Symmetry

15 pages, 3078 KiB

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 813

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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12 pages, 659 KiB

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 2 | Viewed by 783

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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12 pages, 13526 KiB

Open AccessEditor’s ChoiceArticle

Constraint of d = 8 Lorentz Invariance Violation with New Experimental Design

by Tao Jin, Jia-Rui Li, Yu-Jie Tan, Pan-Pan Wang, Cheng-Gang Qin and Cheng-Gang Shao

Symmetry 2024, 16(11), 1432; https://doi.org/10.3390/sym16111432 - 28 Oct 2024

Viewed by 1202

Abstract

Short-range gravity experiments are more suitable for the testing of high-order Lorentz symmetry breaking effects. In our previous work, we proposed a new experimental design based on precision torsion balance technology to test the Lorentz violation force effect that varies inversely with the [...] Read more.

Short-range gravity experiments are more suitable for the testing of high-order Lorentz symmetry breaking effects. In our previous work, we proposed a new experimental design based on precision torsion balance technology to test the Lorentz violation force effect that varies inversely with the fourth power of distance (corresponding to mass dimension d = 6 term), and the corresponding experiment is currently underway. In this paper, we focus on analyzing the potential of this experimental scheme to test the Lorentz violation force that varies inversely with the sixth power of distance (corresponding to mass dimension d = 8 term). The results show that, compared with the current best limit, the new experimental scheme can improve the constraints on the Lorentz violation coefficients with d = 8 by at least one order of magnitude. Full article

(This article belongs to the Special Issue Lorentz Symmetry and General Relativity)

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13 pages, 1294 KiB

Open AccessEditor’s ChoiceArticle

Asymmetry in Galaxy Spin Directions: A Fully Reproducible Experiment Using HSC Data

by Lior Shamir

Symmetry 2024, 16(10), 1389; https://doi.org/10.3390/sym16101389 - 18 Oct 2024

Cited by 2 | Viewed by 2655

Abstract

The asymmetry in the large-scale distribution of the directions in which spiral galaxies rotate has been observed by multiple telescopes, all showing a consistent asymmetry in the distribution of galaxy spin directions as observed from Earth. Here, galaxies with a redshift from HSC [...] Read more.

The asymmetry in the large-scale distribution of the directions in which spiral galaxies rotate has been observed by multiple telescopes, all showing a consistent asymmetry in the distribution of galaxy spin directions as observed from Earth. Here, galaxies with a redshift from HSC DR3 are annotated by their direction of rotation, and their distribution is analyzed. The results show that galaxies that rotate in the opposite direction relative to the Milky Way as observed from Earth are significantly more prevalent compared to galaxies that rotate in the same direction relative to the Milky Way. The asymmetry also forms a dipole axis that becomes stronger when the redshift gets higher. These results are aligned with observations from virtually all premier digital sky surveys, as well as space telescopes such as the HST and the JWST. This shows that the distribution of galaxy spin directions as observed from Earth is not symmetrical, and has a possible link to the rotational velocity of the Milky Way. This experiment provides data, code, and a full protocol that allows the results to be easily reproduced in a transparent manner. This practice is used to overcome the “reproducibility crisis” in science. Full article

(This article belongs to the Special Issue Global and Local Scale Symmetry in Gravitation and Cosmology)

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19 pages, 22914 KiB

Open AccessEditor’s ChoiceReview

Multilevel Diffractive Lenses: Recent Advances and Applications

by Chenyu Shi, Weipeng Zhao, Sai Chen and Wenli Li

Symmetry 2024, 16(10), 1377; https://doi.org/10.3390/sym16101377 - 16 Oct 2024

Cited by 2 | Viewed by 6794

Abstract

Multilevel diffractive lenses (MDLs) has undergone considerable advancements, marked by their exceptional efficiency and diverse focusing capabilities, resulting in their widespread use in optical systems. In recent times, MDLs have consistently been juxtaposed with metalenses, which have experienced swift progress over the last [...] Read more.

Multilevel diffractive lenses (MDLs) has undergone considerable advancements, marked by their exceptional efficiency and diverse focusing capabilities, resulting in their widespread use in optical systems. In recent times, MDLs have consistently been juxtaposed with metalenses, which have experienced swift progress over the last decade. Concurrently, MDLs have continued to evolve, propelled by their distinct advantages, such as cost-effective production and adaptability for mass manufacturing. This article explores the evolution and foundational concepts of MDLs, highlighting the advantages of their circular symmetry in enhancing simulation and optimization efficiency. Furthermore, we present several innovative fabrication methods for MDLs that capitalize on the latest advancements in 3D printing technology. We also show the practical applications and potential future developments of MDLs. Full article

(This article belongs to the Special Issue Metamaterials and Symmetry: Recent Advances and Applications)

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15 pages, 2734 KiB

Open AccessEditor’s ChoiceReview

Comprehensive Analysis of Pelvic Asymmetries in Low Back Pain, Scoliosis, Post-Traumatic Pelvic Dysfunctions and Obstetric Changes: A Narrative Review Focused on Clinical Relevance

by Inés Cruz-Medel, Daiana Priscila Rodrigues-de-Souza and Francisco Alburquerque-Sendín

Symmetry 2024, 16(10), 1304; https://doi.org/10.3390/sym16101304 - 3 Oct 2024

Cited by 2 | Viewed by 4875

Abstract

The human pelvis is a complex structure, which participates in the biomechanical functioning of the musculoskeletal system. Although it is considered a symmetrical entity, the morphology of the pelvis is subject to different factors that alter its anatomy, function or biomechanics, such as [...] Read more.

The human pelvis is a complex structure, which participates in the biomechanical functioning of the musculoskeletal system. Although it is considered a symmetrical entity, the morphology of the pelvis is subject to different factors that alter its anatomy, function or biomechanics, such as age, bipedal locomotion, obstetric changes and sexual dimorphism. However, how these factors influence pelvic asymmetry is unknown. Some evidence suggests that this condition leads to different pathological states, such as chronic low back pain, scoliosis, post-traumatic pelvic dysfunctions and obstetric changes. Therefore, pelvic asymmetries present a significant challenge in clinical practice due to their multifactorial nature and their potential impact on quality of life. Multidisciplinary research and collaboration are essential to improve understanding and develop more effective and specific identification and treatment approaches in the presence of pelvic asymmetries. Full article

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

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18 pages, 5645 KiB

Open AccessEditor’s ChoiceArticle

Assessing Vulnerabilities in Line Length Parameterization and the Per-Unit-Length Paradigm for Phase Modulation and Figure-of-Merit Evaluation in 60 GHz Liquid Crystal Phase Shifters

by Jinfeng Li and Haorong Li

Symmetry 2024, 16(10), 1261; https://doi.org/10.3390/sym16101261 - 25 Sep 2024

Cited by 7 | Viewed by 4194

Abstract

The figure-of-merit (FoM) is a crucial metric in evaluating liquid crystal (LC) phase shifters, significantly influencing the selection of superior device candidates. This paper identifies, for the first time, a fundamental limitation in the widely-used High-Frequency Structure Simulator (HFSS), a closed-source commercial tool, [...] Read more.

The figure-of-merit (FoM) is a crucial metric in evaluating liquid crystal (LC) phase shifters, significantly influencing the selection of superior device candidates. This paper identifies, for the first time, a fundamental limitation in the widely-used High-Frequency Structure Simulator (HFSS), a closed-source commercial tool, when modeling reconfigurable delay line phase shifters (RDLPS) based on LC at millimeter-wave (mmW) frequencies for Beyond 5G (B5G) and Sixth-Generation (6G) applications. Specifically, the study reveals unreliable predictions of differential phase shifts (DPS) when using the line length parameterization (LLP) approach, with an accuracy of only 47.22%. These LLP-induced inaccuracies lead to misleading FoM calculations, potentially skewing comparative analyses against phase shifters implemented with different geometries or advanced technologies. Additionally, the per-unit-length (PUL) paradigm, commonly employed by microwave circuit engineers for evaluating and optimizing microwave transmission line designs, is also found to have limitations in the context of mmW RDLPS based on LC. The PUL methodology underestimates the FoM by 1.38206°/dB for an LC coaxial RDLPS at 60 GHz. These findings underscore a critical symmetry implication, where the assumed symmetry in phase shift response is violated, resulting in inconsistent performance assessments. To address these challenges, a remediation strategy based on a scenario-based “Length-for-π” (LFP) framework is proposed, offering more accurate performance characterization and enabling better-informed decision-making in mmW phase shifter design. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

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32 pages, 6740 KiB

Open AccessEditor’s ChoiceReview

Magnetohydrodynamic Waves in Asymmetric Waveguides and Their Applications in Solar Physics—A Review

by Robertus Erdélyi and Noémi Kinga Zsámberger

Symmetry 2024, 16(9), 1228; https://doi.org/10.3390/sym16091228 - 18 Sep 2024

Cited by 1 | Viewed by 1200

Abstract

The solar atmosphere is a complex, coupled, highly dynamic plasma environment, which shows rich structuring due to the presence of gravitational and magnetic fields. Several features of the Sun’s atmosphere can serve as guiding media for magnetohydrodynamic (MHD) waves. At the same time, [...] Read more.

