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Symmetry
Volume 14
Issue 9
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Symmetry, Volume 14, Issue 9 (September 2022) – 201 articles

Cover Story (view full-size image): Wave–particle duality, which implies that particles may behave like waves and waves like particles, is a widely accepted principle of quantum physics. Hence, it is not surprising that people are questioning theories that do not support a wave function description of single photons. Here, we compare two equivalent approaches that make such a description possible. One of these approaches localises field vectors, but requires non-Hermitian methods. The other, which localises the carriers of fields, so-called blips, does not. The fields of each distinct blip are non-local and blend together, much like how the canopy of a line of trees becomes homogeneous despite each tree having a distinct trunk. Careful attention needs to be paid to the physical interpretation of non-Hermitian descriptions. View this paper
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9 pages, 507 KiB  
Article
Cosmic Ray Antihelium Probe for the Origin of the Baryonic Matter in the Universe
by Vladislav Golubkov, Maxim Khlopov, Anastasia Kirichenko, Alexandra Kravtsova, Andrey Mayorov and Rustam Yulbarisov
Symmetry 2022, 14(9), 1953; https://doi.org/10.3390/sym14091953 - 19 Sep 2022
Cited by 2 | Viewed by 1747
Abstract
Several candidates for antihelium events have been found in the AMS-02 experiment. They cannot be created by natural astrophysical sources and, if confirmed, imply the existence of antimatter stars in our galaxy. This immediately reduces the class of inflationary models with baryosynthesis to [...] Read more.
Several candidates for antihelium events have been found in the AMS-02 experiment. They cannot be created by natural astrophysical sources and, if confirmed, imply the existence of antimatter stars in our galaxy. This immediately reduces the class of inflationary models with baryosynthesis to those that can provide the creation of an antimatter domain of surviving size together with the general baryon asymmetry of the Universe. To confront the future results of experimental searches for cosmic antihelium with predictions of this hypothesis, we develop numerical studies of the creation and propagation of antihelium flux from antimatter globular clusters in the Galaxy. This article presents the results of such a simulation: a function of the magnetic cut-off for the penetration of antihelium nuclei into the Galaxy disk and an estimate of the energy range in which the search and detection of antihelium is most optimal. Full article
(This article belongs to the Special Issue Cosmic Rays: From Fundamental Symmetry Tests to Civil Applications)
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18 pages, 1926 KiB  
Article
Modern Dimensional Analysis-Based Steel Column Heat Transfer Evaluation Using Multiple Experiments
by Renáta-Ildikó Száva, Ioan Száva, Sorin Vlase, Pál-Botond Gálfi, Károly Jármai, Teofil Gălățeanu, Gabriel Popa and Zsolt Asztalos
Symmetry 2022, 14(9), 1952; https://doi.org/10.3390/sym14091952 - 19 Sep 2022
Cited by 4 | Viewed by 1407
Abstract
In order to foresee the response during the fire of a real symmetrical structure (prototype), nowadays engineers apply methods which involve the associated reduced-scale model’s behaviors, mainly dimensional analysis behaviors. Between the dimensional analysis methods, the so-called Modern Dimensional Analysis (MDA), [...] Read more.
In order to foresee the response during the fire of a real symmetrical structure (prototype), nowadays engineers apply methods which involve the associated reduced-scale model’s behaviors, mainly dimensional analysis behaviors. Between the dimensional analysis methods, the so-called Modern Dimensional Analysis (MDA), developed by Szirtes, fulfills all engineering requirements compared with the classical one. The authors used this new proposed method to describe their original electric fire simulation testing bench, as well as the Model Law (using MDA) for the heat transfer in tubular rectangular bars. So, a validation of the Model Law was performed based on several scrupulous experimental investigations both on a real column’s segment and its associated reduced-scale models manufactured at 1:2; 1:4, as well as 1:10 scales. The original heating system, the elaborated protocol, the deduced Model Law, and the results of the experimental investigations represent the contributions of the authors in the field of metallic structures subject to fires. The results validate the possibility of using MDA in the case of heat transmission. Full article
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13 pages, 3297 KiB  
Article
Realization of Quantum Swap Gate and Generation of Entangled Coherent States
by Ziqiu Zhang, Xi Jiang and Shiqing Tang
Symmetry 2022, 14(9), 1951; https://doi.org/10.3390/sym14091951 - 19 Sep 2022
Cited by 4 | Viewed by 2310
Abstract
The cross fusion of quantum mechanics and information science forms quantum information science. Quantum logic gates and quantum entanglement are very important building blocks in quantum information processing. In this paper, we propose one-step schemes for realizing quantum swap gates and generating two-mode [...] Read more.
The cross fusion of quantum mechanics and information science forms quantum information science. Quantum logic gates and quantum entanglement are very important building blocks in quantum information processing. In this paper, we propose one-step schemes for realizing quantum swap gates and generating two-mode entangled coherent states via circuit QED. In our scheme, due to the adiabatic elimination of the excited state of the qutrit under the condition of large detuning, the decoherence of the spontaneous emission of the qutrit can be ignored. The fidelity of the quantum swap gate remains at a very high level. In addition, we also explore the nonclassical properties of two-mode entangled coherent states prepared in our scheme by addressing the second-order correlation function and intermodal squeezing. In particular, two classes of entangled coherent states demonstrate distinct entanglement and nonclassical behavior. Full article
(This article belongs to the Special Issue Advances in Quantum Information)
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13 pages, 2665 KiB  
Article
Conductive Heat Transfer in Materials under Intense Heat Flows
by Gregory Fedotenkov, Lev Rabinskiy and Sergey Lurie
Symmetry 2022, 14(9), 1950; https://doi.org/10.3390/sym14091950 - 19 Sep 2022
Cited by 26 | Viewed by 1955
Abstract
The paper presents the solution of the spatial transient problem of the impact of a moving heat flux source induced by the laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The hyperbolic equation [...] Read more.
