Symmetry

47 pages, 700 KB

Open AccessEditor’s ChoiceReview

Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics

by Chengyi Li and Bo-Qiang Ma

Symmetry 2025, 17(6), 974; https://doi.org/10.3390/sym17060974 - 19 Jun 2025

Cited by 4 | Viewed by 2601

Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, [...] Read more.

Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, we examine, among other scenarios, such instances in supercritical (Liouville) string theory, particularly in some brane models for “quantum foam”. Using the phenomenological formalism introduced here, we analyze the observational hints of Lorentz violation in time-of-flight lags of cosmic photons and neutrinos which fit excellently stringy space–time foam scenarios. We further demonstrate how stringent constraints from other astrophysical data, including the recent first detections of multi-TeV events in

γ

-ray burst 221009A and PeV cosmic photons by the Large High Altitude Air Shower Observatory (LHAASO), are satisfied in this context. Such models thus provide a unified framework for all currently observed phenomenologies of space–time symmetry breaking at Planckian scales. Full article

(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)

23 pages, 925 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Bi-Symmetric Polyhedral Cages with Nearly Maximally Connected Faces and Small Holes

by Bernard Piette

Symmetry 2025, 17(6), 940; https://doi.org/10.3390/sym17060940 - 12 Jun 2025

Cited by 2 | Viewed by 1803

Abstract

Polyhedral cages (p-cages) provide a good description of the geometry of some families of artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces/protein rings, where each face has at least four neighbours and where [...] Read more.

Polyhedral cages (p-cages) provide a good description of the geometry of some families of artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces/protein rings, where each face has at least four neighbours and where the holes are contributed by at most four faces. We start the construction from a planar graph made out of two families of equivalent nodes. We construct the dual of the solid corresponding to that graph, and we tile its faces with regular or nearly regular polygons. We define an energy function describing the amount of irregularity of the p-cages, which we then minimise using a simulated annealing algorithm. We analyse over 600,000 possible geometries but restrict ourselves to p-cages made out of faces with deformations not exceeding 10%. We then present graphically some of the most promising geometries for protein nanocages. Full article

(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)

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21 pages, 439 KB

Open AccessEditor’s ChoiceArticle

Exploring the Interpretations of Charmonia and cc

\bar{c} \bar{c}

Tetraquarks in the Relativistic Flux Tube Model

by Wen-Chao Dong, Zhi-Gang Wang and Jian-Wen Zhou

Symmetry 2025, 17(6), 931; https://doi.org/10.3390/sym17060931 - 11 Jun 2025

Cited by 1 | Viewed by 1493

Abstract

Incited by the scant understanding of unsettled charmonia and newly observed

c c \bar{c} \bar{c}

tetraquarks, this work aims to explore the canonical interpretations and spectroscopic properties of these fully hidden-charm states. In the framework of a relativistic flux tube model, [...] Read more.

Incited by the scant understanding of unsettled charmonia and newly observed

c c \bar{c} \bar{c}

tetraquarks, this work aims to explore the canonical interpretations and spectroscopic properties of these fully hidden-charm states. In the framework of a relativistic flux tube model, the centroid masses of the low-lying

n L

-wave states with

1 \leq n + L \leq 4

are unraveled. In order to pin down the complete mass spectra, the hyperfine splittings induced by the spin-dependent interactions are incorporated into the final predictions. Accordingly, fourteen charmonia are well identified, including the

η_{c} (1 S)

,

J / ψ (1 S)

,

χ_{c 0} (1 P)

,

h_{c} (1 P)

,

χ_{c 1} (1 P)

,

χ_{c 2} (1 P)

,

η_{c} (2 S)

,

ψ (2 S)

,

ψ (3770)

,

ψ_{2} (3823)

,

ψ_{3} (3842)

,

χ_{c 0} (3915)

,

χ_{c 2} (3930)

, and

ψ (4040)

states. Additionally, the exotic

T_{ψ ψ} (6400)

,

T_{ψ ψ} (6600)

,

T_{ψ ψ} (6900)

, and

T_{ψ ψ} (7300)

states are interpreted as the

1 S

-wave,

1 P / 2 S

-wave,

1 D / 2 P

-wave, and

2 D / 3 P / 4 S

-wave

c c \bar{c} \bar{c}

tetraquarks, respectively. Based on the achieved outcomes, the spin-parity quantum number is imperative to discriminate the nature of the

c c \bar{c} \bar{c}

structures, pending further experimental measurement in the future. Full article

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

31 pages, 833 KB

Open AccessEditor’s ChoiceReview

Boltzmann Equation and Its Cosmological Applications

by Seishi Enomoto, Yu-Hang Su, Man-Zhu Zheng and Hong-Hao Zhang

Symmetry 2025, 17(6), 921; https://doi.org/10.3390/sym17060921 - 10 Jun 2025

Cited by 1 | Viewed by 3121

Abstract

We review the derivation of the Boltzmann equation and its cosmological applications in this paper. A novel derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of quantum field theory without any assumption of a finite [...] Read more.

We review the derivation of the Boltzmann equation and its cosmological applications in this paper. A novel derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of quantum field theory without any assumption of a finite temperature system. We also discuss the integrated Boltzmann equation, incorporating the temperature parameter as an extension of the standard equation. Among a number of its cosmological applications, we mainly target two familiar examples, the dynamics of the dark matter abundance through the freeze-out/in process and a baryogenesis scenario. The formulations in those systems are briefly discussed with techniques in their calculations. Full article

(This article belongs to the Special Issue Quantum Gravity and Cosmology: Exploring the Astroparticle Interface)

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24 pages, 274 KB

Open AccessEditor’s ChoiceReview

Steven Weinberg’s Life for Physics

by Ralf Hofmann

Symmetry 2025, 17(6), 840; https://doi.org/10.3390/sym17060840 - 27 May 2025

Viewed by 5733

Abstract

This is a personal review of Steven Weinberg’s scientific autobiography “A Life in Physics”. A reflection on both, personal aspects and scientific milestones of Professor Weinberg’s role-model life is conducted to honour his lasting accomplishments as a great physicist, academic teacher, and public [...] Read more.

This is a personal review of Steven Weinberg’s scientific autobiography “A Life in Physics”. A reflection on both, personal aspects and scientific milestones of Professor Weinberg’s role-model life is conducted to honour his lasting accomplishments as a great physicist, academic teacher, and public activist in progressing high-energy particle theory and theoretical cosmology, and in raising public support for fundamental physics. Full article

(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)

40 pages, 40200 KB

Open AccessEditor’s ChoiceReview

Fundamentals of Symmetry and Topology: Applications to Materials Science and Condensed Matter Physics

by Mengdi Yin, Jing Zhang and Dimitri D. Vvedensky

Symmetry 2025, 17(6), 807; https://doi.org/10.3390/sym17060807 - 22 May 2025

Viewed by 4218

Abstract

We review the connections between condensed matter physics, symmetry, and topology. Physics goes back to at least the time of Galileo, but condensed matter physics, or solid-state physics, is a much newer, emerging only as a separate subject in the 1940s. The subject [...] Read more.

We review the connections between condensed matter physics, symmetry, and topology. Physics goes back to at least the time of Galileo, but condensed matter physics, or solid-state physics, is a much newer, emerging only as a separate subject in the 1940s. The subject of symmetry, which is the mathematics of groups and representations, only came to the fore with the advent of quantum mechanics. Early applications to crystalline solids include Bloch’s theorem, the symmetry of electronic and phononic energy bands, and selection rules. Topology, on the other hand, did not exist as a mathematical subject before the twentieth century, but has had a profound influence on physics in general, and on condensed matter physics in particular. The quantum Hall effect is recognized as the first solid-state topological phenomenon and, along with the Berry phase, led to the development of topological materials. This, in turn, led to the topological description of energy bands and to the development of topological quantum chemistry and the energy band representation. Topology has also led to the description of martensitic transformations and the shape memory effect in terms of topological transformations. Apart from a concise statement of martensitic transformations, topology provides a fast-screening method for the discovery of new shape-memory materials. We review these phenomena, providing background material in topology and differential geometry to enable the reader to understand applications to topological materials and to materials physics. Full article

(This article belongs to the Special Issue The Benefits That Physics Derives from the Concept of Symmetry)

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57 pages, 2571 KB

Open AccessEditor’s ChoiceReview

Heavy–Heavy and Heavy–Light Mesons in Cold Nuclear Matter

by J. J. Cobos-Martínez, Guilherme N. Zeminiani and Kazuo Tsushima

Symmetry 2025, 17(5), 787; https://doi.org/10.3390/sym17050787 - 19 May 2025

Cited by 1 | Viewed by 1174

Abstract

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and [...] Read more.

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and an effective Lagrangian. As demonstrated by the cases of pionic and kaonic atoms, studies of the meson–nucleus bound state can provide us with important information on chiral symmetry in a dense nuclear medium. In this review, we examine the mesons,

K, K^{*}, D, D^{*}, B, B^{*}, η, η^{'}, ϕ, η_{c}, J / ψ, η_{b}, Υ

, and

B_{c}

, where our emphasis is on the heavy mesons. In addition, we also present some new results for the

B_{c}

-nucleus bound states. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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17 pages, 285 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Convergence Analysis of Reinforcement Learning Algorithms Using Generalized Weak Contraction Mappings

by Abdelkader Belhenniche, Roman Chertovskih and Rui Gonçalves

Symmetry 2025, 17(5), 750; https://doi.org/10.3390/sym17050750 - 13 May 2025

Cited by 2 | Viewed by 4218

Abstract

We investigate the convergence properties of policy iteration and value iteration algorithms in reinforcement learning by leveraging fixed-point theory, with a focus on mappings that exhibit weak contractive behavior. Unlike traditional studies that rely on strong contraction properties, such as those defined by [...] Read more.

