Symmetry

21 pages, 746 KiB

Open AccessArticle

Probabilistic Hesitant Intuitionistic Fuzzy Linguistic Term Sets and Their Application in Multiple Attribute Group Decision Making

by You Peng, Yifang Tao, Boyi Wu and Xiaoxin Wang

Symmetry 2020, 12(11), 1932; https://doi.org/10.3390/sym12111932 - 23 Nov 2020

Cited by 10 | Viewed by 1865

Abstract

Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic [...] Read more.

Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic terms rather than concrete numerical values. Thus, several linguistic models, such as the fuzzy linguistic approach (FLA), hesitant fuzzy linguistic term sets (HFLTSs), hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), and probabilistic linguistic term sets (PLTS) have been proposed successively. Due to the flexibility and comprehensiveness of PLTS, it has aroused growing concern. However, it also has a big limitation of requiring the membership degree to be 1 by default, and it does not consider the degree of non-membership and hesitancy of a linguistic variable. Therefore, the probabilistic hesitant intuitionistic fuzzy linguistic term sets (PHIFLTSs) have been presented to extend the PLTS by combining the membership and non-membership in symmetry to depict the evaluation of the experts. To overcome the existing shortcomings and enrich the methodology framework of PHIFLTSs, some novel operational laws are defined to extend the applicability and methodology of the PHIFLTSs in MAGDM. Furthermore, the distance and correlation measures for the PHIFLTSs are improved to make up the shortage of the current distance measures. In addition, the unbalanced linguistic terms are taken into account to represent the cognitive complex information of experts. At last, a MAGDM model based on the multiplicative multi-objective optimization by ratio analysis (MULTIMOORA) approach with the use of the developed novel operational laws and correlation measures is presented, which results in more accuracy and effectiveness. A real-word application example is presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison is done with related existing works in order to show the validity of this methodology. Full article

(This article belongs to the Section Mathematics)

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19 pages, 2473 KiB

Open AccessArticle

Cyber Attack Prevention Based on Evolutionary Cybernetics Approach

by Dmitry Zegzhda, Daria Lavrova, Evgeny Pavlenko and Anna Shtyrkina

Symmetry 2020, 12(11), 1931; https://doi.org/10.3390/sym12111931 - 23 Nov 2020

Cited by 17 | Viewed by 4215

Abstract

The paper looks at the problem of cybersecurity in modern cyber–physical systems and proposes an evolutionary model approach to counteract cyber attacks by self-regulating the structure of the system, as well as several evolutionary indicators to assess the state of the system. The [...] Read more.

The paper looks at the problem of cybersecurity in modern cyber–physical systems and proposes an evolutionary model approach to counteract cyber attacks by self-regulating the structure of the system, as well as several evolutionary indicators to assess the state of the system. The application of evolutionary models makes it possible to describe the regularities of systems behavior and their technical development, which is especially important regarding cyber attacks, which are the cause of a discontinuous evolution of complex systems. A practical example describes a system behavior during attacks and the self-regulation of its structure. The methodological approach consists of using evolutionary models to describe how modern cyber–physical systems can counteract cyber attacks and evolve, building on the experience of past security incidents. The main conclusions and recommendations are presented in the Discussion section, and they consist of the fact that using an evolutionary approach will not only increase the security of cyber–physical systems, but also define the principles of building systems that are resistant to cyber attacks. Full article

(This article belongs to the Section Computer)

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17 pages, 1954 KiB

Open AccessArticle

Evolving Hierarchical and Tag Information via the Deeply Enhanced Weighted Non-Negative Matrix Factorization of Rating Predictions

by Alpamis Kutlimuratov, Akmalbek Abdusalomov and Taeg Keun Whangbo

Symmetry 2020, 12(11), 1930; https://doi.org/10.3390/sym12111930 - 23 Nov 2020

Cited by 17 | Viewed by 2337

Abstract

Identifying the hidden features of items and users of a modern recommendation system, wherein features are represented as hierarchical structures, allows us to understand the association between the two entities. Moreover, when tag information that is added to items by users themselves is [...] Read more.

Identifying the hidden features of items and users of a modern recommendation system, wherein features are represented as hierarchical structures, allows us to understand the association between the two entities. Moreover, when tag information that is added to items by users themselves is coupled with hierarchically structured features, the rating prediction efficiency and system personalization are improved. To this effect, we developed a novel model that acquires hidden-level hierarchical features of users and items and combines them with the tag information of items that regularizes the matrix factorization process of a basic weighted non-negative matrix factorization (WNMF) model to complete our prediction model. The idea behind the proposed approach was to deeply factorize a basic WNMF model to obtain hidden hierarchical features of user’s preferences and item characteristics that reveal a deep relationship between them by regularizing the process with tag information as an auxiliary parameter. Experiments were conducted on the MovieLens 100K dataset, and the empirical results confirmed the potential of the proposed approach and its superiority over models that use the primary features of users and items or tag information separately in the prediction process. Full article

(This article belongs to the Special Issue Recent Advances in Social Data and Artificial Intelligence 2019)

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11 pages, 284 KiB

Open AccessArticle

Total Domination in Rooted Product Graphs

by Abel Cabrera Martínez and Juan A. Rodríguez-Velázquez

Symmetry 2020, 12(11), 1929; https://doi.org/10.3390/sym12111929 - 23 Nov 2020

Cited by 7 | Viewed by 2446

Abstract

During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 [...] Read more.

