Elizaveta Konstantinova

Symmetry 2022, 14(12), 2678; https://doi.org/10.3390/sym14122678 - 18 Dec 2022

Cited by 2 | Viewed by 1820

Abstract

Symmetric titania nanotube arrays (TiO₂ NTs) are a well-known photocatalyst with a large surface area and band edge potentials suitable for redox reactions. Thermal treatment of symmetrical arrays of TiO₂ nanotubes in argon was used to change the carbon content of [...] Read more.

Symmetric titania nanotube arrays (TiO₂ NTs) are a well-known photocatalyst with a large surface area and band edge potentials suitable for redox reactions. Thermal treatment of symmetrical arrays of TiO₂ nanotubes in argon was used to change the carbon content of the samples. The influence of the carbon content in the structure of symmetrical TiO₂ NTs on their photoelectrochemical properties and photocatalytic activity in the conversion of CO₂ into organic fuel precursors has been studied. The structure, chemical, and phase composition of obtained samples were studied by X-ray analysis, Raman spectroscopy, and SEM with energy dispersive analysis. It is established that carbon-related defects in the samples accumulate electrons on the surface required for the CO₂ conversion reaction. It has been shown for the first time that varying the carbon content in symmetric TiO₂ NTs arrays by annealing at different temperatures in argon makes it possible to control the yield of methane and methanol in CO₂ conversion. It is revealed that too high a concentration of carbon dangling bonds promotes the growth of CO₂ conversion efficiency but causes instability in this process. The obtained results show a high promise of symmetric carbon-doped TiO₂ NTs arrays for the photocatalytic conversion of CO₂. Full article

(This article belongs to the Collection Feature Papers in Chemistry)

► Show Figures

Figure 1

23 pages, 1173 KiB

Open AccessArticle

Exploiting Asymmetric EEG Signals with EFD in Deep Learning Domain for Robust BCI

by Binwen Huang, Haiqin Xu, Miao Yuan, Muhammad Zulkifal Aziz and Xiaojun Yu

Symmetry 2022, 14(12), 2677; https://doi.org/10.3390/sym14122677 - 18 Dec 2022

Cited by 4 | Viewed by 1679

Abstract

Motor imagery (MI) is a domineering paradigm in brain–computer interface (BCI) composition, personifying the imaginary limb motion into digital commandments for neural rehabilitation and automation exertions, while many researchers fathomed myriad solutions for asymmetric MI EEG signals classification, the existence of a robust, [...] Read more.

Motor imagery (MI) is a domineering paradigm in brain–computer interface (BCI) composition, personifying the imaginary limb motion into digital commandments for neural rehabilitation and automation exertions, while many researchers fathomed myriad solutions for asymmetric MI EEG signals classification, the existence of a robust, non-complex, and subject-invariant system is far-reaching. Thereupon, we put forward an MI EEG segregation pipeline in the deep-learning domain in an effort to curtail the existing limitations. Our method amalgamates multiscale principal component analysis (MSPCA), a novel empirical Fourier decomposition (EFD) signal resolution method with Hilbert transform (HT), followed by four pre-trained convolutional neural networks for automatic feature estimation and segregation. The conceived architecture is validated upon three binary class datasets: IVa, IVb from BCI Competition III, GigaDB from the GigaScience repository, and one tertiary class dataset V from BCI competition III. The average 10-fold outcomes capitulate 98.63%, 96.33%, and 89.96%, the highest classification accuracy for the aforesaid datasets accordingly using the AlexNet CNN model in a subject-dependent context, while in subject-independent cases, the highest success score was 97.69%, outperforming the contemporary studies by a fair margin. Further experiments such as the resolution scale of EFD, comparison with other signal decomposition (SD) methods, deep feature extraction, and classification with machine learning methods also accredits the supremacy of our proposed EEG signal processing pipeline. The overall findings imply that pre-trained models are reliable in identifying EEG signals due to their capacity to maintain the time-frequency structure of EEG signals, non-complex architecture, and their potential for robust classification performance. Full article

(This article belongs to the Special Issue Symmetry Applied in EEG and Brain Research: Theory and Applications)

► Show Figures

Figure 1

16 pages, 1405 KiB

Open AccessReview

Skeletal Muscle Stem Cells in Aging: Asymmetric/Symmetric Division Switching

by Emilia Manole, Gisela Gaina, Laura Cristina Ceafalan and Mihail Eugen Hinescu

Symmetry 2022, 14(12), 2676; https://doi.org/10.3390/sym14122676 - 17 Dec 2022

Cited by 2 | Viewed by 2285

Abstract

In aged muscle, satellite cells’ symmetric and asymmetric divisions are impaired, and intrinsic and extrinsic complex mechanisms govern these processes. This review presents many updated aspects regarding muscle stem cells’ fate in normal and aging conditions. The balance between self-renewal and commitment divisions [...] Read more.

