Symmetry

27 pages, 2549 KiB

Open AccessEditor’s ChoiceArticle

Tensor-Based Adaptive Filtering Algorithms

by Laura-Maria Dogariu, Cristian-Lucian Stanciu, Camelia Elisei-Iliescu, Constantin Paleologu, Jacob Benesty and Silviu Ciochină

Symmetry 2021, 13(3), 481; https://doi.org/10.3390/sym13030481 - 15 Mar 2021

Cited by 26 | Viewed by 3521

Abstract

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is [...] Read more.

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria. Full article

(This article belongs to the Special Issue Advances in Symmetric Tensor Decomposition Methods)

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9 pages, 284 KiB

Open AccessEditor’s ChoiceArticle

Connecting in the Dirac Equation the Clifford Algebra of Lorentz Invariance with the Lie Algebra of SU(N) Gauge Symmetry

by Eckart Marsch and Yasuhito Narita

Symmetry 2021, 13(3), 475; https://doi.org/10.3390/sym13030475 - 14 Mar 2021

Cited by 6 | Viewed by 1853

Abstract

In this paper, we study possible mathematical connections of the Clifford algebra with the

s u (N)

-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal

S U (N)

gauge-symmetry for a [...] Read more.

In this paper, we study possible mathematical connections of the Clifford algebra with the

s u (N)

-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal

S U (N)

gauge-symmetry for a massive spin one-half fermion described by the Dirac equation. The related matrix algebra is worked out in particular for the

S U (2)

symmetry and outlined as well for the color gauge group

S U (3)

. Possible perspectives of this approach to unification of symmetries are briefly discussed. The calculations make extensive use of tensor multiplication of the matrices involved, whereby our focus is on revisiting the Coleman–Mandula theorem. This permits us to construct unified symmetries between Lorentz invariance and gauge symmetry in a direct product sense. Full article

(This article belongs to the Section Physics)

10 pages, 919 KiB

Open AccessEditor’s ChoiceArticle

Theoretical Study of closo-Borate Anions [B_nH_n]²⁻ (n = 5–12): Bonding, Atomic Charges, and Reactivity Analysis

by Ilya N. Klyukin, Yulia S. Vlasova, Alexander S. Novikov, Andrey P. Zhdanov, Konstantin Y. Zhizhin and Nikolay T. Kuznetsov

Symmetry 2021, 13(3), 464; https://doi.org/10.3390/sym13030464 - 12 Mar 2021

Cited by 21 | Viewed by 3414

Abstract

This study has focused on the structure, bonding, and reactivity analysis of closo-borate anions [B_nH_n]²⁻ (n = 5–12). Several descriptors of B–H interactions have been calculated. It has been found that the values of electron density [...] Read more.

This study has focused on the structure, bonding, and reactivity analysis of closo-borate anions [B_nH_n]²⁻ (n = 5–12). Several descriptors of B–H interactions have been calculated. It has been found that the values of electron density and total energy at bond critical point are the most useful descriptors for investigation of B–H interactions. Using results from the descriptor analysis, one may conclude that orbital interactions in [B_nH_n]²⁻ increase with increasing the boron cluster size. Several approaches to estimate atomic charges have been applied. Boron atoms in apical positions have more negative values of atomic charges as compared with atoms from equatorial positions. The mean values of boron and hydrogen atomic charges tend to be more positive with the increasing of boron cluster size. Global and local reactivity descriptors using conceptual density functional theory (DFT) theory have been calculated. Based on this theory, the closo-borate anions [B_nH_n]²⁻ (n = 5–9) can be considered strong and moderate electrophiles, while the closo-borate anions [B_nH_n]²⁻ (n = 10–12) can be considered marginal electrophiles. Fukui functions for electrophilic attack have been calculated. Fukui functions correlate well with atomic charges of the closo-borate anions. Boron atoms in apical positions have the most positive values of Fukui functions. Full article

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

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14 pages, 1749 KiB

Open AccessEditor’s ChoiceArticle

Two Faces of Water in the Formation and Stabilization of Multicomponent Crystals of Zwitterionic Drug-Like Compounds

by Artem O. Surov, Nikita A. Vasilev, Andrei V. Churakov, Olga D. Parashchuk, Sergei V. Artobolevskii, Oleg A. Alatortsev, Denis E. Makhrov and Mikhail V. Vener

Symmetry 2021, 13(3), 425; https://doi.org/10.3390/sym13030425 - 6 Mar 2021

Cited by 15 | Viewed by 3603

Abstract

Two new hydrated multicomponent crystals of zwitterionic 2-aminonicotinic acid with maleic and fumaric acids have been obtained and thoroughly characterized by a variety of experimental (X-ray analysis and terahertz Raman spectroscopy) and theoretical periodic density functional theory calculations, followed by Bader analysis of [...] Read more.

Two new hydrated multicomponent crystals of zwitterionic 2-aminonicotinic acid with maleic and fumaric acids have been obtained and thoroughly characterized by a variety of experimental (X-ray analysis and terahertz Raman spectroscopy) and theoretical periodic density functional theory calculations, followed by Bader analysis of the crystalline electron density) techniques. It has been found that the Raman-active band in the region of 300 cm⁻¹ is due to the vibrations of the intramolecular O-H...O bond in the maleate anion. The energy/enthalpy of the intermolecular hydrogen bonds was estimated by several empirical approaches. An analysis of the interaction networks reflects the structure-directing role of the water molecule in the examined multicomponent crystals. A general scheme has been proposed to explain the proton transfer between the components during the formation of multicomponent crystals in water. Water molecules were found to play the key role in this process, forming a “water wire” between the COOH group of the dicarboxylic acid and the COO^– group of the zwitterion and the rendering crystal lattice of the considered multicomponent crystals. Full article

(This article belongs to the Special Issue Quantum Chemistry)

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56 pages, 725 KiB

Open AccessEditor’s ChoiceArticle

Lorentz Symmetry Group, Retardation and Energy Transformations in a Relativistic Engine

by Shailendra Rajput, Asher Yahalom and Hong Qin

Symmetry 2021, 13(3), 420; https://doi.org/10.3390/sym13030420 - 5 Mar 2021

Cited by 13 | Viewed by 2011

Abstract

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot [...] Read more.

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in

\frac{1}{c}

and no lower order relativistic engine effect on the energy exists. Full article

(This article belongs to the Special Issue Symmetry and Geometry in Physics)

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50 pages, 639 KiB

Open AccessEditor’s ChoiceArticle

Power Law Duality in Classical and Quantum Mechanics

by Akira Inomata and Georg Junker

Symmetry 2021, 13(3), 409; https://doi.org/10.3390/sym13030409 - 3 Mar 2021

Cited by 5 | Viewed by 2800

Abstract

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is [...] Read more.

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of the Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb–Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential. Full article

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

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26 pages, 1194 KiB

Open AccessEditor’s ChoiceReview

Siberian Snakes, Figure-8 and Spin Transparency Techniques for High Precision Experiments with Polarized Hadron Beams in Colliders

by Yaroslav S. Derbenev, Yury N. Filatov, Anatoliy M. Kondratenko, Mikhail A. Kondratenko and Vasiliy S. Morozov

Symmetry 2021, 13(3), 398; https://doi.org/10.3390/sym13030398 - 28 Feb 2021

Cited by 9 | Viewed by 2630

Abstract

We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the [...] Read more.