We investigate the convergence properties of policy iteration and value iteration algorithms in reinforcement learning by leveraging fixed-point theory, with a focus on mappings that exhibit weak contractive behavior. Unlike traditional studies that rely on strong contraction properties, such as those defined by the Banach contraction principle, we consider a more general class of mappings that includes weak contractions. Employing Zamfirscu’s fixed-point theorem, we establish sufficient conditions for norm convergence in infinite-dimensional policy spaces under broad assumptions. Our approach extends the applicability of these algorithms to feedback control problems in reinforcement learning, where standard contraction conditions may not hold. Through illustrative examples, we demonstrate that this framework encompasses a wider range of operators, offering new insights into the robustness and flexibility of iterative methods in dynamic programming. Full article

(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Optimization: Computations and Applications)

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21 pages, 20352 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Handheld 3D Scanning-Based Robotic Trajectory Planning for Multi-Layer Multi-Pass Welding of a Large Intersecting Line Workpiece with Asymmetric Profiles

by Xinlei Li, Shida Yao, Jiawei Ma, Guanxin Chi and Guangjun Zhang

Symmetry 2025, 17(5), 738; https://doi.org/10.3390/sym17050738 - 11 May 2025

Cited by 3 | Viewed by 2226

Abstract

Traditional offline programming has limitations for large parts with significant machining or assembly deviations. This study proposes a 3D scanning-assisted method that generates accurate STereoLithography (STL) models and enables multi-layer multi-bead welding trajectory planning for large intersecting line workpieces. The proposed framework implements [...] Read more.

Traditional offline programming has limitations for large parts with significant machining or assembly deviations. This study proposes a 3D scanning-assisted method that generates accurate STereoLithography (STL) models and enables multi-layer multi-bead welding trajectory planning for large intersecting line workpieces. The proposed framework implements a robust STL model processing pipeline incorporating Random Sample Consensus (RANSAC)-based cylindrical approximation, cross-sectional slicing, and automated feature detection to achieve high-precision groove feature recognition. For asymmetric variable-section grooves, a multi-layer and multi-pass path-planning algorithm based on template affine projection transformation is developed to ensure accurate deposition of welds along complex geometric contours. Experimental validation demonstrates sub-millimeter trajectory accuracy (positional errors < 1.0 mm), meeting stringent arc welding specifications and substantially expanding the applicability of offline programming systems. Full article

(This article belongs to the Special Issue Symmetry Application in Metals and Alloys)

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31 pages, 1438 KB

Open AccessEditor’s ChoiceArticle

FIMP Dark Matter in Bulk Viscous Non-Standard Cosmologies

by Esteban González, Carlos Maldonado, N. Stefanía Mite and Rodrigo Salinas

Symmetry 2025, 17(5), 731; https://doi.org/10.3390/sym17050731 - 9 May 2025

Cited by 3 | Viewed by 987

Abstract

In this paper, we revisit the extension of the classical non-standard cosmological model in which dissipative processes are considered through a bulk viscous term in the new field

ϕ

, which interacts with the radiation component during the early universe. Specifically, we consider [...] Read more.

In this paper, we revisit the extension of the classical non-standard cosmological model in which dissipative processes are considered through a bulk viscous term in the new field

ϕ

, which interacts with the radiation component during the early universe. Specifically, we consider an interaction term of the form

Γ_{ϕ} ρ_{ϕ}

, where

Γ_{ϕ}

represents the decay rate of the field and

ρ_{ϕ}

denotes its energy density and a bulk viscosity described by

ξ = ξ_{0} ρ_{ϕ}^{1 / 2}

, within the framework of Eckart’s theory. This extended non-standard cosmology is employed to explore the parameter space for the production of Feebly Interacting Massive Particles (FIMPs) as Dark Matter candidates, assuming a constant thermal averaged Dark Matter production cross-section (

⟨ σ v ⟩

), as well as a preliminary analysis of the non-constant case. In particular, for certain combinations of the model and Dark Matter parameters, namely (

T_{end}

,

κ

) and

(m_{χ}, ⟨ σ v ⟩)

, where

T_{end}

corresponds to the temperature at which

ϕ

decays,

κ

is the ratio between the initial energy density of

ϕ

and radiation, and

m_{χ}

is the Dark Matter mass, we identify extensive new parameter regions where Dark Matter can be successfully established while reproducing the currently observed relic density, in contrast to the predictions of

Λ

CDM and classical non-standard cosmological scenarios. Full article

(This article belongs to the Special Issue Matter and Antimatter Asymmetry in Cosmology and Particle Physics)

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35 pages, 7169 KB

Open AccessEditor’s ChoiceArticle

Symmetries in High-Temperature Lattice QCD with (u, d, s, c, b) Optimal Domain-Wall Quarks

by Ting-Wai Chiu

Symmetry 2025, 17(5), 700; https://doi.org/10.3390/sym17050700 - 3 May 2025

Cited by 1 | Viewed by 654

Abstract

We investigate the spatial z-correlators of meson operators in

N_{f} = 2 + 1 + 1 + 1

lattice QCD with optimal domain-wall quarks across eight temperatures ranging from 325 to 3250 MeV. The meson operators include a complete set of [...] Read more.

We investigate the spatial z-correlators of meson operators in

N_{f} = 2 + 1 + 1 + 1

lattice QCD with optimal domain-wall quarks across eight temperatures ranging from 325 to 3250 MeV. The meson operators include a complete set of Dirac bilinears for ten flavor combinations. Our findings reveal a hierarchical restoration of chiral symmetry in QCD with

(u, d, s, c, b)

quarks, progressing sequentially from

S U {(2)}_{L} \times S U {(2)}_{R} \times U {(1)}_{A}

to

S U {(3)}_{L} \times S U {(3)}_{R} \times U {(1)}_{A}

, then to

S U {(4)}_{L} \times S U {(4)}_{R} \times U {(1)}_{A}

, and finally to

S U {(5)}_{L} \times S U {(5)}_{R} \times U {(1)}_{A}

as the temperature increases. Additionally, we explore the emergence of the

S U {(2)}_{C S}

chiral-spin symmetry and compare the temperature windows for all flavor combinations. Our results indicate that the temperature windows for the emergent

S U {(2)}_{C S}

symmetry are primarily dominated by the

\bar{u} b

and

\bar{s} b

sectors. Full article

(This article belongs to the Section Physics)

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46 pages, 1618 KB

Open AccessEditor’s ChoiceReview

Electroweak Form Factors of Baryons in Dense Nuclear Matter

by G. Ramalho, K. Tsushima and Myung-Ki Cheoun

Symmetry 2025, 17(5), 681; https://doi.org/10.3390/sym17050681 - 29 Apr 2025

Cited by 2 | Viewed by 1159

Abstract

There is evidence that the properties of hadrons are modified in a nuclear medium. Information about the medium modifications of the internal structure of hadrons is fundamental for the study of dense nuclear matter and high-energy processes, including heavy-ion and nucleus–nucleus collisions. At [...] Read more.

There is evidence that the properties of hadrons are modified in a nuclear medium. Information about the medium modifications of the internal structure of hadrons is fundamental for the study of dense nuclear matter and high-energy processes, including heavy-ion and nucleus–nucleus collisions. At the moment, however, empirical information about medium modifications of hadrons is limited; therefore, theoretical studies are essential for progress in the field. In the present work, we review theoretical studies of the electromagnetic and axial form factors of octet baryons in symmetric nuclear matter. The calculations are based on a model that takes into account the degrees of freedom revealed in experimental studies of low and intermediate square transfer momentum

q^{2} = - Q^{2}

: valence quarks and meson cloud excitations of baryon cores. The formalism combines a covariant constituent quark model, developed for a free space (vacuum) with the quark–meson coupling model for extension to the nuclear medium. We conclude that the nuclear medium modifies the baryon properties differently according to the flavor content of the baryons and the medium density. The effects of the medium increase with density and are stronger (quenched or enhanced) for light baryons than for heavy baryons. In particular, the in-medium neutrino–nucleon and antineutrino–nucleon cross-sections are reduced compared to the values in free space. The proposed formalism can be extended to densities above the normal nuclear density and applied to neutrino–hyperon and antineutrino–hyperon scattering in dense nuclear matter. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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20 pages, 3728 KB

Open AccessEditor’s ChoiceArticle

Adaptive Switching Control of Voltage Source Converters in Renewable Energy Station Based on Operating Short Circuit Ratio

by Zhan Zhang, Huangqing Xiao, Wenze Liu and Ying Huang

Symmetry 2025, 17(5), 629; https://doi.org/10.3390/sym17050629 - 22 Apr 2025

Cited by 3 | Viewed by 1500

Abstract

By integrating the grid-following control and grid-forming control, the adaptability of grid-connected converters to the grid impedance fluctuation can be effectively improved, and a stable operation in a wide short circuit ratio range can be realized. The existing fusion control schemes focus on [...] Read more.

By integrating the grid-following control and grid-forming control, the adaptability of grid-connected converters to the grid impedance fluctuation can be effectively improved, and a stable operation in a wide short circuit ratio range can be realized. The existing fusion control schemes focus on the influence of the short circuit ratio on the stability of the converter, ignoring the influence of the active power fluctuation of the renewable energy in the design of the fusion scheme. In order to improve this shortcoming, an adaptive switching control of voltage source converters in the renewable energy station is proposed in this paper. Based on the oscillation characteristics of the grid-following converter and the grid-forming converter, this method selects the operating short circuit ratio as the switching index of the grid-following mode and the grid-forming mode. Compared with the current switching schemes based on the short circuit ratio, the operating short circuit ratio replaces the rated capacity of the station with the active output of the station, so it can more reasonably reflect changes in stability caused by active power fluctuations and then give the appropriate switching command, which means that unnecessary switching can be reduced and the control mode can be correctly converted to enhance stability when the system state changes. Full article

(This article belongs to the Section Engineering and Materials)

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81 pages, 2075 KB

Open AccessEditor’s ChoiceReview

A Comprehensive Review on Solving the System of Equations AX = C and XB = D

by Qing-Wen Wang, Zi-Han Gao and Jia-Le Gao

Symmetry 2025, 17(4), 625; https://doi.org/10.3390/sym17040625 - 21 Apr 2025

Cited by 10 | Viewed by 1463

Abstract

This survey provides a review of the theoretical research on the classic system of matrix equations

A X = C

and

X B = D

, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper [...] Read more.

