Journal Description

Symmetry

Symmetry is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, SCIE (Web of Science), CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics); Q1 (Physics and Astronomy); Q1 (Computer Science)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.2 days after submission; acceptance to publication is undertaken in 3.5 days (median values for papers published in this journal in the second half of 2023).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Testimonials: See what our editors and authors say about Symmetry.

Impact Factor: 2.7 (2022); 5-Year Impact Factor: 2.7 (2022)

Imprint Information Journal Flyer Open Access ISSN: 2073-8994

Latest Articles

18 pages, 5214 KiB

Open AccessArticle

An Efficient Trajectory Planning Approach for Autonomous Ground Vehicles Using Improved Artificial Potential Field

Xianjian Jin

Zhiwei Li

Nonsly Valerienne Opinat Ikiela

and

Symmetry 2024, 16(1), 106; https://doi.org/10.3390/sym16010106 (registering DOI) - 15 Jan 2024

Abstract

In this paper, the concept of symmetry is utilized in the promising trajectory planning design of autonomous ground vehicles—that is, the construction and the solution of improved artificial potential field-based trajectory planning approach are symmetrical. Despite existing artificial potential fields (APF) achievements on trajectory planning in autonomous ground vehicles (AGV), applying the traditional approach to dynamic traffic scenarios is inappropriate without considering vehicle dynamics environment and road regulations. This paper introduces a highly efficient approach for planning trajectories using improved artificial potential fields (IAPF) to handle dynamic road participants and address the issue of local minima in artificial potential fields. To begin with, potential fields are created with data obtained from other sensors. By incorporating rotational factors, the potential field will spin when the obstacle executes a maneuver; then, a safety distance model is also developed to limit the range of influence in order to minimize the computational burden. Furthermore, during the planning process, virtual forces using the gradient descent method are generated to direct the vehicle’s movement. During each timestep, the vehicle will assess whether it is likely to encounter a local minimum in the future. Once a local minimum is discovered, the method will create multiple temporary objectives to guide the vehicle toward the global minimum. Consequently, a trajectory that is both collision-free and feasible is planned. Traffic scenarios are carried out to validate the effectiveness of the proposed approach. The simulation results demonstrate that the improved artificial potential field approach is capable of generating a secure trajectory with both comfort and stability. Full article

(This article belongs to the Special Issue Emerging Applications of Machine Learning in Smart Systems Symmetry)

13 pages, 2313 KiB

Open AccessArticle

A New Symmetry-Enhanced Simulation Approach Considering Poromechanical Effects and Its Application in the Hydraulic Fracturing of a Carbonate Reservoir

and

Symmetry 2024, 16(1), 105; https://doi.org/10.3390/sym16010105 - 15 Jan 2024

Abstract

The exploration of fractured-vuggy carbonate reservoirs usually involves hydraulic fracturing to maximize recovery. At present, effectively communicating natural discontinuities is a technical challenge. In this article, we investigated the origin and propagation of cracks in fractured-vuggy reservoirs using discrete element hydraulic fracturing simulations that included poromechanical effects. A particular focus on the microscopic force-displacement symmetry of adjacent pore pressures is introduced. Our results demonstrate that the poromechanical effect significantly increases the strength of overpressurized reservoir formations. Moreover, the effect of injected fluid viscosity on the hydraulic fracturing effectiveness was studied through two simulation tests. The outcomes highlight the critical influence of fluid viscosity on the propagation of micro-cracks in overpressure fractured-vuggy reservoirs. Full article

(This article belongs to the Special Issue Physically Data-Driven Research on Symmetry/Asymmetry in Underground Engineering Construction and Maintenance)

11 pages, 500 KiB

Open AccessArticle

Selectivity in Catalytic Asymmetric Formal [3 + 3] Annulation of 2-Enoyl-pyridine N-Oxide with Benzyl Methyl Ketone