During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 published papers, and 50 of them concern the case of product graphs. However, none of these papers discusses the case of rooted product graphs. Precisely, the present paper covers this gap in the theory. Our goal is to provide closed formulas for the total domination number of rooted product graphs. In particular, we show that there are four possible expressions for the total domination number of a rooted product graph, and we characterize the graphs reaching these expressions. Full article

(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics)

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25 pages, 10570 KiB

Open AccessArticle

Automated Sustainable Multi-Object Segmentation and Recognition via Modified Sampling Consensus and Kernel Sliding Perceptron

by Adnan Ahmed Rafique, Ahmad Jalal and Kibum Kim

Symmetry 2020, 12(11), 1928; https://doi.org/10.3390/sym12111928 - 23 Nov 2020

Cited by 57 | Viewed by 2645

Abstract

Object recognition in depth images is challenging and persistent task in machine vision, robotics, and automation of sustainability. Object recognition tasks are a challenging part of various multimedia technologies for video surveillance, human–computer interaction, robotic navigation, drone targeting, tourist guidance, and medical diagnostics. [...] Read more.

Object recognition in depth images is challenging and persistent task in machine vision, robotics, and automation of sustainability. Object recognition tasks are a challenging part of various multimedia technologies for video surveillance, human–computer interaction, robotic navigation, drone targeting, tourist guidance, and medical diagnostics. However, the symmetry that exists in real-world objects plays a significant role in perception and recognition of objects in both humans and machines. With advances in depth sensor technology, numerous researchers have recently proposed RGB-D object recognition techniques. In this paper, we introduce a sustainable object recognition framework that is consistent despite any change in the environment, and can recognize and analyze RGB-D objects in complex indoor scenarios. Firstly, after acquiring a depth image, the point cloud and the depth maps are extracted to obtain the planes. Then, the plane fitting model and the proposed modified maximum likelihood estimation sampling consensus (MMLESAC) are applied as a segmentation process. Then, depth kernel descriptors (DKDES) over segmented objects are computed for single and multiple object scenarios separately. These DKDES are subsequently carried forward to isometric mapping (IsoMap) for feature space reduction. Finally, the reduced feature vector is forwarded to a kernel sliding perceptron (KSP) for the recognition of objects. Three datasets are used to evaluate four different experiments by employing a cross-validation scheme to validate the proposed model. The experimental results over RGB-D object, RGB-D scene, and NYUDv1 datasets demonstrate overall accuracies of 92.2%, 88.5%, and 90.5% respectively. These results outperform existing state-of-the-art methods and verify the suitability of the method. Full article

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8 pages, 740 KiB

Open AccessArticle

Exploring Finite-Sized Scale Invariance in Stochastic Variability with Toy Models: The Ornstein–Uhlenbeck Model

by Nachiketa Chakraborty

Symmetry 2020, 12(11), 1927; https://doi.org/10.3390/sym12111927 - 23 Nov 2020

Viewed by 2139

Abstract

Stochastic variability is ubiquitous among astrophysical sources. Quantifying stochastic properties of observed time-series or lightcurves, can provide insights into the underlying physical mechanisms driving variability, especially those of the particles that radiate the observed emission. Toy models mimicking cosmic ray transport are particularly [...] Read more.

Stochastic variability is ubiquitous among astrophysical sources. Quantifying stochastic properties of observed time-series or lightcurves, can provide insights into the underlying physical mechanisms driving variability, especially those of the particles that radiate the observed emission. Toy models mimicking cosmic ray transport are particularly useful in providing a means of linking the statistical analyses of observed lightcurves to the physical properties and parameters. Here, we explore a very commonly observed feature; finite sized self-similarity or scale invariance which is a fundamental property of complex, dynamical systems. This is important to the general theme of physics and symmetry. We investigate it through the probability density function of time-varying fluxes arising from a Ornstein–Uhlenbeck Model, as this model provides an excellent description of several time-domain observations of sources like active galactic nuclei. The probability density function approach stems directly from the mathematical definition of self-similarity and is nonparametric. We show that the OU model provides an intuitive description of scale-limited self-similarity and stationary Gaussian distribution while potentially showing a way to link to the underlying cosmic ray transport. This finite size of the scale invariance depends upon the decay time in the OU model. Full article

(This article belongs to the Special Issue Cosmic Rays)

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17 pages, 4421 KiB

Open AccessArticle

Interaction Patterns for Staggered Assembly of Fibrils from Semiflexible Chains

by Arnoud Jongeling, Carsten Svaneborg and Renko de Vries

Symmetry 2020, 12(11), 1926; https://doi.org/10.3390/sym12111926 - 23 Nov 2020

Viewed by 2061

Abstract

The design of colloidal interactions to achieve target self-assembled structures has especially been done for compact objects such as spheres with isotropic interaction potentials, patchy spheres and other compact objects with patchy interactions. Inspired by the self-assembly of collagen-I fibrils and intermediate filaments, [...] Read more.