In aged muscle, satellite cells’ symmetric and asymmetric divisions are impaired, and intrinsic and extrinsic complex mechanisms govern these processes. This review presents many updated aspects regarding muscle stem cells’ fate in normal and aging conditions. The balance between self-renewal and commitment divisions contributes to muscle regeneration, muscle homeostasis, aging, and disease. Stimulating muscle regeneration in aging could be a therapeutic target, but there is still a need to understand the many mechanisms that influence each other in satellite cells and their niche. We highlight here the general outlines regarding satellite cell divisions, the primary markers present in muscle stem cells, the aging aspects concerning signaling pathways involved in symmetric/asymmetric divisions, the regenerative capacity of satellite cells and their niche alteration in senescent muscle, genetics and epigenetics mechanisms implied in satellite cells aging and exercise effect on muscle regeneration in the elderly. Full article

(This article belongs to the Section Life Sciences)

► Show Figures

Graphical abstract

11 pages, 2393 KiB

Open AccessArticle

Percolative, Multifractal, and Symmetry Properties of the Surface at Nanoscale of Cu-Ni Bimetallic Thin Films Deposited by RF-PECVD

by Robert S. Matos, Nilson S. Ferreira, Ştefan Ţălu, Atefeh Ghaderi, Shahram Solaymani, Marcelo A. Pires, Edgar Aparecido Sanches and Henrique D. da Fonseca Filho

Symmetry 2022, 14(12), 2675; https://doi.org/10.3390/sym14122675 - 17 Dec 2022

Cited by 9 | Viewed by 1220

Abstract

We explored the morphological and 3D spatial properties of Cu/Ni thin films obtained by a co-deposition process. The 3D AFM topographic maps analysis indicated that the films displayed different morphologies and rough profiles dictated by their singular directional inhomogeneities. Moreover, Minkowski’s volume showed [...] Read more.

We explored the morphological and 3D spatial properties of Cu/Ni thin films obtained by a co-deposition process. The 3D AFM topographic maps analysis indicated that the films displayed different morphologies and rough profiles dictated by their singular directional inhomogeneities. Moreover, Minkowski’s volume showed that the Cu/Ni films deposited after 15 and 20 min had a similar relative distribution of matter as a function of height, which is different from the individual Cu films. The Minkowski boundary and connectivity point out that the percolative properties of the Cu/Ni samples were similar to each other. However, they were distinct from the percolative features of the Cu sample. It was also observed that the surface microtexture of the films showed similar spatial complexity, dominant spatial frequencies, and topographical uniformity. For the Cu/Ni thin films, the Minkowski functionals morphological analysis showed that the type of film dictated the surface percolation. In contrast, clear fingerprints of multifractal behavior in all the samples were also observed, indicating that the multifractality degree increased with the sputtering time, supporting the significant vertical growth of the Cu/Ni thin film deposited after 20 min. Aside from that, the results from a symmetry-based approach indicated that the vertical growth dynamics of individual Cu and Cu/Ni thin films were different in terms of scaling symmetry, where we observed that the sputtering induced the formation of less asymmetric topographies regarding their multiscaling behavior. Finally, our findings suggested that the sputtering process can be employed to tune the percolative properties, multifractality, and scaling symmetry of the films, inducing different vertical growth dynamics, which can be useful in the optimization of the fabrication of bimetallic surfaces for technological purposes. Full article

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

► Show Figures

Figure 1

15 pages, 313 KiB

Open AccessArticle

Dynamic Inequalities of Two-Dimensional Hardy Type via Alpha-Conformable Derivatives on Time Scales

by Ahmed A. El-Deeb, Alaa A. El-Bary, Jan Awrejcewicz and Kamsing Nonlaopon

Symmetry 2022, 14(12), 2674; https://doi.org/10.3390/sym14122674 - 17 Dec 2022

Viewed by 883

Abstract

We established some new

α

-conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of

α

-conformable Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions of

α

-conformable calculus. Our [...] Read more.

