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Volume 16
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Symmetry, Volume 16, Issue 7 (July 2024) – 41 articles

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16 pages, 2405 KiB  
Article
High Resilient Asymmetry and Anomaly Detection Based on Data Causality
by Zhiyong Hao, Chenhao Yu, Junyi Zhu and Leilei Chang
Symmetry 2024, 16(7), 819; https://doi.org/10.3390/sym16070819 (registering DOI) - 29 Jun 2024
Abstract
In the tunnel construction practice, multiple buildings’ tilt rate data are collected. In this study, data causality is defined to reflect the causal relation between the input and output of the building tilt rate detection data. Upon defining and calculating the data causality, [...] Read more.
In the tunnel construction practice, multiple buildings’ tilt rate data are collected. In this study, data causality is defined to reflect the causal relation between the input and output of the building tilt rate detection data. Upon defining and calculating the data causality, a new high resilient causality detection (HiReCau) method is proposed for abnormal building tilt rate detection. A numerical case and another practical case are studied for validation purposes. The case study results show that the proposed HiReCau method can accurately detect high-causality data and low-causality data among the building tilt rate detection data and produces superior results compared with the direct adoption of a machine learning approach. Furthermore, the resilience of HiReCau is validated by investigations testing varied levels of additional low-causality data in the training dataset. Presently, HiReCau is limited to handling problems with a single output. Furthermore, only the back-propagation neural network (BPNN) is tested as the baseline model and there is also room to further expand the data size. The proposed approach is versatile and able to be adjusted to handle fault diagnosis and safety assessment problems in varied theoretical and engineering backgrounds. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Data Mining)
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14 pages, 861 KiB  
Article
Crystallographic Quaternions
by Andrzej Katrusiak and Stiv Llenga
Symmetry 2024, 16(7), 818; https://doi.org/10.3390/sym16070818 (registering DOI) - 29 Jun 2024
Abstract
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 [...] Read more.
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 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)
16 pages, 280 KiB  
Article
New Monotonic Properties for Solutions of Odd-Order Advanced Nonlinear Differential Equations
by Asma Al-Jaser, Belgees Qaraad, Faizah Alharbi and Stefano Serra-Capizzano
Symmetry 2024, 16(7), 817; https://doi.org/10.3390/sym16070817 (registering DOI) - 29 Jun 2024
Abstract
The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for [...] Read more.
The present paper studies the asymptotic and oscillatory properties of solutions of odd-order differential equations with advanced arguments and in a noncanonical case. By providing new and effective relationships between the corresponding function and the solution, we present strict and new criteria for testing whether the studied equation exhibits oscillatory behavior or converges to zero. Our results contribute uniquely to oscillation theory by presenting some theorems that improve and expand upon the results found in the existing literature. We also provide an example to corroborate the validity of our proposed criteria. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
19 pages, 423 KiB  
Article
Quantum Gravity Corrections to the Inflationary Spectrum in a Bohmian Approach
by Giulia Maniccia and Giovanni Montani
Symmetry 2024, 16(7), 816; https://doi.org/10.3390/sym16070816 (registering DOI) - 29 Jun 2024
Abstract
A precise interpretation of the universe wave function is forbidden in the spirit of the Copenhagen School since a precise notion of measure operation cannot be satisfactorily defined. Here, we propose a Bohmian interpretation of the isotropic universe quantum dynamics, in which the [...] Read more.
A precise interpretation of the universe wave function is forbidden in the spirit of the Copenhagen School since a precise notion of measure operation cannot be satisfactorily defined. Here, we propose a Bohmian interpretation of the isotropic universe quantum dynamics, in which the Hamilton–Jacobi equation is restated by including quantum corrections, which lead to a classical trajectory containing effects of order ℏ2. This solution is then used to determine the spectrum of gauge-invariant quantum fluctuations living on the obtained background model. The analysis is performed adopting the wave function approach to describe the fluctuation dynamics, which gives a time-dependent harmonic oscillator for each Fourier mode and whose frequency is affected by the ℏ2 corrections. The properties of the emerging spectrum are discussed, outlining the modification induced with respect to the scale-invariant result, and the hierarchy of the spectral index running is discussed. Full article
(This article belongs to the Section Physics)
18 pages, 1039 KiB  
Article
The Reliability and Availability Analysis of a Single-Unit System under the Influence of Random Shocks and the Variation in Demand from Production with Erlang Distribution
by Zienab M. Hussien and Mohamed S. El-Sherbeny
Symmetry 2024, 16(7), 815; https://doi.org/10.3390/sym16070815 (registering DOI) - 28 Jun 2024
Abstract
This study evaluates the reliability measures for a system consisting of a single unit that is subject to random shocks at random times with mismatches between demand and production. The system may sometimes be subject to random shocks leading to a system failure [...] Read more.