We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the recently elicited advantageous possibility to conduct high precision experiments in a regime of the spin transparency (ST) when the design global spin tune is close to zero. In this regime, the polarization control is realized by use of spin navigators (SN), which are compact special insertions of magnets dedicated to a high flexibility spin manipulation including frequent spin flips. Full article

(This article belongs to the Special Issue Advances in Spin Physics)

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19 pages, 20807 KiB

Open AccessEditor’s ChoiceArticle

A Novel Plaintext-Related Color Image Encryption Scheme Based on Cellular Neural Network and Chen’s Chaotic System

by Renxiu Zhang, Longfei Yu, Donghua Jiang, Wei Ding, Jian Song, Kuncheng He and Qun Ding

Symmetry 2021, 13(3), 393; https://doi.org/10.3390/sym13030393 - 28 Feb 2021

Cited by 23 | Viewed by 2309

Abstract

To address the problem that traditional stream ciphers are not sensitive to changes in the plaintext, a novel plaintext-related color image encryption scheme is proposed in this paper, which combines the 6-dimensional cellular neural network (CNN) and Chen’s chaotic system. This encryption scheme [...] Read more.

To address the problem that traditional stream ciphers are not sensitive to changes in the plaintext, a novel plaintext-related color image encryption scheme is proposed in this paper, which combines the 6-dimensional cellular neural network (CNN) and Chen’s chaotic system. This encryption scheme belongs to symmetric cryptography. In the proposed scheme, the initial key and switching function generated by the plaintext image are first utilized to control the CNN to complete the scrambling process. Then, Chen’s chaotic system is used to diffuse the scrambled image for realizing higher security. Finally, extensive performance evaluation is undertaken to validate the proposed scheme’s ability to offer the necessary security. Furthermore, the scheme is compared alongside state-of-the-art algorithms to establish its efficiency. Full article

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16 pages, 587 KiB

Open AccessEditor’s ChoiceArticle

A Modern View of the Equation of State in Nuclear and Neutron Star Matter

by G. Fiorella Burgio, Hans-Josef Schulze, Isaac Vidaña and Jin-Biao Wei

Symmetry 2021, 13(3), 400; https://doi.org/10.3390/sym13030400 - 28 Feb 2021

Cited by 15 | Viewed by 3329

Abstract

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use [...] Read more.

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use a set of different models that include several phenomenological EOSs based on Skyrme and relativistic mean field models as well as microscopic calculations based on different many-body approaches, i.e., the (Dirac–)Brueckner–Hartree–Fock theories, Quantum Monte Carlo techniques, and the variational method. Results: We find that almost all the models considered are compatible with the laboratory constraints of the nuclear matter properties as well as with the largest NS mass observed up to now,

2 . 14_{- 0.09}^{+ 0.10} M_{⊙}

for the object PSR J0740+6620, and with the upper limit of the maximum mass of about 2.3–2.5

M_{⊙}

deduced from the analysis of the GW170817 NS merger event. Conclusion: Our study shows that whereas no correlation exists between the tidal deformability and the value of the nuclear symmetry energy at saturation for any value of the NS mass, very weak correlations seem to exist with the derivative of the nuclear symmetry energy and with the nuclear incompressibility. Full article

(This article belongs to the Special Issue The Nuclear Physics of Neutron Stars)

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16 pages, 3495 KiB

Open AccessEditor’s ChoiceArticle

A Model Predictive Control with Preview-Follower Theory Algorithm for Trajectory Tracking Control in Autonomous Vehicles

by Ying Xu, Wentao Tang, Biyun Chen, Li Qiu and Rong Yang

Symmetry 2021, 13(3), 381; https://doi.org/10.3390/sym13030381 - 26 Feb 2021

Cited by 30 | Viewed by 3808

Abstract

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module [...] Read more.

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module could calculate reference lateral acceleration at the preview point by PFT to update state variables, and generate a reference yaw rate in each prediction point. Since the preview range is increased, PFT makes the calculation of yaw rate more accurate. Through physical constraints, the MPC controller can achieve the best tracking of the reference path. The MPC problem is formulated as a linear time-varying (LTV) MPC controller to achieve a predictive model from nonlinear vehicle dynamics to continuous online linearization. The MPC-PFT controller method performs well by increasing the effective length of the reference path. Compared with MPC and PFT controllers, the effectiveness and robustness of the proposed method are proved by simulations of two typical working conditions. Full article

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10 pages, 265 KiB

Open AccessEditor’s ChoiceArticle

Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function

by Alina Alb Lupaş and Georgia Irina Oros

Symmetry 2021, 13(2), 327; https://doi.org/10.3390/sym13020327 - 17 Feb 2021

Cited by 31 | Viewed by 2875

Abstract

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types [...] Read more.

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories. Full article

(This article belongs to the Section Mathematics)

24 pages, 544 KiB

Open AccessEditor’s ChoiceArticle

Coupling Hadron-Hadron Thresholds within a Chiral Quark Model Approach

by Pablo G. Ortega and David R. Entem

Symmetry 2021, 13(2), 279; https://doi.org/10.3390/sym13020279 - 6 Feb 2021

Cited by 16 | Viewed by 2424

Abstract

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the

X (3872)

was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state [...] Read more.

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the

X (3872)

was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance. Full article

(This article belongs to the Special Issue Advances in Chiral Quark Models)

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14 pages, 2702 KiB

Open AccessEditor’s ChoiceArticle

Supramolecular Chirogenesis in Bis-Porphyrin: Crystallographic Structure and CD Spectra for a Complex with a Chiral Guanidine Derivative

by Irina Osadchuk, Nele Konrad, Khai-Nghi Truong, Kari Rissanen, Eric Clot, Riina Aav, Dzmitry Kananovich and Victor Borovkov

Symmetry 2021, 13(2), 275; https://doi.org/10.3390/sym13020275 - 5 Feb 2021

Cited by 8 | Viewed by 4102

Abstract

The complexation of (3aR,7aR)-N-(3,5-bis(trifluoromethyl)phenyl)octahydro-2H-benzo[d]imidazol-2-imine (BTI), as a guest, to ethane-bridged bis(zinc octaethylporphyrin), bis(ZnOEP), as a host, has been studied by means of ultraviolet-visible (UV-Vis) and circular dichroism (CD) absorption spectroscopies, single crystal X-ray [...] Read more.