The paper presents the solution of the spatial transient problem of the impact of a moving heat flux source induced by the laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The hyperbolic equation of transient thermal conductivity accounting for the relaxation time is used to model the laser heating process. It is assumed that the heat flux is distributed symmetrically with respect to the center of the heating spot. The combined numerical and analytical algorithm has been developed and implemented, which allows one to determine the temperature distribution both on the surface and on the depth of the half-space. In this case, the principle of superposition is used with the use of a special symmetric Gaussian distribution to describe the model of a source of high-intensity heat flux. The use of such a symmetric distribution made it possible to calculate the integrals over the spatial variables analytically. The results of the work could be used to estimate the contribution of the conductive component in the overall heat transfer of materials exposed to intense heat flows (laser surface treatment, laser additive technologies, streamlining and heating of materials by high-enthalpy gases, etc.). Full article
(This article belongs to the Special Issue Foundations of Continuum Mechanics and Mathematical Physics)
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18 pages, 826 KiB  
Article
Event-Triggered Adaptive Neural Network Tracking Control with Dynamic Gain and Prespecified Tracking Accuracy for a Class of Pure-Feedback Systems
by Shuiyan Wu, Han Liu and Xiaobo Li
Symmetry 2022, 14(9), 1949; https://doi.org/10.3390/sym14091949 - 19 Sep 2022
Viewed by 1318
Abstract
This paper studies the event-triggered adaptive tracking control problem of a class of pure-feedback systems. Via the backstepping method and the neural network approximation with the central symmetric distribution, an event-triggered adaptive neural network controller is designed. In particular, a dynamic gain driven [...] Read more.
This paper studies the event-triggered adaptive tracking control problem of a class of pure-feedback systems. Via the backstepping method and the neural network approximation with the central symmetric distribution, an event-triggered adaptive neural network controller is designed. In particular, a dynamic gain driven by the tracking error is introduced into the event-triggering mechanism. Then, by using the Lyapunov stability theory, the boundedness of all the closed-loop signals is proved, and the tracking error falls into a prespecified ϵ-neighbourhood of zero. Meanwhile, the Zeno behaviour is avoided. Finally, two simulations verify the effectiveness of the proposed control scheme. Full article
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22 pages, 433 KiB  
Article
Existence Results for Nonlinear Coupled Hilfer Fractional Differential Equations with Nonlocal Riemann–Liouville and Hadamard-Type Iterated Integral Boundary Conditions
by Sunisa Theswan, Sotiris K. Ntouyas, Bashir Ahmad and Jessada Tariboon
Symmetry 2022, 14(9), 1948; https://doi.org/10.3390/sym14091948 - 19 Sep 2022
Cited by 6 | Viewed by 1760
Abstract
We introduce and study a new class of nonlinear coupled Hilfer differential equations with nonlocal boundary conditions involving Riemann–Liouville and Hadamard-type iterated fractional integral operators. By applying the Leray–Schauder alternative and Krasnosel’skiĭ’s fixed point theorem, two results presenting different criteria for the existence [...] Read more.
We introduce and study a new class of nonlinear coupled Hilfer differential equations with nonlocal boundary conditions involving Riemann–Liouville and Hadamard-type iterated fractional integral operators. By applying the Leray–Schauder alternative and Krasnosel’skiĭ’s fixed point theorem, two results presenting different criteria for the existence of solutions to the given problem are proven. The third result provides a sufficient criterion for the existence of a unique solution to the problem at hand. Numerical examples are constructed to demonstrate the application of the results obtained. Two graphs show asymmetric solutions when a Hilfer parameter is varied. The work presented in this paper is novel and significantly enriches the literature on the topic. Full article
(This article belongs to the Special Issue Symmetry in Computational and Mathematical Methods of Fractional Calculus)
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8 pages, 252 KiB  
Article
Tachyons as a Consequence of Light-Cone Reflection Symmetry
by Alan Chodos
Symmetry 2022, 14(9), 1947; https://doi.org/10.3390/sym14091947 - 19 Sep 2022
Cited by 2 | Viewed by 1423
Abstract
We introduce a new symmetry, light-cone reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to [...] Read more.
We introduce a new symmetry, light-cone reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry. Full article
(This article belongs to the Special Issue Tachyons and Fundamental Symmetries)
18 pages, 5590 KiB  
Article
Modified Golden Jackal Optimization Assisted Adaptive Fuzzy PIDF Controller for Virtual Inertia Control of Micro Grid with Renewable Energy
by S. Nanda Kumar and Nalin Kant Mohanty
Symmetry 2022, 14(9), 1946; https://doi.org/10.3390/sym14091946 - 19 Sep 2022
Cited by 9 | Viewed by 1984
Abstract
Frequency regulation of low inertia symmetric micro grids with the incorporation of asymmetric renewable sources such as solar and wind is a challenging task. Virtual Inertia Control (VIC) is the idea of increasing micro grids’ inertia by energy storage systems. In the current [...] Read more.