This study evaluates the reliability measures for a system consisting of a single unit that is subject to random shocks at random times with mismatches between demand and production. The system may sometimes be subject to random shocks leading to a system failure with probability p. The system may also fail completely for various reasons other than shocks. The unit is serviced by a technician if it is affected by a shock. However, the system may fail during operation for various other reasons, such as a programming error, human error, operational continuity and stress, and weather conditions. A single technician immediately repairs or maintains the failed unit. The system is in an operational state when there is demand or in an idle state when there is no demand. The distributions of all times in this system follow a negative exponential, while the time to repair follows a two-stage Erlang distribution. The expressions for the reliability metrics are obtained as functions of time using the Laplace transform and the supplementary variables technique. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, the efficiency of the system is illustrated using numerical examples. Full article
(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)
24 pages, 352 KiB  
Article
A Factory of Fractional Derivatives
by Manuel D. Ortigueira
Symmetry 2024, 16(7), 814; https://doi.org/10.3390/sym16070814 (registering DOI) - 28 Jun 2024
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)
13 pages, 444 KiB  
Article
Knowledge-Guided Parallel Hybrid Local Search Algorithm for Solving Time-Dependent Agile Satellite Scheduling Problems
by Yuyuan Shan, Xueping Wang, Shi Cheng, Mingming Zhang and Lining Xing
Symmetry 2024, 16(7), 813; https://doi.org/10.3390/sym16070813 (registering DOI) - 28 Jun 2024
Viewed by 59
Abstract
As satellite capabilities have evolved and new observation requirements have emerged, satellites have become essential tools in disaster relief, emergency monitoring, and other fields. However, the efficiency of satellite scheduling still needs to be enhanced. Learning and optimization are symmetrical processes of solving [...] Read more.
As satellite capabilities have evolved and new observation requirements have emerged, satellites have become essential tools in disaster relief, emergency monitoring, and other fields. However, the efficiency of satellite scheduling still needs to be enhanced. Learning and optimization are symmetrical processes of solving problems. Learning problem knowledge could provide efficient optimization strategies for solving problems. A knowledge-guided parallel hybrid local search algorithm (KG-PHLS) is proposed in this paper to solve time-dependent agile Earth observation satellite (AEOS) scheduling problems more efficiently. Firstly, the algorithm uses heuristic algorithms to generate initial solutions. Secondly, a knowledge-based parallel hybrid local search algorithm is employed to solve the problem in parallel. Meanwhile, data mining techniques are used to extract knowledge to guide the construction of new solutions. Finally, the proposed algorithm has demonstrated superior efficiency and computation time through simulations across multiple scenarios. Notably, compared to benchmark algorithms, the algorithm improves overall efficiency by approximately 7.4% and 8.9% in large-scale data scenarios while requiring only about 60.66% and 31.89% of the computation time of classic algorithms. Moreover, the proposed algorithm exhibits scalability to larger problem sizes. Full article
(This article belongs to the Special Issue Symmetric Machine Learning Method Enhanced by Evolutionary Computation and Its Applications in Big Data Analytics II)
17 pages, 2103 KiB  
Article
Structural Study of Four-Layered Cylindrical Shell Comprising Ring Support
by Madiha Ghamkhar, Ahmad N. Al-Kenani and Naveed Hussain
Symmetry 2024, 16(7), 812; https://doi.org/10.3390/sym16070812 (registering DOI) - 28 Jun 2024
Viewed by 94
Abstract
In this work, the vibration analysis of a layered, cylinder-shaped shell is undertaken. The structure of the shell layers is composed of functionally graded and isotropic materials. The vibrations of four-layered cylindrical shells with a ring support along the axial direction are investigated [...] Read more.