The solar atmosphere is a complex, coupled, highly dynamic plasma environment, which shows rich structuring due to the presence of gravitational and magnetic fields. Several features of the Sun’s atmosphere can serve as guiding media for magnetohydrodynamic (MHD) waves. At the same time, these waveguides may contain flows of various magnitudes, which can then destabilise the waveguides themselves. MHD waves were found to be ubiquitously present in the solar atmosphere, thanks to the continuous improvement in the spatial, temporal, and spectral resolution of both space-born and ground-based observatories. These detections, coupled with recent theoretical advancements, have been used to obtain diagnostic information about the solar plasma and the magnetic fields that permeate it, by applying the powerful concept of solar magneto-seismology (SMS). The inclusion of asymmetric shear flows in the MHD waveguide models used may considerably affect the seismological results obtained. Further, they also influence the threshold for the onset of the Kelvin–Helmholtz instability, which, at high enough relative flow speeds, can lead to energy dissipation and contribute to the heating of the solar atmosphere—one of the long-standing and most intensely studied questions in solar physics. Full article

(This article belongs to the Special Issue Symmetry in Magnetohydrodynamic Flows and Their Applications)

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17 pages, 17490 KiB

Open AccessEditor’s ChoiceArticle

Ar+ Ion Irradiation Response of LPBF AlSi10Mg Alloy in As-Built and KOBO-Processed Conditions

by Przemysław Snopiński, Marek Barlak and Katarzyna Nowakowska-Langier

Symmetry 2024, 16(9), 1158; https://doi.org/10.3390/sym16091158 - 5 Sep 2024

Cited by 1 | Viewed by 1007

Abstract

In recent years, revolutionary improvements in the properties of certain FCC metals have been achieved by increasing the proportion of twin-related, highly symmetric grain boundaries. Various thermomechanical routes of grain boundary engineering (GBE) processing have been employed to enhance the fraction of low [...] Read more.

In recent years, revolutionary improvements in the properties of certain FCC metals have been achieved by increasing the proportion of twin-related, highly symmetric grain boundaries. Various thermomechanical routes of grain boundary engineering (GBE) processing have been employed to enhance the fraction of low ΣCSL grain boundaries, thereby improving the radiation tolerance of many polycrystalline materials. This improvement is due to symmetric twin boundaries acting as effective sinks for defects caused by radiation, thus enhancing the material’s performance. In this study, the LPBF AlSi10Mg alloy was post-processed via the KOBO extrusion method. Subsequently, the samples were subjected to irradiation with Ar+ ions at an ion fluence of 5 × 10¹⁷ cm⁻². The microstructures of the samples were thoroughly investigated using electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and high-resolution TEM (HRTEM). The results showed that KOBO processing led to the formation of an ultrafine-grained microstructure with a mean grain size of 0.8 µm. Moreover, it was revealed that the microstructure of the KOBO-processed sample exhibited an increased fraction of low-ΣCSL boundaries. Specifically, the fraction of Σ11 boundaries increased from approximately 2% to 8%. Post-irradiation microstructural analysis revealed improved radiation tolerance in the KOBO-processed sample, indicating a beneficial influence of the increased grain boundary fraction and low-ΣCSL boundary fraction on the irradiation resistance of the AlSi10Mg alloy. This research provides valuable insights for the development of customized microstructures with enhanced radiation tolerance, which has significant implications for the advancement of materials in nuclear and aerospace applications. Full article

(This article belongs to the Section Engineering and Materials)

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15 pages, 1867 KiB

Open AccessEditor’s ChoiceArticle

Enzymatic Deracemization of Fluorinated Arylcarboxylic Acids: Chiral Enzymatic Analysis and Absolute Stereochemistry Using Chiral HPLC

by Oleg I. Kolodiazhnyi, Anastasiia O. Kolodiazhna, Oleh Faiziiev and Yuliia Gurova

Symmetry 2024, 16(9), 1150; https://doi.org/10.3390/sym16091150 - 4 Sep 2024

Cited by 1 | Viewed by 1420

Abstract

The hydrolase-catalyzed kinetic resolution of fluorinated racemates of 3-arylcarboxylic acids is described. Hydrolysis of ethyl esters of fluorinated acids by esterases and hydrolases in all cases resulted in the formation of hydrolyzed (S)-carboxylic acids and unreacted (R)-esters in high [...] Read more.

The hydrolase-catalyzed kinetic resolution of fluorinated racemates of 3-arylcarboxylic acids is described. Hydrolysis of ethyl esters of fluorinated acids by esterases and hydrolases in all cases resulted in the formation of hydrolyzed (S)-carboxylic acids and unreacted (R)-esters in high yields and high enantiomeric purity. The influence of separation conditions on the efficiency and enantioselectivity of biocatalytic conversion was also studied. The reactions were carried out under normal conditions (stirring with a magnetic stirrer at room temperature) and microwave irradiation in the presence of hydrolases. Amano PS showed excellent selectivity and good yields in the hydrolysis of fluorinated aromatic compounds. The absolute configuration of the resulting compounds was based on biokinetic studies and the use of chiral HPLC. A molecular modeling of the kinetic resolution of carboxylic acid esters was carried out. Full article

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

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16 pages, 9639 KiB

Open AccessEditor’s ChoiceArticle

Hierarchical Hypervapotron Structure Integrated with Microchannels for Advancement of Thermohydraulic Performance

by Xin Meng, Kai Cheng, Qi Zhao and Xuemei Chen

Symmetry 2024, 16(8), 1089; https://doi.org/10.3390/sym16081089 - 22 Aug 2024

Cited by 2 | Viewed by 1296

Abstract

The hypervapotron structure was considered to be a feasible configuration to meet the high heat-dissipating requirement of divertors in nuclear fusion devices. In this work, symmetric CuCrZr-based transverse microchannels (TMHC) and longitudinal microchannels (LMHC) with an integrated hypervapotron channel were proposed and manufactured, [...] Read more.

The hypervapotron structure was considered to be a feasible configuration to meet the high heat-dissipating requirement of divertors in nuclear fusion devices. In this work, symmetric CuCrZr-based transverse microchannels (TMHC) and longitudinal microchannels (LMHC) with an integrated hypervapotron channel were proposed and manufactured, and subcooled flow boiling experiments were conducted using deionized water at an inlet temperature of 20 °C with a traditional flat-type hypervapotron channel (FHC) for comparison. The LMHC and TMHC obtained lower wall temperatures than the FHC for all conditions, and the TMHC yielded the lowest temperatures. The heat transfer coefficients of the LMHC and TMHC outperformed the FHC due to the enlarged heat transfer area, and the TMHC had the greatest heat transfer coefficient (maximumly increased by 132% compared to the FHC) because the transverse-arranged microchannels were conductive, promoting the convection and liquid replenishment ability by introducing branch flow between fins; however, the microchannels of the LMHC were insensible to flow velocities due to the block effect of longitudinal microchannels. The LMHC obtained the largest pressure drop, and the pressure drop for the FHC and TMHC were comparable since the transverse-placed microchannels had little effect on frictional pressure loss. The TMHC attained the greatest comprehensive thermohydraulic performance which might bring significant insight to the structural design of hypervapotron devices. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

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18 pages, 1023 KiB

Open AccessEditor’s ChoiceReview

Nuclear Symmetry Energy in Strongly Interacting Matter: Past, Present and Future

by Jirina R. Stone

Symmetry 2024, 16(8), 1038; https://doi.org/10.3390/sym16081038 - 13 Aug 2024

Cited by 1 | Viewed by 1949

Abstract

The concept of symmetry under various transformations of quantities describing basic natural phenomena is one of the fundamental principles in the mathematical formulation of physical laws. Starting with Noether’s theorems, we highlight some well–known examples of global symmetries and symmetry breaking on the [...] Read more.

The concept of symmetry under various transformations of quantities describing basic natural phenomena is one of the fundamental principles in the mathematical formulation of physical laws. Starting with Noether’s theorems, we highlight some well–known examples of global symmetries and symmetry breaking on the particle level, such as the separation of strong and electroweak interactions and the Higgs mechanism, which gives mass to leptons and quarks. The relation between symmetry energy and charge symmetry breaking at both the nuclear level (under the interchange of protons and neutrons) and the particle level (under the interchange of u and d quarks) forms the main subject of this work. We trace the concept of symmetry energy from its introduction in the simple semi-empirical mass formula and liquid drop models to the most sophisticated non-relativistic, relativistic, and ab initio models. Methods used to extract symmetry energy attributes, utilizing the most significant combined terrestrial and astrophysical data and theoretical predictions, are reviewed. This includes properties of finite nuclei, heavy-ion collisions, neutron stars, gravitational waves, and parity–violating electron scattering experiments such as CREX and PREX, for which selected examples are provided. Finally, future approaches to investigation of the symmetry energy and its properties are discussed. Full article

(This article belongs to the Special Issue Strongly Interacting Matter at Extreme Conditions—the Role of Symmetry Energy in Nuclear Physics and Astrophysics)

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15 pages, 452 KiB

Open AccessEditor’s ChoiceArticle

Strong Decays of the ϕ(2170) as a Fully Strange Tetraquark State

by Yi-Wei Jiang, Wei-Han Tan, Hua-Xing Chen and Er-Liang Cui

Symmetry 2024, 16(8), 1021; https://doi.org/10.3390/sym16081021 - 9 Aug 2024

Cited by 2 | Viewed by 823

Abstract

We study the strong decays of the

ϕ (2170)

, along with its possible partner

X (2436)

, as two fully strange tetraquark states of

J^{P C} = 1^{- -}

. These two states are assumed to [...] Read more.