Frequency regulation of low inertia symmetric micro grids with the incorporation of asymmetric renewable sources such as solar and wind is a challenging task. Virtual Inertia Control (VIC) is the idea of increasing micro grids’ inertia by energy storage systems. In the current study, an adaptive fuzzy PID structure with a derivative filter (AFPIDF) controller is suggested for VIC of a micro grid with renewable sources. To optimize the proposed controllers, a modified Golden Jackal Optimization (mGJO) has been proposed, where variable Sine Cosine adopted Scaling Factor (SCaSF) is employed to adjust the Jackal’s location in the course of search process to improve the exploration and exploitation capability of the original Golden Jackal Optimization (GJO) algorithm. The performance of the mGJO algorithm is verified by equating it with original GJO, as well as Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Teaching Learning Based Optimization (TLBO) and Ant Lion Optimizer (ALO), considering various standard benchmark test functions. In the next stage, conventional PID and proposed FPIDF controller parameters are optimized using the proposed mGJO technique and the superiority of mGJO over other symmetric optimization algorithms is demonstrated. The robustness of the controller is also investigated under intermittent load disturbances, as well as different levels of asymmetric RESs integration. Full article
(This article belongs to the Section Engineering and Materials)
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23 pages, 6680 KiB  
Article
Analysis of Heat Transfer of Mono and Hybrid Nanofluid Flow between Two Parallel Plates in a Darcy Porous Medium with Thermal Radiation and Heat Generation/Absorption
by Moh Yaseen, Sawan Kumar Rawat, Anum Shafiq, Manoj Kumar and Kamsing Nonlaopon
Symmetry 2022, 14(9), 1943; https://doi.org/10.3390/sym14091943 - 19 Sep 2022
Cited by 53 | Viewed by 3243
Abstract
In the last two decades, academicians have concentrated on the nanofluid squeezing flow between parallel plates. The increasing energy demands and their applications have seen the focus shifted to the hybrid nanofluid flows, but so much is still left to be investigated. This [...] Read more.
In the last two decades, academicians have concentrated on the nanofluid squeezing flow between parallel plates. The increasing energy demands and their applications have seen the focus shifted to the hybrid nanofluid flows, but so much is still left to be investigated. This analysis is executed to explore the symmetry of the MHD squeezing nanofluid (MoS2/H2O) flow and the hybrid nanofluid (MoS2–SiO2/H2O–C2H6O2) flow between the parallel plates and their heat transport property. The heat transport phenomenon is analyzed with the magnetic field, thermal radiation, heat source/sink, suction/injection effect, and porous medium. In the present model, the plate situated above is in the movement towards the lower plate, and the latter is stretching with a linear velocity. The prevailing PDEs depicting the modeled problem with the aforementioned effects are transformed via similarity transformations and solved via the “bvp4c” function, which is an inbuilt function in MATLAB software. The control of the factors on the fields of velocity and temperature, heat transfer rate, velocity boundary layer patterns, and streamlines is investigated. The solution profiles are visually shown and explained. Furthermore, the Nusselt number at the bottom plate is larger for the (MoS2–SiO2/H2O–C2H6O2) hybrid nanofluid than for the (MoS2/H2O) nanofluid flow. In the presence of suction/injection, the streamlines appear to be denser. In addition, the magnetic field has a thinning consequence on the velocity boundary layer region. The results of this study apply to several thermal systems, engineering, and industrial processes, which utilize nanofluid and hybrid nanofluid for cooling and heating processes. Full article
(This article belongs to the Special Issue Symmetry of Nanofluids and Their Applications in Engineering)
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13 pages, 2920 KiB  
Article
On the Symmetry Importance in a Relative Entropy Analysis for Some Engineering Problems
by Marcin Kamiński
Symmetry 2022, 14(9), 1945; https://doi.org/10.3390/sym14091945 - 18 Sep 2022
Cited by 1 | Viewed by 1260
Abstract
This paper aims at certain theoretical studies and additional computational analysis on symmetry and its lack in Kullback-Leibler and Jeffreys probabilistic divergences related to some engineering applications. As it is known, the Kullback-Leibler distance in between two different uncertainty sources exhibits a lack [...] Read more.
This paper aims at certain theoretical studies and additional computational analysis on symmetry and its lack in Kullback-Leibler and Jeffreys probabilistic divergences related to some engineering applications. As it is known, the Kullback-Leibler distance in between two different uncertainty sources exhibits a lack of symmetry, while the Jeffreys model represents its symmetrization. The basic probabilistic computational implementation has been delivered in the computer algebra system MAPLE 2019®, whereas engineering illustrations have been prepared with the use of the Finite Element Method systems Autodesk ROBOT® & ABAQUS®. Determination of the first two probabilistic moments fundamental in the calculation of both relative entropies has been made (i) analytically, using a semi-analytical approach (based upon the series of the FEM experiments), and (ii) the iterative generalized stochastic perturbation technique, where some reference solutions have been delivered using (iii) Monte-Carlo simulation. Numerical analysis proves the fundamental role of computer algebra systems in probabilistic entropy determination and shows remarkable differences obtained with the two aforementioned relative entropy models, which, in some specific cases, may be neglected. As it is demonstrated in this work, a lack of symmetry in probabilistic divergence may have a decisive role in engineering reliability, where extreme and admissible responses cannot be simply replaced with each other in any case. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Damage Detection, Wavelet Transformation and Applied Mechanics)
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20 pages, 3217 KiB  
Article
Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series
by Aisha Abdullah Alderremy, Rasool Shah, Naveed Iqbal, Shaban Aly and Kamsing Nonlaopon
Symmetry 2022, 14(9), 1944; https://doi.org/10.3390/sym14091944 - 18 Sep 2022
Cited by 49 | Viewed by 1941
Abstract
This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination of the Laplace transformation and the residual power series technique, we achieve analytic and [...] Read more.
This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination of the Laplace transformation and the residual power series technique, we achieve analytic and approximation results in rapid convergent series form by employing the notion of the limit, with less time and effort than the residual power series method. Three challenges are evaluated and simulated to validate the suggested method’s practicability, efficiency, and simplicity. The analysis of the acquired findings demonstrates that the method mentioned above is simple, accurate, and appropriate for investigating the solutions to nonlinear applied sciences models. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry)
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13 pages, 3650 KiB  
Article
Transmission Properties of Electromagnetic Waves in Magneto-Electro-Elastic Piezoelectric Electromagnetic Metamaterials
by Wen-Chao Bai, Hui Hu, Ben-Hu Zhou, Gui-Xiang Liu, Ge Tang, Yang-Yu Huang, Yan Cao, Han Zhang and Han-Zhuang Zhang
Symmetry 2022, 14(9), 1942; https://doi.org/10.3390/sym14091942 - 18 Sep 2022
Viewed by 1799
Abstract
We designed magneto-electro-elastic piezoelectric, electromagnetic (EM) metamaterials (MEEPEM) by using a square lattice of the periodic arrays of conducting wires, piezoelectric photonic crystal (PPC), and split-ring resonators (SRRs). We analyzed the mechanism for multi-field coupling in MEEPEM. The magnetic field of the EM [...] Read more.