In this work, the vibration analysis of a layered, cylinder-shaped shell is undertaken. The structure of the shell layers is composed of functionally graded and isotropic materials. The vibrations of four-layered cylindrical shells with a ring support along the axial direction are investigated in this research. The two internal layers are composed of isotropic materials, and the external two layers are composed of functionally graded materials. The outer functionally graded material layers considered are stainless steel, zirconia, and nickel. The inner two isotropic layers considered are aluminum and stainless steel. The shell frequency equation is acquired by employing the Rayleigh–Ritz method under the shell theory of Sanders. The trigonometric volume fraction law is used to sort the functionally graded material composition of the FGM layers. The natural frequencies are attained under two boundary conditions, namely simply supported–simply supported and clamped–clamped. Full article
(This article belongs to the Special Issue Applied Mechanics, Engineering and Modeling - Volume II)
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16 pages, 2975 KiB  
Article
Asymmetry Considerations in Constructing Control Charts: When Symmetry Is Not the Norm
by Ran Etgar
Symmetry 2024, 16(7), 811; https://doi.org/10.3390/sym16070811 (registering DOI) - 28 Jun 2024
Viewed by 99
Abstract
Control charts (esp. X¯-chart) are proven and useful tools to preserve process alignment with its design mean. The control charts’ limits are designed symmetrically around the process’s mean. The assumption of symmetry is justifiable when assuming that the measurements are infinite. [...] Read more.
Control charts (esp. X¯-chart) are proven and useful tools to preserve process alignment with its design mean. The control charts’ limits are designed symmetrically around the process’s mean. The assumption of symmetry is justifiable when assuming that the measurements are infinite. Typically, these assumptions are warranted since the measuring resolution is significantly (by orders of magnitude) lower than the deviation of the controlled process. However, when the measuring device has a resolution of the same order of magnitude as the standard deviation of the controlled process, the symmetrical nature is no longer justified. In low-resolution measurement process control, symmetry is not the norm and both these control limits should be built asymmetrically. To help remedy this issue, this article explores the asymmetrical nature of the low-resolution measurement and suggests a new (asymmetric) control limit based on false-alarm-required probabilities. This represents a novel approach to the problem Full article
(This article belongs to the Section Engineering and Materials)
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11 pages, 2816 KiB  
Article
Energy Efficiency Measurement of Mechanical Crushing Based on Non-Contact Identification Method
by Xiaoquan Lu, Meimei Duan, Huiling Su, Bo Li and Ying Liu
Symmetry 2024, 16(7), 810; https://doi.org/10.3390/sym16070810 (registering DOI) - 28 Jun 2024
Viewed by 125
Abstract
The efficiency of mechanical crushing is a key metric for evaluating machinery performance. However, traditional contact-based methods for measuring this efficiency are unable to provide real-time data monitoring and can potentially disrupt the production process. In this paper, we introduce a non-contact measurement [...] Read more.
The efficiency of mechanical crushing is a key metric for evaluating machinery performance. However, traditional contact-based methods for measuring this efficiency are unable to provide real-time data monitoring and can potentially disrupt the production process. In this paper, we introduce a non-contact measurement technique for mechanical crushing efficiency based on deep learning algorithms. This technique utilizes close-range imaging equipment to capture images of crushed particles and employs deeply trained algorithmic programs rooted in symmetrical logical structures to extract statistical data on particle size. Additionally, we establish a relationship between particle size and crushing energy through experimental analysis, enabling the calculation of crushing efficiency data. Taking cement crushing equipment as an example, we apply this non-contact measurement technique to inspect cement particles of different sizes. Using deep learning algorithms, we automatically categorize and summarize the particle size ranges of cement particles. The results demonstrate that the crushing efficiencies of ore crushing particles, raw material crushing particles, and cement crushing particles can respectively reach 80.7%, 70.15%, and 80.27%, which exhibit a high degree of consistency with the rated value of the samples. The method proposed in this paper holds significant importance for energy efficiency monitoring in industries that require mechanical crushing. Full article
(This article belongs to the Special Issue Symmetry in the Mechanical Behavior of Materials)
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10 pages, 724 KiB  
Article
Minimization over Nonconvex Sets
by José Antonio Vilchez Membrilla, Víctor Salas Moreno, Soledad Moreno-Pulido, Alberto Sánchez-Alzola, Clemente Cobos Sánchez and Francisco Javier García-Pacheco
Symmetry 2024, 16(7), 809; https://doi.org/10.3390/sym16070809 - 27 Jun 2024
Viewed by 203
Abstract
Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques [...] Read more.
Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and algorithms to compute the distance of a closed convex set to the origin, which mostly exist in the Hilbert space setting. In this manuscript, we consider nonconvex minimum norm problems that arise from Bioengineering and reformulate them in such a way that the solution to their reformulation is already known. In particular, we tackle the problem of min∥x∥ subject to ∥Rk(x)∥ ≥ ak for k = 1,…,l, where x∈X and Rk:X→Y are continuous linear operators between real normed spaces X,Y, and ak > 0 for k = 1,…,l. Notice that the region of constraints of the previous problem is neither convex nor balanced. However, it is additively symmetric, which is also the case for the objective function, due to the properties satisfied by norms, which makes possible the analytic resolution of such a nonconvex minimization. The recent literature shows that the design of optimal coils for electronics applications can be achieved by solving problems like this. However, in this work, we apply our analytical solutions to design an optimal coil for an electromagnetic sensor. Full article
(This article belongs to the Section Mathematics)
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22 pages, 6275 KiB  
Review
Type-B Energetic Processes: Their Identification and Implications
by James Weifu Lee
Symmetry 2024, 16(7), 808; https://doi.org/10.3390/sym16070808 - 27 Jun 2024
Viewed by 185
Abstract
We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type-A energy processes, such as classical heat engines, apparently well follow the second law of thermodynamics; Type-B energy processes, such as the newly discovered thermotrophic [...] Read more.
We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type-A energy processes, such as classical heat engines, apparently well follow the second law of thermodynamics; Type-B energy processes, such as the newly discovered thermotrophic function that isothermally utilizes environmental heat energy to perform useful work in driving ATP synthesis, follow the first law of thermodynamics (conservation of mass and energy) but do not have to be constrained by the second law, owing to their special asymmetric functions. Several Type-B energy processes such as asymmetric function-gated isothermal electricity production and epicatalysis have been created through human efforts. The innovative efforts in Type-B processes to enable isothermally utilizing endless environmental heat energy could help to liberate all peoples from their dependence on fossil fuel energy, thus helping to reduce greenhouse gas CO2 emissions and control climate change towards a sustainable future for humanity on Earth. In addition to the needed support for further research, development, and commercialization efforts, currently, better messaging and education on Type-B energetic processes are also highly needed to achieve the mission. Full article
(This article belongs to the Section Chemistry: Symmetry/Asymmetry)
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18 pages, 704 KiB  
Article
Radial Oscillations of Strange Quark Stars Admixed with Dark Matter
by Yu Zhen, Ting-Ting Sun, Jin-Biao Wei, Zi-Yue Zheng and Huan Chen
Symmetry 2024, 16(7), 807; https://doi.org/10.3390/sym16070807 - 27 Jun 2024
Viewed by 164
Abstract
We investigate the equilibrium structure and radial oscillations of strange quark stars admixed with fermionic dark matter. For strange quark matter, we employ a stiff equation of state from a color-superconductivity improved bag model. For dark matter, we adopt the cold free Fermi [...] Read more.
We investigate the equilibrium structure and radial oscillations of strange quark stars admixed with fermionic dark matter. For strange quark matter, we employ a stiff equation of state from a color-superconductivity improved bag model. For dark matter, we adopt the cold free Fermi gas model. We rederive and numerically solve the radial oscillation equations of two-fluid stars based on general relativity, in which the dark matter and strange quark matter couple through gravity and oscillate with the same frequency. Our results show that the stellar maximum mass and radius are reduced by inclusion of dark matter. As to the fundamental mode of the radial oscillations, the frequency f0 is also reduced comparing to pure strange stars, and f02 reaches the zero point at the maximum stellar mass with dM/dϵq,c=0. Therefore, the stability criteria f02>0 and dM/dϵq,c>0 are consistent in our dark matter-mixed strange quark stars with a fixed fraction of dark matter. We also find a discontinuity of f0 as functions of the stellar mass, in contrast to the continuous function in pure strange stars. And it is also accompanied with discontinuity of the oscillation amplitudes as well as a discontinuous in-phase-to-out-phase transition between oscillations of dark matter and strange quark matter. Full article
(This article belongs to the Special Issue Symmetry in Hadron Physics)
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12 pages, 2061 KiB  
Article
Optimal Harvesting Strategies for Timber and Non-Timber Forest Products with Nonlinear Harvesting Terms
by Yaning Zhang, Lina Hao and Shan Zhang
Symmetry 2024, 16(7), 806; https://doi.org/10.3390/sym16070806 - 27 Jun 2024
Viewed by 148
Abstract
Forest resources are renewable, and the rational exploitation and utilization of forest resources are not only conducive to sustainable development on a population scale, they can also lead to higher economic benefits. Based on the actual timber harvest problem, this paper establishes the [...] Read more.
