Symmetry

13 pages, 1499 KB

Open AccessEditor’s ChoiceArticle

Fungal Biocatalysis in Stereoselective Oxidation of 2-Phenylethanol

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

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

Viewed by 851

Abstract

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

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

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

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63 pages, 14545 KB

Open AccessEditor’s ChoiceReview

Sum-Frequency Generation Spectroscopy at Aqueous Electrochemical Interfaces

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

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

Cited by 1 | Viewed by 2960

Abstract

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

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

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

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80 pages, 858 KB

Open AccessEditor’s ChoiceArticle

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

by Salim Bouzebda

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

Cited by 5 | Viewed by 1524

Abstract

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

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

r^{(m)} (φ, t)

, defined as

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

for

t \in X^{m}

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

(This article belongs to the Section Mathematics)

15 pages, 3078 KB

Open AccessEditor’s ChoiceArticle

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

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

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

Viewed by 867

Abstract

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

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

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

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27 pages, 5704 KB

Open AccessEditor’s ChoiceReview

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

by Takashiro Akitsu, Daisuke Nakane and Barbara Miroslaw

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

Cited by 3 | Viewed by 2158

Abstract

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

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

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

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12 pages, 659 KB

Open AccessEditor’s ChoiceArticle

Evaluating Time Irreversibility Tests Using Geometric Brownian Motions with Stochastic Resetting

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

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

Cited by 2 | Viewed by 854

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 KB

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

Cited by 1 | Viewed by 1501

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 KB

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 3405

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, 1413 KB

Open AccessEditor’s ChoiceArticle

In Silico Comparison of Quantum and Bioactivity Parameters of a Series of Natural Diphenyl Acetone Analogues, and In Vitro Caco-2 Studies on Three Main Chalcone Derivatives

by Amalia Stefaniu, Georgeta Neagu, Adrian Albulescu, Nicoleta Radu and Lucia Camelia Pirvu

Symmetry 2024, 16(10), 1383; https://doi.org/10.3390/sym16101383 - 17 Oct 2024

Cited by 2 | Viewed by 2114

Abstract

This paper aims to compare the in silico and in vitro properties of a series of diphenyl acetone derivatives, specifically six chalcone analogues, namely benzophenone, chalcone, phloretin, phloridzin, nothofagin and 4-methylchalcone. The in silico studies were conducted using the Spartan’14 mechanistic program to [...] Read more.

This paper aims to compare the in silico and in vitro properties of a series of diphenyl acetone derivatives, specifically six chalcone analogues, namely benzophenone, chalcone, phloretin, phloridzin, nothofagin and 4-methylchalcone. The in silico studies were conducted using the Spartan’14 mechanistic program to perform a comparative analysis of the molecular, quantum and bioactivity parameters of the six analogues under study. The in vitro MTS studies were designed to investigate the cytotoxic and anti-proliferative effect of the reference substances (r.s.) of three main chalcone derivatives in nature, namely phloretin, phloridzin and 4-methylchalcone, on the Caco-2 cell line. Overall, the in silico results foremost suggested the potential of phloretin to traverse the blood–brain barrier, and the abilities of phloridzin and nothofagin to act as broad cell enzyme inhibitors; the in vitro results demonstrated that phloretin and 4-methylchalcone have the potential to induce both cytotoxic and anti-proliferative effects, depending on their concentration level: the antiproliferative effects were noticed in the interval from 1 to 50 µg of r.s. per sample, while the cytotoxic effects were noticed from 1 to 50 µg of r.s. per sample in the case of 4-methychalcone, and at 50 µg of r.s. per sample in the case of phloretin. Phloridzin did not affect the viability of the Caco-2 line. Full article

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

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19 pages, 22914 KB

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 3 | Viewed by 7345

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 KB

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 6006

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 KB

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 4295

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 KB

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 3 | Viewed by 1263

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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24 pages, 3763 KB

Open AccessEditor’s ChoiceArticle

Intelligent Fuzzy Traffic Signal Control System for Complex Intersections Using Fuzzy Rule Base Reduction

by Tamrat D. Chala and László T. Kóczy

Symmetry 2024, 16(9), 1177; https://doi.org/10.3390/sym16091177 - 9 Sep 2024

Cited by 5 | Viewed by 2868

Abstract

In this study, the concept of symmetry is employed to implement an intelligent fuzzy traffic signal control system for complex intersections. This approach suggests that the implementation of reduced fuzzy rules through the reduction method, without compromising the performance of the original fuzzy [...] Read more.