We study the strong decays of the

ϕ (2170)

, along with its possible partner

X (2436)

, as two fully strange tetraquark states of

J^{P C} = 1^{- -}

. These two states are assumed to contain two strange quarks and two anti-strange quarks, with the flavor symmetry

6_{s s} \otimes {\bar{6}}_{\bar{s} \bar{s}}

. We consider seven decay channels:

ϕ η

,

ϕ η^{'}

,

ϕ f_{0} (980)

,

ϕ f_{1} (1420)

,

h_{1} (1415) η

,

h_{1} (1415) η^{'}

, and

h_{1} (1415) f_{1} (1420)

. Some of these channels are kinematically possible, and we calculate their relative branching ratios through the Fierz rearrangement. Future experimental measurements on these ratios could be useful in determining the nature of the

ϕ (2170)

and

X (2436)

. The

ϕ (2170)

has been observed in the

ϕ f_{0} (980)

,

ϕ η

, and

ϕ η^{'}

channels, and we propose to further examine it in the

h_{1} (1415) η

channel. Evidences of the

X (2436)

have been observed in the

ϕ f_{0} (980)

channel, and we propose to verify whether this structure exists or not in the

ϕ η

,

ϕ η^{'}

,

h_{1} (1415) η

, and

h_{1} (1415) η^{'}

channels. Full article

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

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29 pages, 429 KiB

Open AccessEditor’s ChoiceReview

A Review of Stable, Traversable Wormholes in f(R) Gravity Theories

by Ramesh Radhakrishnan, Patrick Brown, Jacob Matulevich, Eric Davis, Delaram Mirfendereski and Gerald Cleaver

Symmetry 2024, 16(8), 1007; https://doi.org/10.3390/sym16081007 - 7 Aug 2024

Cited by 8 | Viewed by 5776

Abstract

It has been proven that in standard Einstein gravity, exotic matter (i.e., matter violating the pointwise and averaged Weak and Null Energy Conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in [...] Read more.

It has been proven that in standard Einstein gravity, exotic matter (i.e., matter violating the pointwise and averaged Weak and Null Energy Conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore

f (R)

theories and then explore some wormhole solutions in

f (R)

theories, including Lovelock gravity and Einstein Dilaton Gauss–Bonnet (EdGB) gravity. For completeness, we have also reviewed ‘Other wormholes’ such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity (NLG) wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required. Full article

(This article belongs to the Special Issue Symmetry in Gravity Theories and Cosmology)

23 pages, 940 KiB

Open AccessEditor’s ChoiceReview

Overview of B→K^(∗)ℓℓ Theoretical Calculations and Uncertainties

by Farvah Mahmoudi and Yann Monceaux

Symmetry 2024, 16(8), 1006; https://doi.org/10.3390/sym16081006 - 7 Aug 2024

Cited by 6 | Viewed by 1194

Abstract

The search for New Physics (NP) beyond the Standard Model (SM) has been a central focus of particle physics, including in the context of B-meson decays involving

b \to s ℓ ℓ

transitions. These transitions, mediated by flavour-changing neutral currents, are highly [...] Read more.

The search for New Physics (NP) beyond the Standard Model (SM) has been a central focus of particle physics, including in the context of B-meson decays involving

b \to s ℓ ℓ

transitions. These transitions, mediated by flavour-changing neutral currents, are highly sensitive to small NP effects due to their suppression in the SM. While direct searches at colliders have not yet led to NP discoveries, indirect probes through semi-leptonic decays have revealed anomalies in observables such as the branching fraction

B (B \to K μ μ)

and the angular observable

P_{5}^{'} (B \to K^{*} μ μ)

. In order to assess the observed tensions, it is essential to ensure an accurate SM prediction. In this review, we examine the theoretical basis of the

B \to K^{(*)} ℓ ℓ

decays, addressing in particular key uncertainties arising from local and non-local form factors. We also discuss the impact of QED corrections to the Wilson coefficients, as well as the effect of CKM matrix elements on the predictions and the tension with the experimental measurements. We discuss the most recent results, highlighting ongoing efforts to refine predictions and to constrain potential signs of NP in these critical decay processes. Full article

(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)

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16 pages, 532 KiB

Open AccessEditor’s ChoiceReview

Current Status of the Standard Model Prediction for the B_s → μ⁺μ⁻ Branching Ratio

by Mateusz Czaja and Mikołaj Misiak

Symmetry 2024, 16(7), 917; https://doi.org/10.3390/sym16070917 - 18 Jul 2024

Cited by 6 | Viewed by 1453

Abstract

The rare decay

B_{s} \to μ^{+} μ^{-}

provides an important constraint on possible deviations from the Standard Model in b-s-ℓ-ℓ interactions. The present weighted average of its branching ratio measurements amounts to [...] Read more.

The rare decay

B_{s} \to μ^{+} μ^{-}

provides an important constraint on possible deviations from the Standard Model in b-s-ℓ-ℓ interactions. The present weighted average of its branching ratio measurements amounts to

(3.34 \pm 0.27) \times 10^{- 9}

, which remains in good agreement with the theoretical prediction of

(3.64 \pm 0.12) \times 10^{- 9}

within the Standard Model. In the present paper, we review calculations that have contributed to this prediction and discuss the associated uncertainties. Full article

(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)

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16 pages, 515 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Evaporation of Primordial Charged Black Holes: Timescale and Evolution of Thermodynamic Parameters

by José Antonio de Freitas Pacheco

Symmetry 2024, 16(7), 895; https://doi.org/10.3390/sym16070895 - 13 Jul 2024

Cited by 1 | Viewed by 1240

Abstract

The evolution of primordial black holes formed during the reheating phase is revisited. For reheating temperatures in the range of

10^{12}

–

10^{13}

GeV, the initial masses are respectively of the order of

10^{10}

–

10^{8}

M_{P}

, [...] Read more.

The evolution of primordial black holes formed during the reheating phase is revisited. For reheating temperatures in the range of

10^{12}

–

10^{13}

GeV, the initial masses are respectively of the order of

10^{10}

–

10^{8}

M_{P}

, where

M_{P}

is the Planck mass. These newborn black holes have a small charge-to-mass ratio of the order of

10^{- 3}

, a consequence of statistical fluctuations present in the plasma constituting the collapsing matter. Charged black holes can be rapidly discharged by the Schwinger mechanism, but one expects that, for very light black holes satisfying the condition

M / M_{P} < < M_{P} / m_{W}

(

m_{W}

is the mass of the heaviest standard model charged W-boson), the pair production process is probably strongly quenched. Under these conditions, these black holes evaporate until attaining extremality with final masses of about

10^{7}

–

10^{5} M_{P}

. Timescales to reach extremality as a function of the initial charge excess were computed, as well as the evolution of the horizon temperature and the charge-to-mass ratio. The behavior of the horizon temperature can be understood in terms of the well-known discontinuity present in the heat capacity for a critical charge-to-mass ratio

Q / \sqrt{G} M = \sqrt{3} / 2

. Full article

(This article belongs to the Special Issue Symmetry in Gravity Theories and Cosmology)

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16 pages, 303 KiB

Open AccessEditor’s ChoiceArticle

Extension of Buchdahl’s Theorem on Reciprocal Solutions

by David S. Pereira, José Pedro Mimoso and Francisco S. N. Lobo

Symmetry 2024, 16(7), 881; https://doi.org/10.3390/sym16070881 - 11 Jul 2024

Cited by 1 | Viewed by 1458

Abstract

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as [...] Read more.

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as the Einstein frame, Brans–Dicke gravity is reformulated as General Relativity supplemented by an additional scalar field. In 1959, Hans Adolf Buchdahl utilized an elegant technique to derive a set of solutions for the vacuum field equations within this gravitational framework. In this paper, we extend Buchdahl’s method to incorporate the cosmological constant and to the scalar-tensor cases beyond the Brans–Dicke archetypal theory, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans–Dicke theory that includes a quadratic potential. More specifically, we obtain synchronous solutions in the following contexts: in scalar-tensor gravity with massless scalar fields, Brans–Dicke theory with a quadratic potential, where we obtain specific synchronous metrics to the Schwarzschild–de Sitter metric, the Nariai solution, and a hyperbolically foliated solution. Full article

(This article belongs to the Special Issue Symmetry in Gravity Theories and Cosmology)

17 pages, 943 KiB

Open AccessEditor’s ChoiceArticle

The Combined Additive Effect of Inter-Limb Muscle Mass Asymmetries and Body Composition Indices on Lower Limb Injuries in Physically Active Young Adults

by Jarosław Domaradzki

Symmetry 2024, 16(7), 876; https://doi.org/10.3390/sym16070876 - 10 Jul 2024

Viewed by 1667

Abstract

Biological measurements that predict injury risk are crucial diagnostic tools. Yet, research on improving diagnostic accuracy in detecting accidents is insufficient. Combining multiple predictors and assessing them via ROC curves can enhance this accuracy. This study aimed to (1) evaluate the importance of [...] Read more.