Forest resources are renewable, and the rational exploitation and utilization of forest resources are not only conducive to sustainable development on a population scale, they can also lead to higher economic benefits. Based on the actual timber harvest problem, this paper establishes the joint harvest model of timber and non-timber with nonlinear harvest items. In the numerical simulation, by comparing the existing proportional harvest model, it is concluded that the optimal harvest strategy of nonlinear harvest items in this paper can obtain larger ecological benefits and be more conducive to the sustainable development of a population. Firstly, using the qualitative theory of ordinary differential equations, the dynamic behavior of the model is studied, and the existence and stability of the equilibrium point of the model are proven. Secondly, the optimal control solution is obtained by using the optimal control theory. Finally, the optimal harvesting strategy of timber and non-timber products is given based on the numerical simulation results, and a comparison of the effects of different parameters on the optimal harvest strategy, which provides a certain theoretical basis for the sustainable development of the ecological economy of forestry, is carried out. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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16 pages, 1690 KiB  
Article
Cold Chain Logistics Center Layout Optimization Based on Improved Dung Beetle Algorithm
by Jinhui Li and Qing Zhou
Symmetry 2024, 16(7), 805; https://doi.org/10.3390/sym16070805 - 27 Jun 2024
Viewed by 140
Abstract
To reduce the impact of the cold chain logistics center layout on economic benefits, operating efficiency and carbon emissions, a layout optimization method is proposed based on the improved dung beetle algorithm. Firstly, based on the analysis of the relationship between logistics and [...] Read more.
To reduce the impact of the cold chain logistics center layout on economic benefits, operating efficiency and carbon emissions, a layout optimization method is proposed based on the improved dung beetle algorithm. Firstly, based on the analysis of the relationship between logistics and non-logistics, a multi-objective optimization model is established to minimize the total logistics cost, maximize the adjacency correlation and minimize the carbon emissions; secondly, based on the standard Dung Beetle Optimization (DBO) algorithm, in order to further improve the global exploration ability of the algorithm, Chebyshev chaotic mapping and an adaptive Gaussian–Cauchy hybrid mutation disturbance strategy are introduced to improve the DBO (IDBO) algorithm; finally, taking an actual cold chain logistics center as an example, the DBO algorithm and the improved DBO algorithm are applied to optimize its layout, respectively. The results show that the total logistics cost after optimization of the IDBO algorithm is reduced by 25.54% compared with the original layout, the adjacency correlation is improved by 29.93%, and the carbon emission is reduced by 6.75%, verifying the effectiveness of the proposed method and providing a reference for the layout design of cold chain logistics centers. Full article
(This article belongs to the Special Issue Symmetry: Recent Developments in Engineering Science and Applications)
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21 pages, 3192 KiB  
Article
Cutting-Edge Machine Learning Techniques for Accurate Prediction of Agglomeration Size in Water–Alumina Nanofluids
by Behzad Vaferi, Mohsen Dehbashi and Ali Hosin Alibak
Symmetry 2024, 16(7), 804; https://doi.org/10.3390/sym16070804 - 27 Jun 2024
Viewed by 185
Abstract
Nanoparticle agglomeration is one of the most problematic phenomena during nanofluid synthesis by a two-step procedure. Understanding and accurately estimating agglomeration size is crucial, as it significantly affects nanofluids’ properties, behavior, and successful applications. To the best of our knowledge, the literature has [...] Read more.