This survey provides a review of the theoretical research on the classic system of matrix equations

A X = C

and

X B = D

, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper discusses various solution methods for the system, focusing on specialized approaches, including generalized inverse methods, matrix decomposition techniques, and solutions in the forms of Hermitian, extreme rank, reflexive, and conjugate solutions. Additionally, specialized solving methods for specific algebraic structures, such as Hilbert spaces, Hilbert

C^{*}

-modules, and quaternions, are presented. The paper explores the existence conditions and explicit expressions for these solutions, along with examples of their application in color images. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

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24 pages, 2062 KB

Open AccessEditor’s ChoiceArticle

Hybrid Optimization of Phase Masks: Integrating Non-Iterative Methods with Simulated Annealing and Validation via Tomographic Measurements

by Zhiwen Li, Chao Sun, Haihua Wang and Rui-Feng Wang

Symmetry 2025, 17(4), 530; https://doi.org/10.3390/sym17040530 - 31 Mar 2025

Cited by 8 | Viewed by 2096

Abstract

The development of holography has facilitated significant advancements across a wide range of disciplines. A phase-only spatial light modulator (SLM) plays a crucial role in realizing digital holography, typically requiring a phase mask as its input. Non-iterative (NI) algorithms are widely used for [...] Read more.

The development of holography has facilitated significant advancements across a wide range of disciplines. A phase-only spatial light modulator (SLM) plays a crucial role in realizing digital holography, typically requiring a phase mask as its input. Non-iterative (NI) algorithms are widely used for phase mask generation, yet they often fall short in delivering precise solutions and lack adaptability in complex scenarios. In contrast, the Simulated Annealing (SA) algorithm provides a global optimization approach capable of addressing these limitations. This study investigates the integration of NI algorithms with the SA algorithm to enhance the optimization of phase mask generation in digital holography. Furthermore, we examine how adjusting annealing parameters, especially the cooling strategy, can significantly improve system optimization performance and symmetry. Notably, we observe a considerable improvement in the efficiency of the SA algorithm when non-iterative methods are employed to generate the initial phase mask. Our method achieves a perfect representation of the symmetry in desired light fields. The efficacy of the optimized phase masks is evaluated through optical tomographic measurements using two-dimensional mutually unbiased bases (MUBs), with the resulting average similarity reaching 0.99. These findings validate the effectiveness of our methodin optimizing phase mask generation and underscore its potential for high-precision optical mode recognition and analysis. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

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25 pages, 717 KB

Open AccessEditor’s ChoiceReview

Baryon Construction with η^′ Meson Field

by Fan Lin and Yong-Liang Ma

Symmetry 2025, 17(4), 477; https://doi.org/10.3390/sym17040477 - 21 Mar 2025

Cited by 1 | Viewed by 1338

Abstract

In the low-energy regime, baryons with

N_{f} \geq 2

have long been constructed as skyrmions or through bag models, but such constructions for

N_{f} = 1

are hindered by the trivial topological structure of the meson field. Recent proposals suggest that [...] Read more.

In the low-energy regime, baryons with

N_{f} \geq 2

have long been constructed as skyrmions or through bag models, but such constructions for

N_{f} = 1

are hindered by the trivial topological structure of the meson field. Recent proposals suggest that one-flavor baryons can instead be interpreted as quantum Hall droplets on the

η^{'}

domain wall, providing a potential link to quark–hadron continuity at high density. In retrospect, the qualitative or semi-qualitative construction of one-flavor baryons on the

η^{'}

domain wall reveals that these baryons can be described as quantum Hall droplets, resembling topological solitons akin to skyrmions. Using an effective theory on the

η^{'}

domain wall, which is conjectured to be the Chern–Simons–Higgs theory, it is discussed that its vortex solution with unit baryon numbers naturally has a spin of

N_{c} / 2

, and thus can be interpreted as a baryon or multi-baryon structure. The particle–vortex duality suggests that quarks carry a fractional topological charge of

1 / N_{c}

and obey fractional statistics. In terms of chiral bag models, confinement can be attributed to the monopoles confined within the bag, and the vector meson fields on the bag surface are essential for ensuring the correct baryon number in the chiral bag framework, thereby providing deeper insights into baryons as non-trivial topological structures of the meson field. In this paper, we review the progress in this development, with a special focus on the

η^{'}

domain wall dynamics. Naive extensions to

N_{f} \geq 2

are also discussed. Full article

(This article belongs to the Section Physics)

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19 pages, 3861 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Mechanical Properties of 3D-Printed PLA Structures Observed in Framework of Different Rotational Symmetry Orders in Infill Patterns

by Sanja Mahović Poljaček, Davor Donevski, Tamara Tomašegović, Urška Vrabič Brodnjak and Mirjam Leskovšek

Symmetry 2025, 17(3), 466; https://doi.org/10.3390/sym17030466 - 20 Mar 2025

Cited by 3 | Viewed by 3182

Abstract

In this research, eco-friendly PLA filaments were 3D-printed using FDM. Three geometric shapes with different orders of rotational symmetry were selected to create infill patterns: an equilateral triangle, a square, and a regular hexagon. Additionally, each of these three infill patterns was modified [...] Read more.

In this research, eco-friendly PLA filaments were 3D-printed using FDM. Three geometric shapes with different orders of rotational symmetry were selected to create infill patterns: an equilateral triangle, a square, and a regular hexagon. Additionally, each of these three infill patterns was modified by rotating the basic shape used to form the infill pattern by 0°, 15°, and 30°. The objective of this study was to analyze how the order of rotational symmetry within the infill pattern affects the mechanical properties of the printed specimens. To ensure consistency, infill density was kept as uniform as possible across all samples produced. DMA and tensile tests were performed on the produced specimens. The obtained mean values in the tensile measurements were compared using the Kruskal–Wallis test. Dunn’s test was used for post hoc pairwise multiple comparisons. DMA showed that when comparing different infill patterns, the specimens with an order of rotational symmetry of 3 (triangle) showed the highest modulus of elasticity, and the specimens with a 15° rotation regardless of shape generally had the highest storage modulus. Statistical analysis showed that the maximum force of the infill pattern with an order of rotational symmetry of 3 (triangle) was the least affected by the rotation angle, while the infill pattern with an order of rotational symmetry of 4 (square) and a 0° rotation displayed a significantly higher value of the maximum force than other patterns. The infill pattern with an order of rotational symmetry of 6 (hexagon) was moderately affected by the angle of rotation. Given the numerous infill patterns utilized in FDM, the results of this research offered a new viewpoint and insights into optimizing the mechanical properties of 3D-printed infill patterns. Full article

(This article belongs to the Section Engineering and Materials)

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29 pages, 1184 KB

Open AccessEditor’s ChoiceReview

AI-Driven Technology in Heart Failure Detection and Diagnosis: A Review of the Advancement in Personalized Healthcare

by Ikteder Akhand Udoy and Omiya Hassan

Symmetry 2025, 17(3), 469; https://doi.org/10.3390/sym17030469 - 20 Mar 2025

Cited by 12 | Viewed by 7830

Abstract

Artificial intelligence (AI) is playing a dominant role in advancing heart failure detection and diagnosis, significantly furthering personalized healthcare. This review synthesizes AI-driven innovations by examining methodologies, applications, and outcomes. We investigate the integration of machine learning algorithms, diverse datasets including electronic health [...] Read more.

Artificial intelligence (AI) is playing a dominant role in advancing heart failure detection and diagnosis, significantly furthering personalized healthcare. This review synthesizes AI-driven innovations by examining methodologies, applications, and outcomes. We investigate the integration of machine learning algorithms, diverse datasets including electronic health records (EHRs), medical records, imaging data, and clinical notes, deep learning models, and neural networks to enhance diagnostic accuracy. Key advancements include prediction models that leverage real-time data from wearable devices alongside state-of-the-art AI systems trained on patient data from hospitals and clinics. Notably, recent studies have reported diagnostic accuracies ranging from 86.7% to as high as 99.9%, with sensitivity and specificity values often exceeding 97%, underscoring the potential of these AI systems to improve early detection and clinical decision-making substantially. Our review further explores the impact of symmetry and asymmetry in model design, highlighting that symmetric architectures like U-Net offer computational efficiency and structured feature extraction. In contrast, asymmetric models improve the sensitivity to rare conditions and subtle clinical patterns. Incorporating these deep learning (DL) methods in anomaly detection and disease progression modeling further reinforces their positive impact on diagnostic accuracy and patient outcomes. Furthermore, this review identifies challenges in current AI applications, such as data quality, algorithmic transparency, model bias, and evaluation metrics, while outlining future research directions, including integrating generative models, hybrid architectures, and explainable AI techniques to optimize clinical practice. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric in Deep Computer Vision and Generative Modeling)

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17 pages, 295 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras

by Simone Fiori

Symmetry 2025, 17(3), 463; https://doi.org/10.3390/sym17030463 - 19 Mar 2025

Cited by 2 | Viewed by 1009

Abstract

The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equations in physics, and it was shown that discrete-time systems on finite- [...] Read more.

The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equations in physics, and it was shown that discrete-time systems on finite- (albeit high-) dimensional structured state spaces possess solid applications to structured signal processing and nonlinear system identification, modeling and control. With reference to the state-space representation of dynamical systems, the present contribution tackles the core system-theoretic problem of determining suitable laws to express a system’s state transition. In particular, the present contribution aims at formulating a fairly general class of state-transition laws over the Lie algebra associated to a Lie group and at extending some properties of classical dynamical systems to process Lie-algebra-valued state signals. Full article

(This article belongs to the Special Issue Symmetry and Lie Algebras)

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20 pages, 6074 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Investigation of Turbulence Characteristics Influenced by Flow Velocity, Roughness, and Eccentricity in Horizontal Annuli Based on Numerical Simulation

by Yanchao Sun, Jialiang Sun, Jie Zhang and Ning Huang

Symmetry 2025, 17(3), 409; https://doi.org/10.3390/sym17030409 - 9 Mar 2025

Cited by 2 | Viewed by 1857

Abstract

Annular flow channels, which are distinct from circular pipes, represent a complex flow structure widely applied in fields such as food engineering and petroleum engineering. Discovering the internal flow patterns is conducive to the study of heat and mass transfer laws, thereby playing [...] Read more.