The complexation of (3aR,7aR)-N-(3,5-bis(trifluoromethyl)phenyl)octahydro-2H-benzo[d]imidazol-2-imine (BTI), as a guest, to ethane-bridged bis(zinc octaethylporphyrin), bis(ZnOEP), as a host, has been studied by means of ultraviolet-visible (UV-Vis) and circular dichroism (CD) absorption spectroscopies, single crystal X-ray diffraction, and computational simulation. The formation of 1:2 host-guest complex was established by X-ray diffraction and UV-Vis titration studies. Two guest BTI molecules are located at the opposite sides of two porphyrin subunits of bis(ZnOEP) host, which is resting in the anti-conformation. The complexation of BTI molecules proceed via coordination of the imine nitrogens to the zinc ions of each porphyrin subunit of the host. Such supramolecular organization of the complex results in a screw arrangement of the two porphyrin subunits, inducing a strong CD signal in the Soret (B) band region. The corresponding DFT computational studies are in a good agreement with the experimental results and prove the presence of 1:2 host-guest complex as the major component in the solution (97.7%), but its optimized geometry differs from that observed in the solid-state. The UV-Vis and CD spectra simulated by using the solution-state geometry and the TD-DFT/ωB97X-D/cc-pVDZ + SMD (CH2Cl2) level of theory reproduced the experimentally obtained UV-Vis and CD spectra and confirmed the difference between the solid-state and solution structures. Moreover, it was shown that CD spectrum is very sensitive to the spatial arrangement of porphyrin subunits. Full article

(This article belongs to the Special Issue Chiral Auxiliaries and Chirogenesis II)

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21 pages, 10706 KiB

Open AccessEditor’s ChoiceArticle

Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

by Zdeněk Kala

Symmetry 2021, 13(2), 263; https://doi.org/10.3390/sym13020263 - 4 Feb 2021

Cited by 14 | Viewed by 6239

Abstract

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to [...] Read more.

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance. Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models)

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12 pages, 1704 KiB

Open AccessEditor’s ChoiceArticle

Self-Assembly of Hydrogen-Bonded Cage Tetramers of Phosphonic Acid

by Ivan S. Giba and Peter M. Tolstoy

Symmetry 2021, 13(2), 258; https://doi.org/10.3390/sym13020258 - 4 Feb 2021

Cited by 9 | Viewed by 3161

Abstract

The self-association of phosphonic acids with general formula RP(O)(OH)₂ in solution state remains largely unexplored. The general understanding is that such molecules form multiple intermolecular hydrogen bonds, but the stoichiometry of self-associates and the bonding motifs are unclear. In this work, we [...] Read more.

The self-association of phosphonic acids with general formula RP(O)(OH)₂ in solution state remains largely unexplored. The general understanding is that such molecules form multiple intermolecular hydrogen bonds, but the stoichiometry of self-associates and the bonding motifs are unclear. In this work, we report the results of the study of self-association of tert-butylphosphonic acid using low temperature liquid-state ¹H and ³¹P NMR spectroscopy (100 K; CDF₃/CDF₂Cl) and density functional theory (DFT) calculations. For the first time, we demonstrate conclusively that polar aprotic medium tert-butylphosphonic acid forms highly symmetric cage-like tetramers held by eight OHO hydrogen bonds, which makes the complex quite stable. In these associates. each phosphonic acid molecule is bonded to three other molecules by forming two hydrogen bonds as proton donor and two hydrogen bonds as proton acceptor. Though the structure of such cage-like tetramers is close to tetrahedral, the formal symmetry of the self-associate is C₂. Full article

(This article belongs to the Special Issue Exploring Inter- and Intramolecular Interactions as Building Blocks of Larger Systems)

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9 pages, 276 KiB

Open AccessEditor’s ChoiceArticle

Historical Introduction to Chiral Quark Models

by Francisco Fernández and Jorge Segovia

Symmetry 2021, 13(2), 252; https://doi.org/10.3390/sym13020252 - 2 Feb 2021

Cited by 10 | Viewed by 2142

Abstract

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to [...] Read more.

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to incorporate, among other important non-perturbative features of quantum chromodynamics (QCD), the dynamical chiral symmetry breaking mechanism. This effort has delivered different models such as the chiral bag model, the cloudy bag model, the chiral quark model or the chiral constituent quark model. Our main aim herein is to provide a brief introduction of the Special Issue “Advances in Chiral Quark Models” in Symmetry and contribute to the clarification of the differences among the above-mentioned models that include the adjective chiral in their nomenclature. Full article

(This article belongs to the Section Physics)

15 pages, 275 KiB

Open AccessEditor’s ChoiceArticle

Adjoint Operations in Twist-Products of Lattices

by Ivan Chajda and Helmut Länger

Symmetry 2021, 13(2), 253; https://doi.org/10.3390/sym13020253 - 2 Feb 2021

Cited by 1 | Viewed by 2225

Abstract

Given an integral commutative residuated lattices

L = (L, \lor, \land)

, its full twist-product

(L^{2}, ⊔, ⊓)

can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and [...] Read more.

Given an integral commutative residuated lattices

L = (L, \lor, \land)

, its full twist-product

(L^{2}, ⊔, ⊓)

can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every

a \in L

we define a certain subset

P_{a} (L)

of

L^{2}

. We characterize when

P_{a} (L)

is a sublattice of the full twist-product

(L^{2}, ⊔, ⊓)

. In this case

P_{a} (L)

together with some natural antitone involution

^{'}

becomes a pseudo-Kleene lattice. If

L

is distributive then

(P_{a} (L), ⊔, ⊓,^{'})

becomes a Kleene lattice. We present sufficient conditions for

P_{a} (L)

being a subalgebra of

(L^{2}, ⊔, ⊓, ⊙, \Rightarrow)

and thus for ⊙ and ⇒ being a pair of adjoint operations on

P_{a} (L)

. Finally, we introduce another pair ⊙ and ⇒ of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when

P_{a} (L)

is closed under these new operations. Full article

(This article belongs to the Section Mathematics)

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25 pages, 3327 KiB

Open AccessEditor’s ChoiceArticle

An Improved Whale Optimization Algorithm with Random Evolution and Special Reinforcement Dual-Operation Strategy Collaboration

by Qibing Jin, Zhonghua Xu and Wu Cai

Symmetry 2021, 13(2), 238; https://doi.org/10.3390/sym13020238 - 31 Jan 2021

Cited by 30 | Viewed by 3848

Abstract

In view of the slow convergence speed, difficulty of escaping from the local optimum, and difficulty maintaining the stability associated with the basic whale optimization algorithm (WOA), an improved WOA algorithm (REWOA) is proposed based on dual-operation strategy collaboration. Firstly, different evolutionary strategies [...] Read more.

In view of the slow convergence speed, difficulty of escaping from the local optimum, and difficulty maintaining the stability associated with the basic whale optimization algorithm (WOA), an improved WOA algorithm (REWOA) is proposed based on dual-operation strategy collaboration. Firstly, different evolutionary strategies are integrated into different dimensions of the algorithm structure to improve the convergence accuracy and the randomization operation of the random Gaussian distribution is used to increase the diversity of the population. Secondly, special reinforcements are made to the process involving whales searching for prey to enhance their exclusive exploration or exploitation capabilities, and a new skip step factor is proposed to enhance the optimizer’s ability to escape the local optimum. Finally, an adaptive weight factor is added to improve the stability of the algorithm and maintain a balance between exploration and exploitation. The effectiveness and feasibility of the proposed REWOA are verified with the benchmark functions and different experiments related to the identification of the Hammerstein model. Full article

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10 pages, 2216 KiB

Open AccessEditor’s ChoiceArticle

Bootstrapped Motion of an Agent on an Adaptive Resource Landscape

by Trung V. Phan, Gao Wang, Liyu Liu and Robert H. Austin

Symmetry 2021, 13(2), 225; https://doi.org/10.3390/sym13020225 - 29 Jan 2021

Cited by 7 | Viewed by 2472

Abstract

We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. [...] Read more.