The design of colloidal interactions to achieve target self-assembled structures has especially been done for compact objects such as spheres with isotropic interaction potentials, patchy spheres and other compact objects with patchy interactions. Inspired by the self-assembly of collagen-I fibrils and intermediate filaments, we here consider the design of interaction patterns on semiflexible chains that could drive their staggered assembly into regular (para)crystalline fibrils. We consider semiflexible chains composed of a finite number of types of interaction beads (uncharged hydrophilic, hydrophobic, positively charged and negatively charged) and optimize the sequence of these interaction beads with respect to the interaction energy of the semiflexible chains in a number of target-staggered crystalline packings. We find that structures with the lowest interaction energies, that form simple lattices, also have low values of L/D (where L is chain length and D is stagger). In the low interaction energy sequences, similar types of interaction beads cluster together to form stretches. Langevin Dynamics simulations confirm that semiflexible chains with optimal sequences self-assemble into the designed staggered (para)crystalline fibrils. We conclude that very simple interaction patterns should suffice to drive the assembly of long semiflexible chains into staggered (para)crystalline fibrils. Full article

(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)

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Graphical abstract

26 pages, 5513 KiB

Open AccessArticle

Symmetry/Asymmetry of the NHN Hydrogen Bond in Protonated 1,8-Bis(dimethylamino)naphthalene

by Patrycja Piękoś, Aneta Jezierska, Jarosław J. Panek, Eugene A. Goremychkin, Alexander F. Pozharskii, Alexander S. Antonov, Peter M. Tolstoy and Aleksander Filarowski

Symmetry 2020, 12(11), 1924; https://doi.org/10.3390/sym12111924 - 23 Nov 2020

Cited by 8 | Viewed by 3148

Abstract

Experimental and theoretical results are presented based on vibrational spectra and motional dynamics of 1,8-bis(dimethylamino)naphthalene (DMAN) and its protonated forms (DMANH⁺ and the DMANH⁺ HSO₄⁻ complex). The studies of these compounds have been performed in the gas phase and [...] Read more.

Experimental and theoretical results are presented based on vibrational spectra and motional dynamics of 1,8-bis(dimethylamino)naphthalene (DMAN) and its protonated forms (DMANH⁺ and the DMANH⁺ HSO₄⁻ complex). The studies of these compounds have been performed in the gas phase and solid-state. Spectroscopic investigations were carried out by infrared spectroscopy (IR), Raman, and incoherent inelastic neutron scattering (IINS) experimental methods. Density functional theory (DFT) and Car–Parrinello molecular dynamics (CPMD) methods were applied to support our experimental findings. The fundamental investigations of hydrogen bridge vibrations were accomplished on the basis of isotopic substitutions (NH → ND). Special attention was paid to the bridged proton dynamics in the DMANH⁺ complex, which was found to be affected by interactions with the HSO₄⁻ anion. Full article

(This article belongs to the Special Issue Quantum Chemistry)

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14 pages, 303 KiB

Open AccessArticle

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

by Ali Yousef, Emad E. H. Hassan, Ayman A. Amin and Hosny I. Hamdy

Symmetry 2020, 12(11), 1925; https://doi.org/10.3390/sym12111925 - 22 Nov 2020

Cited by 5 | Viewed by 2050

Abstract

This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal [...] Read more.

This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation. Full article

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

20 pages, 4511 KiB

Open AccessArticle

Performance Evaluation of Keyword Extraction Methods and Visualization for Student Online Comments

by Feng Liu, Xiaodi Huang, Weidong Huang and Sophia Xiaoxia Duan

Symmetry 2020, 12(11), 1923; https://doi.org/10.3390/sym12111923 - 22 Nov 2020

Cited by 10 | Viewed by 5969

Abstract

Topic keyword extraction (as a typical task in information retrieval) refers to extracting the core keywords from document topics. In an online environment, students often post comments in subject forums. The automatic and accurate extraction of keywords from these comments are beneficial to [...] Read more.

Topic keyword extraction (as a typical task in information retrieval) refers to extracting the core keywords from document topics. In an online environment, students often post comments in subject forums. The automatic and accurate extraction of keywords from these comments are beneficial to lecturers (particular when it comes to repeatedly delivered subjects). In this paper, we compare the performance of traditional machine learning algorithms and two deep learning methods in extracting topic keywords from student comments posted in subject forums. For this purpose, we collected student comment data from a period of two years, manually tagging part of the raw data for our experiments. Based on this dataset, we comprehensively compared the five typical algorithms of naïve Bayes, logistic regression, support vector machine, convolutional neural networks, and Long Short-Term Memory with Attention (Att-LSTM). The performances were measured by the four evaluation metrics. We further examined the keywords by visualization. From the results of our experiment and visualization, we conclude that the Att-LSTM method is the best approach for topic keyword extraction from student comments. Further, the results from the algorithms and visualization are symmetry, to some degree. In particular, the extracted topics from the comments posted at the same stages of different teaching sessions are, almost, reflection symmetry. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Communications Engineering)

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14 pages, 487 KiB

Open AccessArticle

The Coulomb Symmetry and a Universal Representation of Rydberg Spectral Line Shapes in Magnetized Plasmas

by Andrei Letunov and Valery Lisitsa

Symmetry 2020, 12(11), 1922; https://doi.org/10.3390/sym12111922 - 21 Nov 2020

Cited by 2 | Viewed by 2184

Abstract

A new method of line shape calculations of hydrogen-like atoms in magnetized plasmas is presented. This algorithm makes it possible to solve two fundamental problems in the broadening theory: the analytical description of the radiation transition array between excited atomic states and an [...] Read more.