Biological measurements that predict injury risk are crucial diagnostic tools. Yet, research on improving diagnostic accuracy in detecting accidents is insufficient. Combining multiple predictors and assessing them via ROC curves can enhance this accuracy. This study aimed to (1) evaluate the importance of lower limb muscle mass asymmetry and body composition (BMI and FMI) as predictors of injuries, (2) explore the role of the most effective body composition index in the relationship between muscle asymmetry and injury, and (3) assess the prognostic potential of combined predictors. Cross-sectional sampling was used to select students from a university. The sample included 237 physically active young adults (44% males). The independent variables were inter-limb muscle mass asymmetry (absolute asymmetry, AA), BMI, and FMI; the dependent variable was the number of injuries in the past year. Using zero-inflated Poisson regression, we examined the relationships, including a moderation analysis (moderated multiple ZIP regression). The mediation by body composition was tested using ZIP and logistic regression. The predictive power was assessed via ROC curves. The significance level was set at an α-value of 0.05. No significant difference in injury incidence between males and females was found (χ² = 2.12, p = 0.145), though the injury types varied. Males had more muscle strains, while females had more bone fractures (χ² = 6.02, p = 0.014). In males, the inter-limb asymmetry and FMI predicted injuries; in females, the BMI and FMI did, but not asymmetry. No moderating or mediating effects of body composition were found. In males, combined asymmetry and the FMI better predicted injuries (AUC = 0.686) than separate predictors (AA: AUC = 0.650, FMI: AUC = 0.458). For females, the FMI was the best predictor (AUC = 0.662). The most predictive factors for injuries in males were both muscle asymmetry and the FMI (as combined predictors), while in females, it was the single FMI. The hypothesis regarding the mediating role of body composition indicators was rejected, as no moderation or mediation by the FMI was detected in the relationship between absolute asymmetry (AA) and injuries. For clinical practice, the findings suggest that practitioners should incorporate assessments of both muscle asymmetry and body composition into routine screenings for physically active individuals. Identifying those with both high asymmetry and an elevated FMI can help target preventative interventions more effectively. Tailored strength training and conditioning programs aimed at reducing asymmetry and managing body composition may reduce the risk of injury, particularly in populations identified as high-risk. Full article

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

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12 pages, 14261 KiB

Open AccessEditor’s ChoiceArticle

The Bubble Dynamics near Double Cylinders within a Narrow Gap

by Junwei Shen, Jiaze Ying, Wenda Liu, Shurui Zhang, Yuning Zhang and Yuning Zhang

Symmetry 2024, 16(7), 841; https://doi.org/10.3390/sym16070841 - 4 Jul 2024

Cited by 2 | Viewed by 1189

Abstract

In the present paper, the dynamic behaviors of a bubble collapsing at the symmetrical positions of the double cylinders within a narrow gap are qualitatively and quantitatively investigated. Using a high-speed photographic technique, the morphological evolution of a bubble near the double cylinders [...] Read more.

In the present paper, the dynamic behaviors of a bubble collapsing at the symmetrical positions of the double cylinders within a narrow gap are qualitatively and quantitatively investigated. Using a high-speed photographic technique, the morphological evolution of a bubble near the double cylinders in a two-dimensional flow field is explored and qualitatively demonstrated. The mechanism by which the position of the bubble affects its dynamics is revealed. At the symmetrical position of the double cylinders, the bubble’s dimensionless abscissa shows significant impacts on the collapse behaviors, and its increase weakens the bubble deformation and strengthens the centroid movement. Full article

(This article belongs to the Section Physics)

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14 pages, 1329 KiB

Open AccessEditor’s ChoiceArticle

Crystallographic Quaternions

by Andrzej Katrusiak and Stiv Llenga

Symmetry 2024, 16(7), 818; https://doi.org/10.3390/sym16070818 - 29 Jun 2024

Cited by 1 | Viewed by 1665

Abstract

Symmetry transformations in crystallography are traditionally represented as equations and matrices, which can be suitable both for orthonormal and crystal reference systems. Quaternion representations, easily constructed for any orientations of symmetry operations, owing to the vector structure based on the direction of the [...] Read more.

Symmetry transformations in crystallography are traditionally represented as equations and matrices, which can be suitable both for orthonormal and crystal reference systems. Quaternion representations, easily constructed for any orientations of symmetry operations, owing to the vector structure based on the direction of the rotation axes or of the normal vectors to the mirror plane, are known to be advantageous for optimizing numerical computing. However, quaternions are described in Cartesian coordinates only. Here, we present the quaternion representations of crystallographic point-group symmetry operations for the crystallographic reference coordinates in triclinic, monoclinic, orthorhombic, tetragonal, cubic and trigonal (in rhombohedral setting) systems. For these systems, all symmetry operations have been listed and their applications exemplified. Owing to their concise form, quaternions can be used as the symbols of symmetry operations, which contain information about both the orientation and the rotation angle. The shortcomings of quaternions, including different actions for rotations and improper symmetry operations, as well as inadequate representation of the point symmetry in the hexagonal setting, have been discussed. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

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24 pages, 357 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Factory of Fractional Derivatives

by Manuel D. Ortigueira

Symmetry 2024, 16(7), 814; https://doi.org/10.3390/sym16070814 - 28 Jun 2024

Cited by 3 | Viewed by 1328

Abstract

This paper aims to demonstrate that, beyond the small world of Riemann–Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to different paths taken. The notions of [...] Read more.

This paper aims to demonstrate that, beyond the small world of Riemann–Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to different paths taken. The notions of time and scale sequences are introduced, and general associated basic derivatives, namely, right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to obtain both known and new fractional-order derivatives. Several fractional derivatives are considered, mainly Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn. Full article

(This article belongs to the Section Mathematics)

20 pages, 12317 KiB

Open AccessEditor’s ChoiceArticle

Symmetry Implications of a 60 GHz Inverted Microstrip Line Phase Shifter with Nematic Liquid Crystals in Diverse Packaging Boundary Conditions

by Jinfeng Li and Haorong Li

Symmetry 2024, 16(7), 798; https://doi.org/10.3390/sym16070798 - 25 Jun 2024

Cited by 4 | Viewed by 1780

Abstract

This work demystifies the role that packaging boundary conditions (both physically and electromagnetically) can play in a nematic liquid crystal (NLC)-based inverted microstrip (IMS) phase shifter device operating at the 60 GHz band (from 54 GHz to 66 GHz). Most notably, the air [...] Read more.

This work demystifies the role that packaging boundary conditions (both physically and electromagnetically) can play in a nematic liquid crystal (NLC)-based inverted microstrip (IMS) phase shifter device operating at the 60 GHz band (from 54 GHz to 66 GHz). Most notably, the air box radiating boundary and perfect electric conductor (PEC) enclosing boundary are numerically examined and compared statistically for convergence, scattering parameters, and phase-shift-to-insertion-loss ratio, i.e., figure-of-merit (FoM). Notably, the simulated phase tunability of the radiating air box boundary structure is 8.26°/cm higher than that of the encased (enclosed) PEC boundary structure at 60 GHz. However, the maximum insertion loss of the encased PEC structure is 0.47 dB smaller compared to that of the radiant air box boundary structure. This results in an FoM increase of 29.26°/dB at the enclosed PEC limit (relative to the less-than-optimal airbox radiation limit). Arguably, the NLC-filled IMS phase shifter device packaging with metals fully enclosed (in addition to the default ground plane) enhances the symmetry of the structure, both in the geometry and the materials system. In electromagnetic parlance, it contributes to a more homogenously distributed electric field and a more stable monomodal transmission environment with mitigated radiation and noise. Practically, the addition of the enclosure to the well-established NLC-IMS planar fabrication techniques provides a feasible manufacturing (assembling) solution to acquire the reasonably comparable performance advantage exhibited by non-planar structures, e.g., a fully enclosed strip line and rectangular coaxial line, which are technically demanding to manufacture with NLC. Full article

(This article belongs to the Special Issue Symmetric/Asymmetric Design in Microwave Communication Systems & Embedded Systems for Emerging Wireless Technologies)

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22 pages, 796 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Clustering Model for Three-Way Asymmetric Proximities: Unveiling Origins and Destinations

by Laura Bocci and Donatella Vicari

Symmetry 2024, 16(6), 752; https://doi.org/10.3390/sym16060752 - 16 Jun 2024

Viewed by 1458

Abstract

In many real-world situations, the available data consist of a set of several asymmetric pairwise proximity matrices that collect directed exchanges between pairs of objects measured or observed in a number of occasions (three-way data). To unveil patterns of exchange, a clustering model [...] Read more.