Zuzanna Wrzeszcz

Jakub A. Warachim

and

Renata Siedlecka

Symmetry 2024, 16(1), 104; https://doi.org/10.3390/sym16010104 - 15 Jan 2024

Abstract

The asymmetric formal [3 + 3] annulation process of (E)-2-(3-phenylacryloyl)pyridine N-oxide with benzyl methyl ketone was investigated. The possibility of a stereoselective outcome was checked using salts of natural amino acids, as well as chiral bifunctional derivatives containing amino groups and thiourea or squaramide fragments as organocatalysts. Different types of organocatalysts applied led to opposite enantiomers of 2-(3-oxo-4,5-diphenyl-cyclohex-1-en-yl)pyridine 1-oxide (up to 60% ee). Spectroscopic analysis of the isolated product and analysis of the reaction course was carried out, taking into account the obtained regio- and stereoselectivity. In order to verify the postulated results, calculations of the energy of the intermediate reaction products and the final product using the Kohn–Sham Density Functional Theory (KS-DFT) were made. Full article

(This article belongs to the Special Issue Novel Approaches for Asymmetric Synthesis)

15 pages, 4938 KiB

Open AccessArticle

Structure of Current Sheets Formed in 2D Magnetic Configurations with X-Type Null Lines in the Presence of the Hall Currents and Inverse Currents

Anna G. Frank

and

Sergey A. Savinov

Symmetry 2024, 16(1), 103; https://doi.org/10.3390/sym16010103 - 15 Jan 2024

Abstract

We present experimental results on the formation and evolution of current sheets in two-dimensional magnetic configurations with an X-type null line. Typical features of both the initial magnetic field and the current sheet are their symmetry properties. The experiments were carried out using the CS-3D setup. The formation of a current sheet occurs just after the magneto-sonic wave converges at the null line; then, both the electric current and plasma become compressed in a planar 2D sheet, which accumulates an excess of magnetic energy. The excitation of the Hall currents, which build up the out-of-plane magnetic fields inside the 2D current sheet, brings about the modification of the sheet structure. As a result, the magnetic fields and plasma currents become 3D. The dynamic plasma processes give rise to additional current sheet deformations, which are caused by the excitation of inverse currents at the side edges of the sheet. As a consequence, the out-of-plane magnetic fields are reversed, and strong Ampère’s forces of the opposite directions come into play. These forces slow down the previously accelerated high-speed plasma flows so that the flows become limited in time and space. Full article

(This article belongs to the Special Issue Symmetry in Physics of Plasma Technologies II)

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14 pages, 3651 KiB

Open AccessArticle

The Properties of Topological Manifolds of Simplicial Polynomials

Susmit Bagchi

Symmetry 2024, 16(1), 102; https://doi.org/10.3390/sym16010102 - 14 Jan 2024

Abstract

The formulations of polynomials over a topological simplex combine the elements of topology and algebraic geometry. This paper proposes the formulation of simplicial polynomials and the properties of resulting topological manifolds in two classes, non-degenerate forms and degenerate forms, without imposing the conditions of affine topological spaces. The non-degenerate class maintains the degree preservation principle of the atoms of the polynomials of a topological simplex, which is relaxed in the degenerate class. The concept of hybrid decomposition of a simplicial polynomial in the non-degenerate class is introduced. The decompositions of simplicial polynomial for a large set of simplex vertices generate ideal components from the radical, and the components preserve the topologically isolated origin in all cases within the topological manifolds. Interestingly, the topological manifolds generated by a non-degenerate class of simplicial polynomials do not retain the homeomorphism property under polynomial extension by atom addition if the simplicial condition is violated. However, the topological manifolds generated by the degenerate class always preserve isomorphism with varying rotational orientations. The hybrid decompositions of the non-degenerate class of simplicial polynomials give rise to the formation of simplicial chains. The proposed formulations do not impose strict positivity on simplicial polynomials as a precondition. Full article

(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials II)

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13 pages, 389 KiB

Open AccessReview

Gravitational Light Bending in Weyl Gravity and Schwarzschild-de Sitter Spacetime

