Next Issue
Volume 13, October
Previous Issue
Volume 13, August
 
 

Symmetry, Volume 13, Issue 9 (September 2021) – 208 articles

Cover Story (view full-size image): Voronoi diagrams generate new types of the 5-fold symmetry tiling, which are different from the classical Penrose tessellation. Continuous measures of symmetry and the Voronoi Entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. Voronoi tessellations keep the initial symmetry group of the Penrose tiling. The continuous symmetry measure and the Voronoi Entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. View this paper.
  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Select all
Export citation of selected articles as:
12 pages, 3248 KiB  
Article
Comparative Study: Catalytic Activity and Rhodamine Dye Luminescence at the Surface of TiO2-Based Nanoheterostructures
by Elizaveta Konstantinova, Vladimir Zaitsev, Artem Marikutsa and Alexander Ilin
Symmetry 2021, 13(9), 1758; https://doi.org/10.3390/sym13091758 - 21 Sep 2021
Cited by 3 | Viewed by 1484
Abstract
Nanoheterostructures based on titanium, molybdenum, tungsten, and vanadium nanooxides with symmetric crystal structures, morphologies and high photocatalytic activity in under illumination by visible light, have been synthesized and studied. Microscopy, optical spectroscopy, and electron-spin resonance techniques were used. The asymmetric separation of photo-generated [...] Read more.
Nanoheterostructures based on titanium, molybdenum, tungsten, and vanadium nanooxides with symmetric crystal structures, morphologies and high photocatalytic activity in under illumination by visible light, have been synthesized and studied. Microscopy, optical spectroscopy, and electron-spin resonance techniques were used. The asymmetric separation of photo-generated holes and electrons between different nanooxides in their nanoheterostructures suppresses their recombination. Using the method developed by the authors and based on ESR spectroscopy, the energy levels of the active centers inside the band gaps of the studied samples were found. We have shown, for the first time, that under illumination of nanoheterostructures under asymmetric conditions with adsorbed rhodamine dye at the dye-absorption wavelength (500 nm), photocatalytic reactions are mainly determined by light absorption by the nanostructures themselves, and not by energy transfer from the dye. This important result shows that high photocatalytic activity of materials with symmetric crystal structures is the primary criterion for creating energy-efficient photocatalysts. The results will be useful for the development of energy-efficient catalytic devices based on various combinations of metal nanooxides. Full article
(This article belongs to the Special Issue Heterogeneous Catalysis for More Sustainable Symmetry Development)
Show Figures

Graphical abstract

16 pages, 538 KiB  
Article
A Two-Phase Algorithm for Robust Symmetric Non-Negative Matrix Factorization
by Bingjie Li, Xi Shi and Zhenyue Zhang
Symmetry 2021, 13(9), 1757; https://doi.org/10.3390/sym13091757 - 20 Sep 2021
Viewed by 1644
Abstract
As a special class of non-negative matrix factorization, symmetric non-negative matrix factorization (SymNMF) has been widely used in the machine learning field to mine the hidden non-linear structure of data. Due to the non-negative constraint and non-convexity of SymNMF, the efficiency of existing [...] Read more.
As a special class of non-negative matrix factorization, symmetric non-negative matrix factorization (SymNMF) has been widely used in the machine learning field to mine the hidden non-linear structure of data. Due to the non-negative constraint and non-convexity of SymNMF, the efficiency of existing methods is generally unsatisfactory. To tackle this issue, we propose a two-phase algorithm to solve the SymNMF problem efficiently. In the first phase, we drop the non-negative constraint of SymNMF and propose a new model with penalty terms, in order to control the negative component of the factor. Unlike previous methods, the factor sequence in this phase is not required to be non-negative, allowing fast unconstrained optimization algorithms, such as the conjugate gradient method, to be used. In the second phase, we revisit the SymNMF problem, taking the non-negative part of the solution in the first phase as the initial point. To achieve faster convergence, we propose an interpolation projected gradient (IPG) method for SymNMF, which is much more efficient than the classical projected gradient method. Our two-phase algorithm is easy to implement, with convergence guaranteed for both phases. Numerical experiments show that our algorithm performs better than others on synthetic data and unsupervised clustering tasks. Full article
Show Figures

Figure 1

9 pages, 272 KiB  
Article
p-Adic q-Twisted Dedekind-Type Sums
by Abdelmejid Bayad and Yilmaz Simsek
Symmetry 2021, 13(9), 1756; https://doi.org/10.3390/sym13091756 - 20 Sep 2021
Cited by 2 | Viewed by 1716
Abstract
The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral and the Teichmüller character representations of the Bernoulli polynomials, we give reciprocity law of these sums. These sums and their reciprocity law generalized [...] Read more.
The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral and the Teichmüller character representations of the Bernoulli polynomials, we give reciprocity law of these sums. These sums and their reciprocity law generalized some of the classical p-adic Dedekind sums and their reciprocity law. It is to be noted that the Dedekind reciprocity laws, is a fine study of the existing symmetry relations between the finite sums, considered in our study, and their symmetries through permutations of initial parameters. Full article
(This article belongs to the Special Issue Recent Advances in Number Theory and Their Applications)
13 pages, 3445 KiB  
Article
Laboratory Characterization of In-Service Full-Mouth Rehabilitation with Monolithic Translucent Zirconia Restorations
by Susana M. Salazar Marocho, Mary Beth VanLandingham, Firas Mourad, Andres Pappa and Sreenivas Koka
Symmetry 2021, 13(9), 1755; https://doi.org/10.3390/sym13091755 - 20 Sep 2021
Viewed by 1604
Abstract
The chance to critically and microscopically inspect the quality of bonded restorations once they are delivered to the patient after several pre-cementation steps is rare or nonexistent. Replicas of in-service restorations can provide a wealth of information on the integrity of the restorations [...] Read more.
The chance to critically and microscopically inspect the quality of bonded restorations once they are delivered to the patient after several pre-cementation steps is rare or nonexistent. Replicas of in-service restorations can provide a wealth of information on the integrity of the restorations and moreover make it possible to bring this information to the laboratory for further detailed analysis. This study aimed to characterize the epoxy replicas of 27 cemented monolithic yttria-stabilized zirconia crowns of the maxillary and mandibular arch to assess surface roughness, topography, and symmetry. The topography of the facial, lingual, and occlusal/incisal surfaces of each crown was observed under the optical microscope and further characterized using the scanning electron microscope. Surface roughness measurements were performed using the atomic force microscope. The optical microscope was used to measure the golden proportion and visible width of the anterior maxillary crowns. Surface damage consistent with unpolished adjustment was identified mostly in the occlusal surface of the posterior teeth. Other irregularities, such as scratch marks, small pits, and coarse pits were also found. The surface roughness had great variability. Not all of the anterior maxillary and mandibular teeth followed the golden proportion concept. This study design allows in vitro characterization of in-service restorations. It provides a framework for using replicas for early identification of patterns or features that can trigger fracture and for analysis of morphology and symmetry. Full article
(This article belongs to the Special Issue Symmetry in Dentistry: From the Clinic to the Lab)
Show Figures