A new method of line shape calculations of hydrogen-like atoms in magnetized plasmas is presented. This algorithm makes it possible to solve two fundamental problems in the broadening theory: the analytical description of the radiation transition array between excited atomic states and an account of a thermal ion motion effect on the line shapes formation. The solution to the first problem is based on the semiclassical approach to dipole matrix elements calculations and the usage of the specific symmetry properties of the Coulomb field. The second one is considered in terms of the kinetic treatment of the frequency fluctuation model (FFM). As the result, one has a universal description of line shapes under the action of the dynamic of ion’s microfield. The final line shape is obtained by the convolution of the ionic line shape with the Voigt electron Doppler profile. The method is applicable formally for large values of principal quantum numbers. However, the efficiency of the results is demonstrated even for well known first members of the hydrogen Balmer series

D_{α}

and

D_{β}

lines. The comparison of obtained results with accurate quantum calculations is presented. The new method may be of interest for investigations of spectral line shapes of hydrogen-like ions presented in different kinds of hot ionized environments with the presence of a magnetic field, including So L and divertor tokamak plasmas. Full article

(This article belongs to the Special Issue New Trends in Plasma Physics)

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18 pages, 2101 KiB

Open AccessArticle

Ontology-Based Decision Support Tool for Automatic Sleep Staging Using Dual-Channel EEG Data

by Bingtao Zhang, Zhifei Yang, Hanshu Cai, Jing Lian, Wenwen Chang and Zhonglin Zhang

Symmetry 2020, 12(11), 1921; https://doi.org/10.3390/sym12111921 - 21 Nov 2020

Cited by 3 | Viewed by 2233

Abstract

Sleep staging has attracted significant attention as a critical step in auxiliary diagnosis of sleep disease. To avoid subjectivity of doctor’s manual sleep staging, and to realize scientific management of massive physiological data, an ontology-based decision support tool is proposed. The tool implements [...] Read more.

Sleep staging has attracted significant attention as a critical step in auxiliary diagnosis of sleep disease. To avoid subjectivity of doctor’s manual sleep staging, and to realize scientific management of massive physiological data, an ontology-based decision support tool is proposed. The tool implements an automated procedure for sleep staging using dual-channel electroencephalogram (EEG) signals. First of all, it encodes EEG features, sleep-related concepts and other contextual information to “EEG-Sleep ontology”. Secondly, a rule-set is constructed based on a data mining technique. Finally, the first two steps are processed in a reasoning engine which is automatically assign each 30 s epoch (segment) sleep stage to one of five possible sleep stages: WA, NREM1, NREM2, SWS and REM. The rule set is obtained using EEG data taken from the Sleep-EDF database [EXPANDED] according to the random forest algorithm (RF), we prove that the performance of the proposed method with 89.12% accuracy, and 0.81 Kappa statistics is superior to other algorithms such as Bayesian network, C4.5, support vector machine, and multilayer perceptron. Additionally, our proposed approach improved performance when compared to other studies using a small subset of the Sleep-EDF database [EXPANDED]. Full article

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18 pages, 4130 KiB

Open AccessArticle

Multi-Parameter Optimization of an InP Electro-Optic Modulator

by Mikhail Stepanenko, Igor Yunusov, Vadim Arykov, Pavel Troyan and Yury Zhidik

Symmetry 2020, 12(11), 1920; https://doi.org/10.3390/sym12111920 - 21 Nov 2020

Cited by 10 | Viewed by 3306

Abstract

In this article, a method for indium phosphide (InP) electro-optic modulator (EOM) optimization is introduced. The method can be used for the design and analysis of an EOM based on the Mach-Zehnder interferometer (MZI) design. This design is based on the division of [...] Read more.

In this article, a method for indium phosphide (InP) electro-optic modulator (EOM) optimization is introduced. The method can be used for the design and analysis of an EOM based on the Mach-Zehnder interferometer (MZI) design. This design is based on the division of the input optical signal into two optical paths and then, after processing, it combines the light into a single waveguide. The symmetry of the structure can provide state-of-the-art EOM characteristics with a push-pull control signal. Using a traveling wave electrode (TWE) design as a starting point, the authors varied the heterostructure design and optical waveguide parameters to obtain the optimal values of initial optical loss, evenness of the initial optical loss in the operating wavelength range, and the extinction ratio and length of the modulator arm. The key features of the proposed optimization method include the following: all independent input parameters are linked into a single system, where the relationship between the electrical and optical parameters of the modulator is realized; all physically realizable combinations of the input parameters are available for analysis; and EOM optimization is possible for one target parameter or for a group of target parameters. The results of the EOM optimization using the described method are presented. Full article

(This article belongs to the Section Computer)

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20 pages, 5672 KiB

Open AccessArticle

Quasi-Delay-Insensitive Implementation of Approximate Addition

by Padmanabhan Balasubramanian and Nikos E. Mastorakis

Symmetry 2020, 12(11), 1919; https://doi.org/10.3390/sym12111919 - 20 Nov 2020

Cited by 1 | Viewed by 2988

Abstract

Asynchronous quasi-delay-insensitive (QDI) implementation of approximate addition is described in this article. The objective is to provide an insight into the optimization in design metrics that can be achieved with approximate addition compared to accurate addition based on a QDI implementation by considering [...] Read more.

Asynchronous quasi-delay-insensitive (QDI) implementation of approximate addition is described in this article. The objective is to provide an insight into the optimization in design metrics that can be achieved with approximate addition compared to accurate addition based on a QDI implementation by considering a practical digital image processing application. For the QDI implementation, some approximate adder architectures are considered which are deemed suitable for both ASIC and FPGA based implementations. The accurate and approximate adders considered are of size 32-bits. The delay-insensitive dual-rail code was used for data encoding, and four-phase return-to-zero (RTZ) and return-to-one (RTO) handshake protocols were used separately for data communication. The implementations used a 32/28-nm complementary metal oxide semiconductor (CMOS) technology. The simulation results show that an approximate adder HOERAA achieves a 19.7% reduction in cycle time, a 12.5% reduction in area, and an 17.7% reduction in energy compared to the accurate adder for RTZ handshaking. For RTO handshaking, HOERAA achieves an 18.7% reduction in cycle time, a 12.4% reduction in area, and a 16.6% reduction in energy compared to the accurate adder. Another approximate adder HEAA achieves a 19.7% reduction in cycle time, a 12.9% reduction in area, and a 20.2% reduction in energy, compared to the accurate adder for RTZ handshaking. For RTO handshaking, HEAA achieves an 18.7% reduction in cycle time, a 12.9% reduction in area, and a 19.2% reduction in energy compared to the accurate adder. Nevertheless, the RTO handshaking is preferable to RTZ handshaking as the former facilitates slightly better optimizations in design metrics compared to the latter. The mean absolute error (MAE) and the root mean square error (RMSE), which are popular error metrics used in approximate computing, were calculated for the approximate adders and are given for a comparison. While the MAE of HOERAA and HEAA are comparable, HOERAA has 8.6% reduced RMSE compared to HEAA. Digital image processing results based on accurate and approximate additions are also given, to substantiate the usefulness of approximate addition. Full article