In many real-world situations, the available data consist of a set of several asymmetric pairwise proximity matrices that collect directed exchanges between pairs of objects measured or observed in a number of occasions (three-way data). To unveil patterns of exchange, a clustering model is proposed that accounts for the systematic differences across occasions. Specifically, the goal is to identify the groups of objects that are primarily origins or destinations of the directed exchanges, and, together, to measure the extent to which these clusters differ across occasions. The model is based on two clustering structures for the objects, which are linked one-to-one and common to all occasions. The first structure assumes a standard partition of the objects to fit the average amounts of the exchanges, while the second one fits the imbalances using an “incomplete” partition of the objects, allowing some to remain unassigned. In addition, to account for the heterogeneity of the occasions, the amounts and directions of exchange between clusters are modeled by occasion-specific weights. An Alternating Least-Squares algorithm is provided. Results from artificial data and a real application on international student mobility show the capability of the model to identify origin and/or destination clusters with common behavior across occasions. Full article

(This article belongs to the Section Mathematics)

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19 pages, 787 KiB

Open AccessEditor’s ChoiceArticle

Nonexpansiveness and Fractal Maps in Hilbert Spaces

by María A. Navascués

Symmetry 2024, 16(6), 738; https://doi.org/10.3390/sym16060738 - 13 Jun 2024

Cited by 3 | Viewed by 1230

Abstract

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, [...] Read more.

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from

φ

-contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of

α

-fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

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19 pages, 7444 KiB

Open AccessEditor’s ChoiceArticle

Intelligent Detection of Tunnel Leakage Based on Improved Mask R-CNN

by Wenkai Wang, Xiangyang Xu and Hao Yang

Symmetry 2024, 16(6), 709; https://doi.org/10.3390/sym16060709 - 7 Jun 2024

Cited by 6 | Viewed by 1490

Abstract

The instance segmentation model based on deep learning has addressed the challenges in intelligently detecting water leakage in shield tunneling. Due to the limited generalization ability of the baseline model, occurrences of missed detections, false detections, and repeated detections are encountered during the [...] Read more.

The instance segmentation model based on deep learning has addressed the challenges in intelligently detecting water leakage in shield tunneling. Due to the limited generalization ability of the baseline model, occurrences of missed detections, false detections, and repeated detections are encountered during the actual detection of tunnel water leakage. This paper adopts Mask R-CNN as the baseline model and introduces a mask cascade strategy to enhance the quality of positive samples. Additionally, the backbone network in the model is replaced with RegNetX to enlarge the model’s receptive field, and MDConv is introduced to enhance the model’s feature extraction capability in the edge receptive field region. Building upon these improvements, the proposed model is named Cascade-MRegNetX. The backbone network MRegNetX features a symmetrical block structure, which, when combined with deformable convolutions, greatly assists in extracting edge features from corresponding regions. During the dataset preprocessing stage, we augment the dataset through image rotation and classification, thereby improving both the quality and quantity of samples. Finally, by leveraging pre-trained models through transfer learning, we enhance the robustness of the target model. This model can effectively extract features from water leakage areas of different scales or deformations. Through instance segmentation experiments conducted on a dataset comprising 766 images of tunnel water leakage, the experimental results demonstrate that the improved model achieves higher precision in tunnel water leakage mask detection. Through these enhancements, the detection effectiveness, feature extraction capability, and generalization ability of the baseline model are improved. The improved Cascade-MRegNetX model achieves respective improvements of 7.7%, 2.8%, and 10.4% in terms of AP, AP_0.5, and AP_0.75 compared to the existing Cascade Mask R-CNN model. Full article

(This article belongs to the Special Issue Symmetry, Finite Element Analysis, and Intelligent Sensing and Monitoring: Applications in Engineering)

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27 pages, 9799 KiB

Open AccessEditor’s ChoiceArticle

On the Solvatochromism of Fluorescein Sodium

by Corina Cheptea, Alexandru Zara, Ecaterina Ambrosi, Ana Cezarina Morosanu, Maria Diaconu, Mihaela Miron, Dana Ortansa Dorohoi and Dan Gheorghe Dimitriu

Symmetry 2024, 16(6), 673; https://doi.org/10.3390/sym16060673 - 30 May 2024

Cited by 2 | Viewed by 1994

Abstract

Fluorescein sodium is a very important compound for a wide spectrum of applications, from which medical applications prevail. Despite this, there are very few studies in the literature related to the structure and fundamental properties of fluorescein sodium and its solutions, with most [...] Read more.

Fluorescein sodium is a very important compound for a wide spectrum of applications, from which medical applications prevail. Despite this, there are very few studies in the literature related to the structure and fundamental properties of fluorescein sodium and its solutions, with most of the studies dealing with fluorescein. The purpose of the present article is to determine some parameters of the fluorescein sodium molecule approaching the quantum-mechanical modeling and experimental solvatochromism in both binary and ternary solutions. For data analysis, several theoretical models were applied. The results highlight the intermolecular interactions involved in the spectral shift of the electronic absorption band of fluorescein sodium when dissolved in different solvents or binary solvents and allowed the estimation of the difference between the interaction energy in molecular pairs of the type of fluorescein sodium − solvent 1 and fluorescein sodium − solvent 2. By applying a variational method, the dipole moment in the first excited state of the fluorescein sodium molecule and the angle between the dipole moments in the ground and excited states, respectively, were estimated. These results are useful for a better understanding of the behavior of fluorescein sodium when dissolved in different solvents or combinations of solvents, to develop new practical applications. Full article

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

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88 pages, 28724 KiB

Open AccessEditor’s ChoiceArticle

PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process

by Ming Li

Symmetry 2024, 16(5), 635; https://doi.org/10.3390/sym16050635 - 20 May 2024

Cited by 5 | Viewed by 1304

Abstract

This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of [...] Read more.

This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research. Full article

(This article belongs to the Special Issue Symmetry in the Advanced Mechanics of Systems)

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17 pages, 5856 KiB

Open AccessEditor’s ChoiceArticle

Evolution of Hybrid Cellular Automata for Density Classification Problem

by Petre Anghelescu

Symmetry 2024, 16(5), 599; https://doi.org/10.3390/sym16050599 - 12 May 2024

Cited by 5 | Viewed by 2107

Abstract

This paper describes a solution for the image density classification problem (DCP) using an entirely distributed system with only local processing of information named cellular automata (CA). The proposed solution uses two cellular automata’s features, density conserving and translation of the information stored [...] Read more.

This paper describes a solution for the image density classification problem (DCP) using an entirely distributed system with only local processing of information named cellular automata (CA). The proposed solution uses two cellular automata’s features, density conserving and translation of the information stored in the cellular automata’s cells through the lattice, in order to obtain the solution for the density classification problem. The motivation for choosing a bio-inspired technique based on CA for solving the DCP is to investigate the principles of self-organizing decentralized computation and to assess the capabilities of CA to achieve such computation, which is applicable to many real-world decentralized problems that require a decision to be taken by majority voting, such as multi-agent holonic systems, collaborative robots, drones’ fleet, image analysis, traffic optimization, forming and then separating clusters with different values. The entire application is coded using the C# programming language, and the obtained results and comparisons between different cellular automata configurations are also discussed in this research. Full article

(This article belongs to the Section Mathematics)

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21 pages, 2025 KiB

Open AccessEditor’s ChoiceArticle

Global Models of Collapsing Scalar Field: Endstate

by Dario Corona and Roberto Giambò

Symmetry 2024, 16(5), 583; https://doi.org/10.3390/sym16050583 - 9 May 2024

Viewed by 1040

Abstract

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data [...] Read more.

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data in the dynamical system governed by Einstein’s equations, considering variations in parameters that influence naked singularity formation. We illustrate how these results apply to a family of scalar field models, concluding with a discussion on the concept of genericity in singularity studies. Full article

(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)

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23 pages, 15215 KiB

Open AccessEditor’s ChoiceArticle

Engineering Drawing Applied to the Study of the Design of a Two-Cylinder Entablature Steam Engine with Parallel Motion Crosshead

by José Ignacio Rojas-Sola and Juan Carlos Barranco-Molina

Symmetry 2024, 16(5), 578; https://doi.org/10.3390/sym16050578 - 8 May 2024

Cited by 4 | Viewed by 2236

Abstract

This article presents an investigation into a historical invention consisting of a stationary steam engine designed by Henry Muncaster: a two-cylinder entablature steam engine with parallel motion crosshead. The present interdisciplinary research, based on the theoretical and methodological concepts of engineering drawing and [...] Read more.