In this study, the concept of symmetry is employed to implement an intelligent fuzzy traffic signal control system for complex intersections. This approach suggests that the implementation of reduced fuzzy rules through the reduction method, without compromising the performance of the original fuzzy rule base, constitutes a symmetrical approach. In recent decades, urban and city traffic congestion has become a significant issue because of the time lost as a result of heavy traffic, which negatively affects economic productivity and efficiency and leads to energy loss, and also because of the heavy environmental pollution effect. In addition, traffic congestion prevents an immediate response by the ambulance, police, and fire brigades to urgent events. To mitigate these problems, a three-stage intelligent and flexible fuzzy traffic control system for complex intersections, using a novel hybrid reduction approach was proposed. The three-stage fuzzy traffic control system performs four primary functions. The first stage prioritizes emergency car(s) and identifies the degree of urgency of the traffic conditions in the red-light phase. The second stage guarantees a fair distribution of green-light durations even for periods of extremely unbalanced traffic with long vehicle queues in certain directions and, especially, when heavy traffic is loaded for an extended period in one direction and the short vehicle queues in the conflicting directions require passing in a reasonable time. The third stage adjusts the green-light time to the traffic conditions, to the appearance of one or more emergency car(s), and to the overall waiting times of the other vehicles by using a fuzzy inference engine. The original complete fuzzy rule base set up by listing all possible input combinations was reduced using a novel hybrid reduction algorithm for fuzzy rule bases, which resulted in a significant reduction of the original base, namely, by 72.1%. The proposed novel approach, including the model and the hybrid reduction algorithm, were implemented and simulated using Python 3.9 and SUMO (version 1.14.1). Subsequently, the obtained fuzzy rule system was compared in terms of running time and efficiency with a traffic control system using the original fuzzy rules. The results showed that the reduced fuzzy rule base had better results in terms of the average waiting time, calculated fuel consumption, and CO₂ emission. Furthermore, the fuzzy traffic control system with reduced fuzzy rules performed better as it required less execution time and thus lower computational costs. Summarizing the above results, it may be stated that this new approach to intersection traffic light control is a practical solution for managing complex traffic conditions at lower computational costs. Full article

(This article belongs to the Special Issue Symmetry in Optimization and Control with Real World Applications II)

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15 pages, 301 KB

Open AccessEditor’s ChoiceArticle

Generalized Choi–Davis–Jensen’s Operator Inequalities and Their Applications

by Shih Yu Chang and Yimin Wei

Symmetry 2024, 16(9), 1176; https://doi.org/10.3390/sym16091176 - 9 Sep 2024

Cited by 1 | Viewed by 1413

Abstract

The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize [...] Read more.

The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics. Full article

(This article belongs to the Special Issue Research on Structured Matrices and Applications)

17 pages, 17490 KB

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 3 | Viewed by 1084

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 KB

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 1907

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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17 pages, 281 KB

Open AccessEditor’s ChoiceArticle

Three-Dimensional Lorentz-Invariant Velocities

by James M. Hill

Symmetry 2024, 16(9), 1133; https://doi.org/10.3390/sym16091133 - 2 Sep 2024

Cited by 2 | Viewed by 1356

Abstract

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are [...] Read more.

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are automatically invariant under the most general fully three-dimensional Lorentz transformation. For general three-dimensional motion, using rectangular Cartesian coordinates

(x, y, z)

, we determine the first-order partial differential equations for the three velocity components

u (x, y, z, t)

,

v (x, y, z, t)

and

w (x, y, z, t)

in the

x -

,

y -

and

z -

directions respectively. These partial differential equations and the associated partial differential relations connecting energy and momentum are fully compatible with the Lorentz-invariant energy–momentum relations and appear not to have been given previously in the literature. We determine the spatial and temporal dependence of the functional forms for those three-dimensional velocity fields that are automatically invariant under three-dimensional Lorentz transformations. An interesting special case gives rise to families of particle paths for which the magnitude of the velocity is the speed of light. This is indicative of the abundant possibilities existing in the “fast lane”. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Partial Differential Equations)

16 pages, 9639 KB

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 1402

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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41 pages, 10279 KB

Open AccessEditor’s ChoiceReview

Block Copolymer-Based Symmetric Membranes for Direct Methanol Fuel Cells

by Maria Giovanna Buonomenna and Joonwon Bae

Symmetry 2024, 16(8), 1079; https://doi.org/10.3390/sym16081079 - 20 Aug 2024

Cited by 1 | Viewed by 2475

Abstract

Like batteries, fuel cells provide an inherently clean source of energy with no adverse environmental impact during operation. The utilization of methanol as a fuel is advantageous: it has an energy density of about 6 kWh/kg, which is, much higher than that of [...] Read more.