We established some new

α

-conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of

α

-conformable Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions of

α

-conformable calculus. Our results are proved by using two-dimensional dynamic Jensen’s inequality and Fubini’s theorem on time scales. When

α = 1

, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we derived Hardy’s inequality for

T = R, T = Z

and

T = h Z

. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article

(This article belongs to the Section Mathematics)

7 pages, 5863 KiB

Open AccessArticle

Photonic Topological Insulator Based on Frustrated Total Internal Reflection in Array of Coupled Prism Resonators

by Dmitry P. Fedchenko, Petr N. Kim and Ivan V. Timofeev

Symmetry 2022, 14(12), 2673; https://doi.org/10.3390/sym14122673 - 17 Dec 2022

Cited by 3 | Viewed by 1172

Abstract

Total internal reflection occurs at the interface between two media with different refractive indices during propagation of light rays from a medium with a higher refractive index to a medium with a lower refractive index. If the thickness of the second medium is [...] Read more.

Total internal reflection occurs at the interface between two media with different refractive indices during propagation of light rays from a medium with a higher refractive index to a medium with a lower refractive index. If the thickness of the second medium is comparable to a specific light wavelength, then total internal reflection is violated partially or completely. Based on the frustrated total internal reflection, herein we discuss a two-dimensional photonic topological insulator in an array consisting of triangular, quadrangular, or hexagonal transparent prism resonators with a narrow gap between them. An array of prism resonators allows topologically stable edge solutions (eigenwaves) similar to those studied in ring resonators. Moreover, total internal reflection occurs at different angles of incidence of light. This makes it possible to obtain a set of fundamentally new edge solutions. The light is presumably concentrated at the surface; however, in the new solutions it penetrates relatively deep into the photonic topological insulator and excites several layers of prisms positioned beyond the surface. Remarkably, the direction of light propagation is precisely biased, and therefore new solutions exhibit lower symmetry than the resonator array symmetry. Full article

► Show Figures

Figure 1

12 pages, 330 KiB

Open AccessArticle

Approximation by Operators for the Sheffer–Appell Polynomials

by Mdi Begum Jeelani and Abeer S. Alnahdi

Symmetry 2022, 14(12), 2672; https://doi.org/10.3390/sym14122672 - 17 Dec 2022

Cited by 1 | Viewed by 948

Abstract

In this paper, we introduce a generalization of the Kantrovich–Stancu-type Szasz operator asymmetry with hybrid families of special polynomials. Additionally, we construct certain positive linear operators together with the Sheffer–Appell polynomial sequences and then obtain the properties of convergence and the order of [...] Read more.

In this paper, we introduce a generalization of the Kantrovich–Stancu-type Szasz operator asymmetry with hybrid families of special polynomials. Additionally, we construct certain positive linear operators together with the Sheffer–Appell polynomial sequences and then obtain the properties of convergence and the order of convergence, which is symmetric to these operators. For applications, we consider certain explicit examples including mixed-type special polynomials. Full article

(This article belongs to the Section Mathematics)

12 pages, 361 KiB

Open AccessArticle

Modular Version of Edge Irregularity Strength for Fan and Wheel Graphs

by Debi Oktia Haryeni, Zata Yumni Awanis, Martin Bača and Andrea Semaničová-Feňovčíková

Symmetry 2022, 14(12), 2671; https://doi.org/10.3390/sym14122671 - 16 Dec 2022

Cited by 2 | Viewed by 1333

Abstract

A k-labeling from the vertex set of a simple graph

G = (V, E)

to a set of integers

{1, 2, \dots, k}

is defined to be a modular edge irregular if, for every [...] Read more.

A k-labeling from the vertex set of a simple graph

G = (V, E)

to a set of integers

{1, 2, \dots, k}

is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the remainder of the division of the sum of end vertex labels by modulo

| E (G) |

. The modular edge irregularity strength of a graph is known as the maximal vertex label k, minimized over all modular edge irregular k-labelings of the graph. In this paper we describe labeling schemes with symmetrical distribution of even and odd edge weights and investigate the existence of (modular) edge irregular labelings of joins of paths and cycles with isolated vertices. We estimate the bounds of the (modular) edge irregularity strength for the join graphs

P_{n} + \bar{K_{m}}

and

C_{n} + \bar{K_{m}}

and determine the corresponding exact value of the (modular) edge irregularity strength for some fan graphs and wheel graphs in order to prove the sharpness of the presented bounds. Full article

(This article belongs to the Special Issue Labelings, Colorings and Distances in Graphs)

► Show Figures

Figure 1

9 pages, 419 KiB

Open AccessArticle

On the Constant-Roll Tachyon Inflation with Large and Small η_H

by Qin Fei, Waqas Ahmed and Zhen-Lai Wang

Symmetry 2022, 14(12), 2670; https://doi.org/10.3390/sym14122670 - 16 Dec 2022

Viewed by 968

Abstract

We study the constant-roll tachyon inflation with large and small

η

. In previous studies, only the constant-roll tachyon inflation with small

η

is consistent with the observations. We find that the duality between the constant-roll tachyon inflation with large and small

η

[...] Read more.