Annular flow channels, which are distinct from circular pipes, represent a complex flow structure widely applied in fields such as food engineering and petroleum engineering. Discovering the internal flow patterns is conducive to the study of heat and mass transfer laws, thereby playing a crucial role in optimizing flow processes and selecting equipment. However, the mechanism underlying the influence of annular turbulent flow on macro-pressure drop remains to be further investigated. This paper focuses on the roughness of both inner and outer pipes, as well as positive and negative eccentricities. Numerical simulation is employed to study the microscopic characteristics of the flow field, and the numerical model is validated through indoor experimental measurements of pressure drop laws. Further numerical simulations are conducted to explore the microscopic variations in the flow field, analyzed from the perspectives of wall shear force and turbulence characteristics. The results indicate that an increase in inner pipe roughness significantly enhances the wall shear force on both the inner and outer pipes, and vice versa. In the concentric case, wall shear force and turbulence characteristics exhibit central symmetry. Eccentricity leads to uneven distributions of velocity, turbulence intensity, and shear force, with such unevenness presenting axial symmetry under both positive and negative eccentricities. Additionally, eccentricity demonstrates turbulence drag reduction characteristics. This study enhances our understanding of the mechanism by which annular turbulent flow influences pressure drop. Furthermore, it offers theoretical backing for the design and optimization of annular space piping, thereby aiding in the enhancement of the performance and stability of associated industrial systems. Full article

(This article belongs to the Section Physics)

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14 pages, 10252 KB

Open AccessFeature PaperEditor’s ChoiceArticle

A New Log-Transform Histogram Equalization Technique for Deep Learning-Based Document Forgery Detection

by Yong-Yeol Bae, Dae-Jea Cho and Ki-Hyun Jung

Symmetry 2025, 17(3), 395; https://doi.org/10.3390/sym17030395 - 5 Mar 2025

Cited by 5 | Viewed by 2417

Abstract

Recent advancements in image processing technology have positively impacted some fields, such as image, document, and video production. However, the negative implications of these advancements have also increased, with document image manipulation being a prominent issue. Document image manipulation involves the forgery or [...] Read more.

Recent advancements in image processing technology have positively impacted some fields, such as image, document, and video production. However, the negative implications of these advancements have also increased, with document image manipulation being a prominent issue. Document image manipulation involves the forgery or alteration of documents like receipts, invoices, various certificates, and confirmations. The use of such manipulated documents can cause significant economic and social disruption. To prevent these issues, various methods for the detection of forged document images are being researched, with recent proposals focused on deep learning techniques. An essential aspect of using deep learning to detect manipulated documents is to enhance or augment the characteristics of document images before inputting them into a model. Enhancing the distinctive features of manipulated documents before inputting them into a deep learning model is crucial to achieve high accuracy. One crucial characteristic of document images is their inherent symmetrical patterns, such as consistent text alignment, structural balance, and uniform pixel distribution. This study investigates document forgery detection through a symmetry-aware approach. By focusing on the symmetric structures found in document layouts and pixel distribution, the proposed LTHE technique enhances feature extraction in deep learning-based models. Therefore, this study proposes a new image enhancement technique based on the results of three general-purpose CNN models to enhance the characteristics of document images and achieve high accuracy in deep learning-based forgery detection. The proposed LTHE (Log-Transform Histogram Equalization) technique increases low pixel values through log transformation and increases image contrast by performing histogram equalization to make the features of the image more prominent. Experimental results show that the proposed LTHE technique achieves higher accuracy when compared to other enhancement methods, indicating its potential to aid the development of deep learning-based forgery detection algorithms in the future. Full article

(This article belongs to the Special Issue Symmetry in Image Processing: Novel Topics and Advancements)

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17 pages, 5774 KB

Open AccessEditor’s ChoiceArticle

Structural Design and Vibro-Mechanical Characterization Analysis of Variable Cross-Sectional Metal Rubber Isolator

by Jianchao Liu, Xinzhe Liu, Hanbin Wang, Zixiong Ye and Xin Xue

Symmetry 2025, 17(3), 382; https://doi.org/10.3390/sym17030382 - 3 Mar 2025

Cited by 3 | Viewed by 1659

Abstract

Satellites experience complex vibrational environments during their launch and operation, potentially leading to structural failures and equipment damage. This work aimed to mitigate this issue by designing a variable cross-sectional metal rubber isolator (VCMRI), which was fully constructed from metal and featured a [...] Read more.

Satellites experience complex vibrational environments during their launch and operation, potentially leading to structural failures and equipment damage. This work aimed to mitigate this issue by designing a variable cross-sectional metal rubber isolator (VCMRI), which was fully constructed from metal and featured a symmetric structure. Initially, a finite element model of the VCMRI was developed, incorporating symmetric boundary conditions and employing the Bergström–Boyce model to define variable cross-sectional metal rubber (VCMR) parameters. Subsequently, sinusoidal sweep tests were performed to investigate how variations in VCMR density, spring stiffness, and exc itation deflection angle affect the peak acceleration response and natural frequency of the VCMRI. Finally, simulation analyses were conducted and insertion loss was derived from the results to assess the vibration isolation performance of the VCMRI. The results indicate that the finite element model accurately captures the dynamic behavior of the VCMRI with minimal error. In addition, the VCMRI demonstrates robust vibration isolation performance by effectively integrating the influences of VCMR density, spring stiffness, and excitation angle, achieving insertion losses of up to 19.2 dB across a wide frequency range. It provides robust theoretical support for the design and performance optimization of isolation systems, with potential positive impacts on relevant engineering applications. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Mechanics of Materials)

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19 pages, 12391 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Investigation into Enhancing Ultrasonic Cleaning Efficiency Through Symmetrical Transducer Configuration

by Lei Wei, Sheng Liu and Fang Dong

Symmetry 2025, 17(3), 348; https://doi.org/10.3390/sym17030348 - 25 Feb 2025

Cited by 1 | Viewed by 3892

Abstract

This paper investigates the symmetrical layout effect in ultrasonic cleaning via acoustic solid coupling simulation, with emphasis on how the symmetrical arrangement of transducers influences sound pressure distribution. Two specific transducer layout methods are examined: uniform arrangement at the bottom and symmetrical arrangement [...] Read more.

This paper investigates the symmetrical layout effect in ultrasonic cleaning via acoustic solid coupling simulation, with emphasis on how the symmetrical arrangement of transducers influences sound pressure distribution. Two specific transducer layout methods are examined: uniform arrangement at the bottom and symmetrical arrangement along the sides. The findings indicate that when the tank length is an integer multiple of one-quarter of the acoustic wavelength, the symmetrical side arrangement markedly enhances the sound pressure level within the tank and optimizes the propagation and reflection of acoustic waves. In megasonic cleaning, focusing is achieved through a 7 × 7 transducer array by precisely controlling the phase, and the symmetrical arrangement ensures uniform sound pressure distribution. By integrating 1 MHz megasonic sources from both focused and unfocused configurations, the overall sound pressure distribution and peak sound pressure at the focal point are calculated using multi-physics field coupling simulations. A comparative analysis of the sound fields generated by focused and unfocused sources reveals that the focused source can produce significantly higher sound pressure in specific regions. Leveraging the enhanced cleaning capability of the focused acoustic wave in targeted areas while maintaining broad coverage with the unfocused acoustic wave significantly improves the overall cleaning efficiency. Ultrasonic cleaning finds extensive applications in industries such as electronic component manufacturing, medical device sterilization, and automotive parts cleaning. Its efficiency and environmental friendliness make it highly significant for both daily life and industrial production. Full article

(This article belongs to the Section Engineering and Materials)

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37 pages, 3786 KB

Open AccessEditor’s ChoiceReview

Circumstellar and Circumbinary Discs in Multiple Stellar Systems

by Nicolás Cuello, Antoine Alaguero and Pedro P. Poblete

Symmetry 2025, 17(3), 344; https://doi.org/10.3390/sym17030344 - 25 Feb 2025

Cited by 7 | Viewed by 2907

Abstract

The interplay between stellar multiplicity and protoplanetary discs represents a cornerstone of modern astrophysics, offering key insights into the processes behind planet formation. Protoplanetary discs act as cradles for planetary systems, yet their evolution and capacity to form planets are profoundly affected by [...] Read more.

The interplay between stellar multiplicity and protoplanetary discs represents a cornerstone of modern astrophysics, offering key insights into the processes behind planet formation. Protoplanetary discs act as cradles for planetary systems, yet their evolution and capacity to form planets are profoundly affected by gravitational forces within multiple stellar systems. This review synthesizes recent advancements in observational and theoretical studies to explore the rich diversity of circumstellar and circumbinary discs within multiple stellar systems. We examine how stellar companions shape disc morphology through truncation, spirals, and misalignment. We also outline how dust dynamics and planetesimal formation are impacted by stellar multiplicity. On top of this, observations at a high angular resolution reveal detailed disc structures, while simulations offer key insights into their evolution. Lastly, we consider the implications of stellar multiplicity for planetary system architectures, emphasizing the diversity of planetary outcomes in such environments. Looking ahead, coordinated efforts combining high-resolution observations with advanced numerical models will be critical for unraveling the role of multiple stellar systems in shaping planetary formation and evolution. Full article

(This article belongs to the Section Physics)

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19 pages, 292 KB

Open AccessEditor’s ChoiceArticle

A Novel Method to Calculate Nonlocal Symmetries from Local Symmetries

by Andronikos Paliathanasis

Symmetry 2025, 17(3), 340; https://doi.org/10.3390/sym17030340 - 24 Feb 2025

Cited by 1 | Viewed by 645

Abstract

We explore nonlocal symmetries in a class of Hamiltonian dynamical systems governed by second-order differential equations. Specifically, we establish an algorithm for deriving nonlocal symmetries by utilizing the Jacobi metric and the Eisenhart–Duval lift to geometrize the dynamical systems. The geometrized systems often [...] Read more.