We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. This self-generated agent motion can be coupled with neighboring agents to act as a spontaneously broken symmetry seed for emergent collective dynamics. We also show that in a sufficiently weak externally imposed gradient, it is possible for an agent to move against an external resource gradient due to the local resource depression on the landscape created by an agent. This counter-intuitive boot-strapped motion against an external gradient is demonstrated with a simple robot system on an light-emitting diode (LED) light-board. Full article

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

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26 pages, 5952 KiB

Open AccessEditor’s ChoiceArticle

An Improved Whale Algorithm for Support Vector Machine Prediction of Photovoltaic Power Generation

by Yu-Wei Liu, Huan Feng, Heng-Yi Li and Ling-Ling Li

Symmetry 2021, 13(2), 212; https://doi.org/10.3390/sym13020212 - 28 Jan 2021

Cited by 16 | Viewed by 2358

Abstract

Accurate prediction of photovoltaic power is conducive to the application of clean energy and sustainable development. An improved whale algorithm is proposed to optimize the Support Vector Machine model. The characteristic of the model is that it needs less training data to symmetrically [...] Read more.

Accurate prediction of photovoltaic power is conducive to the application of clean energy and sustainable development. An improved whale algorithm is proposed to optimize the Support Vector Machine model. The characteristic of the model is that it needs less training data to symmetrically adapt to the prediction conditions of different weather, and has high prediction accuracy in different weather conditions. This study aims to (1) select light intensity, ambient temperature and relative humidity, which are strictly related to photovoltaic output power as the input data; (2) apply wavelet soft threshold denoising to preprocess input data to reduce the noise contained in input data to symmetrically enhance the adaptability of the prediction model in different weather conditions; (3) improve the whale algorithm by using tent chaotic mapping, nonlinear disturbance and differential evolution algorithm; (4) apply the improved whale algorithm to optimize the Support Vector Machine model in order to improve the prediction accuracy of the prediction model. The experiment proves that the short-term prediction model of photovoltaic power based on symmetry concept achieves ideal accuracy in different weather. The systematic method for output power prediction of renewable energy is conductive to reducing the workload of predicting the output power and to promoting the application of clean energy and sustainable development. Full article

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47 pages, 5068 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

by Dietrich Haase, Gunter Hermann, Jörn Manz, Vincent Pohl and Jean Christophe Tremblay

Symmetry 2021, 13(2), 205; https://doi.org/10.3390/sym13020205 - 27 Jan 2021

Cited by 11 | Viewed by 3119

Abstract

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D_6h [...] Read more.

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D_6h and D_4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses. Full article

(This article belongs to the Special Issue Symmetry in Quantum Systems)

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22 pages, 2529 KiB

Open AccessEditor’s ChoiceArticle

Probing the Nuclear Equation of State from the Existence of a ∼2.6 M_⊙ Neutron Star: The GW190814 Puzzle

by Alkiviadis Kanakis-Pegios, Polychronis S. Koliogiannis and Charalampos C. Moustakidis

Symmetry 2021, 13(2), 183; https://doi.org/10.3390/sym13020183 - 24 Jan 2021

Cited by 37 | Viewed by 3327

Abstract

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass

\sim {2.59}_{- 0.09}^{+ 0.08} M_{⊙}

, as a component of a system where the main companion was a black hole with mass

\sim 23 M_{⊙}

. [...] Read more.

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass

\sim {2.59}_{- 0.09}^{+ 0.08} M_{⊙}

, as a component of a system where the main companion was a black hole with mass

\sim 23 M_{⊙}

. A scientific debate initiated concerning the identification of the low mass component, as it falls into the neutron star–black hole mass gap. The understanding of the nature of GW190814 event will offer rich information concerning open issues, the speed of sound and the possible phase transition into other degrees of freedom. In the present work, we made an effort to probe the nuclear equation of state along with the GW190814 event. Firstly, we examine possible constraints on the nuclear equation of state inferred from the consideration that the low mass companion is a slow or rapidly rotating neutron star. In this case, the role of the upper bounds on the speed of sound is revealed, in connection with the dense nuclear matter properties. Secondly, we systematically study the tidal deformability of a possible high mass candidate existing as an individual star or as a component one in a binary neutron star system. As the tidal deformability and radius are quantities very sensitive on the neutron star equation of state, they are excellent counters on dense matter properties. We conjecture that similar isolated neutron stars or systems may exist in the universe and their possible future observation will shed light on the maximum neutron star mass problem. Full article

(This article belongs to the Special Issue The Nuclear Physics of Neutron Stars)

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20 pages, 623 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nucleon Structure and Spin Effects in Elastic Hadron Scattering

by Oleg Selyugin

Symmetry 2021, 13(2), 164; https://doi.org/10.3390/sym13020164 - 21 Jan 2021

Cited by 6 | Viewed by 1944

Abstract

Soft diffraction phenomena in elastic nucleon scattering are considered from the viewpoint of the spin dependence of the interaction potential. Spin-dependent pomeron effects are analyzed for elastic

p p

scattering, and spin-dependent differential cross sections and spin correlation parameters are calculated. The spin [...] Read more.

Soft diffraction phenomena in elastic nucleon scattering are considered from the viewpoint of the spin dependence of the interaction potential. Spin-dependent pomeron effects are analyzed for elastic

p p

scattering, and spin-dependent differential cross sections and spin correlation parameters are calculated. The spin correlation parameter

A_{N}

is examined on the basis of experimental data from

\sqrt{s} = 4.9

GeV up to

23.4

GeV in the framework of the extended High Energy Generalized Structure (HEGS) model. It is shown that the existing experimental data of proton-proton and proton-antiproton elastic scattering at high energy in the region of the diffraction minimum and at large momentum transfer give the support of the existence of the energy-independent part of the hadron spin flip amplitude. Full article

(This article belongs to the Special Issue Advances in Spin Physics)

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17 pages, 15366 KiB

Open AccessEditor’s ChoiceArticle

The Symmetric Nature of the Position Distribution of the Human Body Center of Gravity during Propelling Manual Wheelchairs with Innovative Propulsion Systems

by Bartosz Wieczorek, Mateusz Kukla and Łukasz Warguła

Symmetry 2021, 13(1), 154; https://doi.org/10.3390/sym13010154 - 19 Jan 2021

Cited by 14 | Viewed by 3675

Abstract

Objective: The main objective of the tests conducted was to analyze the position variability of the human body’s center of gravity during propelling the wheelchair, and to demonstrate the properties enabling the description of this variability by means of plane figures with a [...] Read more.