We study the constant-roll tachyon inflation with large and small

η

. In previous studies, only the constant-roll tachyon inflation with small

η

is consistent with the observations. We find that the duality between the constant-roll tachyon inflation with large and small

η

may exist. The apparent duality suggests that the constant-roll tachyon inflationary model with large

η

may also be consistent with the observations. By fitting the spectral tilde

n_{s}

and tensor to scalar ratio r, which is a measure of primordial gravitational waves with the observations, we get small and large

η

in this range

- 0.01629 \leq η_{H} \leq - 0.00079

and

3.00081 \leq η_{H} \leq 3.01621

at the 2

σ

C.L for

N = 60

efolds. Full article

(This article belongs to the Special Issue Symmetry in Inflationary Cosmology)

► Show Figures

Figure 1

25 pages, 387 KiB

Open AccessArticle

Some Enhanced Distance Measuring Approaches Based on Pythagorean Fuzzy Information with Applications in Decision Making

by Keke Wu, Paul Augustine Ejegwa, Yuming Feng, Idoko Charles Onyeke, Samuel Ebimobowei Johnny and Sesugh Ahemen

Symmetry 2022, 14(12), 2669; https://doi.org/10.3390/sym14122669 - 16 Dec 2022

Cited by 7 | Viewed by 1202

Abstract

The construct of Pythagorean fuzzy distance measure (PFDM) is a competent measuring tool to curb incomplete information often encountered in decision making. PFDM possesses a wider scope of applications than distance measure under intuitionistic fuzzy information. Some Pythagorean fuzzy distance measure approaches (PFDMAs) [...] Read more.

The construct of Pythagorean fuzzy distance measure (PFDM) is a competent measuring tool to curb incomplete information often encountered in decision making. PFDM possesses a wider scope of applications than distance measure under intuitionistic fuzzy information. Some Pythagorean fuzzy distance measure approaches (PFDMAs) have been developed and applied in decision making, albeit with some setbacks in terms of accuracy and precision. In this paper, some novel PFDMAs are developed with better accuracy and reliability rates compared to the already developed PFDMAs. In an effort to validate the novel PFDMAs, some of their properties are discussed in terms of theorems with proofs. In addition, some applications of the novel PFDMAs in problems of disease diagnosis and pattern recognition are discussed. Furthermore, we present comparative studies of the novel PFDMAs in conjunction to the existing PFDMAs to buttress the merit of the novel approaches in terms of consistency and precision. To end with, some new Pythagorean fuzzy similarity measuring approaches (PFDSAs) based on the novel PFDMAs are presented and applied to solve the problems of disease diagnosis and pattern recognition as well. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

17 pages, 2383 KiB

Open AccessArticle

Firewall Anomaly Detection Based on Double Decision Tree

by Zhiming Lin and Zhiqiang Yao

Symmetry 2022, 14(12), 2668; https://doi.org/10.3390/sym14122668 - 16 Dec 2022

Cited by 1 | Viewed by 1676

Abstract

To solve the problems regarding how to detect anomalous rules with an asymmetric structure, which leads to the firewall not being able to control the packets in and out according to the administrator’s idea, and how to carry out an incremental detection efficiently [...] Read more.

To solve the problems regarding how to detect anomalous rules with an asymmetric structure, which leads to the firewall not being able to control the packets in and out according to the administrator’s idea, and how to carry out an incremental detection efficiently when the new rules are added, anomaly detection algorithms based on an asymmetric double decision tree were considered. We considered the packet filter, the most common and used type of First Matching Rule, for the practical decision space of each rule and the whole policy. We adopted, based on the asymmetric double decision tree detection model, the policy equivalent decision tree and the policy decision tree of anomalies. Therefore, we can separate the policy’s effective decision space and the anomalous decision space. Using the separated decision trees can realize the optimization of the original policy and the faster incremental detection when adding new rules and generating a detailed report. The simulation results demonstrate that the proposed algorithms are superior to the other decision tree algorithms in detection speed and can achieve incremental detection. The results demonstrate that our approach can save about 33% of the time for complete detection compared with the other approaches, and the time of incremental anomaly detection compared to complete detection is about 90% of the time saved in a complex policy. Full article

(This article belongs to the Special Issue Advances in Internet of Things with Symmetric/Asymmetric Structure, Computing and Interaction)

► Show Figures

Figure 1

16 pages, 1807 KiB

Open AccessArticle

New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS

by Zahra Eidinejad, Reza Saadati, Radko Mesiar and Chenkuan Li

Symmetry 2022, 14(12), 2667; https://doi.org/10.3390/sym14122667 - 16 Dec 2022

Cited by 1 | Viewed by 1080

Abstract

By using a class of aggregation control functions, we introduce the concept of multiple-HU-

O S_{1}

-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We apply an alternative fixed-point theorem to prove [...] Read more.