We designed magneto-electro-elastic piezoelectric, electromagnetic (EM) metamaterials (MEEPEM) by using a square lattice of the periodic arrays of conducting wires, piezoelectric photonic crystal (PPC), and split-ring resonators (SRRs). We analyzed the mechanism for multi-field coupling in MEEPEM. The magnetic field of the EM wave excites an attractive Ampère force in SRRs, which periodically compress MEEPEM, and this can create electric polarization due to the piezoelectric effect. The electric field of the EM wave can excite a longitudinal superlattice vibration in the PPC, which can also create electric polarization. The electric polarization can couple to the electric field of the periodic arrays of conducting wires. The coupled electric field will couple to the EM wave. These interactions result in multi-field coupling in MEEPEM. The coupling creates a type of polariton, called multi-field coupling polaritons, corresponding to a photonic band gap, namely, the multi-field coupling photonic band gap. We calculated the dielectric functions, the reflection coefficients, and the effective magnetic permeability of MEEPEM. By using them, we analyzed the transmission properties of EM waves in the MEEPEM. We analyzed the possibility of MEEPEM as left-handed metamaterials and zero refractive index material. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Study on Quantum Optics)
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27 pages, 430 KiB  
Article
Proportional Caputo Fractional Differential Inclusions in Banach Spaces
by Abdelkader Rahmani, Wei-Shih Du, Mohammed Taha Khalladi, Marko Kostić and Daniel Velinov
Symmetry 2022, 14(9), 1941; https://doi.org/10.3390/sym14091941 - 18 Sep 2022
Cited by 6 | Viewed by 1712
Abstract
In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order α∈(0,1) for a continuous (locally integrable) function u:[0,∞)→E, where E is a [...] Read more.
In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order α∈(0,1) for a continuous (locally integrable) function u:[0,∞)→E, where E is a complex Banach space. In our definition, we do not require that the function u(·) is continuously differentiable, which enables us to consider the wellposedness of the corresponding fractional relaxation problems in a much better theoretical way. More precisely, we systematically investigate several new classes of (degenerate) fractional solution operator families connected with the use of this type of fractional derivatives, obeying the multivalued linear approach to the abstract Volterra integro-differential inclusions. The quasi-periodic properties of the proportional fractional integrals as well as the existence and uniqueness of almost periodic-type solutions for various classes of proportional Caputo fractional differential inclusions in Banach spaces are also considered. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Boundary Value Problems)
25 pages, 11085 KiB  
Article
Quasi-Linearization Analysis for Entropy Generation in MHD Mixed-Convection Flow of Casson Nanofluid over Nonlinear Stretching Sheet with Arrhenius Activation Energy
by Kashif Ali, Aftab Ahmed Faridi, Sohail Ahmad, Wasim Jamshed, Syed M. Hussain and El Sayed M. Tag-Eldin
Symmetry 2022, 14(9), 1940; https://doi.org/10.3390/sym14091940 - 18 Sep 2022
Cited by 5 | Viewed by 1745
Abstract
Thermal performance of magnetically driven Casson nanofluid over a nonlinear stretching sheet under the influence of entropy, activation energy and convective boundary conditions was analyzed numerically, employing the quasi-linearization method (QLM). The collective behavior of thermophoretic diffusion and Brownian motion along with special [...] Read more.
Thermal performance of magnetically driven Casson nanofluid over a nonlinear stretching sheet under the influence of entropy, activation energy and convective boundary conditions was analyzed numerically, employing the quasi-linearization method (QLM). The collective behavior of thermophoretic diffusion and Brownian motion along with special effects of viscous dissipation, thermal radiation, heat generation and joule heating are considered in the energy equation for the flow problem. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and maintain the symmetry of the flowing structure. The governing highly nonlinear coupled differential equations of velocity, temperature, concentration and entropy are simulated through an iterative scheme encoded with MATLAB programming language. The geometric model is, therefore, described using a symmetry technique. A comparative analysis of linear and nonlinear stretching in sheets is presented via graphs and tables regarding pertinent dimensionless parameters. It is worth noting that the Nusselt number and Sherwood number decrease at relatively higher rates with growing values of activation energy in the case of nonlinear stretching. Moreover, the entropy generation rate near the stretching surface decreases due to the strong effects of Brownian motion and thermophoretic diffusion while it goes on improving far off the stretching surface. Full article
(This article belongs to the Special Issue Symmetry of Nanofluids and Their Applications in Engineering)
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18 pages, 4733 KiB  
Article
Critical Dynamics in Stratospheric Potential Energy Variations Prior to Significant (M > 6.7) Earthquakes
by Dimitrios Z. Politis, Stelios M. Potirakis, Subrata Kundu, Swati Chowdhury, Sudipta Sasmal and Masashi Hayakawa
Symmetry 2022, 14(9), 1939; https://doi.org/10.3390/sym14091939 - 18 Sep 2022
Cited by 12 | Viewed by 1874
Abstract
Lithosphere–atmosphere–ionosphere coupling (LAIC) is studied through various physical or chemical quantities, obtained from different sources, which are observables of the involved complex processes. LAIC has been proposed to be achieved through three major channels: the chemical, the acoustic, and the electromagnetic. Accumulated evidence [...] Read more.