Objective: The main objective of the tests conducted was to analyze the position variability of the human body’s center of gravity during propelling the wheelchair, and to demonstrate the properties enabling the description of this variability by means of plane figures with a symmetry axis. A secondary objective was to show the impact of the used manual propulsion type and the wheelchair inclination angle in relation to the plane on the dimensions of the position variability areas of the center of gravity. Method and materials: Three patients participated in the research representing 50 centiles of anthropometric dimensions. Each patient carried out fifteen measurement tests on three wheelchairs for three inclination angles of the wheelchair frame in relation to the level. Each measurement test consisted of five propulsion cycles for which the positions of the center of gravity were determined with the sampling frequency of 100 Hz. The measured positions of the center of gravity were approximated with ellipses containing 95.4% of the measurements conducted, assuming their dimension scaling basis in the form of the double value of standard deviation defined based on the registered results. Results: Based on the measurements conducted, the average values of five ellipses parameters were determined for nine cases in which a variable was the type of wheelchair propulsion and its inclination angle in relation to the level. The area of the highest variability of the position of the center of gravity was measured for the wheelchair with a multispeed transmission. The average dimensions of the ellipse semi-axis amounted to 108.53 mm for the semi-axis a and 29.75 for the semi-axis b, the average position of the ellipse center amounted to x = 114.51 mm and y = −10.53 mm, and the average inclination angle of the ellipse α amounted to −6.92°. The area of the lowest variability of the position of the center of gravity was measured for the wheelchair with a hybrid transmission. In this case, the average dimensions of the ellipse semi-axis amounted to 64.07 mm for the semi-axis a and 33.85 for the semi-axis b; whereas, the average position of the ellipse center amounted to x = 245.13 mm and y = −28.24 mm, and the average inclination angle of the ellipse α amounted to −0.56°. Full article

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20 pages, 1204 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

by Mária Hypiusová and Danica Rosinová

Symmetry 2021, 13(1), 142; https://doi.org/10.3390/sym13010142 - 16 Jan 2021

Cited by 8 | Viewed by 2620

Abstract

Robust pole-placement based on convex

D_{R}

-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is [...] Read more.

Robust pole-placement based on convex

D_{R}

-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant. Full article

(This article belongs to the Special Issue PID Control and Symmetry)

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19 pages, 3476 KiB

Open AccessEditor’s ChoiceArticle

Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields

by Konstantin Zhukovsky and Igor Fedorov

Symmetry 2021, 13(1), 135; https://doi.org/10.3390/sym13010135 - 15 Jan 2021

Cited by 18 | Viewed by 2306

Abstract

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of [...] Read more.

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (ρ)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (k) were considered. The effect of the k parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained. Full article

(This article belongs to the Special Issue Advances in Synchrotron and Undulator Radiation Studies)

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17 pages, 319 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Properties of Quantizer and Dequantizer Operators for Qudit States and Parametric Down-Conversion

by Peter Adam, Vladimir A. Andreev, Margarita A. Man’ko, Vladimir I. Man’ko and Matyas Mechler

Symmetry 2021, 13(1), 131; https://doi.org/10.3390/sym13010131 - 14 Jan 2021

Cited by 10 | Viewed by 2215

Abstract

We review the method of quantizers and dequantizers to construct an invertible map of the density operators onto functions including probability distributions and discuss in detail examples of qubit and qutrit states. The biphoton states existing in the process of parametric down-conversion are [...] Read more.

We review the method of quantizers and dequantizers to construct an invertible map of the density operators onto functions including probability distributions and discuss in detail examples of qubit and qutrit states. The biphoton states existing in the process of parametric down-conversion are studied in the probability representation of quantum mechanics. Full article

11 pages, 10679 KiB

Open AccessEditor’s ChoiceArticle

Analysis of Fractal Structures in Dehydrated Films of Protein Solutions

by Maksim Baranov, Elena Velichko and Konstantin Greshnevikov

Symmetry 2021, 13(1), 123; https://doi.org/10.3390/sym13010123 - 13 Jan 2021

Cited by 8 | Viewed by 2779

Abstract

The article deals with dendritic structures resulting from self-organization processes in aqueous solutions of albumin proteins. The methods for obtaining the structures and experimental results are presented. It is shown that dendrites are fractal structures that are symmetric under certain conditions of their [...] Read more.

The article deals with dendritic structures resulting from self-organization processes in aqueous solutions of albumin proteins. The methods for obtaining the structures and experimental results are presented. It is shown that dendrites are fractal structures that are symmetric under certain conditions of their formation and can have different characteristics depending on the isothermal dehydration of liquid samples. The fractal dimension of the structures in films of the albumin protein solution has been calculated. Dependences of the fractal dimension on the concentrations of salts and protein in the initial solutions and also on the dehydration temperature have been revealed. It has been shown that as the protein concentration in the solution grows, the salt concentration for the initiation of the dendritic structure formation increases. It has been found that the temperature dependences of the fractal dimension of the structures become smoother with increasing protein concentration in solutions. The relationship between geometric characteristics of dendrites and self-organization parameters during drying is discussed. Full article

(This article belongs to the Section Life Sciences)

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24 pages, 867 KiB

Open AccessEditor’s ChoiceArticle

On the Arcsecant Hyperbolic Normal Distribution. Properties, Quantile Regression Modeling and Applications

by Mustafa Ç. Korkmaz, Christophe Chesneau and Zehra Sedef Korkmaz

Symmetry 2021, 13(1), 117; https://doi.org/10.3390/sym13010117 - 12 Jan 2021

Cited by 32 | Viewed by 3683

Abstract

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received [...] Read more.

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models. Full article

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17 pages, 664 KiB

Open AccessEditor’s ChoiceArticle

Scalarized Nutty Wormholes

by Rustam Ibadov, Burkhard Kleihaus, Jutta Kunz and Sardor Murodov

Symmetry 2021, 13(1), 89; https://doi.org/10.3390/sym13010089 - 6 Jan 2021

Cited by 6 | Viewed by 1781

Abstract

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the [...] Read more.

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes is reached in the limit of vanishing NUT charge. In the Chern-Simons case, however, the limit is peculiar, since with vanishing NUT charge the coupling constant diverges. We focus on scalarized nutty wormholes with a single throat and study their properties. All these scalarized nutty wormholes feature a critical polar angle, beyond which closed timelike curves are present. Full article

(This article belongs to the Special Issue Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars)

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10 pages, 262 KiB

Open AccessEditor’s ChoiceArticle

New Conditions for Univalence of Confluent Hypergeometric Function

by Georgia Irina Oros

Symmetry 2021, 13(1), 82; https://doi.org/10.3390/sym13010082 - 5 Jan 2021

Cited by 15 | Viewed by 2253

Abstract

Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to [...] Read more.

Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to determine conditions of starlikeness and convexity for the confluent (Kummer) hypergeometric function of the first kind. Having in mind the results obtained by Miller and Mocanu in 1990 who used

a, c \in R

, for the confluent (Kummer) hypergeometric function, in this investigation a and c complex numbers are used and two criteria for univalence of the investigated function are stated. An example is also included in order to show the relevance of the original results of the paper. Full article

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

20 pages, 2956 KiB

Open AccessEditor’s ChoiceReview

Functional Lateralization of the Mirror Neuron System in Monkey and Humans

by Antonino Errante and Leonardo Fogassi

Symmetry 2021, 13(1), 77; https://doi.org/10.3390/sym13010077 - 5 Jan 2021

Cited by 7 | Viewed by 4878

Abstract

To date, both in monkeys and humans, very few studies have addressed the issue of the lateralization of the cortical parietal and premotor areas involved in the organization of voluntary movements and in-action understanding. In this review, we will first analyze studies in [...] Read more.