We explore nonlocal symmetries in a class of Hamiltonian dynamical systems governed by second-order differential equations. Specifically, we establish an algorithm for deriving nonlocal symmetries by utilizing the Jacobi metric and the Eisenhart–Duval lift to geometrize the dynamical systems. The geometrized systems often exhibit additional local symmetries compared to the original systems, some of which correspond to nonlocal symmetries for the original formulation. This novel approach allows us to determine nonlocal symmetries in a systematic way. Within this geometric framework, we demonstrate that the second-order differential equation

\ddot{q} - F (q) = 0

admits an infinite number of nonlocal symmetries generated by the infinite-dimensional conformal algebra of a two-dimensional Riemannian manifold. Applications to higher-dimensional systems are also discussed. Full article

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

63 pages, 23959 KB

Open AccessEditor’s ChoiceReview

A Century of Azulene Chemistry; A Brief Look at Azulenes Building

by Alexandru C. Razus

Symmetry 2025, 17(3), 335; https://doi.org/10.3390/sym17030335 - 22 Feb 2025

Cited by 3 | Viewed by 6389

Abstract

The target of this review is to familiarize researchers from the field, especially for those who want to find out information about the synthesis pathways of azulenes. The properties of the azulene system are very different from those of its isomer, naphthalene. This [...] Read more.

The target of this review is to familiarize researchers from the field, especially for those who want to find out information about the synthesis pathways of azulenes. The properties of the azulene system are very different from those of its isomer, naphthalene. This difference is a consequence of the monoaxial symmetry of azulene geometry and its non-alternating aromatic structure as opposed to the biaxial symmetry and benzenoid structure of naphthalene. The processing of the information from the literature on azulene synthesis is based on the raw materials from which the procedures start. In many cases, instead of the description of reaction pathways, presentation in the form of schemes was preferred, in which the steps and reaction conditions chosen for them, as well as the yields obtained, were highlighted. Full article

(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)

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19 pages, 1331 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Hybrid Neural Network-Based Intrusion Detection System: Leveraging LightGBM and MobileNetV2 for IoT Security

by Yi-Min Yang, Ko-Chin Chang and Jia-Ning Luo

Symmetry 2025, 17(3), 314; https://doi.org/10.3390/sym17030314 - 20 Feb 2025

Cited by 15 | Viewed by 4967

Abstract

The rapid expansion of the Internet of Things (IoT) has uncovered a significant asymmetry in cybersecurity, where low-power edge devices must face sophisticated threats from adversaries backed by ample resources. In our study, we employ a symmetry-based approach to rebalance these uneven scenarios. [...] Read more.

The rapid expansion of the Internet of Things (IoT) has uncovered a significant asymmetry in cybersecurity, where low-power edge devices must face sophisticated threats from adversaries backed by ample resources. In our study, we employ a symmetry-based approach to rebalance these uneven scenarios. We propose a Hybrid Neural Network Intrusion Detection System (Hybrid NNIDS) that uses LightGBM to filter anomalies at the traffic level and MobileNetV2 for further detection at the packet level, creating a viable compromise between detection accuracy and computational cost. Additionally, the proposed Hybrid NNIDS model, on the ACI-IoT-2023 dataset, outperformed other intrusion detection models with an accuracy of 94%, an F1-score of 91%, and a precision rate of 93% in attack detection. The results indicate the developed asymmetry algorithm can greatly reduce processing overhead while still being able to be implemented in IoT environments. The focus of future work will be on the real-world deployment of these security infrastructures in the IoT and their adaptation to newer types of attack vectors that may be developed by malware. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Cyber Security, IoTs and Privacy)

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29 pages, 3567 KB

Open AccessEditor’s ChoiceArticle

Kinematic Fuzzy Logic-Based Controller for Trajectory Tracking of Wheeled Mobile Robots in Virtual Environments

by José G. Pérez-Juárez, José R. García-Martínez, Alejandro Medina Santiago, Edson E. Cruz-Miguel, Luis F. Olmedo-García, Omar A. Barra-Vázquez and Miguel A. Rojas-Hernández

Symmetry 2025, 17(2), 301; https://doi.org/10.3390/sym17020301 - 17 Feb 2025

Cited by 12 | Viewed by 2660

Abstract

Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller [...] Read more.

Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller with a symmetric distribution of fuzzy numbers is proposed and designed for implementation in the kinematic model of a non-holonomic mobile robot. The symmetry in the distribution of triangular fuzzy numbers contributes to a balanced response to disturbances and minimizes systematic errors in direction estimation. Additionally, it improves the system’s adaptability to various reference paths, ensuring accurate tracking and optimized performance in robot navigation. Furthermore, this fuzzy logic-based controller emulates the behavior of a classic PID controller by offering a robust and flexible alternative to traditional methods. A virtual environment was also developed using the UNITY platform to evaluate the performance of the fuzzy controller. The results were evaluated by considering the average tracking error, maximum error, steady-state error, settling time, and total distance traveled, emphasizing the trajectory error. The circular trajectory showed high accuracy with an average error of 0.0089 m, while the cross trajectory presented 0.01814 m, reflecting slight deviations in the turns. The point-to-point trajectory registered a more significant error of 0.9531 m due to abrupt transitions, although with effective corrections in a steady state. The simulation results validate the robustness of the proposed fuzzy controller, providing quantitative insights into its precision and efficiency in a virtual environment, and demonstrating the effectiveness of the proposal. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)

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66 pages, 24939 KB

Open AccessEditor’s ChoiceReview

Dynamic Point-to-Helical and Point-to-Axial Chirality Transmission and Induction of Optical Activity in Multichromophoric Systems: Basic Principles and Relevant Applications in Chirality Sensing

by Tomasz Mądry, Jadwiga Gajewy and Marcin Kwit

Symmetry 2025, 17(2), 293; https://doi.org/10.3390/sym17020293 - 14 Feb 2025

Cited by 2 | Viewed by 4812

Abstract

The analysis of natural and artificial chiral compounds is vital wherever the nuances in the three-dimensional structure are decisive for the possibility of their further use, e.g., as pharmaceuticals or catalysts. The qualitative determination of the structure of a chiral entity requires either [...] Read more.

The analysis of natural and artificial chiral compounds is vital wherever the nuances in the three-dimensional structure are decisive for the possibility of their further use, e.g., as pharmaceuticals or catalysts. The qualitative determination of the structure of a chiral entity requires either an anomalous scattering of X-ray radiation or chiroptical techniques, of which electronic circular dichroism (ECD) is one of the most useful. Chiroptical sensing that uses stereodynamic probes remains one of the remedies for the problem of the lack of a suitable chromophore in the molecules of the chiral compound. A covalent or non-covalent binding of an ECD-silent chiral molecule (the inducer) to the UV-active chromophoric system (chiroptical probe) led to obtaining complex ECD active at a given spectral region. The transfer of structural information from a permanently chiral inducer molecule to the structurally labile chromophoric system of the probe results in adjusting the latter’s structure to the chiral environment. This contribution focuses on some fundamental aspects of chirality sensing using conformationally labile probes. It discusses the mechanism of action of arbitrarily chosen stereodynamic chirality sensors, with particular emphasis on probes based on di- and triarylmethyl derivatives and biphenyl and its congeners. Full article

(This article belongs to the Collection Feature Papers in Chemistry)

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25 pages, 3165 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Estimation and Bayesian Prediction for the Generalized Exponential Distribution Under Type-II Censoring

by Wei Wang and Wenhao Gui

Symmetry 2025, 17(2), 222; https://doi.org/10.3390/sym17020222 - 2 Feb 2025

Cited by 3 | Viewed by 1976

Abstract

This research focuses on the prediction and estimation problems for the generalized exponential distribution under Type-II censoring. Firstly, maximum likelihood estimations for the parameters of the generalized exponential distribution are computed using the EM algorithm. Additionally, confidence intervals derived from the Fisher information [...] Read more.

This research focuses on the prediction and estimation problems for the generalized exponential distribution under Type-II censoring. Firstly, maximum likelihood estimations for the parameters of the generalized exponential distribution are computed using the EM algorithm. Additionally, confidence intervals derived from the Fisher information matrix are developed and analyzed alongside two bootstrap confidence intervals for comparison. Compared to classical maximum likelihood estimation, Bayesian inference proves to be highly effective in handling censored data. This study explores Bayesian inference for estimating the unknown parameters, considering both symmetrical and asymmetrical loss functions. Utilizing Gibbs sampling to produce Markov Chain Monte Carlo samples, we employ an importance sampling approach to obtain Bayesian estimates and compute the corresponding highest posterior density (HPD) intervals. Furthermore, for one-sample prediction and, separately, for the two-sample case, we provide the corresponding posterior distributions, along with methods for computing point predictions and predictive intervals. Through Monte Carlo simulations, we evaluate the performance of Bayesian estimation in contrast to maximum likelihood estimation. Finally, we conduct an analysis of a real dataset derived from deep groove ball bearings, calculating Bayesian point predictions and predictive intervals for future samples. Full article

(This article belongs to the Special Issue Bayesian Statistical Methods for Forecasting)

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21 pages, 5110 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Leveraging Quantum Machine Learning to Address Class Imbalance: A Novel Approach for Enhanced Predictive Accuracy

by Seongjun Kwon, Jihye Huh, Sang Ji Kwon, Sang-ho Choi and Ohbyung Kwon

Symmetry 2025, 17(2), 186; https://doi.org/10.3390/sym17020186 - 25 Jan 2025

Cited by 9 | Viewed by 3631

Abstract

The class imbalance problem presents a critical challenge in real-world applications, particularly in high-stakes domains such as healthcare, finance, disaster management, and fault diagnosis, where accurate anomaly detection is paramount. Class imbalance often disrupts the inherent symmetry of data distributions, resulting in suboptimal [...] Read more.