Figure 1

12 pages, 4340 KiB  
Article
Cobalt Oxide on a Nanoporous TUD-1 Catalyst for Methylene Blue Dye Interaction DFT Studies and Degradation
by Muthusamy Poomalai Pachamuthu, Sambath Baskaran, Chandrakumar Manivannan, Somasundaram Chandra Kishore, Stefano Bellucci and Ramasamy Boopathy
Symmetry 2021, 13(9), 1754; https://doi.org/10.3390/sym13091754 - 20 Sep 2021
Cited by 1 | Viewed by 2025
Abstract
Fenton and Fenton-like advanced oxidation processes (AOP) have been substantially utilized in wastewater treatment for the removal of organic contaminants. The present investigation explores the catalytic activity of cobalt dispersed over nanoporous silicate material (CoO/TUD-1), TUD-1, for the Fenton-type degradation of methylene blue [...] Read more.
Fenton and Fenton-like advanced oxidation processes (AOP) have been substantially utilized in wastewater treatment for the removal of organic contaminants. The present investigation explores the catalytic activity of cobalt dispersed over nanoporous silicate material (CoO/TUD-1), TUD-1, for the Fenton-type degradation of methylene blue (MB) dye present in wastewater, with hydrogen peroxide (H2O2) as an oxidant. The catalyst, which was prepared using the hydrothermal method, was characterized using analytical and spectroscopic techniques, such as X-ray diffraction (XRD), N2 adsorption–desorption isotherms, UV-visible diffuse reflectance (DR), scanning electron microscope (SEM), transmission electron microscopy (TEM) and Fourier transform infrared (FTIR). The results indicated that the CoO/TUD-1 possessed three-dimensional structures with a high surface area and a pore diameter capable of the uniform dispersion of cobalt species. Density functional theory (DFT) simulations were performed to study the most stable tetra coordinate adsorption configuration of a single Co atom on amorphous SiO2. To understand the geometric and electronic structure of this configuration, electron density differences, Bader charge, and partial density of states were examined. The results obtained from the DFT calculations confirmed the occurrence of electron transfer from the Co atom to the amorphous SiO2. The calculated adsorption energy was found to be −1.58 eV, which indicated that the MB dye was strongly adsorbed by parallel configuration mode and degraded more easily. Further, the addition of a 0.1g/L dose of the prepared CoO /TUD degraded the MB dye effectively (~95%) within 240 min of contact. Thus, CoO/TUD-1 is a potential material for the removal of organic contaminants and the degradation of dyes in wastewater treatment. Full article
(This article belongs to the Special Issue Nanotechnology and Symmetry)
Show Figures

Figure 1

14 pages, 1466 KiB  
Article
Can an Intermediate Rate of Nitrogen Inversion Affect Drug Efficacy?
by Raphael R. Steimbach, Gergely Tihanyi, Magalie N. E. Géraldy, Alicja Wzorek, Aubry K. Miller and Karel D. Klika
Symmetry 2021, 13(9), 1753; https://doi.org/10.3390/sym13091753 - 20 Sep 2021
Cited by 1 | Viewed by 1960
Abstract
Nitrogen-inversion rates and diffusion coefficients were measured using 1H NMR for 14 drug-like molecules. The slow nitrogen-inversion rates interconverting the enantiomers of these molecules lay within a postulated intermediate range in terms of their ability to bind to proteins bounded by diffusion [...] Read more.
Nitrogen-inversion rates and diffusion coefficients were measured using 1H NMR for 14 drug-like molecules. The slow nitrogen-inversion rates interconverting the enantiomers of these molecules lay within a postulated intermediate range in terms of their ability to bind to proteins bounded by diffusion constraints, potentially affecting the availability, hence efficacy, of these compounds if they were utilized as drugs. The postulated intermediate range is based on a capture-volume concept, whereby the nitrogen inversion during the time a ligand takes to pass through a volume surrounding the protein binding site, as calculated by the diffusion rate, determines if it will influence ligand binding to the protein. In the systems examined here, the measured nitrogen-inversion rates and the times required to traverse the capture volume differed by a few orders of magnitude. Potentially more consequential are intermediate nitrogen-inversion rates in epimeric cases—since the energies of the interconverting species are unequal, a heavy bias against the eutomer might occur. The implications of an intermediate nitrogen-inversion rate are significant for in silico drug design, drug efficacy, molecular modeling of drug–protein binding, pharmacokinetics, drug enantiomer evaluation, etc. Due consideration of the process should thus be taken into account for drug development directions and in vitro evaluation. Full article
(This article belongs to the Special Issue Chiral Molecules - Production and Biological Properties)
Show Figures