To date, both in monkeys and humans, very few studies have addressed the issue of the lateralization of the cortical parietal and premotor areas involved in the organization of voluntary movements and in-action understanding. In this review, we will first analyze studies in the monkey, describing the functional properties of neurons of the parieto-frontal circuits, involved in the organization of reaching-grasping actions, in terms of unilateral or bilateral control. We will concentrate, in particular, on the properties of the mirror neuron system (MNS). Then, we will consider the evidence about the mirror neuron mechanism in humans, describing studies in which action perception, as well as action execution, produces unilateral or bilateral brain activation. Finally, we will report some investigations demonstrating plastic changes of the MNS following specific unilateral brain damage, discussing how this plasticity can be related to the rehabilitation outcome Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Brain Behavior and Perception)

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19 pages, 645 KiB

Open AccessEditor’s ChoiceArticle

Fluctuation–Dissipation Relations in Active Matter Systems

by Lorenzo Caprini, Andrea Puglisi and Alessandro Sarracino

Symmetry 2021, 13(1), 81; https://doi.org/10.3390/sym13010081 - 5 Jan 2021

Cited by 26 | Viewed by 4726

Abstract

We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable [...] Read more.

We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation–dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation. Full article

(This article belongs to the Special Issue Thermodynamics for Finite-Size and Time-Dependent Behavior: Small Systems, Fluctuations, Correlations, and Internal Heterogeneity)

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20 pages, 6777 KiB

Open AccessEditor’s ChoiceReview

Elastic Organic Crystals of π-Conjugated Molecules: New Concept for Materials Chemistry

by Shotaro Hayashi

Symmetry 2020, 12(12), 2022; https://doi.org/10.3390/sym12122022 - 7 Dec 2020

Cited by 19 | Viewed by 6870

Abstract

It is generally believed that organic single crystals composed of a densely packed arrangement of anisotropic, organic small molecules are less useful as functional materials due to their mechanically inflexible and brittle nature, compared to polymers bearing flexible chains and thereby exhibiting viscoelasticity. [...] Read more.

It is generally believed that organic single crystals composed of a densely packed arrangement of anisotropic, organic small molecules are less useful as functional materials due to their mechanically inflexible and brittle nature, compared to polymers bearing flexible chains and thereby exhibiting viscoelasticity. Nevertheless, organic crystals have attracted much attention because of their tunable optoelectronic properties and a variety of elegant crystal habits and unique ordered or disordered molecular packings arising from the anisotropic molecular structures. However, the recent emergence of flexible organic crystal materials showing plasticity and elasticity has considerably changed the concept of organic single crystals. In this review, the author summarizes the state-of-the-art development of flexible organic crystal materials, especially functional elastic organic crystals which are expected to provide a foothold for the next generation of organic crystal materials. Full article

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

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16 pages, 1617 KiB

Open AccessEditor’s ChoiceArticle

Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

by Mohammad Malikan, Victor A. Eremeyev and Krzysztof Kamil Żur

Symmetry 2020, 12(12), 1935; https://doi.org/10.3390/sym12121935 - 24 Nov 2020

Cited by 42 | Viewed by 4692

Abstract

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. [...] Read more.

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant. Full article

(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)

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78 pages, 1348 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Tetra- and Penta-Quark Structures in the Constituent Quark Model

by Gang Yang, Jialun Ping and Jorge Segovia

Symmetry 2020, 12(11), 1869; https://doi.org/10.3390/sym12111869 - 13 Nov 2020

Cited by 92 | Viewed by 4559

Abstract

With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the [...] Read more.

With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the Gaussian expansion method, has been employed systematically in real- and complex-range investigations. We review herein the double- and fully-heavy tetraquarks, but also the hidden-charm, hidden-bottom and doubly charmed pentaquarks. Several exotic hadrons observed experimentally were well reproduced within our approach; moreover, their possible compositeness and other properties, such as their decay widths and general patterns in the spectrum, are analyzed. Besides, we report also some theoretical predictions of tetra- and penta-quark states which have not seen by experiment yet. Full article

(This article belongs to the Special Issue Advances in Chiral Quark Models)

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13 pages, 2018 KiB

Open AccessEditor’s ChoiceReview

Breaking Symmetry: Fluctuating Asymmetry and Geometric Morphometrics as Tools for Evaluating Developmental Instability under Diverse Agroecosystems

by Hugo A. Benítez, Darija Lemic, Amado Villalobos-Leiva, Renata Bažok, Rodrigo Órdenes-Claveria, Ivana Pajač Živković and Katarina M. Mikac

Symmetry 2020, 12(11), 1789; https://doi.org/10.3390/sym12111789 - 29 Oct 2020

Cited by 39 | Viewed by 12490

Abstract

Fluctuating asymmetry (FA), in contrast with other asymmetries, is the bilateral asymmetry that represents small, random developmental differences between right and left sides. After nearly a century of using traditional morphometrics in the estimation of FA, geometric morphometrics (GM) now provides new insights [...] Read more.

Fluctuating asymmetry (FA), in contrast with other asymmetries, is the bilateral asymmetry that represents small, random developmental differences between right and left sides. After nearly a century of using traditional morphometrics in the estimation of FA, geometric morphometrics (GM) now provides new insights into the use of FA as a tool, especially for assessing environmental and developmental stress. Thus, it will be possible to assess adaptation to various environmental stressors as particular triggers for unavoidable selection pressures. In this review, we describe measures of FA that use geometric morphometrics, and we include a flow chart of the methodology. We also describe how this combination (GM + FA) has been tested in several agroecosystems. Nutritional stress, temperature, chemical pollution, and population density are known stressors experienced by populations in agroecosystems. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry as a Measure of Stress)

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36 pages, 4068 KiB

Open AccessEditor’s ChoiceArticle

On Confinement and Quarantine Concerns on an SEIAR Epidemic Model with Simulated Parameterizations for the COVID-19 Pandemic

by Manuel De la Sen, Asier Ibeas and Ravi P. Agarwal

Symmetry 2020, 12(10), 1646; https://doi.org/10.3390/sym12101646 - 7 Oct 2020

Cited by 23 | Viewed by 3335

Abstract

This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability [...] Read more.

This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations. The seriously infectious individuals are assumed to be a part of the total infectious being described by a time-varying proportional function. A time-varying upper-bound of those seriously infected individuals has to be satisfied as objective by either a total confinement or partial quarantine intervention of the susceptible subpopulation. Afterwards, a new extended SEIR (susceptible-exposed-infectious-recovered) epidemic model, which is referred to as an SEIAR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-recovered) epidemic model with demography and disease mortality is given and focused on so as to extend the above developed ideas on the SIR model. A proportionally gain in the model parameterization is assumed to distribute the transition from the exposed to the infectious into the two infectious individuals (namely, symptomatic and asymptomatic individuals). Such a model is evaluated under total or partial quarantines of all or of some of the subpopulations which have the effect of decreasing the number of contagions. Simulated numerical examples are also discussed related to model parameterizations of usefulness related to the current COVID-19 pandemic outbreaks. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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13 pages, 473 KiB

Open AccessEditor’s ChoiceArticle

Exploring Possible Triangle Singularities in the Ξ b − → K − J / ψ Λ Decay

by Chao-Wei Shen, Hao-Jie Jing, Feng-Kun Guo and Jia-Jun Wu

Symmetry 2020, 12(10), 1611; https://doi.org/10.3390/sym12101611 - 28 Sep 2020

Cited by 27 | Viewed by 2775

Abstract

We analyze possible singularities in the

J / ψ Λ

invariant mass distribution of the

Ξ_{b}^{-} \to K^{-} J / ψ Λ

process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop [...] Read more.