This article presents an investigation into a historical invention consisting of a stationary steam engine designed by Henry Muncaster: a two-cylinder entablature steam engine with parallel motion crosshead. The present interdisciplinary research, based on the theoretical and methodological concepts of engineering drawing and computer-aided design, has allowed us to understand the operation of this invention from the 3D CAD model of the invention obtained thanks to the original drawings published in the magazine Model Engineer in 1957 and reproduced in 2017, since there is no descriptive information related to the invention. However, there have been drawbacks in the geometric modeling process since the dimensions of some components did not exist and in other cases they were erroneous. For this reason, dimensional, geometric and movement constraints (degrees of freedom) had to be applied so that said 3D CAD model would be coherent and functional, and an interference analysis also had to be performed. Finally, the existing symmetry in the arrangement of the cylinders and the crosshead has been discovered, it being essential to guarantee that the forces and movements are uniform on both sides of the steam engine, and allowing the work to be carried out in a more balanced manner by reducing vibrations and improving the overall efficiency of the invention. Full article

(This article belongs to the Special Issue Graphic Representation and Symmetry Applied to the Technical Historical Heritage)

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29 pages, 11919 KiB

Open AccessEditor’s ChoiceArticle

Integration of Decentralized Graph-Based Multi-Agent Reinforcement Learning with Digital Twin for Traffic Signal Optimization

by Vijayalakshmi K. Kumarasamy, Abhilasha Jairam Saroj, Yu Liang, Dalei Wu, Michael P. Hunter, Angshuman Guin and Mina Sartipi

Symmetry 2024, 16(4), 448; https://doi.org/10.3390/sym16040448 - 7 Apr 2024

Cited by 10 | Viewed by 4161

Abstract

Machine learning (ML) methods, particularly Reinforcement Learning (RL), have gained widespread attention for optimizing traffic signal control in intelligent transportation systems. However, existing ML approaches often exhibit limitations in scalability and adaptability, particularly within large traffic networks. This paper introduces an innovative solution [...] Read more.

Machine learning (ML) methods, particularly Reinforcement Learning (RL), have gained widespread attention for optimizing traffic signal control in intelligent transportation systems. However, existing ML approaches often exhibit limitations in scalability and adaptability, particularly within large traffic networks. This paper introduces an innovative solution by integrating decentralized graph-based multi-agent reinforcement learning (DGMARL) with a Digital Twin to enhance traffic signal optimization, targeting the reduction of traffic congestion and network-wide fuel consumption associated with vehicle stops and stop delays. In this approach, DGMARL agents are employed to learn traffic state patterns and make informed decisions regarding traffic signal control. The integration with a Digital Twin module further facilitates this process by simulating and replicating the real-time asymmetric traffic behaviors of a complex traffic network. The evaluation of this proposed methodology utilized PTV-Vissim, a traffic simulation software, which also serves as the simulation engine for the Digital Twin. The study focused on the Martin Luther King (MLK) Smart Corridor in Chattanooga, Tennessee, USA, by considering symmetric and asymmetric road layouts and traffic conditions. Comparative analysis against an actuated signal control baseline approach revealed significant improvements. Experiment results demonstrate a remarkable 55.38% reduction in Eco_PI, a developed performance measure capturing the cumulative impact of stops and penalized stop delays on fuel consumption, over a 24 h scenario. In a PM-peak-hour scenario, the average reduction in Eco_PI reached 38.94%, indicating the substantial improvement achieved in optimizing traffic flow and reducing fuel consumption during high-demand periods. These findings underscore the effectiveness of the integrated DGMARL and Digital Twin approach in optimizing traffic signals, contributing to a more sustainable and efficient traffic management system. Full article

(This article belongs to the Special Issue Selected Papers from The 2023 International Conference on Digital Twin (Digital Twin 2023))

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20 pages, 1741 KiB

Open AccessEditor’s ChoiceArticle

The Relation between Infants’ Manual Lateralization and Their Performance of Object Manipulation and Tool Use

by Iryna Babik, Kylie Llamas and George F. Michel

Symmetry 2024, 16(4), 434; https://doi.org/10.3390/sym16040434 - 5 Apr 2024

Cited by 1 | Viewed by 3197

Abstract

Previous research yielded inconsistent findings regarding whether manual lateralization (e.g., a distinct and consistent hand preference) affects manual performance during infancy and early childhood. The aim of the current study was to determine whether manual lateralization, viewed as a marker of hemispheric lateralization, [...] Read more.

Previous research yielded inconsistent findings regarding whether manual lateralization (e.g., a distinct and consistent hand preference) affects manual performance during infancy and early childhood. The aim of the current study was to determine whether manual lateralization, viewed as a marker of hemispheric lateralization, is associated with infants’ performance in role-differentiated bimanual manipulation (RDBM) and tool use. This longitudinal study assessed 158 typically developing infants (91 males, aged 9.13 ± 0.15 months at baseline) monthly during the 9–14-month period. Developmental trajectories for manual lateralization in object acquisition were related to those for RDBM and tool use, even after accounting for potential sex differences. All statistical analyses were conducted using Hierarchical Linear Modeling software (version 6). Advanced RDBM performance was associated with a lower magnitude of manual lateralization and a higher tendency among infants to use both hands for object acquisition. No significant relation was found between the magnitude of manual lateralization and tool-use performance. Thus, the current results highlight the importance of hand coupling for enhanced RDBM performance. Moreover, across all ages, females outperformed males in sophisticated RDBMs, possibly due to their less pronounced manual lateralization and a greater inclination towards bimanual object acquisition—factors that appear to facilitate RDBM performance. Full article

(This article belongs to the Special Issue Neuroscience, Neurophysiology and Asymmetry—Volume II)

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16 pages, 877 KiB

Open AccessEditor’s ChoiceArticle

Explanatory Model for Elite Canoeists’ Performance Using a Functional Electromechanical Dynamometer Based on Detected Lateral Asymmetry

by Tania Álvarez-Yates, Mario Iglesias-Caamaño, Alba Cuba-Dorado, Virginia Serrano-Gómez, Victor Ferreira-Lima, Fábio Yuzo Nakamura and Oscar García-García

Symmetry 2024, 16(3), 347; https://doi.org/10.3390/sym16030347 - 14 Mar 2024

Cited by 6 | Viewed by 1852

Abstract

Canoe modality in flatwater canoeing has a clear asymmetrical nature. This study aimed (1) to determine the magnitude and direction of neuromuscular properties, range of motion (ROM) and lower-limb strength asymmetries in female and male canoeists; (2) to establish sex-individualized asymmetry thresholds for [...] Read more.

Canoe modality in flatwater canoeing has a clear asymmetrical nature. This study aimed (1) to determine the magnitude and direction of neuromuscular properties, range of motion (ROM) and lower-limb strength asymmetries in female and male canoeists; (2) to establish sex-individualized asymmetry thresholds for canoeists’ neuromuscular properties, ROM and lower-limb strength; and (3) to determine the relationship of canoeists’ neuromuscular properties, ROM and lower-limb strength asymmetries with a specific canoe–dynamometer performance test. Twenty-one international canoeists were assessed through tensiomyography (TMG), ROM, lower-limb explosive strength, and a specific canoe incremental dynamometric test. The magnitude of asymmetry assessed through TMG and ROM was not modulated either by sex or performance level (international medal vs. non-medal). Females showed greater asymmetry than males on muscle tone of the erector spinae towards non-stroke side (22.75% vs. 9.72%) and the tibialis anterior (30.97% vs. 16.29%), and Fmax in explosive leg press (2.41% vs. 0.63%) towards the stroke side. International medalists showed greater asymmetry in semitendinosus contraction time towards non-stroke side (20.51% vs. 9.43%) and reached Vmax earlier in explosive leg press towards stroke side leg (19.20% vs. 9.40%). A greater asymmetry in Fmax and in Vm, and a smaller asymmetry in Tvmax and in leg press showed a small predictive capacity for canoeists’ performance on a specific canoe incremental dynamometry test. Reporting reference data from world-class canoeists’ asymmetries can be of great importance for coaches to periodically control lateral asymmetry. Full article

(This article belongs to the Section Life Sciences)

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20 pages, 18983 KiB

Open AccessEditor’s ChoiceArticle

A Lagrangian Analysis of Tip Leakage Vortex in a Low-Speed Axial Compressor Rotor

by Jiexuan Hou, Yangwei Liu and Yumeng Tang

Symmetry 2024, 16(3), 344; https://doi.org/10.3390/sym16030344 - 13 Mar 2024

Cited by 5 | Viewed by 1626

Abstract

A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent [...] Read more.

A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent structures (LCSs). The computational method of the FTLE field in three-dimensional unsteady flow fields is discussed and then applied to the instantaneous flow fields at both the design and near-stall conditions. Results show that the accuracy of the particle trajectory and the density of the initial grid of the particle trajectory greatly affect the results of the FTLE field and, thus, the LCSs. Compared to the Eulerian Q method, which is calculated based on the symmetric and anti-symmetric components of the local velocity gradient tensor, the Lagrangian method has great potential in unraveling the mechanism of complex vortex structures. The LCSs show a transport barrier between the TLV and the secondary TLV, indicating two separate vortices. The aLCSs show the bubble-like and bar-like structure in the isosurfaces corresponding to the bubble and spiral breakdown patterns. Full article

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

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14 pages, 1755 KiB

Open AccessEditor’s ChoiceArticle

Partial Control and Beyond: Controlling Chaotic Transients with the Safety Function

by Rubén Capeáns and Miguel A. F. Sanjuan

Symmetry 2024, 16(3), 338; https://doi.org/10.3390/sym16030338 - 11 Mar 2024

Cited by 3 | Viewed by 1713

Abstract

Chaotic dynamical systems often exhibit transient chaos, where trajectories behave chaotically for a short amount of time before escaping to an external attractor. Sustaining transient chaotic dynamics under disturbances is challenging yet desirable for many applications. The partial control approach exploits the inherent [...] Read more.