Nanoparticle agglomeration is one of the most problematic phenomena during nanofluid synthesis by a two-step procedure. Understanding and accurately estimating agglomeration size is crucial, as it significantly affects nanofluids’ properties, behavior, and successful applications. To the best of our knowledge, the literature has not yet applied machine learning methods to estimate alumina agglomeration size in water-based nanofluids. So, this research employs a range of machine learning models—Random Forest, Adaptive Boosting, Extra Trees, Categorical Boosting, and Multilayer Perceptron Neural Networks—to predict alumina agglomeration sizes in water-based nanofluids. To this end, a comprehensive experimental database, including 345 alumina agglomeration sizes in water-based nanofluids, compiled from 29 various sources from the literature, is utilized to train these models and monitor their generalization ability in the testing stage. The models estimate agglomeration size based on multiple factors: alumina concentration, ultrasonic time, power, frequency, temperature, surfactant type and concentration, and pH levels. The relevancy test based on the Pearson method clarifies that Al2O3 agglomeration size in water primarily depends on ultrasonic frequency, ultrasonic power, alumina concentration in water, and surfactant concentration. Comparative analyses based on numerical and graphical techniques reveal that the Categorical Boosting model surpasses others in accurately simulating this complex phenomenon. It effectively captures the intricate relationships between key features and alumina agglomeration size, achieving an average absolute relative deviation of 6.75%, a relative absolute error of 12.83%, and a correlation coefficient of 0.9762. Furthermore, applying the leverage method to the experimental data helps identify two problematic measurements within the database. These results validate the effectiveness of the Categorical Boosting model and contribute to the broader goal of enhancing our understanding and control of nanofluid properties, thereby aiding in improving their practical applications. Full article
(This article belongs to the Special Issue Machine Learning and Data Analysis II)
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13 pages, 1513 KiB  
Article
Optical Bistability of Graphene Incorporated into All-Superconducting Photonic Crystals
by Qun Xiao, Jun Liu, Dong Zhao, Miaomiao Zhao and Haiyang Hu
Symmetry 2024, 16(7), 803; https://doi.org/10.3390/sym16070803 - 26 Jun 2024
Viewed by 160
Abstract
We investigated optical bistability and its temperature dependence in a composite system composed of an all-superconducting photonic crystal and graphene. The photonic crystal, constructed from two types of superconducting sheets, and which is temperature-sensitive and can greatly localize the electric field, alternately supports [...] Read more.
We investigated optical bistability and its temperature dependence in a composite system composed of an all-superconducting photonic crystal and graphene. The photonic crystal, constructed from two types of superconducting sheets, and which is temperature-sensitive and can greatly localize the electric field, alternately supports a defect mode in a cryogenic environment. Graphene is located at the strongest site in the electric field, so the third-order nonlinearity of graphene is enhanced tremendously, and, subsequently, low thresholds of optical bistability are achieved in the near-infrared region. The thresholds of optical bistability and the interval between the upper and lower thresholds decrease with the increase in environmental temperature, while the bistable thresholds increase with the addition of the incident wavelength. Furthermore, the critical threshold triggering optical bistability can be modulated by environment temperature and the periodic number of photonic crystals as well. The simulations may be found to be applicable for all temperature-sensitive optical switches or sensors in cryogenic environments. Full article
(This article belongs to the Section Physics)
34 pages, 2197 KiB  
Article
Advanced Statistical Approach for the Mathematical Modeling of Transfer Processes in a Layer Based on Experimental Data at the Boundary
by Olha Chernukha, Petro Pukach, Halyna Bilushchak, Yurii Bilushchak and Myroslava Vovk
Symmetry 2024, 16(7), 802; https://doi.org/10.3390/sym16070802 - 26 Jun 2024
Viewed by 156
Abstract
In this work, a mathematical model of the transfer process in a layer under the condition of given experimental data on a part of the layer boundary is presented and investigated. Such research is important for the mathematical description of the objects and [...] Read more.