The class imbalance problem presents a critical challenge in real-world applications, particularly in high-stakes domains such as healthcare, finance, disaster management, and fault diagnosis, where accurate anomaly detection is paramount. Class imbalance often disrupts the inherent symmetry of data distributions, resulting in suboptimal performance of traditional machine learning models. Conventional approaches such as undersampling and oversampling are commonly employed to address this issue; however, these methods can introduce additional asymmetries, including information loss and overfitting, which ultimately compromise model efficacy. This study introduces an innovative approach leveraging quantum machine learning (QML), specifically the Variational Quantum Classifier (VQC), to restore and capitalize on the symmetrical properties of data distributions without relying on resampling techniques. By employing quantum circuits optimized to mitigate the asymmetries inherent in imbalanced datasets, the proposed method demonstrates consistently superior performance across diverse datasets, with notable improvements in Recall for minority classes. These findings underscore the potential of quantum machine learning as a robust alternative to classical methods, offering a symmetry-aware solution to class imbalance and advancing QML-driven technologies in fields where equitable representation and symmetry are of critical importance. Full article

(This article belongs to the Section Computer)

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20 pages, 840 KB

Open AccessEditor’s ChoiceReview

Continuum Effect on Mirror Symmetry Breaking Within the Gamow Frameworks

by Shuang Zhang, Zhicheng Xu and Simin Wang

Symmetry 2025, 17(2), 169; https://doi.org/10.3390/sym17020169 - 23 Jan 2025

Cited by 1 | Viewed by 1308

Abstract

Nuclear physics provides a natural laboratory for studying two kinds of fermions: protons and neutrons. These particles share similarities in mass and strong nuclear interactions, which are often described by isospin symmetry. However, isospin is not a good quantum number due to the [...] Read more.

Nuclear physics provides a natural laboratory for studying two kinds of fermions: protons and neutrons. These particles share similarities in mass and strong nuclear interactions, which are often described by isospin symmetry. However, isospin is not a good quantum number due to the differences between protons and neutrons in charge and quark mass. These differences become more pronounced as we approach or move beyond the dripline, affecting the structures and decay properties of mirror nuclei. To explore these intriguing phenomena, researchers have developed novel theoretical frameworks. In this article, we review the results from the Gamow shell model and Gamow coupled-channel, which account for the mirror symmetry breaking influenced by nuclear forces and continuum effects. Specifically, we discuss the recently observed mirror asymmetries in nuclei at the boundaries of the nuclide landscape and their theoretical explanations. We examine the breaking of mirror symmetry in the spectra of

N = 8

isotones versus

Z = 8

isotopes, as well as the decay properties of the ²²Al-²²F mirror pair. Such studies enhance our understanding of strong interactions and the behavior of open quantum systems. Full article

(This article belongs to the Special Issue Isospin Symmetry/Asymmetry in Experimental Nuclear Physics)

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18 pages, 7744 KB

Open AccessFeature PaperEditor’s ChoiceArticle

High-Performance Carrier Phase Recovery for Local Local Oscillator Continuous-Variable Quantum Key Distribution

by Jiayu Ma, Chao Zhou, Dengke Qi, Ziyang Chen, Yongmei Sun, Song Yu and Xiangyu Wang

Symmetry 2025, 17(1), 139; https://doi.org/10.3390/sym17010139 - 18 Jan 2025

Cited by 2 | Viewed by 1997

Abstract

Continuous-variable quantum key distribution (CV-QKD) has been increasingly studied, which offers the advantage of compatibility with modern coherent optical communication systems. In contrast to CV-QKD with a transmitting local oscillator, the local local oscillator CV-QKD avoids the security vulnerabilities of a local oscillator [...] Read more.

Continuous-variable quantum key distribution (CV-QKD) has been increasingly studied, which offers the advantage of compatibility with modern coherent optical communication systems. In contrast to CV-QKD with a transmitting local oscillator, the local local oscillator CV-QKD avoids the security vulnerabilities of a local oscillator by generating a local oscillator at the receiver. In practice, the frequency offset of the two lasers introduces extra phase noise, which is generally suppressed by various carrier phase recovery algorithms. However, the accuracy of carrier phase recovery can be influenced by the power of the pilot tone, particularly as the transmission distance increases. To further improve accuracy, we propose a method based on the unscented particle filter algorithm, to increase the accuracy of phase estimation, effectively restore the quantum signal and reduce excess noise. In our work, we demonstrated a local local oscillator CV-QKD experiment with a finite-size block of

1 \times 10^{8}

under a transmission distance of 50 km. Through our method, we achieved a secret key rate of 525 kbps, which represents a 28% improvement. These results confirm that our proposed method not only improves the accuracy of carrier phase recovery, but also provides a new approach for future research on algorithms for long-distance CV-QKD. Furthermore, our study improves the phase compensation performance, enabling the orthogonal components of the quantum signal to exhibit enhanced symmetry in phase space. Full article

(This article belongs to the Section Physics)

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14 pages, 1143 KB

Open AccessEditor’s ChoiceArticle

On the Horizontal Divergence Asymmetry in the Gulf of Mexico

by Tianshu Zhou, Jin-Han Xie and Dhruv Balwada

Symmetry 2025, 17(1), 136; https://doi.org/10.3390/sym17010136 - 17 Jan 2025

Cited by 2 | Viewed by 964

Abstract

Due to the geostrophic balance, horizontal divergence-free is often assumed when analyzing large-scale oceanic flows. However, the geostrophic balance is a leading-order approximation. We investigate the statistical feature of weak horizontal compressibility in the Gulf of Mexico by analyzing drifter data (the Grand [...] Read more.

Due to the geostrophic balance, horizontal divergence-free is often assumed when analyzing large-scale oceanic flows. However, the geostrophic balance is a leading-order approximation. We investigate the statistical feature of weak horizontal compressibility in the Gulf of Mexico by analyzing drifter data (the Grand LAgrangian Deployment (GLAD) experiment and the LAgrangian Submesoscale ExpeRiment (LASER)) based on the asymptotic probability density function of the angle between velocity and acceleration difference vectors in a strain-dominant model. The results reveal a notable divergence at scales between 10 km and 300 km, which is stronger in winter (LASER) than in summer (GLAD). We conjecture that the divergence is induced by wind stress with its curl parallel to the Earth’s rotation. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

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34 pages, 13140 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Characterization of Spatial Cognitive EEG Signals Using Normalized Adjusted Permutation Conditional Mutual Information

by Xianglong Wan, Yue Sun, Zhenzhen Wu and Dong Wen

Symmetry 2025, 17(1), 130; https://doi.org/10.3390/sym17010130 - 17 Jan 2025

Cited by 5 | Viewed by 1651

Abstract

Spatial cognitive ability, a fundamental domain within the human cognitive system, involves the perception, interpretation, and manipulation of spatial environments. This study introduces a new EEG feature extraction algorithm, Normalized Adjusted Permutation Conditional Mutual Information (NAPCMI), to improve the accuracy of spatial cognition [...] Read more.

Spatial cognitive ability, a fundamental domain within the human cognitive system, involves the perception, interpretation, and manipulation of spatial environments. This study introduces a new EEG feature extraction algorithm, Normalized Adjusted Permutation Conditional Mutual Information (NAPCMI), to improve the accuracy of spatial cognition assessments. By capturing the symmetry and temporal dependencies within EEG signals during spatial cognition tasks, NAPCMI enhances the ability to extract relevant features. The study validates NAPCMI using a BCI-VR spatial cognition assessment system, incorporating gesture recognition. Results demonstrate that NAPCMI outperforms traditional methods in feature extraction, highlighting its potential for advancing the understanding and assessment of spatial cognitive abilities. The findings also emphasize the significance of specific EEG frequency bands, such as Delta and Beta1, in spatial cognition tasks, further validating NAPCMI’s effectiveness. Full article

(This article belongs to the Special Issue Advances in Symmetry/Asymmetry and Biomedical Engineering)

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45 pages, 4574 KB

Open AccessEditor’s ChoiceReview

Chiral Effective Model of Cold and Dense Two-Color QCD: The Linear Sigma Model Approach

by Daiki Suenaga

Symmetry 2025, 17(1), 124; https://doi.org/10.3390/sym17010124 - 15 Jan 2025

Cited by 6 | Viewed by 1770

Abstract

This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC₂D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC₂D, both [...] Read more.

This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC₂D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC₂D, both theoretical and numerical studies derive the presence of the so-called baryon superfluid phase at a sufficiently large chemical potential (

μ_{q}

), where diquark condensates govern the ground state. The hadron mass spectrum simulated in this phase shows that the mass of an iso-singlet (

I = 0

) and

0^{-}

state is remarkably reduced, but such a mode cannot be described by the chiral perturbation theory. Motivated by this fact, I have invented a LSM constructed upon the linear representation of chiral symmetry, more precisely Pauli–Gürsey symmetry. It is shown that my LSM successfully reproduces the low-lying hadron mass spectrum in a broad range of

μ_{q}

simulated on the lattice. As applications of the LSM, topological susceptibility and sound velocity in cold and dense QC₂D are evaluated to compare with the lattice results. Additionally, the generalized Gell–Mann–Oakes–Renner relation and hardon mass spectrum in the presence of a diquark source are analyzed. I also introduce an extended version of the LSM incorporating spin-1 hadrons. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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25 pages, 2721 KB

Open AccessEditor’s ChoiceArticle

Spatial Kinetic Modeling of Crowd Evacuation: Coupling Social Behavior and Infectious Disease Contagion

by Juan Pablo Agnelli, Claudio Armas and Damián A. Knopoff

Symmetry 2025, 17(1), 123; https://doi.org/10.3390/sym17010123 - 15 Jan 2025

Cited by 3 | Viewed by 1785

Abstract

This paper introduces a kinetic model of crowd evacuation from a bounded domain, integrating social behavior and contagion dynamics. The model describes the spatial movement of individuals in a crowd, taking into account interactions with other people and the geometry of the environment. [...] Read more.