We analyze possible singularities in the

J / ψ Λ

invariant mass distribution of the

Ξ_{b}^{-} \to K^{-} J / ψ Λ

process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with

Ξ^{*}

-charmonium-

Λ

intermediate states, the one from the

χ_{c 1} Ξ (2120) Λ

loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs S- and P-waves in

χ_{c 1} Λ

and

J / ψ Λ

systems, respectively, when the quantum numbers of these systems are

1 / 2^{+}

or

3 / 2^{+}

. When the quantum numbers of the

Ξ (2120)

are

J^{P} = 1 / 2^{+}

,

1 / 2^{-}

or

3 / 2^{+}

, the peak structure should be sharper than the other

J^{P}

choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the

Ξ^{*}

-charmonium-

Λ

triangle diagram if structures are observed in the

J / ψ Λ

invariant mass spectrum experimentally. In addition, a few triangle diagrams with the

D_{s 1}^{*} (2700)

as one of the intermediate particles can also produce singularities in the

J / ψ Λ

distribution, but at higher energies above 4.9 GeV. Full article

(This article belongs to the Special Issue Advances in Chiral Quark Models)

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20 pages, 3110 KiB

Open AccessEditor’s ChoiceArticle

Clar Covers of Overlapping Benzenoids: Case of Two Identically-Oriented Parallelograms

by Henryk A. Witek and Johanna Langner

Symmetry 2020, 12(10), 1599; https://doi.org/10.3390/sym12101599 - 25 Sep 2020

Cited by 9 | Viewed by 1853

Abstract

We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons

R b

, parallelograms M, vertically overlapping parallelograms

M v M

, horizontally [...] Read more.

We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons

R b

, parallelograms M, vertically overlapping parallelograms

M v M

, horizontally overlapping parallelograms

M h M

, and intersecting parallelograms

M x M

. All formulas have the form of multiple sums over binomial coefficients. Three of the formulas are given with a proof based on the interface theory of benzenoids, while the remaining two formulas are presented as conjectures verified via extensive numerical tests. Both of the conjectured formulas have the form of a

2 \times 2

determinant bearing close structural resemblance to analogous formulas for the number of Kekulé structures derived from the John-Sachs theory of Kekulé structures. Full article

(This article belongs to the Special Issue Symmetry on the Genealogy of Conjugated Acyclic Polyenes ‑ Dedicated to the Two Active Mathematical Chemists, Diudea and Aihara)

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35 pages, 3704 KiB

Open AccessEditor’s ChoiceArticle

A New Approach to Identifying a Multi-Criteria Decision Model Based on Stochastic Optimization Techniques

by Bartłomiej Kizielewicz and Wojciech Sałabun

Symmetry 2020, 12(9), 1551; https://doi.org/10.3390/sym12091551 - 20 Sep 2020

Cited by 48 | Viewed by 3636

Abstract

Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet [...] Read more.

Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet identification of preferences makes it impossible to determine the preferences for new alternatives. In this work, we propose a new approach to identifying a multi-criteria decision model to address this challenge. Our proposal is based on stochastic optimization techniques and the characteristic objects method (COMET). An extensive work comparing the use of hill-climbing, simulated annealing, and particle swarm optimization algorithms are presented in this paper. The paper also contains preliminary studies on initial conditions. Finally, our approach has been demonstrated using a simple numerical example. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)

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56 pages, 2440 KiB

Open AccessEditor’s ChoiceArticle

Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods

by Wojciech Sałabun, Jarosław Wątróbski and Andrii Shekhovtsov

Symmetry 2020, 12(9), 1549; https://doi.org/10.3390/sym12091549 - 20 Sep 2020

Cited by 268 | Viewed by 9708

Abstract

Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) [...] Read more.

Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) methods. To achieve that, a set of feasible MCDA methods was identified. Based on reference literature guidelines, a simulation experiment was planned. The formal foundations of the authors’ approach provide a reference set of MCDA methods ( Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Complex Proportional Assessment (COPRAS), and PROMETHEE II: Preference Ranking Organization Method for Enrichment of Evaluations) along with their similarity coefficients (Spearman correlation coefficients and WS coefficient). This allowed the generation of a set of models differentiated by the number of attributes and decision variants, as well as similarity research for the obtained rankings sets. As the authors aim to build a complex benchmarking model, additional dimensions were taken into account during the simulation experiments. The aspects of the performed analysis and benchmarking methods include various weighing methods (results obtained using entropy and standard deviation methods) and varied techniques of normalization of MCDA model input data. Comparative analyses showed the detailed influence of values of particular parameters on the final form and a similarity of the final rankings obtained by different MCDA methods. Full article

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)

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35 pages, 2694 KiB

Open AccessEditor’s ChoiceArticle

Empirical Consequences of Emergent Mass

by Craig D. Roberts

Symmetry 2020, 12(9), 1468; https://doi.org/10.3390/sym12091468 - 7 Sep 2020

Cited by 70 | Viewed by 3859

Abstract

The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The [...] Read more.

The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The source of all these things can be traced to emergent mass, which might itself be QCD’s self-stabilising mechanism. A background to this perspective is provided, presenting, inter alia, a discussion of the gluon mass and QCD’s process-independent effective charge and highlighting an array of observable expressions of emergent mass, ranging from its manifestations in pion parton distributions to those in nucleon electromagnetic form factors. Full article

(This article belongs to the Special Issue Chiral Symmetry in Physics)

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73 pages, 8657 KiB

Open AccessFeature PaperEditor’s ChoiceReview

On the Remarkable Superconductivity of FeSe and Its Close Cousins

by Andreas Kreisel, Peter J. Hirschfeld and Brian M. Andersen

Symmetry 2020, 12(9), 1402; https://doi.org/10.3390/sym12091402 - 23 Aug 2020

Cited by 100 | Viewed by 15373

Abstract

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of [...] Read more.

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe

_{1 - x}

Se

_{x}

, intercalated FeSe materials, and monolayer FeSe and FeTe

_{1 - x}

Se

_{x}

on SrTiO

_{3}

. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity. Full article

(This article belongs to the Special Issue Gap Symmetry and Structure of Superconductors)

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10 pages, 1751 KiB

Open AccessEditor’s ChoiceArticle

Increase in Absolute Leaf Water Content Tends to Keep Pace with That of Leaf Dry Mass—Evidence from Bamboo Plants

by Weiwei Huang, Gadi V. P. Reddy, Yueyi Li, Jørgen Bo Larsen and Peijian Shi

Symmetry 2020, 12(8), 1345; https://doi.org/10.3390/sym12081345 - 12 Aug 2020

Cited by 23 | Viewed by 4700

Abstract

Leaves, as the most important photosynthetic organ of plants, are intimately associated with plant function and adaptation to environmental changes. The scaling relationship of the leaf dry mass (or the fresh mass) vs. leaf surface area has been referred to as “diminishing returns”, [...] Read more.