(This article belongs to the Special Issue Simulation and Modelling in Natural Sciences, Economics, Biomedicine and Engineering)

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12 pages, 283 KiB

Open AccessArticle

Best Approximations by Increasing Invariant Subspaces of Self-Adjoint Operators

by Oleh Lopushansky and Renata Tłuczek-Piȩciak

Symmetry 2020, 12(11), 1918; https://doi.org/10.3390/sym12111918 - 20 Nov 2020

Cited by 1 | Viewed by 2197

Abstract

The paper describes approximations properties of monotonically increasing sequences of invariant subspaces of a self-adjoint operator, as well as their symmetric generalizations in a complex Hilbert space, generated by its positive powers. It is established that the operator keeps its spectrum over the [...] Read more.

The paper describes approximations properties of monotonically increasing sequences of invariant subspaces of a self-adjoint operator, as well as their symmetric generalizations in a complex Hilbert space, generated by its positive powers. It is established that the operator keeps its spectrum over the dense union of these subspaces, equipped with quasi-norms, and that it is contractive. The main result is an inequality that provides an accurate estimate of errors for the best approximations in Hilbert spaces by these invariant subspaces. Full article

(This article belongs to the Section Mathematics)

28 pages, 407 KiB

Open AccessArticle

A New Approach for Euler-Lagrange Orbits on Compact Manifolds with Boundary

by Dario Corona and Fabio Giannoni

Symmetry 2020, 12(11), 1917; https://doi.org/10.3390/sym12111917 - 20 Nov 2020

Cited by 2 | Viewed by 1661

Abstract

Consider a compact manifold with boundary, homeomorphic to the N-dimensional disk, and a Tonelli Lagrangian function defined on the tangent bundle. In this paper, we study the multiplicity problem for Euler-Lagrange orbits that satisfy the conormal boundary conditions and that lay on [...] Read more.

Consider a compact manifold with boundary, homeomorphic to the N-dimensional disk, and a Tonelli Lagrangian function defined on the tangent bundle. In this paper, we study the multiplicity problem for Euler-Lagrange orbits that satisfy the conormal boundary conditions and that lay on the boundary only in their extreme points. In particular, for suitable values of the energy function and under mild hypotheses, if the Tonelli Lagrangian is reversible then the minimal number of Euler-Lagrange orbits with prescribed energy that satisfies the conormal boundary conditions is N. If L is not reversible, then this number is two. Full article

(This article belongs to the Special Issue Recent Advance in Mathematical Physics)

16 pages, 5808 KiB

Open AccessArticle

Optimization by Context Refinement for Development of Incremental Granular Models

by Myung-Won Lee and Keun-Chang Kwak

Symmetry 2020, 12(11), 1916; https://doi.org/10.3390/sym12111916 - 20 Nov 2020

Viewed by 1510

Abstract

Optimization by refinement of linguistic contexts produced from an output variable in the construction of an incremental granular model (IGM) is presented herein. In contrast to the conventional learning method using the backpropagation algorithm, we use a novel method to learn both the [...] Read more.

Optimization by refinement of linguistic contexts produced from an output variable in the construction of an incremental granular model (IGM) is presented herein. In contrast to the conventional learning method using the backpropagation algorithm, we use a novel method to learn both the cluster centers of Gaussian fuzzy sets representing the symmetry in the premise part and the contexts of the consequent part in the if–then fuzzy rules. Hence, we use the fundamental concept of context-based fuzzy clustering and design with an integration of linear regression (LR) and granular fuzzy models (GFMs). This GFM is constructed based on the association between the triangular membership function produced both in the input–output variables. The context can be established by the system user or using an optimization method. Hence, we can obtain superior performances based on the combination of simple linear regression and local GFMs optimized by context refinement. Experimental results pertaining to coagulant dosing in a water purification plant and automobile miles per gallon prediction revealed that the presented method performed better than linear regression, multilinear perceptron, radial basis function networks, linguistic model, and the IGM. Full article

(This article belongs to the Section Computer)

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22 pages, 419 KiB

Open AccessArticle

An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings

by Lateef Olakunle Jolaoso and Maggie Aphane

Symmetry 2020, 12(11), 1915; https://doi.org/10.3390/sym12111915 - 20 Nov 2020

Cited by 4 | Viewed by 1738

Abstract

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which [...] Read more.

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)

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11 pages, 603 KiB

Open AccessArticle

Kinetics of Nanostructuring Processes of Material Surface under Influence of Laser Radiation

by Alexei Khomenko, Olga Yushchenko and Anna Badalian

Symmetry 2020, 12(11), 1914; https://doi.org/10.3390/sym12111914 - 20 Nov 2020

Cited by 2 | Viewed by 1776

Abstract

In this paper, further research is conducted for a synergetic model that describes the state of the material surface in the process of laser irradiation. Namely, the previously studied approach of mutually coordinated behavior of the relaxation field, concentration of relaxation zones, and [...] Read more.