Chaotic dynamical systems often exhibit transient chaos, where trajectories behave chaotically for a short amount of time before escaping to an external attractor. Sustaining transient chaotic dynamics under disturbances is challenging yet desirable for many applications. The partial control approach exploits the inherent symmetry and geometric structure of chaotic saddles, the topological object responsible of transient chaos, to enable surprising control with only small perturbations. Here, we review the latest findings in partial control techniques with the aim to sustain chaos or accelerate escapes by exploiting these intricate invariant sets. We introduce the fundamental concept of safe sets regions where orbits persist despite noise. This paper presents recent generalizations through safety functions and escape functions that automatically find the minimum control needed. Efficient numerical algorithms are presented and several examples of application are illustrated. Rather than eliminating chaos entirely, partial control techniques provide a framework to reliably control transient chaotic dynamics with minimal interventions. This approach has promising applications across diverse fields including physics, engineering, biology, and more. Full article

(This article belongs to the Special Issue Selected Papers on Nonlinear Dynamics)

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24 pages, 2695 KiB

Open AccessEditor’s ChoiceArticle

Implicit and Explicit Preferences for Golden Ratio

by Claudia Salera, Camilla Vallebella, Marco Iosa and Anna Pecchinenda

Symmetry 2024, 16(3), 333; https://doi.org/10.3390/sym16030333 - 9 Mar 2024

Cited by 4 | Viewed by 4056

Abstract

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in [...] Read more.

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for the golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking them to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimatum Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio. Full article

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

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32 pages, 448 KiB

Open AccessEditor’s ChoiceArticle

Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

by David Chester, Xerxes D. Arsiwalla, Louis H. Kauffman, Michel Planat and Klee Irwin

Symmetry 2024, 16(3), 316; https://doi.org/10.3390/sym16030316 - 6 Mar 2024

Cited by 6 | Viewed by 1764

Abstract

We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the [...] Read more.

We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras. Full article

(This article belongs to the Section Physics)

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15 pages, 3848 KiB

Open AccessEditor’s ChoiceArticle

Unsymmetrical and C₃-Symmetrical Partially Fluorinated Hexaarylbenzenes: Effect of Terminal Alkoxy Chain Length on Photophysical and Thermophysical Behavior

by Yizhou Wang, Shigeyuki Yamada, Motohiro Yasui and Tsutomu Konno

Symmetry 2024, 16(3), 314; https://doi.org/10.3390/sym16030314 - 6 Mar 2024

Viewed by 2006

Abstract

Solution-state photoluminescence (PL) is affected by the electronic state; however, solid-state PL varies widely depending on the aggregated state. Although the synthesis and photophysical properties of unsymmetrical and C₃-symmetrical hexaarylbenzenes (HABs) have been reported, the influence of their terminal alkoxy chains [...] Read more.

Solution-state photoluminescence (PL) is affected by the electronic state; however, solid-state PL varies widely depending on the aggregated state. Although the synthesis and photophysical properties of unsymmetrical and C₃-symmetrical hexaarylbenzenes (HABs) have been reported, the influence of their terminal alkoxy chains on their physical properties remains unclear. Therefore, we synthesized a series of unsymmetrical and C₃-symmetrical partially fluorinated HABs with different alkoxy chains and investigated the effects of alkoxy chain length on the thermophysical and photophysical properties. While investigating phase transition behavior, the ethoxy-substituted unsymmetrical derivative revealed a columnar liquid-crystalline phase, whereas the other derivatives only exhibited a phase transition between crystalline and isotropic phases. While evaluating PL behavior, both the unsymmetrical and C₃-symmetrical analogs exhibited relatively strong blue PL, independent of the alkoxy chain length. Through-space π-conjugation caused the PL spectra of C₃-symmetrical derivatives to redshift compared to those of unsymmetrical derivatives. Partially fluorinated HABs exhibited relatively strong fluorescence, even in the crystalline state, depending on the alkoxy chain length, owing to the formation of various aggregated structures. Crystalline fluorinated HABs exhibited photochromism, resulting in the appearance of long-wavelength PL bands when exposed to ultraviolet (UV) irradiation, making them promising candidates for PL sensing materials for UV detection. Full article

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

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21 pages, 895 KiB

Open AccessEditor’s ChoiceReview

Analysis of

B_{(s)}^{0}

→ μ⁺μ⁻ Decays at the Large Hadron Collider

by Kai-Feng Chen, Titus Mombächer and Umberto De Sanctis

Symmetry 2024, 16(2), 251; https://doi.org/10.3390/sym16020251 - 18 Feb 2024

Cited by 3 | Viewed by 1890

Abstract

This article reviews the most recent measurements of

B_{(s)}^{0}

→ μ⁺μ⁻ decay properties at the Large Hadron Collider (LHC) which are the most precise to date. The measurements of the branching fraction and effective lifetime of [...] Read more.

This article reviews the most recent measurements of

B_{(s)}^{0}

→ μ⁺μ⁻ decay properties at the Large Hadron Collider (LHC) which are the most precise to date. The measurements of the branching fraction and effective lifetime of the

B_{s}^{0}

→ μ⁺μ⁻ decay by the ATLAS, CMS, and LHCb collaborations, as well as the search for

B^{0}

→ μ⁺μ⁻ decays, are summarized with a focus on the experimental challenges. Furthermore, prospects are given for these measurements and new observables that become accessible with the foreseen amounts of data by the end of the LHC. Full article

(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)

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25 pages, 897 KiB

Open AccessEditor’s ChoiceArticle

Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation

by Mariusz Ciesielski

Symmetry 2024, 16(2), 252; https://doi.org/10.3390/sym16020252 - 18 Feb 2024

Cited by 4 | Viewed by 1908

Abstract

Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, [...] Read more.

Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, but the linear and cubic splines are also considered to compare the quality of the developed method and numerical calculations. The estimation of errors for the derived approximation algorithms is presented. Examples of the numerical evaluation of the fractional integrals and derivatives are executed using 128-bit floating-point numbers and arithmetic routines. For each derived algorithm, the experimental orders of convergence are calculated. Also, an illustrative computational example showing the action of the considered fractional operators on the symmetric function in the interval is presented. Full article

(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)

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15 pages, 2129 KiB

Open AccessEditor’s ChoiceArticle

g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

by Takeshi Emura, Koutarou Matsumoto, Ryuji Uozumi and Hirofumi Michimae

Symmetry 2024, 16(2), 223; https://doi.org/10.3390/sym16020223 - 12 Feb 2024

Cited by 3 | Viewed by 3216

Abstract

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to [...] Read more.

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data. Full article

(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)

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33 pages, 1158 KiB

Open AccessEditor’s ChoiceReview

Direct Detection of Dark Matter: A Critical Review

by Marcin Misiaszek and Nicola Rossi

Symmetry 2024, 16(2), 201; https://doi.org/10.3390/sym16020201 - 8 Feb 2024

Cited by 18 | Viewed by 9714

Abstract

The nature of dark matter in the Universe is one of the hardest unsolved problems in modern physics. Indeed, on one hand, the overwhelming indirect evidence from astrophysics seems to leave no doubt about its existence; on the other hand, direct search experiments, [...] Read more.

The nature of dark matter in the Universe is one of the hardest unsolved problems in modern physics. Indeed, on one hand, the overwhelming indirect evidence from astrophysics seems to leave no doubt about its existence; on the other hand, direct search experiments, especially those conducted with low-background detectors in underground laboratories all over the world, seem to deliver only null results with a few debated exceptions. Furthermore, the lack of predicted candidates on the LHC energy scale has made this dichotomy even more puzzling. We will recall the most important phases of this novel branch of experimental astro-particle physics, analyzing the interconnections among the main projects involved in this challenging quest, and we will draw conclusions slightly different from how the problem is commonly understood. Full article

(This article belongs to the Section Physics)

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20 pages, 974 KiB

Open AccessEditor’s ChoiceArticle

Exploring Footedness, Throwing Arm, and Handedness as Predictors of Eyedness Using Cluster Analysis and Machine Learning: Implications for the Origins of Behavioural Asymmetries

by Paul Rodway, Curtis Rodway and Astrid Schepman

Symmetry 2024, 16(2), 177; https://doi.org/10.3390/sym16020177 - 2 Feb 2024

Cited by 2 | Viewed by 2518

Abstract

Behavioural asymmetries displayed by individuals, such as hand preference and foot preference, tend to be lateralized in the same direction (left or right). This may be because their co-ordination conveys functional benefits for a variety of motor behaviours. To explore the potential functional [...] Read more.