Like batteries, fuel cells provide an inherently clean source of energy with no adverse environmental impact during operation. The utilization of methanol as a fuel is advantageous: it has an energy density of about 6 kWh/kg, which is, much higher than that of other commercialized batteries. This review is focused on the core of a DMFC, i.e., the symmetric membrane, in particular on the block copolymers used for its preparation as an alternative to well-known Nafion. The synthesis of block copolymer ionomers based on different building block types, with special emphasis on the critical issue of methanol permeability and proton/methanol selectivity, as well as the effect of block length and crosslinking are described and discussed. Full article

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

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10 pages, 2222 KB

Open AccessEditor’s ChoiceArticle

A Robust Zn-Hydroxamate Metal–Organic Framework Constructed from an Unsymmetrical Ligand for Iodine Capture

by Ting Song, Yinning Zhu, Zhehao Li, Zhewei Mei, Zhen-Wu Shao and Chong Liu

Symmetry 2024, 16(8), 1049; https://doi.org/10.3390/sym16081049 - 15 Aug 2024

Cited by 5 | Viewed by 1572

Abstract

To qualify as competent sorbents for airborne contaminants such as iodine vapor, permanent porosity and chemical stability are key criteria for the selection of candidate metal-organic frameworks (MOFs). To ensure these characteristics, in the present study, an unsymmetrical bifunctional ligand incorporating both carboxylic [...] Read more.

To qualify as competent sorbents for airborne contaminants such as iodine vapor, permanent porosity and chemical stability are key criteria for the selection of candidate metal-organic frameworks (MOFs). To ensure these characteristics, in the present study, an unsymmetrical bifunctional ligand incorporating both carboxylic acid and hydroxamic acid groups was employed for MOF [Zn(CBHA)](DMF) [SUM-13; CPHA = 4-carboxyphenylhydroxamate, DMF = N,N-dimethylformamide] design and synthesis. Though coupled with Zn²⁺, which does not typically yield kinetically robust MOFs with hard acids, the SUM-13 featuring differentiated coordination modes of chelating, bridging and monodentate bonding exhibited exceptional chemical stability and permanent porosity, with a Brunauer–Emmett–Teller (BET) surface area of 296.9 m²/g and a total pore volume of 0.1196 cm³/g. Additionally, with porosity and open metal sites at the five-coordinate Zn²⁺ centers, SUM-13 was demonstrated to be an eligible iodine adsorbent, reaching a maximum uptake of 796 mg/g. These findings underscore the validity and potential of the design strategy in constructing stable metal–organic frameworks. Full article

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

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18 pages, 1023 KB

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 2 | Viewed by 2138

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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21 pages, 305 KB

Open AccessEditor’s ChoiceArticle

Degree of L_p Approximation Using Activated Singular Integrals

by George A. Anastassiou

Symmetry 2024, 16(8), 1022; https://doi.org/10.3390/sym16081022 - 10 Aug 2024

Cited by 1 | Viewed by 850

Abstract

In this article we present the

L_{p}

,

p \geq 1

, approximation properties of activated singular integral operators over the real line. We establish their approximation to the unit operator with rates. The kernels here come from neural network activation functions [...] Read more.

In this article we present the

L_{p}

,

p \geq 1

, approximation properties of activated singular integral operators over the real line. We establish their approximation to the unit operator with rates. The kernels here come from neural network activation functions and we employ the related density functions. The derived inequalities use the high order

L_{p}

modulus of smoothness. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)

15 pages, 452 KB

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 891

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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14 pages, 304 KB

Open AccessEditor’s ChoiceArticle

Regularization and Propagation in a Hamilton–Jacobi–Bellman-Type Equation in Infinite-Dimensional Hilbert Space

by Carlo Bianca and Christian Dogbe

Symmetry 2024, 16(8), 1017; https://doi.org/10.3390/sym16081017 - 9 Aug 2024

Cited by 1 | Viewed by 1268

Abstract

This paper is devoted to new propagation and regularity results for a class of first-order Hamilton–Jacobi–Bellman-type problems in a separable infinite-dimensional Hilbert space. Specifically, the related Cauchy problem is investigated by employing the Faedo–Galerkin approximation method. Under some structural assumptions, the main result [...] Read more.