In this paper, further research is conducted for a synergetic model that describes the state of the material surface in the process of laser irradiation. Namely, the previously studied approach of mutually coordinated behavior of the relaxation field, concentration of relaxation zones, and field of stress is supplemented with a nonlinear term. It is shown that, using this model, we can describe the behavior of different types of systems. During the analysis, five stationary states were found which correspond to different modes of formation of relaxation areas on the surface. The regions of parameters are found at which one or another mode of the system behavior is established. Phase portraits are constructed for each mode and the kinetics of the system is described. The obtained results qualitatively coincide with the experimental data. Full article

(This article belongs to the Special Issue Recent Advances in the Study of Symmetry and Continuum Mechanics)

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10 pages, 317 KiB

Open AccessArticle

Nonadiabatic Atomic-Like State Stabilizing Antiferromagnetism and Mott Insulation in MnO

by Ekkehard Krüger

Symmetry 2020, 12(11), 1913; https://doi.org/10.3390/sym12111913 - 20 Nov 2020

Cited by 4 | Viewed by 2181

Abstract

This paper reports evidence that the antiferromagnetic and insulating ground state of MnO is caused by a nonadiabatic atomic-like motion, as is evidently the case in NiO. In addition, it is shown that experimental findings on the displacements of the Mn and O [...] Read more.

This paper reports evidence that the antiferromagnetic and insulating ground state of MnO is caused by a nonadiabatic atomic-like motion, as is evidently the case in NiO. In addition, it is shown that experimental findings on the displacements of the Mn and O atoms in the antiferromagnetic phase of MnO corroborate the presented suggestion that the rhombohedral-like distortion in antiferromagnetic MnO, as well as in antiferromagnetic NiO is an inner distortion of the monoclinic base-centered Bravais lattice of the antiferromagnetic phases. Full article

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16 pages, 1380 KiB

Open AccessFeature PaperArticle

Cherry Picking: Consumer Choices in Swarm Dynamics, Considering Price and Quality of Goods

by Damian Knopoff, Valeria Secchini and Pietro Terna

Symmetry 2020, 12(11), 1912; https://doi.org/10.3390/sym12111912 - 20 Nov 2020

Cited by 12 | Viewed by 2744

Abstract

This paper proposes a further development of the mathematical theory of swarms to behavioral dynamics of social and economic systems, with an application to the modeling of price series in a market. The complexity features of the system are properly described by modeling [...] Read more.

This paper proposes a further development of the mathematical theory of swarms to behavioral dynamics of social and economic systems, with an application to the modeling of price series in a market. The complexity features of the system are properly described by modeling the asymmetric interactions between buyers and sellers, specifically considering the so-called cherry picking phenomenon, by which not only prices but also qualities are considered when buying a good. Finally, numerical simulations are performed to depict the predictive ability of the model and to show interesting emerging behaviors, as the coordination of buyers and their division in endogenous clusters. Full article

(This article belongs to the Special Issue Complexity and Symmetry in the Science of Living Systems: Active Particle Methods)

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13 pages, 370 KiB

Open AccessArticle

Pricing Various Types of Power Options under Stochastic Volatility

by Youngrok Lee, Yehun Kim and Jaesung Lee

Symmetry 2020, 12(11), 1911; https://doi.org/10.3390/sym12111911 - 20 Nov 2020

Cited by 7 | Viewed by 1970

Abstract

The exotic options with curved nonlinear payoffs have been traded in financial markets, which offer great flexibility to participants in the market. Among them, power options with the payoff depending on a certain power of the underlying asset price are widely used in [...] Read more.

The exotic options with curved nonlinear payoffs have been traded in financial markets, which offer great flexibility to participants in the market. Among them, power options with the payoff depending on a certain power of the underlying asset price are widely used in markets in order to provide high leverage strategy. In pricing power options, the classical Black–Scholes model which assumes a constant volatility is simple and easy to handle, but it has a limit in reflecting movements of real financial markets. As the alternatives of constant volatility, we focus on the stochastic volatility, finding more exact prices for power options. In this paper, we use the stochastic volatility model introduced by Schöbel and Zhu to drive the closed-form expressions for the prices of various power options including soft strike options. We also show the sensitivity of power option prices under changes in the values of each parameter by calculating the resulting values obtained from the formulas. Full article

(This article belongs to the Special Issue Advances in Stochastic Differential Equations)

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29 pages, 10024 KiB

Open AccessFeature PaperReview

Spin Symmetry Breaking: Superparamagnetic and Spin Glass-Like Behavior Observed in Rod-Like Liquid Crystalline Organic Compounds Contacting Nitroxide Radical Spins

by Shuichi Sato, Yoshiaki Uchida and Rui Tamura

Symmetry 2020, 12(11), 1910; https://doi.org/10.3390/sym12111910 - 20 Nov 2020

Cited by 5 | Viewed by 5123

Abstract

Liquid crystalline (LC) organic radicals were expected to show a novel non-linear magnetic response to external magnetic and electric fields due to their coherent collective molecular motion. We have found that a series of chiral and achiral all-organic LC radicals having one or [...] Read more.