Joseph Sultana

Symmetry 2024, 16(1), 101; https://doi.org/10.3390/sym16010101 - 14 Jan 2024

Abstract

The topic of gravitational lensing in the Mannheim–Kazanas solution of Weyl conformal gravity and the Schwarzschild–de Sitter solution in general relativity has featured in numerous publications. These two solutions represent a spherical massive object (lens) embedded in a cosmological background. In both cases, the interest lies in the possible effect of the background non-asymptotically flat spacetime on the geometry of the local light curves, particularly the observed deflection angle of light near the massive object. The main discussion involves possible contributions to the bending angle formula from the cosmological constant

Λ

in the Schwarzschild–de Sitter solution and the linear term

γ r

in the Mannheim–Kazanas metric. These effects from the background geometry, and whether they are significant enough to be important for gravitational lensing, seem to depend on the methodology used to calculate the bending angle. In this paper, we review these techniques and comment on some of the obtained results, particularly those cases that contain unphysical terms in the bending angle formula. Full article

(This article belongs to the Section Physics)

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16 pages, 4602 KiB

Open AccessArticle

Time–Energy Uncertainty Relation in Nonrelativistic Quantum Mechanics

Danko D. Georgiev

Symmetry 2024, 16(1), 100; https://doi.org/10.3390/sym16010100 - 14 Jan 2024

Abstract

The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using [...] Read more.

ℓ_{1}

norm of energy coherence

C

is invariant with respect to the unitary evolution of the quantum state. Thus, the

ℓ_{1}

norm of energy coherence

C

of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal

ℓ_{1}

norm of energy coherence,

C < 1

, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal

ℓ_{1}

norm of energy coherence,

C = 1

, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance. Full article

(This article belongs to the Section Physics)

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12 pages, 263 KiB

Open AccessArticle

An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space

Gonca Durmaz Güngör

and

Ishak Altun

Symmetry 2024, 16(1), 99; https://doi.org/10.3390/sym16010099 - 13 Jan 2024

Abstract

We introduce the new idea of

(α - θ_{σ})

-contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left [...] Read more.

We introduce the new idea of

(α - θ_{σ})

-contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left

S m y t h

-complete quasi-metric spaces. We also apply our results to infer the existence of a solution to a second-order boundary-value problem. Full article

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

20 pages, 1801 KiB

Open AccessArticle

On Some Origins of Tautomeric Preferences in Neutral Creatinine in Vacuo: Search for Analogies and Differences in Cyclic Azoles and Azines

Ewa Daniela Raczyńska

Symmetry 2024, 16(1), 98; https://doi.org/10.3390/sym16010098 - 12 Jan 2024

Abstract

In order to look for the origins of tautomeric preferences in neutral creatinine in vacuo, we examined prototropic conversions for model azoles, namely mono-hydroxy and mono-amino imidazoles, and also for their selected 1-methyl derivatives. All possible isomeric forms of creatinine and model compounds, resulting from intramolecular proton transfer (prototropy), conformational isomerism about –OH, and configurational isomerism about =NH, were studied in the gas phase (model of non-polar environment) by means of quantum-chemical methods. Because the bond-length alternation is a consequence of the resonance phenomenon, it was measured for all DFT-optimized structures by means of the harmonic oscillator model of electron delocalization (HOMED) index. Important HOMED analogies were discussed for investigated azoles and compared with those for previously studied cyclic azines, including pyrimidine nucleic acid bases. The internal effects were taken into account, and the stabilities of the investigated tautomers-rotamers were analyzed. Significant conclusions on the favored factors that can dictate the tautomeric preferences in creatinine were derived. Full article

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16 pages, 323 KiB

Open AccessArticle

A Solvable Algebra for Massless Fermions

Stefan Groote

and

Rein Saar

Symmetry 2024, 16(1), 97; https://doi.org/10.3390/sym16010097 - 11 Jan 2024

Abstract

We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel subgroup. In the absence of [...] Read more.