Lithosphere–atmosphere–ionosphere coupling (LAIC) is studied through various physical or chemical quantities, obtained from different sources, which are observables of the involved complex processes. LAIC has been proposed to be achieved through three major channels: the chemical, the acoustic, and the electromagnetic. Accumulated evidence supporting the acoustic channel hypothesis has been published, while atmospheric gravity waves (AGWs) play a key role in LAIC as the leading mechanism for the transmission of energy from the lower atmosphere to the stratosphere and mesosphere, associated with atmospheric disturbances observed prior to strong earthquakes (EQs). The seismogenic AGW is the result of temperature disturbances, usually studied through stratospheric potential energy (EP). In this work, we examined 11 cases of significant EQs (M > 6.7) that occurred during the last 10 years at different geographic areas by analyzing the temperature profile at the wider location of each one of the examined EQs. The “Sounding of the Atmosphere using Broadband Emission Radiometry” (SABER) instrument, part of the “Thermosphere Ionosphere Mesosphere Energetics Dynamics” (TIMED) satellite, data were employed to compute the potential energy (EP) of the AGW. Using the temperature profile, we first calculated EP and determined the altitudes’ range for which prominent pre-seismic disturbances were observed. Subsequently, the EP time series at specific altitudes, within the determined “disturbed” range, were for the first time analyzed using the criticality analysis method termed the “natural time” (NT) method in order to find any evidence of an approach to a critical state (during a phase transition from a symmetric phase to a low symmetry phase) prior to the EQ occurrence. Our results show criticality indications in the fluctuation of EP a few days (1 to 15 days) prior to the examined EQs, except from one case. In our study, we also examined all of the temperature-related extreme phenomena that have occurred near the examined geographic areas, in order to take into account any possible non-seismic influence on the obtained results. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)
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19 pages, 965 KiB  
Article
A Text Classification Model via Multi-Level Semantic Features
by Keji Mao, Jinyu Xu, Xingda Yao, Jiefan Qiu, Kaikai Chi and Guanglin Dai
Symmetry 2022, 14(9), 1938; https://doi.org/10.3390/sym14091938 - 17 Sep 2022
Cited by 6 | Viewed by 2929
Abstract
Text classification is a major task of NLP (Natural Language Processing) and has been the focus of attention for years. News classification as a branch of text classification is characterized by complex structure, large amounts of information and long text length, which in [...] Read more.
Text classification is a major task of NLP (Natural Language Processing) and has been the focus of attention for years. News classification as a branch of text classification is characterized by complex structure, large amounts of information and long text length, which in turn leads to a decrease in the accuracy of classification. To improve the classification accuracy of Chinese news texts, we present a text classification model based on multi-level semantic features. First, we add the category correlation coefficient to TF-IDF (Term Frequency-Inverse Document Frequency) and the frequency concentration coefficient to CHI (Chi-Square), and extract the keyword semantic features with the improved algorithm. Then, we extract local semantic features with TextCNN with symmetric-channel and global semantic information from a BiLSTM with attention. Finally, we fuse the three semantic features for the prediction of text categories. The results of experiments on THUCNews, LTNews and MCNews show that our presented method is highly accurate, with 98.01%, 90.95% and 94.24% accuracy, respectively. With model parameters two magnitudes smaller than Bert, the improvements relative to the baseline Bert+FC are 1.27%, 1.2%, and 2.81%, respectively. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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10 pages, 268 KiB  
Article
On the Sum and Spread of Reciprocal Distance Laplacian Eigenvalues of Graphs in Terms of Harary Index
by Saleem Khan, Shariefuddin Pirzada and Yilun Shang
Symmetry 2022, 14(9), 1937; https://doi.org/10.3390/sym14091937 - 17 Sep 2022
Cited by 10 | Viewed by 1705
Abstract
The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RT(G)−RD(G), where RT(G) is the diagonal matrix of [...] Read more.
The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RT(G)−RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Clearly, RDL(G) is a real symmetric matrix, and we denote its eigenvalues as λ1(RDL(G))≥λ2(RDL(G))≥…≥λn(RDL(G)). The largest eigenvalue λ1(RDL(G)) of RDL(G), denoted by λ(G), is called the reciprocal distance Laplacian spectral radius. In this paper, we obtain several upper bounds for the sum of k largest reciprocal distance Laplacian eigenvalues of G in terms of various graph parameters, such as order n, maximum reciprocal distance degree RTmax, minimum reciprocal distance degree RTmin, and Harary index H(G) of G. We determine the extremal cases corresponding to these bounds. As a consequence, we obtain the upper bounds for reciprocal distance Laplacian spectral radius λ(G) in terms of the parameters as mentioned above and characterize the extremal cases. Moreover, we attain several upper and lower bounds for reciprocal distance Laplacian spread RDLS(G)=λ1(RDL(G))−λn−1(RDL(G)) in terms of various graph parameters. We determine the extremal graphs in many cases. Full article
(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications)
13 pages, 435 KiB  
Article
Partial Asymmetry Measures for Square Contingency Tables
by Takuma Ishihara, Kouji Yamamoto, Kouji Tahata and Sadao Tomizawa
Symmetry 2022, 14(9), 1936; https://doi.org/10.3390/sym14091936 - 17 Sep 2022
Cited by 1 | Viewed by 1327
Abstract
In square contingency table analysis, we consider a partial measure that represents the degree of departure from symmetry for each of several pairs. It may be useful to pool the values of the measure into a single summary measure of partial asymmetry. We [...] Read more.