This paper introduces a kinetic model of crowd evacuation from a bounded domain, integrating social behavior and contagion dynamics. The model describes the spatial movement of individuals in a crowd, taking into account interactions with other people and the geometry of the environment. Interactions between healthy and infectious individuals can lead to disease transmission and are considered. The approach is grounded in the kinetic theory of active particles, where the activity variable represents both the infectious disease status of individuals (e.g., susceptible, infected) and the psychological state of pedestrians, including contagion awareness. Varying awareness levels influence individual behavior, leading to more cautious movement patterns, potentially reducing the overall infection rate. The performance of the model is evaluated through a series of numerical simulations. Different scenarios are examined to investigate the impact of awareness levels on pedestrian behavior, infectious disease spread, and evacuation times. Additionally, the effects of population immunization and individual contagion awareness are assessed to determine the most effective strategy for reducing infections. The results provide valuable insights into targeted strategies to mitigate contagion. Full article

(This article belongs to the Special Issue Mathematical Modeling of Symmetry in Collective Biological Dynamics)

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25 pages, 8892 KB

Open AccessEditor’s ChoiceArticle

A Symmetry-Inspired Hierarchical Control Strategy for Preventing Rollover in Articulated Rollers

by Quanzhi Xu, Wei Qiang and Hui Xie

Symmetry 2025, 17(1), 118; https://doi.org/10.3390/sym17010118 - 14 Jan 2025

Cited by 1 | Viewed by 1025

Abstract

In off-road environments, the lateral rollover stability of articulated unmanned rollers (URs) is critical to ensure operational safety and efficiency. This paper introduces the concept of a rollover energy barrier (REB), a symmetry-based metric that quantifies the energy margin between the current state [...] Read more.

In off-road environments, the lateral rollover stability of articulated unmanned rollers (URs) is critical to ensure operational safety and efficiency. This paper introduces the concept of a rollover energy barrier (REB), a symmetry-based metric that quantifies the energy margin between the current state and the critical rollover threshold of articulated rollers. URs exhibit dynamic asymmetry due to their hydraulic steering systems, which differ significantly from traditional passenger vehicles. To address these challenges, we propose a hierarchical control framework inspired by the principles of dynamic symmetry. This framework integrates Nonlinear Model Predictive Control (NMPC) and Active Disturbance Rejection Control (ADRC): NMPC is used for trajectory planning by incorporating the REB into the cost function, ensuring rollover stability, while ADRC compensates for dynamic asymmetries, model uncertainties, and external disturbances during trajectory tracking. Simulation and experimental results validate the effectiveness of the proposed control strategy in enhancing the rollover stability and tracking performance of the URs under off-road conditions. Full article

(This article belongs to the Section Engineering and Materials)

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24 pages, 4419 KB

Open AccessEditor’s ChoiceReview

Sugar Asymmetry: The Evolution of De Novo Asymmetric Syntheses of Carbohydrates from Hexoses to Oligosaccharides

by Ian Hicks, Sugyeom Kim, Aneesh Sridhar and George A. O’Doherty

Symmetry 2025, 17(1), 99; https://doi.org/10.3390/sym17010099 - 10 Jan 2025

Cited by 3 | Viewed by 3120

Abstract

The ability to recognize hidden symmetry in a highly asymmetric world is a key factor in how we view and understand the world around us. Despite the fact that it is an intrinsic property of the natural world, we have an innate ability [...] Read more.

The ability to recognize hidden symmetry in a highly asymmetric world is a key factor in how we view and understand the world around us. Despite the fact that it is an intrinsic property of the natural world, we have an innate ability to find hidden symmetry in asymmetric objects. The inherent asymmetry of the natural world is a fundamental property built into its chemical building blocks (e.g., proteins, carbohydrates, etc.). This review highlights the role of asymmetry in the structure of the carbohydrates and how these stereochemical complexities present synthetic challenges. This survey starts with an overview of the role synthetic chemistry plays in the discovery of carbohydrates and their 3D structure. This review then introduces various de novo asymmetric synthetic approaches that have been developed for the synthesis of carbohydrates and, in particular, oligosaccharides. The two most successful strategies for oligosaccharide synthesis rely on diastereoselective palladium-catalyzed glycosylation. The first uses an Achmatowicz reaction to asymmetrically prepare pyranose building blocks along with a substrate-controlled Pd-glycosylation. The other strategy couples a ligand-controlled Pd-glycosylation with a ring-closing metathesis for oligosaccharide assembly. Full article

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

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20 pages, 731 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Bi-Symmetric Polyhedral Cages with Maximally Connected Faces and Small Holes

by Bernard Piette and Árpad Lukács

Symmetry 2025, 17(1), 101; https://doi.org/10.3390/sym17010101 - 10 Jan 2025

Cited by 3 | Viewed by 1098

Abstract

Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and

P_{1}

edges, while those of the [...] Read more.

Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and

P_{1}

edges, while those of the other family have six neighbors and

P_{2}

edges. We restrict ourselves to polyhedral cages where the holes are adjacent to four faces at most. We characterize all p-cages with a deformation of the faces, compared to regular polygons, not exceeding 10%. Full article

(This article belongs to the Section Mathematics)

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14 pages, 9481 KB

Open AccessFeature PaperEditor’s ChoiceArticle

The One-Fault Dimension-Balanced Hamiltonian Problem in Toroidal Mesh Graphs

by Justie Su-Tzu Juan, Hao-Cheng Ciou and Meng-Jyun Lin

Symmetry 2025, 17(1), 93; https://doi.org/10.3390/sym17010093 - 9 Jan 2025

Cited by 4 | Viewed by 1146

Abstract

Finding a Hamiltonian cycle in a graph G = (V, E) is a well-known problem. The challenge of finding a Hamiltonian cycle that avoids these faults when faulty vertices or edges are present has been extensively studied. When the edge [...] Read more.

Finding a Hamiltonian cycle in a graph G = (V, E) is a well-known problem. The challenge of finding a Hamiltonian cycle that avoids these faults when faulty vertices or edges are present has been extensively studied. When the edge set of G is partitioned into k dimensions, the problem of dimension-balanced Hamiltonian cycles arises, where the Hamiltonian cycle uses approximately the same number of edges from each dimension (differing by at most one). This paper studies whether a dimension-balanced Hamiltonian cycle (DBH) exists in toroidal mesh graphs T_m_,n when a single vertex or edge is faulty, called the one-fault DBH problem. We establish that T_m_,n is one-fault DBH, except in the following cases: (1) both m and n are even; (2) one of m and n is 3, while the other satisfies mod 4 = 3 and is greater than 6; (3) one of m and n is odd, while the other satisfies mod 4 = 2. Additionally, this paper resolves a conjecture from prior literature, thereby providing a complete solution to the DBP problem on T_m_,n. Full article

(This article belongs to the Section Mathematics)

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29 pages, 660 KB

Open AccessEditor’s ChoiceArticle

Equivalence of History and Generator ϵ-Machines

by Nicholas F. Travers and James P. Crutchfield

Symmetry 2025, 17(1), 78; https://doi.org/10.3390/sym17010078 - 6 Jan 2025

Cited by 1 | Viewed by 1355

Abstract

ϵ

-Machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization though, [...] Read more.

ϵ

-Machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization though, an alternative generator definition was given as follows: unifilar, edge-emitting hidden Markov models with probabilistically distinct states. The key difference is that history

ϵ

-machines are defined by a process, whereas generator

ϵ

-machines define a process. We show here that these two definitions are equivalent in the finite-state case. Full article

(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)

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16 pages, 4891 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Estimating Large Global Significances with a New Monte Carlo Extrapolation Method

by Liangliang Chen, Yufei Chen, Gerry Bauer, Leonard G. Spiegel, Zhen Hu and Kai Yi

Symmetry 2025, 17(1), 57; https://doi.org/10.3390/sym17010057 - 1 Jan 2025

Viewed by 1110

Abstract

In particle physics, it is needed to evaluate the possibility that excesses of events in mass spectra are due to statistical fluctuations as quantified by the standards of local and global significances. Without prior knowledge of a particle’s mass, it is especially critical [...] Read more.

In particle physics, it is needed to evaluate the possibility that excesses of events in mass spectra are due to statistical fluctuations as quantified by the standards of local and global significances. Without prior knowledge of a particle’s mass, it is especially critical to estimate its global significance. The usual approach is to count the number of times a significance limit is exceeded in a collection of simulated Monte Carlo (MC) “toy experiments”. To demonstrate this conventional method for global significance, we performed simulation studies according to a recent Compact Muon Solenoid (CMS) result to show its effectiveness. However, this counting method is not practical for computing large global significances. To address this problem, we developed a new “extrapolation” method to evaluate the global significance. We compared the global significance estimated by our new method with that of the conventional approach, and verified its feasibility and effectiveness. This method is also applicable for cases where only small toy MC samples are available. In this approach, the significance is calculated based on p-values, assuming symmetrical Gaussian distributions. Full article

(This article belongs to the Section Physics)

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31 pages, 491 KB

Open AccessEditor’s ChoiceArticle

Cosmological Solutions in Teleparallel F(T, B) Gravity

by Fateme Gholami and Alexandre Landry

Symmetry 2025, 17(1), 60; https://doi.org/10.3390/sym17010060 - 1 Jan 2025

Cited by 7 | Viewed by 1397

Abstract

In this paper, we find several teleparallel

F (T, B)

solutions for a Robertson–Walker (TRW) cosmological spacetime. We first set and solve the

F (T, B)

-type field equations for a linear perfect fluid. Using similar techniques, [...] Read more.

In this paper, we find several teleparallel

F (T, B)

solutions for a Robertson–Walker (TRW) cosmological spacetime. We first set and solve the

F (T, B)

-type field equations for a linear perfect fluid. Using similar techniques, we then find new

F (T, B)

solutions for non-linear perfect fluids with a weak quadratic correction term to the linear equation of state (EoS). Finally, we solve for new classes of

F (T, B)

solutions for a scalar field source by assuming a power-law scalar field and then an exponential scalar field in terms of the time coordinate. For flat cosmological cases (

k = 0

cases), we find new exact and approximate

F (T, B)

solutions. For non-flat cases (

k = \pm 1

cases), we only find new teleparallel

F (T, B)

solutions for some specific and well-defined cosmological expansion subcases. We conclude by briefly discussing the impact of these new teleparallel solutions on cosmological processes such as dark energy (DE) quintessence and phantom energy models. Full article

(This article belongs to the Section Physics)

13 pages, 1499 KB

Open AccessEditor’s ChoiceArticle

Fungal Biocatalysis in Stereoselective Oxidation of 2-Phenylethanol

by Agnieszka Raczyńska, Beata Szmigiel-Merena, Małgorzata Brzezińska-Rodak, Magdalena Klimek-Ochab and Ewa Żymańczyk-Duda

Symmetry 2025, 17(1), 17; https://doi.org/10.3390/sym17010017 - 26 Dec 2024

Cited by 2 | Viewed by 1502

Abstract

Three fungal strains were employed for the stereoselective oxidation of the cheap and commercially available substrate 2-phenylethanol, which resulted in chiral building blocks being received. The whole-cell biocatalysts were as follows: Beauveria bassiana DSM 1344, Beauveria brongniartii DSM 6651, and Rhizopus arrhizus DSM [...] Read more.