{sol}_{2}^{\pm}

of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, in our conclusions, it is argued how the spin-flip contribution might be closely related to the occurrence of nonphysical spin operators. Full article

(This article belongs to the Section Physics)

14 pages, 974 KiB

Open AccessArticle

Wave Solutions for a (2 + 1)-Dimensional Burgers–KdV Equation with Variable Coefficients via the Functional Expansion Method

Rodica Cimpoiasu

and

Radu Constantinescu

Symmetry 2024, 16(1), 96; https://doi.org/10.3390/sym16010096 - 11 Jan 2024

Abstract

A (2+1)-dimensional fourth order Burgers–KdV equation with variable coefficients (vcBKdV) is studied here and interesting wave-type solutions with variable amplitudes and velocities are reported. The model has been not previously studied in the chosen form and it presents a twofold interest: as a model describing a rich variety of phenomena and as a higher-order equation solving difficulties generated by the presence of the variable coefficients. The novelty of our approach is related to the use of the functional expansion, a solving method based on an auxiliary equation that generalizes other approaches, such as, for example, the

(\frac{G^{'}}{G})

proved here. We use a similarity reduction with a nonlinear wave variable that leads to a determining system that it is not usually algebraic, but an over-determined system of partial differential equations. It depends on 14 constant or functional parameters and can generate much richer classes of solutions. Three such classes of solutions, corresponding to the case when a specific form of the generalized reaction–diffusion equation is used as auxiliary equation, are considered. The influence on the dynamical behavior of two important factors, the choices of the auxiliary equation and the form of solution, are studied by providing graphical representations of specific solutions for various values of the parameters. Full article

(This article belongs to the Section Physics)

18 pages, 306 KiB

Open AccessArticle

Ricci Curvature Inequalities for Contact CR-Warped Product Submanifolds of an Odd Dimensional Sphere Admitting a Semi-Symmetric Metric Connection

Meraj Ali Khan

Ibrahim Al-Dayel

and

Foued Aloui

Symmetry 2024, 16(1), 95; https://doi.org/10.3390/sym16010095 - 11 Jan 2024

Abstract

The primary objective of this paper is to explore contact CR-warped product submanifolds of Sasakian space forms equipped with a semi-symmetric metric connection. We thoroughly examine these submanifolds and establish various key findings. Furthermore, we derive an inequality relating the Ricci curvature to [...] Read more.

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)

17 pages, 766 KiB

Open AccessArticle

Robust and Exponential Stabilization of a Cart–Pendulum System via Geometric PID Control

and

Symmetry 2024, 16(1), 94; https://doi.org/10.3390/sym16010094 - 11 Jan 2024

Abstract

This paper addresses the robust stabilization problem of a cart–pole system. The controlled dynamics of this interconnected system are deduced by following the analytic framework of Lagrangian mechanics, and the residual terms are formulated as a bias depending on the angle and angular velocity. A geometric definition of Proportional–Integral–Derivative (PID) control algorithm is proposed, and a Lyapunov function is explicitly constructed through two stages of variable change. Local exponential stability of the stable equilibrium is proved, and a criterion for parameter tuning is provided by ensuring an exponential decrease in the Lyapunov function. Enlarging the control parameters to infinity allows for the extension of attraction region almost to the half circle. The effectiveness of geometric PID controller and the local exponential stability of the resulting close system are verified by simulating a numerical example. Full article

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16 pages, 1501 KiB

Open AccessArticle

Wald Intervals via Profile Likelihood for the Mean of the Inverse Gaussian Distribution

Patchanok Srisuradetchai

Ausaina Niyomdecha

and

Wikanda Phaphan

Symmetry 2024, 16(1), 93; https://doi.org/10.3390/sym16010093 - 11 Jan 2024

Abstract

The inverse Gaussian distribution, known for its flexible shape, is widely used across various applications. Existing confidence intervals for the mean parameter, such as profile likelihood, reparametrized profile likelihood, and Wald-type reparametrized profile likelihood with observed Fisher information intervals, are generally effective. However, our simulation study identifies scenarios where the coverage probability falls below the nominal confidence level. Wald-type intervals are widely used in statistics and have a symmetry property. We mathematically derive the Wald-type profile likelihood (WPL) interval and the Wald-type reparametrized profile likelihood with expected Fisher information (WRPLE) interval and compare their performance to existing methods. Our results indicate that the WRPLE interval outperforms others in terms of coverage probability, while the WPL typically yields the shortest interval. Additionally, we apply these proposed intervals to a real dataset, demonstrating their potential applicability to other datasets that follow the IG distribution. Full article