Figure 1

14 pages, 534 KiB  
Article
Stochastic Intermittency Fields in a von Kármán Experiment
by Jürgen Schmiegel and Flavio Pons
Symmetry 2021, 13(9), 1752; https://doi.org/10.3390/sym13091752 - 20 Sep 2021
Cited by 2 | Viewed by 1566
Abstract
We discuss the application of stochastic intermittency fields to describe and analyse the statistical properties of time series of the generalised turbulence intensity in an anisotropic and inhomogeneous turbulent flow and provide a parsimonious description of the one-, two-, and three-point statistics. In [...] Read more.
We discuss the application of stochastic intermittency fields to describe and analyse the statistical properties of time series of the generalised turbulence intensity in an anisotropic and inhomogeneous turbulent flow and provide a parsimonious description of the one-, two-, and three-point statistics. In particular, we show that the three-point correlations can be predicted from observed two-point statistics. Our analysis is motivated by observed stylised features of the energy dissipation in homogeneous and isotropic situations where these statistical properties are well represented within the framework of stochastic intermittency fields. We find a close resemblance and conclude that stochastic intermittency fields may be relevant in more general situations. Full article
Show Figures

Figure 1

26 pages, 1289 KiB  
Article
Polynomial Invariant of Molecular Circuit Topology
by Alireza Mashaghi and Roland van der Veen
Symmetry 2021, 13(9), 1751; https://doi.org/10.3390/sym13091751 - 19 Sep 2021
Cited by 1 | Viewed by 1604
Abstract
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain [...] Read more.
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain entanglements and local or global structural symmetries stabilised by formation contacts between different parts of the chain. Circuit topology captures the arrangements of intra-chain contacts within a given folded linear chain and allows for the classification and comparison of chains. Contacts keep chain segments in physical proximity and can be either mechanically hard attachments or soft entanglements that constrain a physical chain. Contrary to knot theory, which offers many established knot invariants, circuit invariants are just being developed. Here, we present polynomial invariants that are both efficient and sufficiently powerful to deal with any combination of soft and hard contacts. A computer implementation and table of chains with up to three contacts is also provided. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
Show Figures

Figure 1

10 pages, 821 KiB  
Article
Prediction of Partition Coefficients in SDS Micelles by DFT Calculations
by Leila Saranjam, Elisabet Fuguet, Miroslava Nedyalkova, Vasil Simeonov, Francesc Mas and Sergio Madurga
Symmetry 2021, 13(9), 1750; https://doi.org/10.3390/sym13091750 - 19 Sep 2021
Cited by 3 | Viewed by 2108
Abstract
A computational methodology using Density-Functional Theory (DFT) calculations was developed to determine the partition coefficient of a compound in a solution of Sodium Dodecyl Sulfate (SDS) micelles. Different sets of DFT calculations were used to predict the free energy of a set of [...] Read more.
A computational methodology using Density-Functional Theory (DFT) calculations was developed to determine the partition coefficient of a compound in a solution of Sodium Dodecyl Sulfate (SDS) micelles. Different sets of DFT calculations were used to predict the free energy of a set of 63 molecules in 15 different solvents with the purpose of identifying the solvents with similar physicochemical characteristics to the studied micelles. Experimental partition coefficients were obtained from Micellar Electrokinetic Chromatography (MEKC) measurements. The experimental partition coefficient of these molecules was compared with the predicted partition coefficient in heptane/water, cyclohexane/water, N-dodecane/water, pyridine/water, acetic acid/water, decan-1-ol/water, octanol/water, propan-2-ol/water, acetone/water, propan-1-ol/water, methanol/water, 1,2-ethane diol/water, dimethyl sulfoxide/water, formic acid/water, and diethyl sulphide/water systems. It is observed that the combination of pronan-1-ol/water solvent was the most appropriated to estimate the partition coefficient for SDS micelles. This approach allowed us to estimate the partition coefficient orders of magnitude faster than the classical molecular dynamics simulations. The DFT calculations were carried out with the well-known exchange correlation functional B3LYP and with the global hybrid functional M06-2X from the Minnesota functionals with 6-31++G ** basis set. The effect of solvation was considered by the continuum model based on density (SMD). The proposed workflow for the prediction rate of the participation coefficient unveiled the symmetric balance between the experimental data and the computational methods. Full article
(This article belongs to the Special Issue Symmetry, Molecular Modelling and Simulation in Biochemistry)
Show Figures

Figure 1

13 pages, 308 KiB  
Article
Coadjoint Orbits of the Poincaré Group for Discrete-Spin Particles in Any Dimension
by Ismael Ahlouche Lahlali, Nicolas Boulanger and Andrea Campoleoni
Symmetry 2021, 13(9), 1749; https://doi.org/10.3390/sym13091749 - 19 Sep 2021
Cited by 5 | Viewed by 1502
Abstract
Considering the Poincaré group ISO(d1,1) in any dimension d>3, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our [...] Read more.
Considering the Poincaré group ISO(d1,1) in any dimension d>3, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our analysis extends to the case of continuous spin. Full article
(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)
16 pages, 3788 KiB  
Article
Binaural Background Noise Enhances Neuromagnetic Responses from Auditory Cortex
by Dawei Shen, Claude Alain and Bernhard Ross
Symmetry 2021, 13(9), 1748; https://doi.org/10.3390/sym13091748 - 19 Sep 2021
Cited by 2 | Viewed by 1686
Abstract
The presence of binaural low-level background noise has been shown to enhance the transient evoked N1 response at about 100 ms after sound onset. This increase in N1 amplitude is thought to reflect noise-mediated efferent feedback facilitation from the auditory cortex to lower [...] Read more.
The presence of binaural low-level background noise has been shown to enhance the transient evoked N1 response at about 100 ms after sound onset. This increase in N1 amplitude is thought to reflect noise-mediated efferent feedback facilitation from the auditory cortex to lower auditory centers. To test this hypothesis, we recorded auditory-evoked fields using magnetoencephalography while participants were presented with binaural harmonic complex tones embedded in binaural or monaural background noise at signal-to-noise ratios of 25 dB (low noise) or 5 dB (higher noise). Half of the stimuli contained a gap in the middle of the sound. The source activities were measured in bilateral auditory cortices. The onset and gap N1 response increased with low binaural noise, but high binaural and low monaural noise did not affect the N1 amplitudes. P1 and P2 onset and gap responses were consistently attenuated by background noise, and noise level and binaural/monaural presentation showed distinct effects. Moreover, the evoked gamma synchronization was also reduced by background noise, and it showed a lateralized reduction for monaural noise. The effects of noise on the N1 amplitude follow a bell-shaped characteristic that could reflect an optimal representation of acoustic information for transient events embedded in noise. Full article
(This article belongs to the Special Issue Neuroscience, Neurophysiology and Asymmetry)
Show Figures