In this work, a mathematical model of the transfer process in a layer under the condition of given experimental data on a part of the layer boundary is presented and investigated. Such research is important for the mathematical description of the objects and systems for which, based on physical considerations, it is impossible to correctly impose boundary or initial conditions, even in a sufficiently general form, but there are experimental data on the desired function or its derivative at the boundary of the body or at the initial time. The values of the desired function at the boundary are known at certain moments in time. The boundary condition is constructed by the experimental data and the initial-boundary value problem, with such a boundary condition, is formulated and solved. The influence of the statistical characteristics of the sample of experimental data on the solution to the initial-boundary value problem is analyzed, and a two-sided statistical estimation of the solution is determined. The confidence intervals for the coefficients of the regression equation and the corresponding confidence intervals for the sought function are established. The influence of the statistical characteristics of the sample on the sought function at the lower boundary of the layer is investigated. Numerical analysis of the solution to the initial-boundary value problem is carried out depending on the statistical characteristics of the sample. Various cases of samples by size and variance are considered. Numerical solutions are studied under the conditions of large and small time intervals of the considered process. Full article
(This article belongs to the Section Mathematics)
23 pages, 6711 KiB  
Article
Simulation of Dynamic Path Planning of Symmetrical Trajectory of Mobile Robots Based on Improved A* and Artificial Potential Field Fusion for Natural Resource Exploration
by Yuriy Kozhubaev and Ruide Yang
Symmetry 2024, 16(7), 801; https://doi.org/10.3390/sym16070801 - 26 Jun 2024
Viewed by 212
Abstract
With the rapid development of new-generation artificial intelligence and Internet of Things technology, mobile robot technology has been widely used in various fields. Among them, the autonomous path-planning technology of mobile robots is one of the cores for realizing their autonomous driving and [...] Read more.
With the rapid development of new-generation artificial intelligence and Internet of Things technology, mobile robot technology has been widely used in various fields. Among them, the autonomous path-planning technology of mobile robots is one of the cores for realizing their autonomous driving and obstacle avoidance. This study conducts an in-depth discussion on the real-time and dynamic obstacle avoidance capabilities of mobile robot path planning. First, we proposed a preprocessing method for obstacles in the grid map, focusing on the closed processing of the internal space of concave obstacles to ensure the feasibility of the path while effectively reducing the number of grid nodes searched by the A* algorithm, thereby improving path search efficiency. Secondly, in order to achieve static global path planning, this study adopts the A algorithm. However, in practice, algorithm A has problems such as a large number of node traversals, low search efficiency, redundant path nodes, and uneven turning angles. To solve these problems, we optimized the A* algorithm, focusing on optimizing the heuristic function and weight coefficient to reduce the number of node traversals and improve search efficiency. In addition, we use the Bezier curve method to smooth the path and remove redundant nodes, thereby reducing the turning angle. Then, in order to achieve dynamic local path planning, this study adopts the artificial potential field method. However, the artificial potential field method has the problems of unreachable target points and local minima. In order to solve these problems, we optimized the repulsion field so that the target point is at the lowest point of the global energy of the gravitational field and the repulsive field and eliminated the local optimal point. Finally, for the path-planning problem of mobile robots in dynamic environments, this study proposes a hybrid path-planning method based on a combination of the improved A* algorithm and the artificial potential field method. In this study, we not only focus on the efficiency of mobile robot path planning and real-time dynamic obstacle avoidance capabilities but also pay special attention to the symmetry of the final path. By introducing symmetry, we can more intuitively judge whether the path is close to the optimal state. Symmetry is an important criterion for us to evaluate the performance of the final path. Full article
(This article belongs to the Special Issue Computer Science and Symmetry/Asymmetry: Feature Papers)
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16 pages, 2465 KiB  
Article
Dynamics and Optimal Harvesting for Fishery Models with Reserved Areas
by Wenjun Gao, Xiu Jia and Ruiqing Shi
Symmetry 2024, 16(7), 800; https://doi.org/10.3390/sym16070800 - 26 Jun 2024
Viewed by 191
Abstract
This paper analyzes the dynamic behavior of a fishery model described by differential algebraic equations. Two patches, namely free fishing area and protected area, are included in the model. The migration of fish is symmetrical, i.e., the fish can migrate between the two [...] Read more.