In square contingency table analysis, we consider a partial measure that represents the degree of departure from symmetry for each of several pairs. It may be useful to pool the values of the measure into a single summary measure of partial asymmetry. We show that the estimator of partial measures is asymptotically mutually independent for a large sample size. The present paper proposes a symmetry measure in the class of weighted averages that is different from previous studies. The proposed measure is an approximation of the measure in the class of weighted averages that has the smallest variance. Full article
(This article belongs to the Section Mathematics)
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21 pages, 425 KiB  
Article
New Quantum Mercer Estimates of Simpson–Newton-like Inequalities via Convexity
by Saad Ihsan Butt, Hüseyin Budak and Kamsing Nonlaopon
Symmetry 2022, 14(9), 1935; https://doi.org/10.3390/sym14091935 - 16 Sep 2022
Cited by 17 | Viewed by 1529
Abstract
Recently, developments and extensions of quadrature inequalities in quantum calculus have been extensively studied. As a result, several quantum extensions of Simpson’s and Newton’s estimates are examined in order to explore different directions in quantum studies. The main motivation of this article is [...] Read more.
Recently, developments and extensions of quadrature inequalities in quantum calculus have been extensively studied. As a result, several quantum extensions of Simpson’s and Newton’s estimates are examined in order to explore different directions in quantum studies. The main motivation of this article is the development of variants of Simpson–Newton-like inequalities by employing Mercer’s convexity in the context of quantum calculus. The results also give new quantum bounds for Simpson–Newton-like inequalities through Hölder’s inequality and the power mean inequality by employing the Mercer scheme. The validity of our main results is justified by providing examples with graphical representations thereof. The obtained results recapture the discoveries of numerous authors in quantum and classical calculus. Hence, the results of these inequalities lead us to the development of new perspectives and extensions of prior results. Full article
(This article belongs to the Special Issue Symmetry in Quantum Calculus)
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14 pages, 298 KiB  
Article
Application of a Multiplier Transformation to Libera Integral Operator Associated with Generalized Distribution
by Jamiu Olusegun Hamzat, Abiodun Tinuoye Oladipo and Georgia Irina Oros
Symmetry 2022, 14(9), 1934; https://doi.org/10.3390/sym14091934 - 16 Sep 2022
Cited by 2 | Viewed by 1260
Abstract
The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function fs(z) is defined as involving an analytic [...] Read more.
The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function fs(z) is defined as involving an analytic p-valent function and generalized distribution expressed in terms of analytic p-valent functions. Neighborhood properties for functions fs(z) are established. Further, by applying a previously introduced linear transformation to fs(z) and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform. Full article
(This article belongs to the Special Issue Symmetry in Pure Mathematics and Real and Complex Analysis)
15 pages, 747 KiB  
Article
Direct Training via Backpropagation for Ultra-Low-Latency Spiking Neural Networks with Multi-Threshold
by Changqing Xu, Yi Liu, Dongdong Chen and Yintang Yang
Symmetry 2022, 14(9), 1933; https://doi.org/10.3390/sym14091933 - 16 Sep 2022
Cited by 9 | Viewed by 1978
Abstract
Spiking neural networks (SNNs) can utilize spatio-temporal information and have the characteristic of energy efficiency, being a good alternative to deep neural networks (DNNs). The event-driven information processing means that SNNs can reduce the expensive computation of DNNs and save a great deal [...] Read more.
Spiking neural networks (SNNs) can utilize spatio-temporal information and have the characteristic of energy efficiency, being a good alternative to deep neural networks (DNNs). The event-driven information processing means that SNNs can reduce the expensive computation of DNNs and save a great deal of energy consumption. However, high training and inference latency is a limitation of the development of deeper SNNs. SNNs usually need tens or even hundreds of time steps during the training and inference process, which causes not only an increase in latency but also excessive energy consumption. To overcome this problem, we propose a novel training method based on backpropagation (BP) for ultra-low-latency (1–2 time steps) SNNs with multi-threshold. In order to increase the information capacity of each spike, we introduce the multi-threshold Leaky Integrate and Fired (LIF) model. The experimental results show that our proposed method achieves average accuracy of 99.56%, 93.08%, and 87.90% on MNIST, FashionMNIST, and CIFAR10, respectively, with only two time steps. For the CIFAR10 dataset, our proposed method achieves 1.12% accuracy improvement over the previously reported directly trained SNNs with fewer time steps. Full article
(This article belongs to the Section Computer)
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13 pages, 4751 KiB  
Article
Diabetic Retinopathy Classification Using CNN and Hybrid Deep Convolutional Neural Networks
by Yasashvini R., Vergin Raja Sarobin M., Rukmani Panjanathan, Graceline Jasmine S. and Jani Anbarasi L.
Symmetry 2022, 14(9), 1932; https://doi.org/10.3390/sym14091932 - 16 Sep 2022
Cited by 38 | Viewed by 11953
Abstract
Diabetic Retinopathy (DR) is an eye condition that mainly affects individuals who have diabetes and is one of the important causes of blindness in adults. As the infection progresses, it may lead to permanent loss of vision. Diagnosing diabetic retinopathy manually with the [...] Read more.
Diabetic Retinopathy (DR) is an eye condition that mainly affects individuals who have diabetes and is one of the important causes of blindness in adults. As the infection progresses, it may lead to permanent loss of vision. Diagnosing diabetic retinopathy manually with the help of an ophthalmologist has been a tedious and a very laborious procedure. This paper not only focuses on diabetic retinopathy detection but also on the analysis of different DR stages, which is performed with the help of Deep Learning (DL) and transfer learning algorithms. CNN, hybrid CNN with ResNet, hybrid CNN with DenseNet are used on a huge dataset with around 3662 train images to automatically detect which stage DR has progressed. Five DR stages, which are 0 (No DR), 1 (Mild DR), 2 (Moderate), 3 (Severe) and 4 (Proliferative DR) are processed in the proposed work. The patient’s eye images are fed as input to the model. The proposed deep learning architectures like CNN, hybrid CNN with ResNet, hybrid CNN with DenseNet 2.1 are used to extract the features of the eye for effective classification. The models achieved an accuracy of 96.22%, 93.18% and 75.61% respectively. The paper concludes with a comparative study of the CNN, hybrid CNN with ResNet, hybrid CNN with DenseNet architectures that highlights hybrid CNN with DenseNet as the perfect deep learning classification model for automated DR detection. Full article
(This article belongs to the Special Issue Deep Learning and Symmetry)
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15 pages, 302 KiB  
Article
Repdigits as Sums of Four Tribonacci Numbers
by Yuetong Zhou, Peng Yang, Shaonan Zhang and Kaiqiang Zhang
Symmetry 2022, 14(9), 1931; https://doi.org/10.3390/sym14091931 - 16 Sep 2022
Viewed by 1448
Abstract
In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet’s formula, Baker’s theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo [...] Read more.