Leaves, as the most important photosynthetic organ of plants, are intimately associated with plant function and adaptation to environmental changes. The scaling relationship of the leaf dry mass (or the fresh mass) vs. leaf surface area has been referred to as “diminishing returns”, suggesting that the leaf area fails to increase in proportion to leaf dry mass (or fresh mass). However, previous studies used materials across different families, and there is lack of studies testing whether leaf fresh mass is proportional to the leaf dry mass for the species in the same family, and examining the influence of the scaling of leaf dry mass vs. fresh mass on two kinds of diminishing returns based on leaf dry mass and fresh mass. Bamboo plants (Poaceae: Bambusoideae) are good materials for doing such a study, which have astonishingly similar leaf shapes across species. Bamboo leaves have a typical parallel venation pattern. In general, a parallel venation pattern tends to produce a more stable symmetrical leaf shape than the pinnate and palmate venation patterns. The symmetrical parallel veins enable leaves to more regularly hold water, which is more likely to result in a proportional relationship between the leaf dry mass and absolute water content, which consequently determines whether the scaling exponent of the leaf dry mass vs. area is significantly different from (or the same as) that of the leaf fresh mass vs. area. In the present study, we used the data of 101 bamboo species, cultivars, forms and varieties (referred to as 101 (bamboo) taxa below for convenience) to analyze the scaling relationships between the leaf dry mass and area, and between leaf fresh mass and area. We found that the confidence intervals of the scaling exponents of the leaf fresh mass vs. dry mass of 68 out of the 101 taxa included unity, which indicates that for most bamboo species (67.3%), the increase in leaf water mass keeps pace with that of leaf dry mass. There was a significant scaling relationship between either leaf dry mass or fresh mass, and the leaf surface area for each studied species. We found that there was no significant difference between the scaling exponent of the leaf dry mass vs. leaf area and that of the leaf fresh mass vs. leaf area when the leaf dry mass was proportional to the leaf fresh mass. The goodness of fit to the linearized scaling relationship of the leaf fresh mass vs. area was better than that of the leaf dry mass vs. area for each of the 101 bamboo taxa. In addition, there were significant differences in the normalized constants of the leaf dry mass vs. fresh mass among the taxa (i.e., the differences in leaf water content), which implies the difference in the adaptabilities to different environments across the taxa. Full article

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

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38 pages, 3339 KiB

Open AccessEditor’s ChoiceArticle

Fluctuating Asymmetry in Morphological Characteristics of Betula Pendula Roth Leaf under Conditions of Urban Ecosystems: Evaluation of the Multi-Factor Negative Impact

by Elena Shadrina, Nina Turmukhametova, Victoria Soldatova, Yakov Vol'pert, Irina Korotchenko and Galina Pervyshina

Symmetry 2020, 12(8), 1317; https://doi.org/10.3390/sym12081317 - 6 Aug 2020

Cited by 11 | Viewed by 3817

Abstract

The fluctuating asymmetry (FA) in Betula pendula Roth was estimated as an integrated measure of five morphometric characteristics of a lamina. Samples were collected in seven cities that differ both in climatic conditions, moderately to sharply continental. In total, 33 ecotopes were distinguished [...] Read more.

The fluctuating asymmetry (FA) in Betula pendula Roth was estimated as an integrated measure of five morphometric characteristics of a lamina. Samples were collected in seven cities that differ both in climatic conditions, moderately to sharply continental. In total, 33 ecotopes were distinguished with various level of anthropogenic load. The statistical data processing involved correlation, one-way and factorial ANOVA, regression analyses, and principal component analysis (PCA). The impact of 25 climatic and anthropogenic factors on the FA value was considered. In most urban ecotopes, the integrated fluctuating asymmetry (IFA) value was higher than in natural biotopes of the same region. No significant inter-annual differences in IFA values were found. FA dependence on traffic load is noted to be statistically significant. The covariation analysis of IFA, climatic, and anthropogenic variables in various urban ecotopes revealed the impact of three groups of factors that together explain 93% of the variance in environmental parameters. The complex analysis clearly arranged the studied ecotopes by pollution gradient and climatic patterns. The primary effect of the total anthropogenic load on the developmental stability of B. pendula results in an IFA increase. IFA can play a key role in bioindication assessment of environmental quality. The climatic factors have no significant effect on the developmental stability of B. pendula in urban conditions. Full article

(This article belongs to the Section Life Sciences)

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15 pages, 287 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)

by Valeriy Obukhov

Symmetry 2020, 12(8), 1289; https://doi.org/10.3390/sym12081289 - 3 Aug 2020

Cited by 20 | Viewed by 2623

Abstract

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as [...] Read more.

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2020)

10 pages, 241 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

by Omar Bazighifan, Osama Moaaz, Rami Ahmad El-Nabulsi and Ali Muhib

Symmetry 2020, 12(8), 1248; https://doi.org/10.3390/sym12081248 - 29 Jul 2020

Cited by 16 | Viewed by 2329

Abstract

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important [...] Read more.

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given. Full article

(This article belongs to the Special Issue Asymptotic Properties of Solutions of Difference and Differential Equations)

20 pages, 1914 KiB

Open AccessEditor’s ChoiceArticle

An Integrated Approach of Analytic Hierarchy Process and Triangular Fuzzy Sets for Analyzing the Park-and-Ride Facility Location Problem

by Jairo Ortega, János Tóth, Sarbast Moslem, Tamás Péter and Szabolcs Duleba

Symmetry 2020, 12(8), 1225; https://doi.org/10.3390/sym12081225 - 26 Jul 2020

Cited by 22 | Viewed by 3010

Abstract

A park and ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to complete their journey. The main advantage of the system is reducing the congestions problem in the central business district (CBD). Thus, the [...] Read more.

A park and ride (P&R) system is a set of facilities where private vehicle users can transfer to public transport to complete their journey. The main advantage of the system is reducing the congestions problem in the central business district (CBD). Thus, the notion of symmetry is particularly important in multi-criteria decision aid (MCDA) because they are basic characteristics of the binary relationships used in modelling the preferences of decision-makers. The focal point of this study is evaluating the P&R facility system location problem from the experts’ point of view. For this aim, an integrated multicriteria decision-making (MCDM) methodology is proposed to evaluate the location of the facilities of the P&R system. The questionnaire survey was designed and estimated by 10 transport experts in the related field. The famous analytic hierarchy process (AHP) was adopted in a fuzzy environment, where the fuzzy sets have an efficient ability to manage the vague concepts in a specific way; moreover, it can mitigate the evaluator reasoning during decision-making. The hierarchical structure of the problem was established to evaluate a real-life problem in Cuenca city, Ecuador. The outcomes highlighted the “accessibility of public transport” as the most significant issue in the P&R facility location problem. The obtained results provide more flexible facilities than the pure AHP method. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)

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21 pages, 1213 KiB

Open AccessEditor’s ChoiceArticle

Stability and Boundedness of the Solutions of Multi-Parameter Dynamical Systems with Circulatory Forces

by Jan Awrejcewicz, Nataliya Losyeva and Volodymyr Puzyrov

Symmetry 2020, 12(8), 1210; https://doi.org/10.3390/sym12081210 - 23 Jul 2020

Cited by 11 | Viewed by 1885

Abstract

We consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are [...] Read more.

We consider a linear dynamical system under the action of potential and circulatory forces. The matrix of potential forces is positive definite, and the main question is when the circulatory forces induce instability to the system. Different approaches to studying the problem are discussed and illustrated by examples. The case of multiple eigenvalues also is considered, and sufficient conditions of instability are obtained. Some issues of the dynamics of a nonlinear system with an unstable linear approximation are discussed. The behavior of trajectories in the case of unstable equilibrium is investigated, and an example of the chaotic behavior versus the case of bounded solutions is presented and discussed. Full article

(This article belongs to the Special Issue Symmetry in Discrete Dynamical Systems and Ordinary Differential Equations)

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