Figure 1

12 pages, 267 KiB  
Article
Convergence of Certain Baskakov Operators of Integral Type
by Marius Mihai Birou, Carmen Violeta Muraru and Voichiţa Adriana Radu
Symmetry 2021, 13(9), 1747; https://doi.org/10.3390/sym13091747 - 19 Sep 2021
Viewed by 1303
Abstract
In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,) with the properties: φ(0)=0,φ>0 on [0,) and [...] Read more.
In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,) with the properties: φ(0)=0,φ>0 on [0,) and limxφ(x)=. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval (,0] (the symmetric of the interval [0,) from the origin). Full article
(This article belongs to the Special Issue New Directions in Theory of Approximation and Related Problems)
14 pages, 7386 KiB  
Article
Brain Symmetry Analysis during the Use of a BCI Based on Motor Imagery for the Control of a Lower-Limb Exoskeleton
by Laura Ferrero, Mario Ortiz, Vicente Quiles, Eduardo Iáñez, José A. Flores and José M. Azorín
Symmetry 2021, 13(9), 1746; https://doi.org/10.3390/sym13091746 - 19 Sep 2021
Cited by 8 | Viewed by 3200
Abstract
Brain–Computer Interfaces (BCI) are systems that allow external devices to be controlled by means of brain activity. There are different such technologies, and electroencephalography (EEG) is an example. One of the most common EEG control methods is based on detecting changes in sensorimotor [...] Read more.
Brain–Computer Interfaces (BCI) are systems that allow external devices to be controlled by means of brain activity. There are different such technologies, and electroencephalography (EEG) is an example. One of the most common EEG control methods is based on detecting changes in sensorimotor rhythms (SMRs) during motor imagery (MI). The aim of this study was to assess the laterality of cortical function when performing MI of the lower limb. Brain signals from five subjects were analyzed in two conditions, during exoskeleton-assisted gait and while static. Three different EEG electrode configurations were evaluated: covering both hemispheres, covering the non-dominant hemisphere and covering the dominant hemisphere. In addition, the evolution of performance and laterality with practice was assessed. Although sightly superior results were achieved with information from all electrodes, differences between electrode configurations were not statistically significant. Regarding the evolution during the experimental sessions, the performance of the BCI generally evolved positively the higher the experience was. Full article
(This article belongs to the Special Issue Neuroscience, Neurophysiology and Asymmetry)
Show Figures

Figure 1

9 pages, 13485 KiB  
Article
Investigation of Eigenmode-Based Coupled Oscillator Solver Applied to Ising Spin Problems
by Shintaro Murakami, Okuto Ikeda, Yusuke Hirukawa and Toshiharu Saiki
Symmetry 2021, 13(9), 1745; https://doi.org/10.3390/sym13091745 - 19 Sep 2021
Viewed by 1288
Abstract
We evaluate a coupled oscillator solver by applying it to square lattice (N × N) Ising spin problems for N values up to 50. The Ising problems are converted to a classical coupled oscillator model that includes both positive (ferromagnetic-like) and negative (antiferromagnetic-like) [...] Read more.
We evaluate a coupled oscillator solver by applying it to square lattice (N × N) Ising spin problems for N values up to 50. The Ising problems are converted to a classical coupled oscillator model that includes both positive (ferromagnetic-like) and negative (antiferromagnetic-like) coupling between neighboring oscillators (i.e., they are reduced to eigenmode problems). A map of the oscillation amplitudes of lower-frequency eigenmodes enables us to visualize oscillator clusters with a low frustration density (unfrustrated clusters). We found that frustration tends to localize at the boundary between unfrustrated clusters due to the symmetric and asymmetric nature of the eigenmodes. This allows us to reduce frustration simply by flipping the sign of the amplitude of oscillators around which frustrated couplings are highly localized. For problems with N = 20 to 50, the best solutions with an accuracy of 96% (with respect to the exact ground state) can be obtained by simply checking the lowest ~N/2 candidate eigenmodes. Full article
(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)
Show Figures

Figure 1

22 pages, 8141 KiB  
Review
Progress on the Stereoselective Synthesis of Chiral Molecules Based on Metal-Catalyzed Dynamic Kinetic Resolution of Alcohols with Lipases
by Raffaella Ferraccioli
Symmetry 2021, 13(9), 1744; https://doi.org/10.3390/sym13091744 - 19 Sep 2021
Cited by 5 | Viewed by 4171
Abstract
Metal/lipase-combo catalyzed dynamic kinetic resolution (DKR) of racemic chiral alcohols is a general and practical process to obtain the corresponding enantiopure esters R with quantitative conversion. The use of known Ru-catalysts as well as newly developed homogeneous and heterogeneous metal catalysts (Fe, V) [...] Read more.
Metal/lipase-combo catalyzed dynamic kinetic resolution (DKR) of racemic chiral alcohols is a general and practical process to obtain the corresponding enantiopure esters R with quantitative conversion. The use of known Ru-catalysts as well as newly developed homogeneous and heterogeneous metal catalysts (Fe, V) contributed to make the DKR process more sustainable and to expand the substrate scope of the reaction. In addition to classical substrates, challenging allylic alcohols, tertiary alcohols, C1-and C2-symmetric biaryl diols turned out to be competent substrates. Synthetic utility further emerged from the integration of this methodology into cascade reactions leading to linear/cyclic chiral molecules with high ee through the formation of multiple bonds, in a one-pot procedure. Full article
(This article belongs to the Special Issue Novel Approaches for Asymmetric Synthesis)
Show Figures