Three fungal strains were employed for the stereoselective oxidation of the cheap and commercially available substrate 2-phenylethanol, which resulted in chiral building blocks being received. The whole-cell biocatalysts were as follows: Beauveria bassiana DSM 1344, Beauveria brongniartii DSM 6651, and Rhizopus arrhizus DSM 1185. The main product of Beauveria bassiana bioconversion was 1-phenylethane-1,2-diol, obtained, depending on the form of the biocatalyst, as an R-enantiomer (e.g., 99.9%) with fresh biomass application or as a racemic mixture in cases of immobilization in agar-agar. The best and most innovative results for the synthesis of the R-enantiomer of diol were received under precisely defined conditions as a result of a scaling study conducted on an automatic batch reactor. This is a pioneering result, since, in previous studies, fresh mycelium of Aspergillus niger resulted in this product being received as the (S) enantiomer. Also, the use of Rhizopus arrhizus DSM 1185 (immobilized in polyurethane foams) presented important results, as the bioconversion of phenyl ethanol led, indeed, to the racemic mixture of 1-phenylethane-1,2-diol but was accompanied by a noticeable tyrosol synthesis, which had not been reported previously. Full article

(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)

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63 pages, 14545 KB

Open AccessEditor’s ChoiceReview

Sum-Frequency Generation Spectroscopy at Aqueous Electrochemical Interfaces

by Ba Lich Pham, Alireza Ranjbari, Abderrahmane Tadjeddine, Laetitia Dalstein and Christophe Humbert

Symmetry 2024, 16(12), 1699; https://doi.org/10.3390/sym16121699 - 21 Dec 2024

Cited by 4 | Viewed by 6434

Abstract

The electrochemical interface (EI) is the determining factor in the yield and mechanism of sustainable energy storage and conversion systems due to its intrinsic functionality as a dynamic junction with the symmetry breaking of the molecular arrangement for complex reaction fields of mass [...] Read more.

The electrochemical interface (EI) is the determining factor in the yield and mechanism of sustainable energy storage and conversion systems due to its intrinsic functionality as a dynamic junction with the symmetry breaking of the molecular arrangement for complex reaction fields of mass transport and heterogeneous electron transfer. At the EI, the externally applied potential stimulus drives the formation of the electrical double layer (EDL) and governs the adsorption of interfacial adsorbate species in aqueous electrolyte solutions. Water and its aqueous electrolyte systems are integral and quintessential elements in the technological innovation of various fields such as environmental sciences, electrocatalysis, photocatalysis, and biochemistry. Although deciphering the structure and orientation of water molecules at the electrode–electrolyte interface in a quantitative analysis is of utmost importance, assessing chemical phenomena at the buried EI was rather challenging due to the intricacy of selecting interface-specific methodologies. Based on the non-centrosymmetry of the interfaces’ electronic properties, sum-frequency generation (SFG) spectroscopy has been manifested to be specifically well suited for probing the EI with detailed and comprehensive characteristics of adsorbates’ chemical structures and electrochemical events. In this review, we holistically engage in a methodical and scrupulous assessment of the fundamental EDL models and navigate towards the connection of the renowned Stark effect and potential dependence of SFG spectra at heterogeneous electrode–electrolyte interfaces. We dissect the development, advantages, and available geometrical configurations of in situ SFG spectroscopy in harnessing the EI. A broad spectrum of applications in unraveling the water orientations and rationalizing the convoluted mechanism of fuel-generated electrocatalytic reactions with particular encumbrances and potential resolutions is underscored by leveraging SFG spectroscopy. Full article

(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)

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80 pages, 858 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Uniform in Number of Neighbor Consistency and Weak Convergence of k-Nearest Neighbor Single Index Conditional Processes and k-Nearest Neighbor Single Index Conditional U-Processes Involving Functional Mixing Data

by Salim Bouzebda

Symmetry 2024, 16(12), 1576; https://doi.org/10.3390/sym16121576 - 25 Nov 2024

Cited by 8 | Viewed by 2138

Abstract

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced [...] Read more.

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation

r^{(m)} (φ, t)

, defined as

E [φ (Y_{1}, \dots, Y_{m}) | (X_{1}, \dots, X_{m}) = t]

for

t \in X^{m}

. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems. Full article

(This article belongs to the Section Mathematics)

15 pages, 3078 KB

Open AccessEditor’s ChoiceArticle

Bilateral Correlational Behavior of Pyroglutamate Aminopeptidase I Activity in Rat Photoneuroendocrine Locations During a Standard 12:12 h Light–Dark Cycle

by Manuel Ramírez-Sánchez, Isabel Prieto, Ana Belén Segarra, Inmaculada Banegas, Magdalena Martínez-Cañamero, Germán Domínguez-Vías, Raquel Durán and Francisco Vives

Symmetry 2024, 16(11), 1539; https://doi.org/10.3390/sym16111539 - 17 Nov 2024

Viewed by 1899

Abstract

We previously described the circadian variation and bilateral distribution of pyroglutamate aminopeptidase I (pGluPI) activity levels in photoneuroendocrine locations of adult male rats during a standard 12:12 h light–dark cycle. However, the correlational analysis between such locations has not yet been studied. This [...] Read more.

We previously described the circadian variation and bilateral distribution of pyroglutamate aminopeptidase I (pGluPI) activity levels in photoneuroendocrine locations of adult male rats during a standard 12:12 h light–dark cycle. However, the correlational analysis between such locations has not yet been studied. This may provide new data about the unilateral and bilateral functional interaction between photoneuroendocrine locations under light and dark conditions. We analyzed the correlations between locations of a photoneuroendocrine circuit consisting of retina, anterior hypothalamus, superior cervical ganglion, and pineal gland, as well as other related photoneuroendocrine locations: posterior hypothalamus, anterior pituitary, posterior pituitary, occipital cortex, and serum. In particular, we analyzed the correlations between the left retina or the right retina versus the rest of the locations, as well as the correlations between the left and right sides of paired structures at the different time points selected from 12 h light and 12 h dark periods. Also, the profiles of correlational results were compared with the corresponding mean levels. The results demonstrate the complexity of asymmetrical brain behavior. The correlation profile did not always parallel the profile observed with the mean activity values. The diurnal behavior of correlations with the left or right retina differed from one location to another. Likewise, the diurnal variation of correlations between the left and right sides of the paired structures differed between them. Particularly, while most correlations between the left versus right sides of paired structures showed positive values, that of the posterior hypothalamus showed a negative value at 13 h of light period. In addition, except the posterior hypothalamus, most paired locations only correlated significantly with right retina at 07 h of the light period. The results demonstrate the dynamic complexity of brain asymmetry, which represents a challenge for understanding its functional meaning. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Life Sciences: Feature Papers 2024)

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27 pages, 5704 KB

Open AccessEditor’s ChoiceReview

Viewpoints Concerning Crystal Structure from Recent Reports on Schiff Base Compounds and Their Metal Complexes

by Takashiro Akitsu, Daisuke Nakane and Barbara Miroslaw

Symmetry 2024, 16(11), 1525; https://doi.org/10.3390/sym16111525 - 14 Nov 2024

Cited by 6 | Viewed by 3256

Abstract

Schiff bases are organic compounds that are often used as ligands in metal complexes. In addition to the C=N double bond, which is characteristic of Schiff bases, intermolecular hydrogen bonds are frequently observed in both the twisting of planar substituents in organic compounds [...] Read more.

Schiff bases are organic compounds that are often used as ligands in metal complexes. In addition to the C=N double bond, which is characteristic of Schiff bases, intermolecular hydrogen bonds are frequently observed in both the twisting of planar substituents in organic compounds and the geometric structure of the coordination environment in metal complexes. The results of the crystal structure analyses are stored in databases, which can be used to assess three-dimensional structures. To examine the important structural aspects for novel molecular and material designs, this review examines the important discussion of crystal structure “features” from various viewpoints based on papers on Schiff bases and Schiff base metal complexes from recent years. Full article

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

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12 pages, 659 KB

Open AccessEditor’s ChoiceArticle

Evaluating Time Irreversibility Tests Using Geometric Brownian Motions with Stochastic Resetting

by Massimiliano Zanin, Pece Trajanovski, Petar Jolakoski, Trifce Sandev and Ljupco Kocarev

Symmetry 2024, 16(11), 1445; https://doi.org/10.3390/sym16111445 - 31 Oct 2024

Cited by 3 | Viewed by 1250

Abstract

The time irreversibility of a dynamical process refers to the phenomenon where its behaviour or statistical properties change when it is observed under a time-reversal operation, i.e., backwards in time and indicates the presence of an “arrow of time”. It is an important [...] Read more.

The time irreversibility of a dynamical process refers to the phenomenon where its behaviour or statistical properties change when it is observed under a time-reversal operation, i.e., backwards in time and indicates the presence of an “arrow of time”. It is an important feature of both synthetic and real-world systems, as it represents a macroscopic property that describes the mechanisms driving the dynamics at a microscale level and that stems from non-linearities and the presence of non-conservative forces within them. While many alternatives have been proposed in recent decades to assess this feature in experimental time series, the evaluation of their performance is hindered by the lack of benchmark time series of known reversibility. To solve this problem, we here propose and evaluate the use of a geometric Brownian motion model with stochastic resetting. We specifically use synthetic time series generated with this model to evaluate eight irreversibility tests in terms of sensitivity with respect to several characteristics, including their degree of irreversibility and length. We show how tests yield at times contradictory results, including the false detection of irreversible dynamics in time-reversible systems with a frequency higher than expected by chance and how most of them detect a multi-scale irreversibility structure that is not present in the underlying data. Full article

(This article belongs to the Section Physics)

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