In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet’s formula, Baker’s theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo 9 to deal with three individual cases. Full article
(This article belongs to the Topic Engineering Mathematics)
15 pages, 549 KiB  
Article
One-Parameter Lorentzian Dual Spherical Movements and Invariants of the Axodes
by Yanlin Li, Nadia Alluhaibi and Rashad A. Abdel-Baky
Symmetry 2022, 14(9), 1930; https://doi.org/10.3390/sym14091930 - 15 Sep 2022
Cited by 23 | Viewed by 1916
Abstract
E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian [...] Read more.
E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler–Savary, and Disteli’s formulae were derived. Full article
(This article belongs to the Section Mathematics)
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11 pages, 2726 KiB  
Article
A Monopole UWB Antenna for WIFI 7/Bluetooth and Satellite Communication
by Zhonggen Wang, Mingqing Wang and Wenyan Nie
Symmetry 2022, 14(9), 1929; https://doi.org/10.3390/sym14091929 - 15 Sep 2022
Cited by 5 | Viewed by 2503
Abstract
In this paper, a monopole UWB broadband antenna is designed, fabricated, and measured for wireless communication networks. The initial radiator model of the proposed antenna has a short-sleeve shape, and to expand the impedance bandwidth, the right and left angles are subtracted symmetrically [...] Read more.
In this paper, a monopole UWB broadband antenna is designed, fabricated, and measured for wireless communication networks. The initial radiator model of the proposed antenna has a short-sleeve shape, and to expand the impedance bandwidth, the right and left angles are subtracted symmetrically from the lower half of the radiator. The impedance matching is improved by etching slots in the feed line and adding L-shaped patches symmetrically on both sides of the feed line. The results show that the proposed miniaturized antenna system can cover WiFi 7(2.4–2.484 GHz, 5.15–5.35 GHz, 5.725–5.825 GHz, 5.925–7.125 GHz), 4G LTE (2.3–2.39 GHz, 2.555–2.655 GHz), 5G (4.8–5.0 GHz), X-band (7–12.4 GHz), Ku-band (10.7–14.59 GHz), and C-band uplink bands (5.925–6.425 GHz). Moreover, the antenna is found to be omnidirectional at low frequencies, with a maximum peak gain of 5.43 dBi. The antenna can be used for multi-frequency wireless communication applications. Full article
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23 pages, 4433 KiB  
Article
Multi-Effects of Tunneling and Basement Excavation on Existing Pile Group
by Hongguo Diao, Ye Tian, Gang Wei, Xinquan Wang and Xiao Li
Symmetry 2022, 14(9), 1928; https://doi.org/10.3390/sym14091928 - 15 Sep 2022
Cited by 4 | Viewed by 2141
Abstract
Tunnels and foundation pits are two separate types of excavation that are frequently used in urban settings. Excavating tunnels and foundation pits sequentially around existing pile foundations is becoming more and more prevalent as urban underground space utilization rates increase. The deformation and [...] Read more.
Tunnels and foundation pits are two separate types of excavation that are frequently used in urban settings. Excavating tunnels and foundation pits sequentially around existing pile foundations is becoming more and more prevalent as urban underground space utilization rates increase. The deformation and load transfer mechanisms of the pile group foundation under two asymmetric excavation conditions of “first tunnel, then foundation pit” and “first foundation pit, then tunnel” are studied from the perspective of the relative positions of the tunnel–pile–foundation pit based on the constant gravity model test and 3D numerical simulation. The result shows: The pile settlement of the front pile (closer to the tunnel) caused by the excavation condition of the “first foundation pit-then tunnel” is relatively larger, while the pile settlement of the rear pile (closer to the foundation pit) caused by the excavation condition of “first tunnel-then pit” is larger. The transverse tilting of the pile group caused by the excavation of the “first foundation pit-then tunnel” is relatively larger. For the front pile, the pile tip resistance generated by “first excavation-then tunnel” is about 10% greater than it was before the initial excavation, which is greater than the result of “first tunnel-then foundation pit”. For the rear pile, the pile tip resistance generated by “first excavation-then tunnel” is about 85% greater than it was before the initial excavation, which is smaller than the result of “first tunnel-then foundation pit”. The multiple excavation sequence of “tunnel first-then foundation pit” leads to a larger induced bending moment for the front pile, whereas a larger induced bending moment for the rear pile results from the multiple excavation sequence “first foundation pit-then tunnel”. Full article
(This article belongs to the Section Engineering and Materials)
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9 pages, 1007 KiB  
Article
The Impact of Piano Styles on Muscle Force in Pianist Students
by Iulia Toma, Elena Amaricai, Roxana Ramona Onofrei and Mihai Popean
Symmetry 2022, 14(9), 1927; https://doi.org/10.3390/sym14091927 - 15 Sep 2022
Cited by 1 | Viewed by 1852
Abstract
The study of the consequences of different sonata styles (baroque, classical and romantic piano repertoire) on pianists’ upper limbs represents a research topic for both the musical and medical fields. Twenty piano students were examined using a MicroFet2 dynamometer after playing three sonatas [...] Read more.