Scheme 1

14 pages, 2603 KiB  
Article
Identification of Private ICS Protocols Based on Raw Traffic
by Liang Zhai, Qiuhua Zheng, Xu Zhang, Haizhong Hu, Weihao Yin, Yingpei Zeng and Ting Wu
Symmetry 2021, 13(9), 1743; https://doi.org/10.3390/sym13091743 - 19 Sep 2021
Cited by 4 | Viewed by 2112
Abstract
With the development of the Industrial Internet in recent years, security issues have been a hot topic of the industrial control system (ICS) network management. Identifying the protocol traffic in the communication process of the ICS is an important prerequisite to avoid security [...] Read more.
With the development of the Industrial Internet in recent years, security issues have been a hot topic of the industrial control system (ICS) network management. Identifying the protocol traffic in the communication process of the ICS is an important prerequisite to avoid security problems, especially in ICSs that use many private protocols. The private protocols cannot be analyzed due to the unknown internal structure of the protocols, which makes the ICS protocol identification work more difficult. However, the Internet-oriented protocol identification method is not applicable to the scenario of the private ICS protocols network environment. With this problem in mind, this paper proposes a method of ICS protocol identification based on the raw traffic payload. The method firstly performs data preprocessing such as data selection, interception, cleaning conversion, and labeling on the raw traffic of the protocol based on the characteristics of the industrial control protocol. Then it uses an AM-1DCNN + LSTM deep learning model to extract temporal and spatial features of the ICS raw traffic, and performs protocol identification. This method can effectively extract ICS protocol features in scenarios where protocol parsing is impossible compared with existing methods. We constructed a dataset for ICS protocol identification based on open-source data and tested the proposed method for experiments, and the identification accuracy rate reached 93%. Full article
Show Figures

Figure 1

15 pages, 3309 KiB  
Article
MRE: A Military Relation Extraction Model Based on BiGRU and Multi-Head Attention
by Yiwei Lu, Ruopeng Yang, Xuping Jiang, Dan Zhou, Changsheng Yin and Zizhuo Li
Symmetry 2021, 13(9), 1742; https://doi.org/10.3390/sym13091742 - 19 Sep 2021
Cited by 10 | Viewed by 2008
Abstract
A great deal of operational information exists in the form of text. Therefore, extracting operational information from unstructured military text is of great significance for assisting command decision making and operations. Military relation extraction is one of the main tasks of military information [...] Read more.
A great deal of operational information exists in the form of text. Therefore, extracting operational information from unstructured military text is of great significance for assisting command decision making and operations. Military relation extraction is one of the main tasks of military information extraction, which aims at identifying the relation between two named entities from unstructured military texts. However, the traditional methods of extracting military relations cannot easily resolve problems such as inadequate manual features and inaccurate Chinese word segmentation in military fields, failing to make full use of symmetrical entity relations in military texts. With our approach, based on the pre-trained language model, we present a Chinese military relation extraction method, which combines the bi-directional gate recurrent unit (BiGRU) and multi-head attention mechanism (MHATT). More specifically, the conceptual foundation of our method lies in constructing an embedding layer and combining word embedding with position embedding, based on the pre-trained language model; the output vectors of BiGRU neural networks are symmetrically spliced to learn the semantic features of context, and they fuse the multi-head attention mechanism to improve the ability of expressing semantic information. On the military text corpus that we have built, we conduct extensive experiments. We demonstrate the superiority of our method over the traditional non-attention model, attention model, and improved attention model, and the comprehensive evaluation value F1-score of the model is improved by about 4%. Full article
Show Figures

Figure 1

19 pages, 80402 KiB  
Review
Symmetry and Aesthetics in Dentistry
by Christoph Runte and Dieter Dirksen
Symmetry 2021, 13(9), 1741; https://doi.org/10.3390/sym13091741 - 19 Sep 2021
Cited by 6 | Viewed by 6061
Abstract
Animal bodies in general and faces in particular show mirror symmetry with respect to the median-sagittal plane, with exceptions rarely occurring. Bilateral symmetry to the median sagittal plane of the body also evolved very early. From an evolutionary point of view, it should [...] Read more.
Animal bodies in general and faces in particular show mirror symmetry with respect to the median-sagittal plane, with exceptions rarely occurring. Bilateral symmetry to the median sagittal plane of the body also evolved very early. From an evolutionary point of view, it should therefore have fundamental advantages, e.g., more effective locomotion and chewing abilities. On the other hand, the recognition of bilaterally symmetric patterns is an important module in our visual perception. In particular, the recognition of faces with different spatial orientations and their identification is strongly related to the recognition of bilateral symmetry. Maxillofacial surgery and Dentistry affect effective masticatory function and perceived symmetry of the lower third of the face. Both disciplines have the ability to eliminate or mitigate asymmetries with respect to form and function. In our review, we will demonstrate symmetric structures from single teeth to the whole face. We will further describe different approaches to quantify cranial, facial and dental asymmetries by using either landmarks or 3D surface models. Severe facial asymmetries are usually caused by malformations such as hemifacial hyperplasia, injury or other diseases such as Noma or head and neck cancer. This could be an important sociobiological reason for a correlation between asymmetry and perceived disfigurement. The aim of our review is to show how facial symmetry and attractiveness are related and in what way dental and facial structures and the symmetry of their shape and color influence aesthetic perception. We will further demonstrate how modern technology can be used to improve symmetry in facial prostheses and maxillofacial surgery. Full article
(This article belongs to the Special Issue Symmetry in Dentistry: From the Clinic to the Lab)
Show Figures