This paper is devoted to new propagation and regularity results for a class of first-order Hamilton–Jacobi–Bellman-type problems in a separable infinite-dimensional Hilbert space. Specifically, the related Cauchy problem is investigated by employing the Faedo–Galerkin approximation method. Under some structural assumptions, the main result is obtained by using the probabilistic representation formula of the solution in order to define the weak continuity assumptions, by assuming the existence of a symmetric positive definite Hilbert–Schmidt operator and by employing modulus continuity arguments. Full article

(This article belongs to the Section Mathematics)

36 pages, 13944 KB

Open AccessEditor’s ChoiceArticle

Enumeration of n-Dimensional Hypercubes, Icosahedra, Rubik’s Cube Dice, Colorings, Chirality, and Encryptions Based on Their Symmetries

by Krishnan Balasubramanian

Symmetry 2024, 16(8), 1020; https://doi.org/10.3390/sym16081020 - 9 Aug 2024

Cited by 4 | Viewed by 3138

Abstract

The whimsical Las Vegas/Monte Carlo cubic dice are generalized to construct the combinatorial problem of enumerating all n-dimensional hypercube dice and dice of other shapes that exhibit cubic, icosahedral, and higher symmetries. By utilizing powerful generating function techniques for various irreducible representations, we [...] Read more.

The whimsical Las Vegas/Monte Carlo cubic dice are generalized to construct the combinatorial problem of enumerating all n-dimensional hypercube dice and dice of other shapes that exhibit cubic, icosahedral, and higher symmetries. By utilizing powerful generating function techniques for various irreducible representations, we derive the combinatorial enumerations of all possible dice in n-dimensional space with hyperoctahedral symmetries. Likewise, a number of shapes that exhibit icosahedral symmetries such as a truncated dodecahedron and a truncated icosahedron are considered for the combinatorial problem of dice enumerations with the corresponding shapes. We consider several dice with cubic symmetries such as the truncated octahedron, dodecahedron, and Rubik’s cube shapes. It is shown that all enumerated dice are chiral, and we provide the counts of chiral pairs of dice in the n-dimensional space. During the combinatorial enumeration, it was discovered that two different shapes of dice exist with the same chiral pair count culminating to the novel concept of isochiral polyhedra. The combinatorial problem of dice enumeration is generalized to multi-coloring partitions. Applications to chirality in n-dimension, molecular clusters, zeolites, mesoporous materials, cryptography, and biology are also pointed out. Applications to the nonlinear n-dimensional hypercube and other dicey encryptions are exemplified with romantic, clandestine messages: “I love U” and “V Elope at 2”. Full article

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

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29 pages, 429 KB

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 7248

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 KB

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 1276

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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14 pages, 3174 KB

Open AccessEditor’s ChoiceArticle

Non-Selective Reduction of P-Stereogenic Phosphinoylacetic Acid Esters and 3-Phosphorylated Coumarins to Phosphino-Boranes: Discovery of Unexpected 2,3-Dihydrobenzofuran Derivative

by Kamil Dziuba, Natalia Walczak and Katarzyna Szwaczko

Symmetry 2024, 16(8), 976; https://doi.org/10.3390/sym16080976 - 1 Aug 2024

Viewed by 1643

Abstract

This paper presents the efficient reduction of phosphinoylacetic acid esters and 3-phosphorylated coumarin to their corresponding phosphino-boranes using BH₃-THF complexes. Optimized conditions for the reduction of phosphinoylacetic acid esters resulted in high yields of phosphinoborates. The straightforwardness and efficiency of the process were [...] Read more.

This paper presents the efficient reduction of phosphinoylacetic acid esters and 3-phosphorylated coumarin to their corresponding phosphino-boranes using BH₃-THF complexes. Optimized conditions for the reduction of phosphinoylacetic acid esters resulted in high yields of phosphinoborates. The straightforwardness and efficiency of the process were demonstrated for diarylphosphinoylacetic acid ethyl esters, as well as P-stereogenic L-menthyl esters, where the simultaneous reduction of the strong P=O bond and the ester group was exclusively observed for the first time. The study also highlighted the significant influence of steric effects with bulky substituents, such as the menthol group or the 1-naphthyl substituent at phosphorus, on the reduction efficiency. However, the reduction of 3-phosphorylated coumarins produced an unexpected reaction product: a 2,3-dihydrobenzofuran derivative. The present findings provide valuable information on the direct reduction of phosphine oxides and related compounds, demonstrating the versatility of borane complexes in synthetic chemistry, and provide new perspectives for studying the problems of symmetry and asymmetry in the chemistry of such transformations. Full article

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

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23 pages, 5188 KB

Open AccessEditor’s ChoiceArticle

Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests

by Andrea Coccaro, Marco Letizia, Humberto Reyes-González and Riccardo Torre

Symmetry 2024, 16(8), 942; https://doi.org/10.3390/sym16080942 - 23 Jul 2024

Cited by 9 | Viewed by 2420

Abstract

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth comparison of coupling and autoregressive flows, both based [...] Read more.