Behavioural asymmetries displayed by individuals, such as hand preference and foot preference, tend to be lateralized in the same direction (left or right). This may be because their co-ordination conveys functional benefits for a variety of motor behaviours. To explore the potential functional relationship between key motor asymmetries, we examined whether footedness, handedness, or throwing arm was the strongest predictor of eyedness. Behavioural asymmetries were measured by self-report in 578 left-handed and 612 right-handed individuals. Cluster analysis of the asymmetries revealed four handedness groups: consistent right-handers, left-eyed right-handers, consistent left-handers, and inconsistent left-handers (who were left-handed but right-lateralized for footedness, throwing and eyedness). Supervised machine learning models showed the importance of footedness, in addition to handedness, in determining eyedness. In right-handers, handedness was the best predictor of eyedness, followed closely by footedness, and for left-handers it was footedness. Overall, predictors were more informative in predicting eyedness for individuals with consistent lateral preferences. Implications of the findings in relation to the origins and genetics of handedness and sports training are discussed. Findings are related to fighting theories of handedness and to bipedalism, which evolved after manual dexterity, and which may have led to some humans being right-lateralized for ballistic movements and left-lateralized for hand dexterity. Full article

(This article belongs to the Section Life Sciences)

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14 pages, 916 KiB

Open AccessEditor’s ChoiceArticle

A Forecast of the Sensitivity of the DALI Experiment to Galactic Axion Dark Matter

by Juan F. Hernández-Cabrera, Javier De Miguel, Enrique Joven Álvarez, E. Hernández-Suárez, J. Alberto Rubiño-Martín and Chiko Otani

Symmetry 2024, 16(2), 163; https://doi.org/10.3390/sym16020163 - 30 Jan 2024

Cited by 5 | Viewed by 1455

Abstract

The axion is a long-postulated boson that can simultaneously solve two fundamental problems of modern physics: the charge–parity symmetry problem in the strong interaction and the enigma of dark matter. In this work, we estimate, by means of Monte Carlo simulations, the sensitivity [...] Read more.

The axion is a long-postulated boson that can simultaneously solve two fundamental problems of modern physics: the charge–parity symmetry problem in the strong interaction and the enigma of dark matter. In this work, we estimate, by means of Monte Carlo simulations, the sensitivity of the Dark-photons & Axion-Like particles Interferometer (DALI), a new-generation Fabry–Pérot haloscope proposed to probe axion dark matter in the 25–250

μ

eV band. Full article

(This article belongs to the Special Issue The Dark Universe: The Harbinger of a Major Discovery)

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16 pages, 1031 KiB

Open AccessEditor’s ChoiceArticle

Symmetry Breaking and Dynamic Transition in the Negative Mass Term Klein–Gordon Equations

by Ferenc Márkus and Katalin Gambár

Symmetry 2024, 16(2), 144; https://doi.org/10.3390/sym16020144 - 26 Jan 2024

Cited by 3 | Viewed by 1433

Abstract

Through the discussion of three physical processes, we show that the Klein–Gordon equations with a negative mass term describe special dynamics. In the case of two classical disciplines—mechanics and thermodynamics—the Lagrangian-based mathematical description is the same, even though the nature of the investigated [...] Read more.

Through the discussion of three physical processes, we show that the Klein–Gordon equations with a negative mass term describe special dynamics. In the case of two classical disciplines—mechanics and thermodynamics—the Lagrangian-based mathematical description is the same, even though the nature of the investigated processes seems completely different. The unique feature of this type of equation is that it contains wave propagation and dissipative behavior in one framework. The dissipative behavior appears through a repulsive potential. The transition between the two types of dynamics can be specified precisely, and its physical meaning is clear. The success of the two descriptions inspires extension to the case of electrodynamics. We reverse the suggestion here. We create a Klein–Gordon equation with a negative mass term, but first, we modify Maxwell’s equations. The repulsive interaction that appears here results in a charge spike. However, the Coulomb interaction limits this. The charge separation is also associated with the high-speed movement of the charged particle localized in a small space domain. As a result, we arrive at a picture of a fast vibrating phenomenon with an electromagnetism-related Klein–Gordon equation with a negative mass term. The calculated maximal frequency value

ω = 1.74 \times 10^{21}

1/s. Full article

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

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31 pages, 2565 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Revisiting de Broglie’s Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework

by David Darrow and John W. M. Bush

Symmetry 2024, 16(2), 149; https://doi.org/10.3390/sym16020149 - 26 Jan 2024

Cited by 7 | Viewed by 3286

Abstract

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with [...] Read more.

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation

p = ℏ k

at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle. Full article

(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)

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13 pages, 3286 KiB

Open AccessEditor’s ChoiceArticle

Temperature-Dependent Phase Variations in Van Der Waals CdPS₃ Revealed by Raman Spectroscopy

by Sharidya Rahman, Hieu Ngyuen, Daniel Macdonald and Yuerui Lu

Symmetry 2024, 16(2), 140; https://doi.org/10.3390/sym16020140 - 24 Jan 2024

Cited by 1 | Viewed by 2096

Abstract

In addition to graphene, the transition metal dichalcogenides, black phosphorus and multiple other layered materials have undergone immense investigations. Among them, metal thiophosphates (MPS_x) have emerged as a promising material for various applications. While several layered metal thiophosphates with general-formula MPS [...] Read more.

In addition to graphene, the transition metal dichalcogenides, black phosphorus and multiple other layered materials have undergone immense investigations. Among them, metal thiophosphates (MPS_x) have emerged as a promising material for various applications. While several layered metal thiophosphates with general-formula MPS_x have been scrutinized extensively, van der Waals (vdW) CdPS₃ has been overlooked in the literature. Here we report on the extensive Raman scattering of layered CdPS₃, showing structural phase transition at a low temperature. The emergence of multiple new peaks at low frequency and a significant shift in peak position with temperature implied a probable change in crystal symmetry from trigonal D_3d to triclinic C_i below the phase transition temperature, T_K~180 K. In addition, we also showed a p-type performance of CdPS₃ FET fabricated using Au electrodes. This work adds CdPS₃ to the list of potential layered materials for energy application. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in 2D Materials)

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13 pages, 2726 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Revisiting the Absolute Configuration of Peyssonnoside A Using Vibrational Circular Dichroism Spectroscopy

by Andrew R. Puente, Bhuwan Khatri Chhetri, Julia Kubanek and Prasad L. Polavarapu

Symmetry 2024, 16(2), 133; https://doi.org/10.3390/sym16020133 - 23 Jan 2024

Viewed by 1990

Abstract

Peyssonnoside A is an unusual natural product consisting of a diterpene unit and a sulfonated monosaccharide. The experimental and theoretical comparison of Optical Rotatory Dispersion (ORD) and quantitative Nuclear Magnetic Resonance (NMR) data provided strong evidence for the stereochemistry of the diterpene unit. [...] Read more.

Peyssonnoside A is an unusual natural product consisting of a diterpene unit and a sulfonated monosaccharide. The experimental and theoretical comparison of Optical Rotatory Dispersion (ORD) and quantitative Nuclear Magnetic Resonance (NMR) data provided strong evidence for the stereochemistry of the diterpene unit. However, predicted Vibrational Circular Dichroism (VCD) spectra of Peyssonnoside A at the B3LYP/6-311++G(2d,2p) level showed poor correlation to the corresponding experimental spectra, preventing independent absolute configuration (AC) determination from VCD analysis. New calculations using the B3PW91 functional and the 6-311G(3df,2pd) basis set suggest that we can now independently and confidently assign the AC of Peyssonnoside A through VCD analyses. The use of f-polarization functions is responsible for the current successful assignment, compared to previously failed VCD analysis. This study highlights two important points: (a) the importance of using multiple levels of theories for satisfactorily reproducing the experimental spectra and (b) for quantitative comparisons using similarity indices, it is important to consider not only the VCD spectra but also the corresponding absorption spectra. Full article

(This article belongs to the Special Issue From Nanoclusters to Nanoparticles: Symmetry, Theory, Experiments, and Applications)

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15 pages, 13929 KiB

Open AccessEditor’s ChoiceArticle

Effects of KoBo-Processing and Subsequent Annealing Treatment on Grain Boundary Network and Texture Development in Laser Powder Bed Fusion (LPBF) AlSi10Mg Alloy

by Przemysław Snopiński

Symmetry 2024, 16(1), 122; https://doi.org/10.3390/sym16010122 - 19 Jan 2024

Cited by 6 | Viewed by 1957

Abstract

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties [...] Read more.

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties that differ from bulk crystalline domains. Their effects on material properties, including mechanical strength, corrosion resistance, and electrical conductivity, make grain boundaries a focus of intense scientific investigation. In this study, the microstructural transformation of an AlSi10Mg alloy subjected to KoBo extrusion and subsequent annealing is investigated. A notable discovery is the effectiveness of a strain-annealing method for grain boundary engineering (GBE) of the LPBF AlSi10Mg alloy. In particular, this study shows a significant increase in the population of coincidence site lattice boundaries (CSL), which embody the symmetry of the crystal lattice structure. These boundaries, which are characterised by a high degree of symmetry, contribute to their special properties compared to random grain boundaries. The experimental results emphasise the crucial role of strain-induced boundary migration (SIBM) in the development of a brass texture in the microstructure of the alloy after annealing. In addition, the presented results demonstrate the feasibility of applying GBE to materials with high stacking fault energy (SFE), which opens up new possibilities for optimizing their properties. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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