Figure 1

12 pages, 1849 KiB  
Article
Evaluation Process of the Burglary Resistance When Explosives Are Used to Create an Opening in the Barriers
by Zuzana Zvakova, Martin Boros, Lucia Figuli and Andrej Velas
Symmetry 2021, 13(9), 1740; https://doi.org/10.3390/sym13091740 - 18 Sep 2021
Cited by 5 | Viewed by 1444
Abstract
Burglary resistance expresses the time required to overcome the barriers to cause the damage in order to unlawfully enter a place for the purposes of stealing property or committing a felony (i.e., disruption of important assets, e.g., critical infrastructure). Damage to the object [...] Read more.
Burglary resistance expresses the time required to overcome the barriers to cause the damage in order to unlawfully enter a place for the purposes of stealing property or committing a felony (i.e., disruption of important assets, e.g., critical infrastructure). Damage to the object protection system means damage to the symmetry of the system—the balance between protection measures and security threats. Barriers are considered to be the walls of buildings or secure storage units (safe, safe, etc.), i.e., passive barriers that separate asset (protected value) from the security threat. The role of barriers in the security system is also to slow down the attack and create a time reserve for the intervention of a security service. There is no uniform approach to express the burglary resistance of such barriers using explosives; however, burglary by explosion are present. Explosives in the article are a tool that can be used by the offenders. The article uses mainly Delphi method and Saaty method. These methods have made it possible to identify and expertly evaluate scenarios for the use of explosives to break a barrier. Logical methods and interviews were also used. The result of the article is the identification and evaluation of the possibilities of using explosives to overcome barriers and expressing the blast burglary resistance of barriers. The universal assessment approach allows the inclusion of explosives to the burglary resistance protection system assessment schemes. Full article
(This article belongs to the Special Issue Symmetry Applied in Special Engineering)
Show Figures

Figure 1

25 pages, 9123 KiB  
Article
Substructure Shake Table Testing of Frame Structure–Damper System Using Model-Based Integration Algorithms and Finite Element Method: Numerical Study
by Bo Fu, Huanjun Jiang and Jin Chen
Symmetry 2021, 13(9), 1739; https://doi.org/10.3390/sym13091739 - 18 Sep 2021
Cited by 6 | Viewed by 1827
Abstract
Substructure shake table testing (SSTT) is an advanced experimental technique that is suitable for investigating the vibration control of secondary structure-type dampers such as tuned mass dampers (TMDs). The primary structure and damper are considered as analytical and experimental substructures, respectively. The analytical [...] Read more.
Substructure shake table testing (SSTT) is an advanced experimental technique that is suitable for investigating the vibration control of secondary structure-type dampers such as tuned mass dampers (TMDs). The primary structure and damper are considered as analytical and experimental substructures, respectively. The analytical substructures of existing SSTTs have mostly been simplified as SDOF structures or shear-type structures, which is not realistic. A common trend is to simulate the analytical substructure via the finite element (FE) method. In this study, the control effects of four dampers, i.e., TMD, tuned liquid damper (TLD), particle damper (PD) and particle-tuned mass damper (PTMD), on a frame were examined by conducting virtual SSTTs. The frame was modeled through stiffness-based beam-column elements with fiber sections and was solved by a family of model-based integration algorithms. The influences of the auxiliary mass ratio, integration parameters, time step, and time delay on SSTT were investigated. The results indicate that the TLD had the best performance. In addition, SSTT using model-based integration algorithms can provide satisfactory results, even when the time step is relatively large. The effects of integration parameters and time delay are not significant. Full article
(This article belongs to the Special Issue Symmetry in Structural Health Monitoring)
Show Figures

Figure 1

13 pages, 773 KiB  
Article
A Variety of Dynamic Steffensen-Type Inequalities on a General Time Scale
by Ahmed Abdel-Moneim El-Deeb, Omar Bazighifan and Jan Awrejcewicz
Symmetry 2021, 13(9), 1738; https://doi.org/10.3390/sym13091738 - 18 Sep 2021
Cited by 8 | Viewed by 1206
Abstract
This work is motivated by the work of Josip Pečarić in 2013 and 1982 and the work of Srivastava in 2017. By the utilization of the diamond-α dynamic inequalities, which are defined as a linear mixture of the delta and nabla integrals, [...] Read more.
This work is motivated by the work of Josip Pečarić in 2013 and 1982 and the work of Srivastava in 2017. By the utilization of the diamond-α dynamic inequalities, which are defined as a linear mixture of the delta and nabla integrals, we present and prove very important generalized results of diamond-α Steffensen-type inequalities on a general time scale. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. Full article
14 pages, 2014 KiB  
Article
User Selection Approach in Multiantenna Beamforming NOMA Video Communication Systems
by Shu-Ming Tseng and Shih-Chun Kao
Symmetry 2021, 13(9), 1737; https://doi.org/10.3390/sym13091737 - 18 Sep 2021
Cited by 8 | Viewed by 1873
Abstract
For symmetric non-orthogonal multiple access (NOMA)/multiple-input multiple-output (MIMO) systems, radio resource allocation is an important research problem. The optimal solution is of high computational complexity. Thus, one existing solution Kim et al. proposed is a suboptimal user selection and optimal power assignment for [...] Read more.
For symmetric non-orthogonal multiple access (NOMA)/multiple-input multiple-output (MIMO) systems, radio resource allocation is an important research problem. The optimal solution is of high computational complexity. Thus, one existing solution Kim et al. proposed is a suboptimal user selection and optimal power assignment for total data rate maximization. Another existing solution Tseng et al. proposed is different suboptimal user grouping and optimal power assignment for sum video distortion minimization. However, the performance of sub-optimal schemes by Kim et al. and Tseng et al. is still much lower than the optimal user grouping scheme. To approach the optimal scheme and outperform the existing sub-optimal schemes, a deep neural network (DNN) based approach, using the results from the optimal user selection (exhaustive search) as the training data, and a loss function modification specific for NOMA user selection to meet the constraint that a user cannot be in both the strong and weak set, and avoid the post processing online computational complexity, are proposed. The simulation results show that the theoretical peak signal-to-noise ratio (PSNR) of the proposed scheme is higher than the state-of-the-art suboptimal schemes Kim et al. and Tseng et al. by 0.7~2.3 dB and is only 0.4 dB less than the optimal scheme at lower online computational complexity. The online computational complexity (testing stage) of the proposed DNN user selection scheme is 60 times less than the optimal user selection scheme. The proposed DNN-based scheme outperforms the existing suboptimal solution, and slightly underperforms the optimal scheme (exhaustive search) at a much lower computation complexity. Full article
Show Figures