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth comparison of coupling and autoregressive flows, both based on symmetric (affine) and non-symmetric (rational quadratic spline) bijectors, considering four different architectures: real-valued non-Volume preserving (RealNVP), masked autoregressive flow (MAF), coupling rational quadratic spline (C-RQS), and autoregressive rational quadratic spline (A-RQS). We focus on a set of multimodal target distributions of increasing dimensionality ranging from 4 to 400. The performances were compared by means of different test statistics for two-sample tests, built from known distance measures: the sliced Wasserstein distance, the dimension-averaged one-dimensional Kolmogorov–Smirnov test, and the Frobenius norm of the difference between correlation matrices. Furthermore, we included estimations of the variance of both the metrics and the trained models. Our results indicate that the A-RQS algorithm stands out both in terms of accuracy and training speed. Nonetheless, all the algorithms are generally able, without too much fine-tuning, to learn complicated distributions with limited training data and in a reasonable time of the order of hours on a Tesla A40 GPU. The only exception is the C-RQS, which takes significantly longer to train, does not always provide good accuracy, and becomes unstable for large dimensionalities. All algorithms were implemented using TensorFlow2 and TensorFlow Probability and have been made available on GitHub. Full article

(This article belongs to the Special Issue Machine Learning and Data Analysis II)

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21 pages, 712 KB

Open AccessEditor’s ChoiceArticle

OPT-FRAC-CHN: Optimal Fractional Continuous Hopfield Network

by Karim El Moutaouakil, Zakaria Bouhanch, Abdellah Ahourag, Ahmed Aberqi and Touria Karite

Symmetry 2024, 16(7), 921; https://doi.org/10.3390/sym16070921 - 18 Jul 2024

Cited by 4 | Viewed by 1359

Abstract

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution [...] Read more.

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. Full article

(This article belongs to the Special Issue Challenges and New Trends in Optimization and Control Theory in the Era of AI: Analysis, Modelling, and Symmetrical Mathematical Methods)

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16 pages, 532 KB

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 1579

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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15 pages, 8166 KB

Open AccessEditor’s ChoiceArticle

Synthesis, X-ray Diffraction and Computational Druglikeness Evaluation of New Pyrrolo[1,2-a][1,10]Phenanthrolines Bearing a 9-Cyano Group

by Mihaela Cristea, Marcel Mirel Popa, Sergiu Shova, Maria Gdaniec, Amalia Stefaniu, Constantin Draghici, Mihai Raduca, Nicoleta Doriana Banu and Florea Dumitrascu

Symmetry 2024, 16(7), 911; https://doi.org/10.3390/sym16070911 - 17 Jul 2024

Viewed by 1390

Abstract

New 9-cyano-pyrrolo[1,2-a][1,10]phenanthrolines 5a–d, obtained by a 1,3-dipolar cycloaddition reaction between the corresponding N-ylides of 1,10-phenanthrolinium bromides 2a–d, generated in situ and acrylonitrile as a dipolarophile, were investigated by single-crystal X-ray diffraction and computational studies to assess their [...] Read more.

New 9-cyano-pyrrolo[1,2-a][1,10]phenanthrolines 5a–d, obtained by a 1,3-dipolar cycloaddition reaction between the corresponding N-ylides of 1,10-phenanthrolinium bromides 2a–d, generated in situ and acrylonitrile as a dipolarophile, were investigated by single-crystal X-ray diffraction and computational studies to assess their druglikeness and evaluate their structure-activity properties. The non-covalent interactions present within the supramolecular landscape of the new 9-cyano-pyrrolo[1,2-a][1,10]phenanthrolines were correlated with the SAR investigations with the aim of estimating the propensity for bioactivity in these compounds. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry of Molecules Related to Biological Activity)

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16 pages, 515 KB

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 1409

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 KB

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 1524

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 KB

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 1848

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 KB

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 1265

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 KB

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 2044

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 KB

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 1387

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 KB

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 1864

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 KB

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 1531

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 KB

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 4 | Viewed by 1313

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 KB

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 7 | Viewed by 1613

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 KB

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 3 | Viewed by 2198

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 KB

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 6 | Viewed by 1389

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 KB

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 2254

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 KB

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 1102

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 KB

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 2580

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 KB

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 14 | Viewed by 4576

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 KB

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 3291

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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