(This article belongs to the Special Issue Symmetry in Probability Theory and Statistics)

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29 pages, 2758 KiB

Open AccessArticle

Vacuum Currents for a Scalar Field in Models with Compact Dimensions

Aram A. Saharian

Symmetry 2024, 16(1), 92; https://doi.org/10.3390/sym16010092 - 11 Jan 2024

Abstract

This paper presents a review of investigations into the vacuum expectation value of the current density for a charged scalar field in spacetimes that hold toroidally compactified spatial dimensions. As background geometries, the locally Minkowskian (LM), locally de Sitter (LdS), and locally anti-de Sitter (LAdS) spacetimes are considered. Along compact dimensions, quasi-periodicity conditions are imposed on the field operator and the presence of a constant gauge field is assumed. The vacuum current has nonzero components along the compact dimensions only. Those components are periodic functions of the magnetic flux enclosed in compact dimensions, with a period that is equal to the flux quantum. For LdS and LAdS geometries, and for small values of the length of a compact dimension, compared with the curvature radius, the leading term in the expansion of the the vacuum current along that dimension coincides with that for LM bulk. In this limit, the dominant contribution to the mode sum for the current density comes from the vacuum fluctuations with wavelengths smaller to those of the curvature radius; additionally, the influence of the gravitational field is weak. The effects of the gravitational field are essential for lengths of compact dimensions that are larger than the curvature radius. In particular, instead of the exponential suppression of the current density in LM bulk, one can obtain a power law decay in the LdS and LAdS spacetimes. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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25 pages, 4232 KiB

Open AccessArticle

Maintaining Symmetry between Convolutional Neural Network Accuracy and Performance on an Edge TPU with a Focus on Transfer Learning Adjustments

and

Symmetry 2024, 16(1), 91; https://doi.org/10.3390/sym16010091 - 11 Jan 2024

Abstract

Transfer learning has proven to be a valuable technique for deploying machine learning models on edge devices and embedded systems. By leveraging pre-trained models and fine-tuning them on specific tasks, practitioners can effectively adapt existing models to the constraints and requirements of their application. In the process of adapting an existing model, a practitioner may make adjustments to the model architecture, including the input layers, output layers, and intermediate layers. Practitioners must be able to understand whether the modifications to the model will be symmetrical or asymmetrical with respect to the performance. In this study, we examine the effects of these adjustments on the runtime and energy performance of an edge processor performing inferences. Based on our observations, we make recommendations for how to adjust convolutional neural networks during transfer learning to maintain symmetry between the accuracy of the model and its runtime performance. We observe that the edge TPU is generally more efficient than a CPU at performing inferences on convolutional neural networks, and continues to outperform a CPU as the depth and width of the convolutional network increases. We explore multiple strategies for adjusting the input and output layers of an existing model and demonstrate important performance cliffs for practitioners to consider when modifying a convolutional neural network model. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Machine Learning)

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10 pages, 1279 KiB

Open AccessArticle

The Effects of Drop Vertical Jump Task Variation on Landing Mechanics: Implications for Evaluating Limb Asymmetry

Kirsten Tulchin-Francis

and

Tishya A. L. Wren

Symmetry 2024, 16(1), 90; https://doi.org/10.3390/sym16010090 - 11 Jan 2024

Abstract

Limb asymmetry is an important consideration when evaluating rehabilitation progress or re-injury risk. The drop vertical jump (DVJ) task is commonly used to assess landing mechanics; however, the extent to which task setup influences limb asymmetry is unknown. Our purpose was to examine limb asymmetries across DVJ variations. We hypothesized that more demanding variations involving greater jump distance and target use would elicit greater landing asymmetries. Participants performed six DVJ variations while lower extremity joint kinematics and kinetics were collected. Joint angles and internal moments of the hip, knee and ankle were computed at initial contact and over the decent phase of the initial landing. The horizontal jump distance and the verbal instructions provided on how to jump off the box influenced limb asymmetries. The DVJ variation without a horizontal jump distance resulted in significant differences at the hip and knee; specifically, greater hip and knee flexion asymmetry (7.0° and 15.2° differences, respectively) were observed between limbs at initial contact. Instructions restricting take-off and landing strategies reduced asymmetry; this indicates that verbal instructions are critical to avoid altering natural landing mechanics. To best utilize DVJ as a tool, study protocols should be standardized to allow for more generalizable research and clinical findings. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Sport Sciences)