Figure 1

21 pages, 420 KiB  
Article
Integrability and Limit Cycles via First Integrals
by Jaume Llibre
Symmetry 2021, 13(9), 1736; https://doi.org/10.3390/sym13091736 - 18 Sep 2021
Cited by 7 | Viewed by 1626
Abstract
In many problems appearing in applied mathematics in the nonlinear ordinary differential systems, as in physics, chemist, economics, etc., if we have a differential system on a manifold of dimension, two of them having a first integral, then its phase portrait is completely [...] Read more.
In many problems appearing in applied mathematics in the nonlinear ordinary differential systems, as in physics, chemist, economics, etc., if we have a differential system on a manifold of dimension, two of them having a first integral, then its phase portrait is completely determined. While the existence of first integrals for differential systems on manifolds of a dimension higher than two allows to reduce the dimension of the space in as many dimensions as independent first integrals we have. Hence, to know first integrals is important, but the following question appears: Given a differential system, how to know if it has a first integral? The symmetries of many differential systems force the existence of first integrals. This paper has two main objectives. First, we study how to compute first integrals for polynomial differential systems using the so-called Darboux theory of integrability. Furthermore, second, we show how to use the existence of first integrals for finding limit cycles in piecewise differential systems. Full article
(This article belongs to the Special Issue Qualitative Theory and Symmetries of Ordinary Differential Equations)
Show Figures

Figure 1

12 pages, 22266 KiB  
Article
Dynamic Processes in a Superconducting Adiabatic Neuron with Non-Shunted Josephson Contacts
by Marina Bastrakova, Anastasiya Gorchavkina, Andrey Schegolev, Nikolay Klenov, Igor Soloviev, Arkady Satanin and Maxim Tereshonok
Symmetry 2021, 13(9), 1735; https://doi.org/10.3390/sym13091735 - 18 Sep 2021
Cited by 5 | Viewed by 2481
Abstract
We investigated the dynamic processes in a superconducting neuron based on Josephson contacts without resistive shunting (SC-neuron). Such a cell is a key element of perceptron-type neural networks that operate in both classical and quantum modes. The analysis of the obtained [...] Read more.
We investigated the dynamic processes in a superconducting neuron based on Josephson contacts without resistive shunting (SC-neuron). Such a cell is a key element of perceptron-type neural networks that operate in both classical and quantum modes. The analysis of the obtained results allowed us to find the mode when the transfer characteristic of the element implements the “sigmoid” activation function. The numerical approach to the analysis of the equations of motion and the Monte Carlo method revealed the influence of inertia (capacitances), dissipation, and temperature on the dynamic characteristics of the neuron. Full article
(This article belongs to the Section Physics)
Show Figures

Figure 1

12 pages, 2858 KiB  
Article
Improvement of Properties of Stainless Steel Orthodontic Archwire Using TiO2:Ag Coating
by Zofia Kielan-Grabowska, Justyna Bącela, Anna Zięty, Wioletta Seremak, Marta Gawlik-Maj, Beata Kawala, Beata Borak, Jerzy Detyna and Michał Sarul
Symmetry 2021, 13(9), 1734; https://doi.org/10.3390/sym13091734 - 18 Sep 2021
Cited by 9 | Viewed by 3296
Abstract
Orthodontic treatment carries the risk of major complications such as enamel demineralization, tooth decay, gingivitis, and periodontal damage. A large number of elements of fixed orthodontic appliance results in the creation of additional plaque retention sites which increase the risk of biofilm creation. [...] Read more.
Orthodontic treatment carries the risk of major complications such as enamel demineralization, tooth decay, gingivitis, and periodontal damage. A large number of elements of fixed orthodontic appliance results in the creation of additional plaque retention sites which increase the risk of biofilm creation. Modification of the surface of orthodontic elements may prevent the formation of bacterial biofilm. In this paper, surface modification of stainless steel orthodontic wires with TiO2: Ag was carried out by the sol-gel thin film dip-coating method. To obtain the anatase crystal structure, substrates were calcined for 2 h at 500 °C. The properties of the obtained coatings were investigated using scanning electron microscopy, X-ray diffraction, and electrochemical tests. Corrosion studies were performed in a Ringer’s solution, which simulated physiological solution. SEM and XRD analyses of the coated surface confirmed the presence of Ag nanoparticles which may have antimicrobial potential. Full article
(This article belongs to the Special Issue Symmetry Applied in Biomechanics and Mechanical Engineering)
Show Figures

Figure 1

18 pages, 27949 KiB  
Article
Theoretical Modeling and Analysis of Directional Spectrum Emissivity and Its Pattern for Random Rough Surfaces with a Matrix Method
by Jianrui Hu, Zhanqiang Liu, Jinfu Zhao, Bing Wang and Qinghua Song
Symmetry 2021, 13(9), 1733; https://doi.org/10.3390/sym13091733 - 18 Sep 2021
Cited by 3 | Viewed by 2055
Abstract
The emissivity is an important surface property parameter in many fields, including infrared temperature measurement. In this research, a symmetry theoretical model of directional spectral emissivity prediction is proposed based on Gaussian random rough surface theory. A numerical solution based on a matrix [...] Read more.
The emissivity is an important surface property parameter in many fields, including infrared temperature measurement. In this research, a symmetry theoretical model of directional spectral emissivity prediction is proposed based on Gaussian random rough surface theory. A numerical solution based on a matrix method is determined based on its symmetrical characteristics. Influences of the index of refraction n and the root mean square (RMS) roughness σrms on the directional spectrum emissivity ε are analyzed and discussed. The results indicate that surfaces with higher n and lower σrms tend to have a peak in high viewing angles. On the contrary, surfaces with lower n and higher σrms tend to have a peak in low viewing angles. Experimental verifications based on infrared (IR) temperature measurement of Inconel 718 sandblasted surfaces were carried out. This model would contribute to understand random rough surfaces and their emitting properties in fields including machining, process controlling, remote sensing, etc. Full article
(This article belongs to the Section Engineering and Materials)
Show Figures