The study of the consequences of different sonata styles (baroque, classical and romantic piano repertoire) on pianists’ upper limbs represents a research topic for both the musical and medical fields. Twenty piano students were examined using a MicroFet2 dynamometer after playing three sonatas (Scarlatti K. 1 Sonata as a representative of the baroque style, Haydn Sonata no. 60 for the classical style and Chopin second Sonata for the romantic style). The phase sequence was randomised for each subject: firstly, continuous interpretation of 10 bars of a sonata was conducted 10 times, with the metronome tempo set by the investigator; secondly, the subject interpreted 10 bars of a different sonata continuously, standardised by tempo, which was carried out 10 times; finally, the continuous interpretation of 10 bars of the remaining third sonata, standardised by tempo, was carried out 10 times. After each performance of the 10 bars, the elbow extensor’s isometric muscle force was measured. Significant differences were found between the elbow extensor’s isometric muscle force assessed after playing Scarlatti’s sonata and Haydn’s sonata (p = 0.005 for left arm, p = 0.03 for right arm), between Scarlatti’s sonata and Chopin’s sonata (p < 0.0001 for both left and right arms) and between Haydn’s sonata and Chopin’s sonata (p = 0.01 for left arm, p < 0.0001 for right arm). In healthy piano students, the dynamometric assessment of elbow extensors’ isometric muscle force after playing three different sonatas (baroque, classical and romantic) showed that the lowest values were recorded after playing the baroque style. Our results showed bilateral symmetry in the elbow extensor’s isometric muscle force for all three piano styles. The testing of arm muscles, besides that of the fingers, should be considered as a regular evaluation for future professional pianists with regard to the prevention of musculoskeletal complaints. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Musculoskeletal Science)
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25 pages, 695 KiB  
Article
Basic Statistical Properties of the Knot Efficiency
by Ján Šimon and Branislav Ftorek
Symmetry 2022, 14(9), 1926; https://doi.org/10.3390/sym14091926 - 15 Sep 2022
Cited by 1 | Viewed by 2191
Abstract
A knot is the weakest point of every rope, and the knot efficiency measures the portion of original rope strength taken away by the knot. Despite possible safety implications, surprisingly little attention has been paid to this life-critical quantity in research papers. Knot [...] Read more.
A knot is the weakest point of every rope, and the knot efficiency measures the portion of original rope strength taken away by the knot. Despite possible safety implications, surprisingly little attention has been paid to this life-critical quantity in research papers. Knot efficiency is directly immeasurable and the only way to obtain it is by calculation from rope breaking strength. However, this complication makes room for a wide spectrum of misleading concepts. The vast majority of authors do not treat knot efficiency as a random variable, and published results mostly suffer from incorrect statistical processing. The main goal of the presented paper is to fix this issue by proposing correct statistical tools needed for knot efficiency assessment. The probability density function of knot efficiency ψ(η) has been derived in general, as well as for normally distributed breaking strength. Statistical properties of knot efficiency PDF have been discussed, and a less complex approximation of knot efficiency PDF has been proposed and investigated. Full article
(This article belongs to the Section Mathematics)
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19 pages, 508 KiB  
Article
Quantum Integral Inequalities in the Setting of Majorization Theory and Applications
by Bandar Bin-Mohsin, Muhammad Zakria Javed, Muhammad Uzair Awan, Hüseyin Budak, Hasan Kara and Muhammad Aslam Noor
Symmetry 2022, 14(9), 1925; https://doi.org/10.3390/sym14091925 - 14 Sep 2022
Cited by 4 | Viewed by 1463
Abstract
In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another [...] Read more.
In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over Rn known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite–Hadamard type inequalities using the Jensen–Mercer inequality in the frame of q˙-calculus and majorized l-tuples. Firstly we derive q˙-Hermite–Hadamard–Jensen–Mercer (H.H.J.M) type inequalities with the help of Mercer’s inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q˙-differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q˙-identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper. Full article
(This article belongs to the Special Issue Symmetry in Quantum Calculus)
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17 pages, 3905 KiB  
Article
Continuous and Discrete Dynamical Models of Total Nitrogen Transformation in a Constructed Wetland: Sensitivity and Bifurcation Analysis
by Sunarsih, Moch. Fandi Ansori, Siti Khabibah and Dwi Purwantoro Sasongko
Symmetry 2022, 14(9), 1924; https://doi.org/10.3390/sym14091924 - 14 Sep 2022
Cited by 3 | Viewed by 1351
Abstract
In this research, we study a dynamical system of total nitrogen transformation in a mangrove-filled constructed wetland. The system’s variables are the mangrove biomass concentration and total nitrogen concentration in wastewater and in soil solution. We investigate the system’s dynamics by examining the [...] Read more.
In this research, we study a dynamical system of total nitrogen transformation in a mangrove-filled constructed wetland. The system’s variables are the mangrove biomass concentration and total nitrogen concentration in wastewater and in soil solution. We investigate the system’s dynamics by examining the local stability of the equilibriums, simulating the phase portrait and solutions and providing time-dependent parameter sensitivity analyses. The analysis shows that the level of garbage acts as the parameter for when mangrove biomass will disappear. Both the graphs of the system solutions and the sensitivity function in the case of biomass concentration and total nitrogen concentration in soil solution versus time show symmetrical features at specific time intervals. According to the sensitivity index when reaching equilibrium, the level of garbage is the most sensitive parameter to the system. In addition, we explore the model’s discrete form by investigating the conditions for the equilibrium’s local stability and presenting bifurcation diagrams for each parameter. The symmetrical aspects are visible in the visualization of the bifurcation diagram and the solutions’ chaotic behavior. Full article
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