Liquid crystalline (LC) organic radicals were expected to show a novel non-linear magnetic response to external magnetic and electric fields due to their coherent collective molecular motion. We have found that a series of chiral and achiral all-organic LC radicals having one or two five-membered cyclic nitroxide radical (PROXYL) units in the core position and, thereby, with a negative dielectric anisotropy exhibit spin glass (SG)-like superparamagnetic features, such as a magnetic hysteresis (referred to as ‘positive magneto-LC effect’), and thermal and impurity effects during a heating and cooling cycle in weak magnetic fields. Furthermore, for the first time, a nonlinear magneto-electric (ME) effect has been detected with respect to one of the LC radicals showing a ferroelectric (chiral Smectic C) phase. The mechanism of the positive magneto-LC effect is proposed and discussed by comparison of our experimental results with the well-known magnetic properties of SG materials and on the basis of the experimental results of a nonlinear ME effect. A recent theoretical study by means of molecular dynamic simulation and density functional theory calculations suggesting the high possibility of conservation of the memory of spin-spin interactions between magnetic moments owing to the ceaseless molecular contacts in the LC and isotropic states is briefly mentioned as well. Full article

(This article belongs to the Special Issue Chemical Symmetry Breaking)

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10 pages, 1469 KiB

Open AccessArticle

Image Denoising Based on Bivariate Distribution

by Ping Zhao, Xingyu Zhao and Chun Zhao

Symmetry 2020, 12(11), 1909; https://doi.org/10.3390/sym12111909 - 20 Nov 2020

Cited by 3 | Viewed by 2333

Abstract

The literature has shown that the performance of the de-noising algorithm was greatly influenced by the dependencies between wavelet coefficients. In this paper, the bivariate probability density function (PDF) was proposed which was symmetric, and the dependencies between the coefficients were considered. The [...] Read more.

The literature has shown that the performance of the de-noising algorithm was greatly influenced by the dependencies between wavelet coefficients. In this paper, the bivariate probability density function (PDF) was proposed which was symmetric, and the dependencies between the coefficients were considered. The bivariate Cauchy distribution and the bivariate Student’s distribution are special cases of the proposed bivariate PDF. One of the parameters in the probability density function gave the estimation method, and the other parameter can take any real number greater than 2. The algorithm adopted a maximum a posteriori estimator employing the dual-tree complex wavelet transform (DTCWT). Compared with the existing best results, the method is faster and more efficient than the previous numerical integration techniques. The bivariate shrinkage function of the proposed algorithm can be expressed explicitly. The proposed method is simple to implement. Full article

(This article belongs to the Special Issue Symmetry in Artificial Visual Perception and Its Application)

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19 pages, 8743 KiB

Open AccessArticle

Method of Colors and Secure Fonts Used for Source Shaping of Valuable Emissions from Projector in Electromagnetic Eavesdropping Process

by Alexandru Boitan, Ireneusz Kubiak, Simona Halunga, Artur Przybysz and Andrzej Stańczak

Symmetry 2020, 12(11), 1908; https://doi.org/10.3390/sym12111908 - 20 Nov 2020

Cited by 8 | Viewed by 4872

Abstract

The protection of information processed electronically involves a large number of IT devices from computer sets or laptops to monitors, printers, servers, etc. In many cases, classified information processing might be associated with the use of projectors, which are an indispensable element of [...] Read more.

The protection of information processed electronically involves a large number of IT devices from computer sets or laptops to monitors, printers, servers, etc. In many cases, classified information processing might be associated with the use of projectors, which are an indispensable element of meetings for a limited group of people. Such devices are connected to computers through interfaces of various analogue and digital standards and can become an additional source of unwanted emissions, and the distinctive features of these emissions allow the information displayed to be unwantedly reproduced. This paper offers evidence of the existing threat related to electromagnetic infiltration of several projectors, by showing images reconstructed from registered revealing emissions. The paper presents an analysis of several solutions that can be used to reduce the level of infiltration susceptibility of projectors or to highlight this property in the device assessment process. The possibilities of using special computer fonts and the so-called method of colors—background color and text color—is analyzed. The tests were carried out on randomly selected projectors in two independent laboratories, and, based on these results, a number of interesting conclusions have been highlighted at the end. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Communications Engineering)

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18 pages, 961 KiB

Open AccessArticle

A Numerical Schemefor the Probability Density of the First Hitting Time for Some Random Processes

by Jorge E. Macías-Díaz

Symmetry 2020, 12(11), 1907; https://doi.org/10.3390/sym12111907 - 20 Nov 2020

Cited by 1 | Viewed by 2144

Abstract

Departing from a general stochastic model for a moving boundary problem, we consider the density function of probability for the first passing time. It is well known that the distribution of this random variable satisfies a problem ruled by an advection–diffusion system for [...] Read more.

Departing from a general stochastic model for a moving boundary problem, we consider the density function of probability for the first passing time. It is well known that the distribution of this random variable satisfies a problem ruled by an advection–diffusion system for which very few solutions are known in exact form. The model considers also a deterministic source, and the coefficients of this equation are functions with sufficient regularity. A numerical scheme is designed to estimate the solutions of the initial-boundary-value problem. We prove rigorously that the numerical model is capable of preserving the main characteristics of the solutions of the stochastic model, that is, positivity, boundedness and monotonicity. The scheme has spatial symmetry, and it is theoretically analyzed for consistency, stability and convergence. Some numerical simulations are carried out in this work to assess the capability of the discrete model to preserve the main structural features of the solutions of the model. Moreover, a numerical study confirms the efficiency of the scheme, in agreement with the mathematical results obtained in this work. Full article

(This article belongs to the Special Issue Advances in Stochastic Differential Equations)

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12 pages, 256 KiB

Open AccessArticle

Heavy Quark Symmetry and Fine Structure of the Spectrum of Hadronic Dark Matter

by Vladimir Kuksa and Vitaly Beylin

Symmetry 2020, 12(11), 1906; https://doi.org/10.3390/sym12111906 - 20 Nov 2020

Cited by 2 | Viewed by 1630

Abstract

We analyze the structure of excited states of new heavy hadrons in the scenario with hadronic dark matter. Fine mass-splitting in a doublet of new mesons stipulates the existence of charged metastable heavy mesons. We describe the structure of new meson excited states [...] Read more.