Figure 1

34 pages, 1133 KiB  
Review
Symmetries and Geometries of Qubits, and Their Uses
by A. R. P. Rau
Symmetry 2021, 13(9), 1732; https://doi.org/10.3390/sym13091732 - 18 Sep 2021
Cited by 5 | Viewed by 2564
Abstract
The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such [...] Read more.
The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such systems for quantum information processes. In the last two decades, two different approaches, with independent starting points and motivations, have been combined for this purpose. One approach has been to develop the unitary time evolution of two or more qubits in order to study quantum correlations; by exploiting the relevant Lie algebras and, especially, sub-algebras of the Hamiltonians involved, researchers have arrived at connections to finite projective geometries and combinatorial designs. Independently, geometers, by studying projective ring lines and associated finite geometries, have come to parallel conclusions. This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. Altogether, this may be seen as further development of Felix Klein’s Erlangen Program for symmetries and geometries. In particular, the fifteen generators of the continuous SU(4) Lie group for two qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite quaternionic groups. The very different perspectives that we consider may provide further insight into quantum information problems. Extensions are considered for multiple qubits, as well as higher-spin or higher-dimensional qudits. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Show Figures

Figure 1

17 pages, 3687 KiB  
Article
Industrial Laser Welding Defect Detection and Image Defect Recognition Based on Deep Learning Model Developed
by Honggui Deng, Yu Cheng, Yuxin Feng and Junjiang Xiang
Symmetry 2021, 13(9), 1731; https://doi.org/10.3390/sym13091731 - 18 Sep 2021
Cited by 29 | Viewed by 6648
Abstract
Aiming at the problem of the poor robustness of existing methods to deal with diverse industrial weld image data, we collected a series of asymmetric laser weld images in the largest laser equipment workshop in Asia, and studied these data based on an [...] Read more.
Aiming at the problem of the poor robustness of existing methods to deal with diverse industrial weld image data, we collected a series of asymmetric laser weld images in the largest laser equipment workshop in Asia, and studied these data based on an industrial image processing algorithm and deep learning algorithm. The median filter was used to remove the noises in weld images. The image enhancement technique was adopted to increase the image contrast in different areas. The deep convolutional neural network (CNN) was employed for feature extraction; the activation function and the adaptive pooling approach were improved. Transfer Learning (TL) was introduced for defect detection and image classification on the dataset. Finally, a deep learning-based model was constructed for weld defect detection and image recognition. Specific instance datasets verified the model’s performance. The results demonstrate that this model can accurately identify weld defects and eliminate the complexity of manually extracting features, reaching a recognition accuracy of 98.75%. Hence, the reliability and automation of detection and recognition are improved significantly. The research results can provide a theoretical and practical reference for the defect detection of sheet metal laser welding and the development of the industrial laser manufacturing industry. Full article
Show Figures

Figure 1

20 pages, 1797 KiB  
Article
Modeling Extreme Values Utilizing an Asymmetric Probability Function
by Mohammed M. A. Almazah, Muqrin A. Almuqrin, Mohamed. S. Eliwa, Mahmoud El-Morshedy and Haitham M. Yousof
Symmetry 2021, 13(9), 1730; https://doi.org/10.3390/sym13091730 - 18 Sep 2021
Cited by 11 | Viewed by 1445
Abstract
In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment [...] Read more.
In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model. Full article
(This article belongs to the Special Issue Probability, Statistics and Applied Mathematics)
Show Figures

Figure 1

9 pages, 5634 KiB  
Article
Longitudinal Changes in Running Gait Asymmetries and Their Relationship to Personal Record Race Times in Collegiate Cross Country Runners
by Mikel R. Stiffler-Joachim, Stephanie A. Kliethermes, Jack A. Martin, Claire S. Tanaka, Ramsey Benkert and Bryan C. Heiderscheit
Symmetry 2021, 13(9), 1729; https://doi.org/10.3390/sym13091729 - 18 Sep 2021
Cited by 2 | Viewed by 2044
Abstract
Minimizing between-limb asymmetries during running is often a goal of training, as increased asymmetries are related to decreased efficiency and increased energy expenditure. However, it is unknown if asymmetries change with increased running exposure or are related to actual race performance. The purpose [...] Read more.
Minimizing between-limb asymmetries during running is often a goal of training, as increased asymmetries are related to decreased efficiency and increased energy expenditure. However, it is unknown if asymmetries change with increased running exposure or are related to actual race performance. The purpose of this study was to determine (1) if pre-season asymmetries changed year-to-year among collegiate cross country runners, and (2) if these asymmetries were associated with within-season personal records (PRs). Pre-season biomechanical test results and race performance data were analyzed for 54 unique runners (28 female) across six seasons, totaling 152 assessments (age: 19.1 (0.9) years, height: 1.71 (0.10) m, weight: 61.7 (7.7) kg (values = mean [standard deviation])). Biomechanical asymmetries included ground reaction forces; ground contact time; base of gait; foot inclination angle; and peak hip flexion, hip extension, hip adduction, pelvic drop, knee flexion, and ankle dorsiflexion. Year of collegiate eligibility was used to quantify training exposure. Asymmetries during running did not change across years of eligibility (p ≥ 0.12), except propulsive impulse, which decreased over time (p = 0.03). PR times were faster with decreased propulsive impulse asymmetry and increased AVLR and peak ankle dorsiflexion asymmetries. This is the first study to assess longitudinal asymmetries over time and provide potential targets for interventions aimed at modifying asymmetries to improve performance. Full article
(This article belongs to the Special Issue Motion, Gait Analysis and Asymmetry)
Show Figures

Figure 1

Previous Issue
Next Issue
Back to TopTop