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17 pages, 2461 KiB

Open AccessArticle

A Blockchain-Based Privacy-Preserving Healthcare Data Sharing Scheme for Incremental Updates

and

Symmetry 2024, 16(1), 89; https://doi.org/10.3390/sym16010089 - 11 Jan 2024

Abstract

With the rapid development of artificial intelligence (AI) in the healthcare industry, the sharing of personal healthcare data plays an essential role in advancing medical AI. Unfortunately, personal healthcare data sharing is plagued by challenges like ambiguous data ownership and privacy leakage. Blockchain, which stores the hash of shared data on-chain and ciphertext off-chain, is treated as a promising approach to address the above issues. However, this approach lacks a flexible and reliable mechanism for incremental updates of the same case data. To avoid the overhead of authentication, access control, and rewards caused by on-chain data changes, we propose a blockchain and trusted execution environment (TEE)-based privacy-preserving sharing scheme for healthcare data that supports incremental updates. Based on chameleon hash and TEE, the scheme achieves reliable incremental updates and verification without changing the on-chain data. In the scheme, for privacy concerns, off-chain data are protected through symmetric encryption, whereas data verification, decryption, and computation are performed within TEE. The experimental results show the feasibility and effectiveness of the proposed scheme. Full article

(This article belongs to the Special Issue Advances in Multidisciplinary Exploration for Symmetric Key Cryptography and Blockchain Technology)

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17 pages, 754 KiB

Open AccessArticle

Data-Driven Control Based on Information Concentration Estimator and Regularized Online Sequential Extreme Learning Machine

Xiaofei Zhang

Hongbin Ma

and

Huaqing Zhang

Symmetry 2024, 16(1), 88; https://doi.org/10.3390/sym16010088 - 10 Jan 2024

Abstract

Due to the complexity of digital equipment and systems, it is quite difficult to obtain a precise mechanism model in practice. For an unknown discrete-time nonlinear system, in this paper, a semi-parametric model is used to describe this discrete-time nonlinear system, and this semi-parametric model contains a parametric uncertainty part and a nonparametric uncertainty part. Based on this semi-parametric model, a novel data-driven control algorithm based on an information concentration estimator and regularized online sequential extreme learning machine (ReOS-ELM) is designed. The information concentration estimator estimates the parametric uncertainty part; The training data of ReOS-ELM network is obtained, based on symmetry and information concentration estimator, then the training of ReOS-ELM network and the estimate of nonparametric uncertainty part using ReOS-ELM network are carried out online, successively. A stability analysis and three simulation examples were performed, and the simulation results show that the proposed data-driven control algorithm is effective in improving the control accuracy. Full article

(This article belongs to the Special Issue Artificial Intelligence, Adaptation and Symmetry/Asymmetry)

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15 pages, 5176 KiB

Open AccessArticle

Asymmetries Caused by Nonparaxiality and Spin–Orbit Interaction during Light Propagation in a Graded-Index Medium

Nikolai I. Petrov

Symmetry 2024, 16(1), 87; https://doi.org/10.3390/sym16010087 - 10 Jan 2024

Abstract

Spin–orbit coupling and nonparaxiality effects during the propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry-breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally symmetric graded-index optical fiber are considered. The mode-group delay in a graded-index fiber due to spin–orbit interaction is demonstrated. A scheme for observing the temporal spin Hall effect is proposed. It is shown that the relative delay times between vortex pulses of opposite circular polarizations of the order of 10 ps/km can be observed in graded-index fibers for high-order topological charges. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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