We analyze the structure of excited states of new heavy hadrons in the scenario with hadronic dark matter. Fine mass-splitting in a doublet of new mesons stipulates the existence of charged metastable heavy mesons. We describe the structure of new meson excited states in the framework of the heavy quark effective theory. Phenomenological consequences of fine and hyperfine splitting are considered in the hadronic dark matter scenario and beyond. Full article

(This article belongs to the Special Issue Symmetry beyond the Standard Models of Cosmology, High Energy Physics and Quantum Field Theory)

10 pages, 2043 KiB

Open AccessArticle

Hand Preference in Rhinopithecus roxellana Infants: Is It Influenced by Familial Inheritance?

by Wei-Wei Fu, Yi Ren, Cheng-Liang Wang, Xiao-Wei Wang and Bao-Guo Li

Symmetry 2020, 12(11), 1905; https://doi.org/10.3390/sym12111905 - 20 Nov 2020

Cited by 3 | Viewed by 2084

Abstract

The Sichuan snub-nosed monkey (Rhinopithecus roxellana) is a typical arboreal group-living Old-World primate and has been studied broadly in hand preference. However, infants have not been tested independently from other immature individuals to date. The purpose of the present study was [...] Read more.

The Sichuan snub-nosed monkey (Rhinopithecus roxellana) is a typical arboreal group-living Old-World primate and has been studied broadly in hand preference. However, infants have not been tested independently from other immature individuals to date. The purpose of the present study was to investigate hand preference in a spontaneously unimanual feeding task in nine infants at 12 months and the relationship of hand preference with their parents in R. roxellanae. Most infants (89%) showed individual-level hand preference. No correlation was found in the direction of hand preference between infant and its parents, and a significant negative correlation in the strength of hand preference was found between infants and their mothers (r = −0.715, p = 0.03). Moreover, there was no sex difference in the direction and strength of hand preference both in infants and adults (i.e., parents). Meanwhile, the strength of hand preference in adults was stronger than that in infants. This study is a first and preliminary exploration for the expression of hand preference in R. roxellanae infants and whether their hand preference was influenced by familial inheritance. Full article

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26 pages, 2718 KiB

Open AccessArticle

Symmetries in Teleportation Assisted by N-Channels under Indefinite Causal Order and Post-Measurement

by Carlos Cardoso-Isidoro and Francisco Delgado

Symmetry 2020, 12(11), 1904; https://doi.org/10.3390/sym12111904 - 20 Nov 2020

Cited by 7 | Viewed by 2243

Abstract

Quantum teleportation has had notorious advances in the last decade, being successfully deployed in the experimental domain. In other terrains, the understanding of indefinite causal order has demonstrated a valuable enhancement in quantum communication to correct channel imperfections. In this work, we address [...] Read more.

Quantum teleportation has had notorious advances in the last decade, being successfully deployed in the experimental domain. In other terrains, the understanding of indefinite causal order has demonstrated a valuable enhancement in quantum communication to correct channel imperfections. In this work, we address the symmetries underlying imperfect teleportation when it is assisted by indefinite causal order to correct the use of noisy entangled resources. In the strategy being presented, indefinite causal order introduces a control state to address the causal ordering. Then, by using post-selection, it fulfills the teleportation enhancement to recover the teleported state by constructive interference. By analysing primarily sequential teleportation under definite causal order, we perform a comparison basis for notable outcomes derived from indefinite causal order. After, the analysis is conducted by increasing the number of teleportation processes, thus suggesting additional alternatives to exploit the most valuable outcomes in the process by adding weak measurement as a complementary strategy. Finally, we discuss the current affordability for an experimental implementation. Full article

(This article belongs to the Special Issue Symmetries in Quantum Mechanics)

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12 pages, 3688 KiB

Open AccessFeature PaperReview

Vapochromism of Organic Crystals Based on Macrocyclic Compounds and Inclusion Complexes

by Toshikazu Ono and Yoshio Hisaeda

Symmetry 2020, 12(11), 1903; https://doi.org/10.3390/sym12111903 - 19 Nov 2020

Cited by 15 | Viewed by 3659

Abstract

Vapochromic materials, which change color and luminescence when exposed to specific vapors and gases, have attracted considerable attention in recent years owing to their potential applications in a wide range of fields such as chemical sensors and environmental monitors. Although the mechanism of [...] Read more.

Vapochromic materials, which change color and luminescence when exposed to specific vapors and gases, have attracted considerable attention in recent years owing to their potential applications in a wide range of fields such as chemical sensors and environmental monitors. Although the mechanism of vapochromism is still unclear, several studies have elucidated it from the viewpoint of crystal engineering. In this mini-review, we investigate recent advances in the vapochromism of organic crystals. Among them, macrocyclic molecules and inclusion complexes, which have apparent host–guest interactions with analyte molecules (specific vapors and gases), are described. When the host compound is properly designed, its cavity size and symmetry change in response to guest molecules, influencing the optical properties by changing the molecular inclusion and recognition abilities. This information highlights the importance of structure–property relationships resulting from the molecular recognition at the solid–vapor interface. Full article

(This article belongs to the Special Issue Chemical Symmetry Breaking)

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Symmetry, Volume 12, Issue 11 (November 2020) – 184 articles

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