By using a class of aggregation control functions, we introduce the concept of multiple-HU-

O S_{1}

-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We apply an alternative fixed-point theorem to prove the existence of a unique solution and the multiple-HU-

O S_{1}

-stability for the NS-ABC-FDE in the symmetric matrix-valued FBS. Finally, with an example, we show the application of the obtained results. Full article

(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points)

► Show Figures

Figure 1

17 pages, 1732 KiB

Open AccessArticle

Simultaneous Confidence Intervals for All Pairwise Differences between the Coefficients of Variation of Multiple Birnbaum–Saunders Distributions

by Wisunee Puggard, Sa-Aat Niwitpong and Suparat Niwitpong

Symmetry 2022, 14(12), 2666; https://doi.org/10.3390/sym14122666 - 16 Dec 2022

Cited by 1 | Viewed by 966

Abstract

In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and [...] Read more.

In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5

μ

m (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)

► Show Figures

Figure 1

5 pages, 273 KiB

Open AccessEditorial

Special Issue of Symmetry: “Symmetry in Mathematical Analysis and Functional Analysis”

by Octav Olteanu

Symmetry 2022, 14(12), 2665; https://doi.org/10.3390/sym14122665 - 16 Dec 2022

Viewed by 797

Abstract

This Special Issue consists of 11 papers recently published in MDPI’s journal Symmetry under the general thematic title “Symmetry in Mathematical Analysis and Functional Analysis” (see [...] Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis)

14 pages, 15762 KiB

Open AccessArticle

Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations

by Pengfei Li, Yanzhu Wei, Boris A. Malomed and Dumitru Mihalache

Symmetry 2022, 14(12), 2664; https://doi.org/10.3390/sym14122664 - 16 Dec 2022

Cited by 3 | Viewed by 1429

Abstract

The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values

1 \leq α \leq 2

. [...] Read more.

The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values

1 \leq α \leq 2

. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Management is included by making the diffraction and/or nonlinearity coefficients periodic functions of the propagation distance,

ζ

. The management format with the nonlinearity coefficient decaying as

1 / ζ

is considered too. These management schemes maintain stable propagation of the ring-Airy beams, which maintain their axial symmetry, in contrast to the symmetry-breaking splitting instability of ring-shaped patterns in 2D Kerr media. The instability driven by supercritical collapse at all values

α < 2

in the presence of the self-focusing cubic term is eliminated, too, by the means of management. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)

► Show Figures

Figure 1

17 pages, 654 KiB

Open AccessArticle

Explicitly Modeling Stress Softening and Thermal Recovery for Rubber-like Materials

by Xiaoming Wang, Heng Xiao and Shengliang Lu

Symmetry 2022, 14(12), 2663; https://doi.org/10.3390/sym14122663 - 16 Dec 2022

Viewed by 1076

Abstract

Rubber-like materials exhibit stress softening when subject to loading–unloading cycles, i.e., the Mullins effect. However, this phenomenon can be recovered after annealing the previously stretched sample under a stress-free state. The aim of this paper is to establish a constitutive model with thermodynamic [...] Read more.

Rubber-like materials exhibit stress softening when subject to loading–unloading cycles, i.e., the Mullins effect. However, this phenomenon can be recovered after annealing the previously stretched sample under a stress-free state. The aim of this paper is to establish a constitutive model with thermodynamic consistency to account for the stress softening and thermal recovery. Towards this goal, (i) an explicit form of Helmholtz free energy can be found such that the restrictions from thermodynamic law can be satisfied; (ii) a compressible, multi-axial strain-energy function considering energy dissipation is proposed by introducing specific invariants; (iii) a unified shape function based on the symmetry property of the test data in a one-dimensional case with stress softening and thermal recovery is provided by introducing a weight variant; (iv) it is proven that the new potential can automatically reduce to the one-dimensional case, i.e., uniaxial tension, equal biaxial, or plane strain; (v) numerical results for model validation are exactly matched with classical experimental data. Full article

(This article belongs to the Special Issue Advances in Materials Science with Symmetry/Asymmetry)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry, Volume 14, Issue 12 (December 2022) – 222 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI