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Symmetry, Volume 13, Issue 4 (April 2021) – 209 articles

Cover Story (view full-size image): The gate of a potassium channel, from its X-ray structure, has been studied. Parts have been calculated, and, with protons properly placed, calculation and X-ray structure agree. The figure shows four S6 helices bordering the gate. The purple sphere is a K+ ion, the small central molecules are water molecules, and the outer lines are six amino acids. View this paper.
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12 pages, 2810 KiB  
Article
Room Temperature Syntheses of ZnO and Their Structures
by Domenica Tommasa Donia, Elvira Maria Bauer, Mauro Missori, Ludovica Roselli, Daniele Cecchetti, Pietro Tagliatesta, Lorenzo Gontrani and Marilena Carbone
Symmetry 2021, 13(4), 733; https://doi.org/10.3390/sym13040733 - 20 Apr 2021
Cited by 17 | Viewed by 3327
Abstract
ZnO has many technological applications which largely depend on its properties, which can be tuned by controlled synthesis. Ideally, the most convenient ZnO synthesis is carried out at room temperature in an aqueous solvent. However, the correct temperature values are often loosely defined. [...] Read more.
ZnO has many technological applications which largely depend on its properties, which can be tuned by controlled synthesis. Ideally, the most convenient ZnO synthesis is carried out at room temperature in an aqueous solvent. However, the correct temperature values are often loosely defined. In the current paper, we performed the synthesis of ZnO in an aqueous solvent by varying the reaction and drying temperatures by 10 °C steps, and we monitored the synthesis products primarily by XRD). We found out that a simple direct synthesis of ZnO, without additional surfactant, pumping, or freezing, required both a reaction (TP) and a drying (TD) temperature of 40 °C. Higher temperatures also afforded ZnO, but lowering any of the TP or TD below the threshold value resulted either in the achievement of Zn(OH)2 or a mixture of Zn(OH)2/ZnO. A more detailed Rietveld analysis of the ZnO samples revealed a density variation of about 4% (5.44 to 5.68 gcm−3) with the synthesis temperature, and an increase of the nanoparticles’ average size, which was also verified by SEM images. The average size of the ZnO synthesized at TP = TD = 40 °C was 42 nm, as estimated by XRD, and 53 ± 10 nm, as estimated by SEM. For higher synthesis temperatures, they vary between 76 nm and 71 nm (XRD estimate) or 65 ± 12 nm and 69 ± 11 nm (SEM estimate) for TP = 50 °C, TD = 40 °C, or TP = TD = 60 °C, respectively. At TP = TD = 30 °C, micrometric structures aggregated in foils are obtained, which segregate nanoparticles of ZnO if TD is raised to 40 °C. The optical properties of ZnO obtained by UV-Vis reflectance spectroscopy indicate a red shift of the band gap by ~0.1 eV. Full article
(This article belongs to the Special Issue Materials Science and X-Ray Diffraction)
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19 pages, 6465 KiB  
Article
Chirality, Gelation Ability and Crystal Structure: Together or Apart? Alkyl Phenyl Ethers of Glycerol as Simple LMWGs
by Alexander A. Bredikhin, Aidar T. Gubaidullin, Zemfira A. Bredikhina, Robert R. Fayzullin and Olga A. Lodochnikova
Symmetry 2021, 13(4), 732; https://doi.org/10.3390/sym13040732 - 20 Apr 2021
Cited by 4 | Viewed by 2170
Abstract
Chiral recognition plays an important role in the self-assembly of soft materials, in particular supramolecular organogels formed by low molecular weight gelators (LMWGs). Out of 14 pairs of the studied racemic and enantiopure samples of alkyl-substituted phenyl ethers of glycerol, only eight enantiopure [...] Read more.
Chiral recognition plays an important role in the self-assembly of soft materials, in particular supramolecular organogels formed by low molecular weight gelators (LMWGs). Out of 14 pairs of the studied racemic and enantiopure samples of alkyl-substituted phenyl ethers of glycerol, only eight enantiopure diols form the stable gels in nonane. The formation of gels from solutions was studied by polarimetry, and their degradation with the formation of xerogels was studied by the PXRD method. The revealed crystalline characteristics of all studied xerogels corresponded to those for crystalline samples of the parent gelators. In addition to those previously investigated, crystalline samples of enantiopure para-n-alkylphenyl glycerol ethers [alkyl = pentyl (5), hexyl (6), heptyl (7), octyl (8), nonyl (9)] and racemic 3-(3,5-dimethylphenoxy)propane-1,2-diol (rac-14) have been examined by single crystal X-ray diffraction analysis. Among 22 samples of compounds 114 studied by SC-XRD, seven different types of supramolecular motifs are identified, of which only two are realized in crystals of supramolecular gelators. An attempt was made to relate the ability to gel formation with the characteristics of the supramolecular motif of a potential gelling agent, and the frequency of formation of the motif, required for gelation, with the chiral characteristics of the sample. Full article
(This article belongs to the Special Issue Chiral Molecules: Properties, Synthesis and Analysis)
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24 pages, 3063 KiB  
Article
Multi-Criteria Seed Selection for Targeting Multi-Attribute Nodes in Complex Networks
by Artur Karczmarczyk, Jarosław Jankowski and Jarosław Wątrobski
Symmetry 2021, 13(4), 731; https://doi.org/10.3390/sym13040731 - 20 Apr 2021
Cited by 3 | Viewed by 2248
Abstract
Online environments have evolved from the early-stage technical systems to social platforms with social communication mechanisms resembling the interactions which can be found in the real world. Online marketers are using the close relations between the users of social networks to more easily [...] Read more.
Online environments have evolved from the early-stage technical systems to social platforms with social communication mechanisms resembling the interactions which can be found in the real world. Online marketers are using the close relations between the users of social networks to more easily propagate the marketing contents in their advertising campaigns. Such viral marketing campaigns have proven to provide better results than traditional online marketing, hence the increasing research interest in the topic. While the majority of the up-to-date research focuses on maximizing the global coverage and influence in the complete network, some studies have been conducted in the area of budget-constrained conditions as well as in the area of targeting particular groups of nodes. In this paper, a novel approach to targeting multi-attribute nodes in complex networks is presented, in which an MCDA method with various preference weights for all criteria is used to select the initial seeds to best reach the targeted nodes in the network. The proposed approach shows some symmetric characteristics—while the global coverage in the network is decreased, the coverage amongst the targeted nodes grows. Full article
(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
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17 pages, 3005 KiB  
Article
Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations
by Ravi Agarwal, Snezhana Hristova and Donal O’Regan
Symmetry 2021, 13(4), 730; https://doi.org/10.3390/sym13040730 - 20 Apr 2021
Cited by 4 | Viewed by 2003
Abstract
In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has [...] Read more.
In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results. Full article
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7 pages, 241 KiB  
Article
Emergent Space-Time in a Bubble Universe
by James Moffat
Symmetry 2021, 13(4), 729; https://doi.org/10.3390/sym13040729 - 20 Apr 2021
Viewed by 1675
Abstract
I exploit the close connection between the tessellation of space-time in the Regge calculus and an Eilenberg homology to investigate the deep quantum nature of space-time in a simple bubble universe of a size consistent with the Planck regime. Following the mathematics allows [...] Read more.
I exploit the close connection between the tessellation of space-time in the Regge calculus and an Eilenberg homology to investigate the deep quantum nature of space-time in a simple bubble universe of a size consistent with the Planck regime. Following the mathematics allows me to define this granulated space-time as the embedding space of the skeleton of a computational spin network inside a quantum computer. This approach can be regarded as a quantum simulation of the equivalent physics. I can, therefore, define a fundamental characterisation of any high-energy physical process at the Planck scale as equivalent to a quantum simulation inside a quantum computer. Full article
(This article belongs to the Special Issue Quantum Gravity)
16 pages, 4061 KiB  
Article
Examination and Comparison of Theta Band Connectivity in Left- and Right-Hand Dominant Individuals throughout a Motor Skill Acquisition
by Jessica McDonnell, Nicholas P Murray, Sungwoo Ahn, Stefan Clemens, Erik Everhart and J. Chris Mizelle
Symmetry 2021, 13(4), 728; https://doi.org/10.3390/sym13040728 - 20 Apr 2021
Cited by 3 | Viewed by 2211
Abstract
The majority of the population identifies as right-hand dominant, with a minority 10.6% identifying as left-hand dominant. Social factors may partially skew the distribution, but it remains that left-hand dominant individuals make up approximately 40 million people in the United States alone and [...] Read more.
The majority of the population identifies as right-hand dominant, with a minority 10.6% identifying as left-hand dominant. Social factors may partially skew the distribution, but it remains that left-hand dominant individuals make up approximately 40 million people in the United States alone and yet, remain underrepresented in the motor control literature. Recent research has revealed behavioral and neurological differences between populations, therein overturning assumptions of a simple hemispheric flip in motor-related activations. The present work showed differentially adaptable motor programs between populations and found fundamental differences in methods of skill acquisition highlighting underlying neural strategies unique to each population. Difference maps and descriptive metrics of coherent activation patterns showed differences in how theta oscillations were utilized. The right-hand group relied on occipital parietal lobe connectivity for visual information integration necessary to inform the motor task, while the left-hand group relied on a more frontal lobe localized cognitive based approach. The findings provide insight into potential alternative methods of information integration and emphasize the importance for inclusion of the left-hand dominant population in the growing conceptualization of the brain promoting the generation of a more complete, stable, and accurate understanding of our complex biology. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Sport Sciences)
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15 pages, 772 KiB  
Article
Algebra of Symmetry Operators for Klein-Gordon-Fock Equation
by Valeriy V. Obukhov
Symmetry 2021, 13(4), 727; https://doi.org/10.3390/sym13040727 - 20 Apr 2021
Cited by 23 | Viewed by 2184
Abstract
All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time V4 a group of motion G3 acts simply transitively on a non-null subspace of transitivity V3. It is [...] Read more.
All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time V4 a group of motion G3 acts simply transitively on a non-null subspace of transitivity V3. It is shown that in the case of a Riemannian space Vn, in which the group Gr acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group Gr. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2022)
16 pages, 569 KiB  
Article
New Method for Generating New Families of Distributions
by Lamya A. Baharith and Wedad H. Aljuhani
Symmetry 2021, 13(4), 726; https://doi.org/10.3390/sym13040726 - 20 Apr 2021
Cited by 7 | Viewed by 2075
Abstract
This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this [...] Read more.
This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis. Full article
(This article belongs to the Special Issue Recent Advances in Number Theory and Their Applications)
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13 pages, 659 KiB  
Article
Feedback Control for a Diffusive and Delayed Brusselator Model: Semi-Analytical Solutions
by Hassan Yahya Alfifi
Symmetry 2021, 13(4), 725; https://doi.org/10.3390/sym13040725 - 20 Apr 2021
Cited by 13 | Viewed by 2156
Abstract
This paper describes the stability and Hopf bifurcation analysis of the Brusselator system with delayed feedback control in the single domain of a reaction–diffusion cell. The Galerkin analytical technique is used to present a system equation composed of ordinary differential equations. The condition [...] Read more.
This paper describes the stability and Hopf bifurcation analysis of the Brusselator system with delayed feedback control in the single domain of a reaction–diffusion cell. The Galerkin analytical technique is used to present a system equation composed of ordinary differential equations. The condition able to determine the Hopf bifurcation point is found. Full maps of the Hopf bifurcation regions for the interacting chemical species are shown and discussed, indicating that the time delay, feedback control, and diffusion parameters can play a significant and important role in the stability dynamics of the two concentration reactants in the system. As a result, these parameters can be changed to destabilize the model. The results show that the Hopf bifurcation points for chemical control increase as the feedback parameters increase, whereas the Hopf bifurcation points decrease when the diffusion parameters increase. Bifurcation diagrams with examples of periodic oscillation and phase-plane maps are provided to confirm all the outcomes calculated in the model. The benefits and accuracy of this work show that there is excellent agreement between the analytical results and numerical simulation scheme for all the figures and examples that are illustrated. Full article
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17 pages, 332 KiB  
Review
Quantum Orbit Method in the Presence of Symmetries
by Nicola Ciccoli
Symmetry 2021, 13(4), 724; https://doi.org/10.3390/sym13040724 - 19 Apr 2021
Cited by 1 | Viewed by 1543
Abstract
We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C-algebra quantization obtained through groupoid techniques, and we try to put the [...] Read more.
We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C-algebra quantization obtained through groupoid techniques, and we try to put the results obtained in algebraic or representation theoretical contexts in relation with groupoid quantization. Full article
(This article belongs to the Special Issue Quantum Group Symmetry and Quantum Geometry)
14 pages, 465 KiB  
Article
A Modified SIRD Model to Study the Evolution of the COVID-19 Pandemic in Spain
by Vicente Martínez
Symmetry 2021, 13(4), 723; https://doi.org/10.3390/sym13040723 - 19 Apr 2021
Cited by 12 | Viewed by 3913
Abstract
In this paper, we use an SIRD model to analyze the evolution of the COVID-19 pandemic in Spain, caused by a new virus called SARS-CoV-2 from the coronavirus family. This model is governed by a nonlinear system of differential equations that allows us [...] Read more.
In this paper, we use an SIRD model to analyze the evolution of the COVID-19 pandemic in Spain, caused by a new virus called SARS-CoV-2 from the coronavirus family. This model is governed by a nonlinear system of differential equations that allows us to detect trends in the pandemic and make reliable predictions of the evolution of the infection in the short term. This work shows this evolution of the infection in various changing stages throughout the period of maximum alert in Spain. It also shows a quick adaptation of the parameters that define the disease in several stages. In addition, the model confirms the effectiveness of quarantine to avoid the exponential expansion of the pandemic and reduce the number of deaths. The analysis shows good short-term predictions using the SIRD model, which are useful to influence the evolution of the epidemic and thus carry out actions that help reduce its harmful effects. Full article
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12 pages, 274 KiB  
Article
Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior
by Shyam Sundar Santra, Khaled Mohamed Khedher, Osama Moaaz, Ali Muhib and Shao-Wen Yao
Symmetry 2021, 13(4), 722; https://doi.org/10.3390/sym13040722 - 19 Apr 2021
Cited by 12 | Viewed by 2157
Abstract
In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, [...] Read more.
In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results. Full article
26 pages, 2236 KiB  
Article
Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior
by Ralph V. Chamberlin, Michael R. Clark, Vladimiro Mujica and George H. Wolf
Symmetry 2021, 13(4), 721; https://doi.org/10.3390/sym13040721 - 19 Apr 2021
Cited by 8 | Viewed by 2397
Abstract
Here, we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is [...] Read more.
Here, we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this “nanothermodynamics” to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of “atoms” into an ensemble of “regions” of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for particles that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the spins, we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann’s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to the equilibrium thermal fluctuations found in many materials. Full article
(This article belongs to the Section Physics)
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14 pages, 2842 KiB  
Review
Non-Enzymatic Desymmetrization Reactions in Aqueous Media
by Satomi Niwayama
Symmetry 2021, 13(4), 720; https://doi.org/10.3390/sym13040720 - 19 Apr 2021
Cited by 3 | Viewed by 1999
Abstract
Symmetric organic compounds are generally obtained inexpensively, and therefore they can be attractive building blocks for the total synthesis of various pharmaceuticals and natural products. The drawback is that discriminating the identical functional groups in the symmetric compounds is difficult. Water is the [...] Read more.
Symmetric organic compounds are generally obtained inexpensively, and therefore they can be attractive building blocks for the total synthesis of various pharmaceuticals and natural products. The drawback is that discriminating the identical functional groups in the symmetric compounds is difficult. Water is the most environmentally benign and inexpensive solvent. However, successful organic reactions in water are rather limited due to the hydrophobicity of organic compounds in general. Therefore, desymmetrization reactions in aqueous media are expected to offer versatile strategies for the synthesis of a variety of significant organic compounds. This review focuses on the recent progress of desymmetrization reactions of symmetric organic compounds in aqueous media without utilizing enzymes. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Total Synthesis)
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22 pages, 4484 KiB  
Article
Detecting Anonymous Target and Predicting Target Trajectories in Wireless Sensor Networks
by P. Leela Rani and G. A. Sathish Kumar
Symmetry 2021, 13(4), 719; https://doi.org/10.3390/sym13040719 - 19 Apr 2021
Cited by 10 | Viewed by 2515
Abstract
Target Tracking (TT) is an application of Wireless Sensor Networks (WSNs) which necessitates constant assessment of the location of a target. Any change in position of a target and the distance from each intermediate sensor node to the target is passed on to [...] Read more.
Target Tracking (TT) is an application of Wireless Sensor Networks (WSNs) which necessitates constant assessment of the location of a target. Any change in position of a target and the distance from each intermediate sensor node to the target is passed on to base station and these factors play a crucial role in further processing. The drawback of WSN is that it is prone to numerous constraints like low power, faulty sensors, environmental noises, etc. The target should be detected first and its path should be tracked continuously as it moves around the sensing region. This problem of detecting and tracking a target should be conducted with maximum accuracy and minimum energy consumption in each sensor node. In this paper, we propose a Target Detection and Target Tracking (TDTT) model for continuously tracking the target. This model uses prelocalization-based Kalman Filter (KF) for target detection and clique-based estimation for tracking the target trajectories. We evaluated our model by calculating the probability of detecting a target based on distance, then estimating the trajectory. We analyzed the maximum error in position estimation based on density and sensing radius of the sensors. The results were found to be encouraging. The proposed KF-based target detection and clique-based target tracking reduce overall expenditure of energy, thereby increasing network lifetime. This approach is also compared with Dynamic Object Tracking (DOT) and face-based tracking approach. The experimental results prove that employing TDTT improves energy efficiency and extends the lifetime of the network, without compromising the accuracy of tracking. Full article
(This article belongs to the Section Computer)
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13 pages, 1843 KiB  
Article
Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments
by Shuji Shinohara, Nobuhito Manome, Yoshihiro Nakajima, Yukio Pegio Gunji, Toru Moriyama, Hiroshi Okamoto, Shunji Mitsuyoshi and Ung-il Chung
Symmetry 2021, 13(4), 718; https://doi.org/10.3390/sym13040718 - 19 Apr 2021
Cited by 1 | Viewed by 2783
Abstract
The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. [...] Read more.
The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution. Full article
(This article belongs to the Section Computer)
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17 pages, 8724 KiB  
Article
Applying Ateb–Gabor Filters to Biometric Imaging Problems
by Mariia Nazarkevych, Natalia Kryvinska and Yaroslav Voznyi
Symmetry 2021, 13(4), 717; https://doi.org/10.3390/sym13040717 - 19 Apr 2021
Cited by 2 | Viewed by 2536
Abstract
This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible [...] Read more.
This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well. Full article
(This article belongs to the Special Issue Safe and Reliable AI for Smart Sustainable Cities)
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23 pages, 5010 KiB  
Article
Wire Tension Coordination Control of Electro-Hydraulic Servo Driven Double-Rope Winding Hoisting Systems Using a Hybrid Controller Combining the Flatness-Based Control and a Disturbance Observer
by Xiang Li, Zhencai Zhu, Gang Shen and Yu Tang
Symmetry 2021, 13(4), 716; https://doi.org/10.3390/sym13040716 - 19 Apr 2021
Cited by 5 | Viewed by 2531
Abstract
When the double-rope winding hoisting system (DWHS) is in operation, tensions of two wire ropes of the DWHS will not be symmetrical because of some factors such as different manufacturing deviation between the twin winding drum and two wire ropes, different winding groove [...] Read more.
When the double-rope winding hoisting system (DWHS) is in operation, tensions of two wire ropes of the DWHS will not be symmetrical because of some factors such as different manufacturing deviation between the twin winding drum and two wire ropes, different winding groove depths, the winding asynchronism of two wire ropes, and elastic modulus difference of two wire ropes and so on. Therefore, an electro-hydraulic servo system (EHSS) is employed to actively control two wire ropes tensions to guarantee operation security of the DWHS. Dynamic models of the hoisting system and the EHSS are introduced, of which dynamic model of the DWHS is expressed with state representation. The flatness-based controller (FBC) is designed for the hoisting system. A disturbance observer is utilized to deal with the external disturbance and unmodeled characteristics of the EHSS. Hence, a disturbance observer based integral backstepping controller (DO-BIBC) is designed for the EHSS. The stability of the overall control system is proved by de-fining an overall Lyapunov function. To investigate the property of the proposed controller, an experimental setup of the DWHS is established. As well, comparative experimental results indicate that the proposed controller exhibits a better performance on leveling control of the conveyance and tension coordination control on the two wire ropes than a conventional PI controller. Full article
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19 pages, 1162 KiB  
Article
A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models
by Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi and Shanta Kumari Sunanda
Symmetry 2021, 13(4), 715; https://doi.org/10.3390/sym13040715 - 18 Apr 2021
Cited by 5 | Viewed by 1836
Abstract
We study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided [...] Read more.
We study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided difference of order one as well as the first derivative in our analysis. We also provide computable radius of convergence, error estimates, and uniqueness of the solution results not given in earlier studies. Hence, we expand the applicability of these methods. The dynamical analysis of the discussed family is also presented. Numerical experiments complete this article. Full article
(This article belongs to the Section Mathematics)
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15 pages, 287 KiB  
Article
Investigation of the k-Analogue of Gauss Hypergeometric Functions Constructed by the Hadamard Product
by Mohamed Abdalla and Muajebah Hidan
Symmetry 2021, 13(4), 714; https://doi.org/10.3390/sym13040714 - 18 Apr 2021
Cited by 5 | Viewed by 1991
Abstract
Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted [...] Read more.
Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted to the study of the k-analogue of Gauss hypergeometric functions by the Hadamard product. We give a definition of the Hadamard product of k-Gauss hypergeometric functions (HPkGHF) associated with the fourth numerator and two denominator parameters. In addition, convergence properties are derived from this function. We also discuss interesting properties such as derivative formulae, integral representations, and integral transforms including beta transform and Laplace transform. Furthermore, we investigate some contiguous function relations and differential equations connecting the HPkGHF. The current results are more general than previous ones. Moreover, the proposed results are useful in the theory of k-special functions where the hypergeometric function naturally occurs. Full article
(This article belongs to the Special Issue Special Functions and Polynomials)
15 pages, 322 KiB  
Article
Fixed Points Theorems for Unsaturated and Saturated Classes of Contractive Mappings in Banach Spaces
by Vasile Berinde and Mădălina Păcurar
Symmetry 2021, 13(4), 713; https://doi.org/10.3390/sym13040713 - 18 Apr 2021
Cited by 12 | Viewed by 2005
Abstract
Based on the technique of enriching contractive type mappings, a technique that has been used successfully in some recent papers, we introduce the concept of a saturated class of contractive mappings. We show that, from this perspective, the contractive type mappings in the [...] Read more.
Based on the technique of enriching contractive type mappings, a technique that has been used successfully in some recent papers, we introduce the concept of a saturated class of contractive mappings. We show that, from this perspective, the contractive type mappings in the metric fixed point theory can be separated into two distinct classes, unsaturated and saturated, and that, for any unsaturated class of mappings, the technique of enriching contractive type mappings provides genuine new fixed-point results. We illustrate the concept by surveying some significant fixed-point results obtained recently for five remarkable unsaturated classes of contractive mappings. In the second part of the paper, we also identify two important classes of saturated contractive mappings, whose main feature is that they cannot be enlarged by enriching the contractive mappings. Full article
25 pages, 2854 KiB  
Article
Sensitivity Analysis of Key Formulations of Topology Optimization on an Example of Cantilever Bending Beam
by Martin Sotola, Pavel Marsalek, David Rybansky, Martin Fusek and Dusan Gabriel
Symmetry 2021, 13(4), 712; https://doi.org/10.3390/sym13040712 - 18 Apr 2021
Cited by 12 | Viewed by 3504
Abstract
Topology optimization is a modern method for optimizing the material distribution in a given space, automatically searching for the ideal design of the product. The method aims to maximize the design performance of the system regarding given conditions. In engineering practice, a given [...] Read more.
Topology optimization is a modern method for optimizing the material distribution in a given space, automatically searching for the ideal design of the product. The method aims to maximize the design performance of the system regarding given conditions. In engineering practice, a given space is first described using the finite element method and, subsequently, density-based method with solid isotropic material with penalty. Then, the final shape is found using a gradient-based method, such as the optimality criteria algorithm. However, obtaining the ideal shape is highly dependent on the correct setting of numerical parameters. This paper focuses on the sensitivity analysis of key formulations of topology optimization using the implementation of mathematical programming techniques in MATLAB software. For the purposes of the study, sensitivity analysis of a simple spatial task—cantilever bending—is performed. This paper aims to present the formulations of the optimization problem—in this case, minimization of compliance. It should be noted that this paper does not present any new mathematical formulas but rather provides an introduction into the mathematical theory (including filtering methods and calculating large-size problems using the symmetry of matrices) as well as a step-by step guideline for the minimization of compliance within the density-based topology optimization and search for an optimal shape. The results can be used for complex commercial applications produced by traditional manufacturing processes or by additive manufacturing methods. Full article
(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics)
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22 pages, 502 KiB  
Article
A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications
by Rana Ali Bakoban and Ashwaq Mohammad Al-Shehri
Symmetry 2021, 13(4), 711; https://doi.org/10.3390/sym13040711 - 18 Apr 2021
Cited by 3 | Viewed by 2137
Abstract
In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived [...] Read more.
In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data. Full article
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10 pages, 770 KiB  
Article
Orbit Polynomial of Graphs versus Polynomial with Integer Coefficients
by Modjtaba Ghorbani, Maryam Jalali-Rad and Matthias Dehmer
Symmetry 2021, 13(4), 710; https://doi.org/10.3390/sym13040710 - 17 Apr 2021
Cited by 4 | Viewed by 2515
Abstract
Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is [...] Read more.
Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is obtained by subtracting the orbit polynomial from 1. In the present paper, we studied the conditions under which an integer polynomial can arise as an orbit polynomial of a graph. Additionally, we surveyed graphs with a small number of orbits and characterized several classes of graphs with respect to their orbit polynomials. Full article
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16 pages, 3302 KiB  
Article
Self-Adaptive Genetic Programming for Manufacturing Big Data Analysis
by Sanghoun Oh, Woong-Hyun Suh and Chang-Wook Ahn
Symmetry 2021, 13(4), 709; https://doi.org/10.3390/sym13040709 - 17 Apr 2021
Cited by 3 | Viewed by 2353
Abstract
While black-box-based machine learning algorithms have high analytical consistency in manufacturing big data analysis, those algorithms experience difficulties in interpreting the results based on the manufacturing process principle. To overcome this limitation, we present a Self-Adaptive Genetic Programming (SAGP) for manufacturing big data [...] Read more.
While black-box-based machine learning algorithms have high analytical consistency in manufacturing big data analysis, those algorithms experience difficulties in interpreting the results based on the manufacturing process principle. To overcome this limitation, we present a Self-Adaptive Genetic Programming (SAGP) for manufacturing big data analysis. In Genetic Programming (GP), the solution is expressed as a relationship between variables using mathematical symbols, and the solution with the highest explanatory power is finally selected. These advantages enable intuitive interpretation on manufacturing mechanisms and derive manufacturing principles based on the variables represented by formulas. However, GP occasionally has trouble adjusting the balance between high accuracy and detailed interpretation due to an incommensurable symmetry of the solutions. In order to effectively handle this drawback, we apply the self-adaptive mechanism into GP for managing crossover and mutation probabilities regarding the complexity of tree structure solutions in each generation. Our proposed algorithm showed equal or superior performance compared to other machine learning algorithms. We believe our proposed method can be applied in diverse manufacturing big data analytics in the future. Full article
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28 pages, 4077 KiB  
Article
Multi-Objective Caching Optimization for Wireless Backhauled Fog Radio Access Network
by Alaa Bani-Bakr, MHD Nour Hindia, Kaharudin Dimyati, Effariza Hanafi and Tengku Faiz Tengku Mohmed Noor Izam
Symmetry 2021, 13(4), 708; https://doi.org/10.3390/sym13040708 - 17 Apr 2021
Cited by 10 | Viewed by 1787
Abstract
Proactive content caching in a fog radio access network (F-RAN) is an efficient technique used to alleviate delivery delay and traffic congestion. However, the symmetric caching of the content is impractical due to the dissimilarity among the contents popularity. Therefore, in this paper, [...] Read more.
Proactive content caching in a fog radio access network (F-RAN) is an efficient technique used to alleviate delivery delay and traffic congestion. However, the symmetric caching of the content is impractical due to the dissimilarity among the contents popularity. Therefore, in this paper, a multi-objective random caching scheme to balance the successful transmission probability (STP) and delay in wireless backhauled F-RAN is proposed. First, stochastic geometry tools are utilized to derive expressions of the association probability, STP, and average delivery delay. Next, the complexity is reduced by considering the asymptotic STP and delay in the high signal-to-noise ratio (SNR) regime. Then, aiming at maximizing the STP or minimizing the delay, the multi-objective cache placement optimization problem is formulated. A novel projected multi-objective cuckoo search algorithm (PMOCSA) is proposed to obtain the Pareto front of the optimal cache placement. The numerical results show that PMOCSA outperforms the original multi-objective cuckoo search algorithm (MOCSA) in terms of convergence to a feasible Pareto front and its rate. It also shows that the proposed multi-objective caching scheme significantly outperforms the well-known benchmark caching schemes by up to 40% higher STP and 85% lower average delay. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Communications Engineering)
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19 pages, 1962 KiB  
Article
Research on the Design of a Hexagonal Shaft Straightening Machine Based on Quality Function Development and Evidence Theory
by Juan Zhou, Yuhang Huang and Zhonghua Yu
Symmetry 2021, 13(4), 707; https://doi.org/10.3390/sym13040707 - 17 Apr 2021
Cited by 2 | Viewed by 2162
Abstract
In response to the problem that weights in product planning and design are difficult to accurately reflect the real needs of users, a design method for hexagonal shaft straightening machines based on quality function configuration and evidence theory is proposed. First, based on [...] Read more.
In response to the problem that weights in product planning and design are difficult to accurately reflect the real needs of users, a design method for hexagonal shaft straightening machines based on quality function configuration and evidence theory is proposed. First, based on the method of quality function deployment and evidence theory, the demand indicator and its importance are determined by market research and the Kano model. Second, to solve the conflict problem in the process of expert opinion aggregation, combined with evidence theory, taking expert knowledge as evidence, the possible value space of causal strength among nodes constitutes the recognition framework, which is used to synthesize the knowledge of multiple experts. The indicator correlation degree is reflected by using a correlation weight matrix, and effective solutions to the relevant theoretical problems and algorithms, such as those for competitive indicator evaluation, weight calculation and planning target value cases, are proposed. Finally, according to the analysis results for the various structural elements of the house of quality, a hexagonal shaft straightening machine function for master planning house of quality was constructed, and propose a design and build the main experimental platform. The relevant test results show that the technical specifications of the hexagonal shaft straightening machine basically meet the requirements of the overall planning target values, verifying the effectiveness and feasibility of the proposed method. Full article
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16 pages, 3190 KiB  
Article
X-SDD: A New Benchmark for Hot Rolled Steel Strip Surface Defects Detection
by Xinglong Feng, Xianwen Gao and Ling Luo
Symmetry 2021, 13(4), 706; https://doi.org/10.3390/sym13040706 - 17 Apr 2021
Cited by 74 | Viewed by 8471
Abstract
It is important to accurately classify the defects in hot rolled steel strip since the detection of defects in hot rolled steel strip is closely related to the quality of the final product. The lack of actual hot-rolled strip defect data sets currently [...] Read more.
It is important to accurately classify the defects in hot rolled steel strip since the detection of defects in hot rolled steel strip is closely related to the quality of the final product. The lack of actual hot-rolled strip defect data sets currently limits further research on the classification of hot-rolled strip defects to some extent. In real production, the convolutional neural network (CNN)-based algorithm has some difficulties, for example, the algorithm is not particularly accurate in classifying some uncommon defects. Therefore, further research is needed on how to apply deep learning to the actual detection of defects on the surface of hot rolled steel strip. In this paper, we proposed a hot rolled steel strip defect dataset called Xsteel surface defect dataset (X-SDD) which contains seven typical types of hot rolled strip defects with a total of 1360 defect images. Compared with the six defect types of the commonly used NEU surface defect database (NEU-CLS), our proposed X-SDD contains more types. Then, we adopt the newly proposed RepVGG algorithm and combine it with the spatial attention (SA) mechanism to verify the effect on the X-SDD. Finally, we apply multiple algorithms to test on our proposed X-SDD to provide the corresponding benchmarks. The test results show that our algorithm achieves an accuracy of 95.10% on the testset, which exceeds other comparable algorithms by a large margin. Meanwhile, our algorithm achieves the best results in Macro-Precision, Macro-Recall and Macro-F1-score metrics. Full article
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21 pages, 4511 KiB  
Article
Identical Limb Dynamics for Unilateral Impairments through Biomechanical Equivalence
by Fatemeh Rasouli and Kyle B. Reed
Symmetry 2021, 13(4), 705; https://doi.org/10.3390/sym13040705 - 17 Apr 2021
Cited by 1 | Viewed by 2343
Abstract
Dynamic models, such as double pendulums, can generate similar dynamics as human limbs. They are versatile tools for simulating and analyzing the human walking cycle and performance under various conditions. They include multiple links, hinges, and masses that represent physical parameters of a [...] Read more.
Dynamic models, such as double pendulums, can generate similar dynamics as human limbs. They are versatile tools for simulating and analyzing the human walking cycle and performance under various conditions. They include multiple links, hinges, and masses that represent physical parameters of a limb or an assistive device. This study develops a mathematical model of dissimilar double pendulums that mimics human walking with unilateral gait impairment and establishes identical dynamics between asymmetric limbs. It introduces new coefficients that create biomechanical equivalence between two sides of an asymmetric gait. The numerical solution demonstrates that dissimilar double pendulums can have symmetric kinematic and kinetic outcomes. Parallel solutions with different physical parameters but similar biomechanical coefficients enable interchangeable designs that could be incorporated into gait rehabilitation treatments or alternative prosthetic and ambulatory assistive devices. Full article
(This article belongs to the Special Issue Symmetry and Biomechanics)
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12 pages, 295 KiB  
Article
Analogies between Logistic Equation and Relativistic Cosmology
by Steve Dussault, Valerio Faraoni and Andrea Giusti
Symmetry 2021, 13(4), 704; https://doi.org/10.3390/sym13040704 - 17 Apr 2021
Cited by 2 | Viewed by 2016
Abstract
We develop several formal analogies between the logistic equation and the spatially homogeneous and isotropic relativistic cosmology described by the Einstein–Friedmann equations. These analogies produce an effective Lagrangian and Hamiltonian and new symmetries for the logistic equation. Full article
(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2021)
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