This paper analyzes the dynamic behavior of a fishery model described by differential algebraic equations. Two patches, namely free fishing area and protected area, are included in the model. The migration of fish is symmetrical, i.e., the fish can migrate between the two patches. It is observed that a singularity-induced bifurcation occurs when the economic benefit of harvesting changes. When the economic benefit is positive, a state feedback controller is added to stabilize the system. Some examples and numerical simulations are presented to verify the theoretical results. In addition, harvesting of prey populations is used as a control measure to obtain the maximum economic benefits and ecological sustainability. The optimal solution is derived by using Pontryagin’s maximum principle. Through extensive numerical simulations, it is shown that the optimal solution is capable of achieving ecosystem sustainability. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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10 pages, 266 KiB  
Article
Fixed Point of α-Modular Nonexpanive Mappings in Modular Vector Spaces ℓp(·)
by Buthinah A. Bin Dehaish and Mohamed A. Khamsi
Symmetry 2024, 16(7), 799; https://doi.org/10.3390/sym16070799 - 25 Jun 2024
Viewed by 314
Abstract
Let C denote a convex subset within the vector space ℓp(·), and let T represent a mapping from C onto itself. Assume α=(α1,⋯,αn) is a multi-index in [...] Read more.
Let C denote a convex subset within the vector space ℓp(·), and let T represent a mapping from C onto itself. Assume α=(α1,⋯,αn) is a multi-index in [0,1]n such that ∑i=1nαi=1, where α1>0 and αn>0. We define Tα:C→C as Tα=∑i=1nαiTi, known as the mean average of the mapping T. While every fixed point of T remains fixed for Tα, the reverse is not always true. This paper examines necessary and sufficient conditions for the existence of fixed points for T, relating them to the existence of fixed points for Tα and the behavior of T-orbits of points in T’s domain. The primary approach involves a detailed analysis of recurrent sequences in R. Our focus then shifts to variable exponent modular vector spaces ℓp(·), where we explore the essential conditions that guarantee the existence of fixed points for these mappings. This investigation marks the first instance of such results in this framework. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
20 pages, 5324 KiB  
Article
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
Viewed by 184
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)
25 pages, 1614 KiB  
Article
Frequency-Enhanced Transformer with Symmetry-Based Lightweight Multi-Representation for Multivariate Time Series Forecasting
by Chenyue Wang, Zhouyuan Zhang, Xin Wang, Mingyang Liu, Lin Chen and Jiatian Pi
Symmetry 2024, 16(7), 797; https://doi.org/10.3390/sym16070797 - 25 Jun 2024
Viewed by 167
Abstract
Transformer-based methods have recently demonstrated their potential in time series forecasting problems. However, the mainstream approach, primarily utilizing attention to model inter-step correlation in the time domain, is constrained by two significant issues that lead to ineffective and inefficient multivariate forecasting. The first [...] Read more.
Transformer-based methods have recently demonstrated their potential in time series forecasting problems. However, the mainstream approach, primarily utilizing attention to model inter-step correlation in the time domain, is constrained by two significant issues that lead to ineffective and inefficient multivariate forecasting. The first is that key representations in the time domain are scattered and sparse, resulting in parameter bloat and increased difficulty in capturing time dependencies. The second is that treating time step points as uniformly embedded tokens leads to the erasure of inter-variate correlations. To address these challenges, we propose a frequency-wise and variables-oriented transformer-based method. This method leverages the intrinsic conjugate symmetry in the frequency domain, enabling compact frequency domain representations that naturally mix information across time points while reducing spatio-temporal costs. Multivariate inter-correlations can also be captured from similar frequency domain components, which enhances the variables-oriented attention mechanism modeling capability. Further, we employ both polar and complex domain perspectives to enrich the frequency domain representations and decode complicated temporal patterns. We propose frequency-enhanced independent representation multi-head attention (FIR-Attention) to leverage these advantages for improved multivariate interaction. Techniques such as cutting-off frequency and equivalent mapping are used to ensure the model’s lightweight nature. Extensive experiments on eight mainstream datasets show that our approach achieves first-rate satisfactory results and, importantly, requires only one percent of the spatio-temporal cost of mainstream methods. Full article
(This article belongs to the Section Computer)
17 pages, 323 KiB  
Article
Solutions for the Nonlinear Mixed Variational Inequality Problem in the System
by Husain Gissy, Abdullah Ali H. Ahmadini and Salahuddin
Symmetry 2024, 16(7), 796; https://doi.org/10.3390/sym16070796 - 25 Jun 2024
Viewed by 149
Abstract
Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is nonempty, weakly compact, and unique. Additionally, [...] Read more.
Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is nonempty, weakly compact, and unique. Additionally, we suggest a stability result for the SNMVIPs by perturbing the duality mappings. Furthermore, we present an optimal control problem that is governed by the SNMVIPs and show that it can be solved. Full article
(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)
40 pages, 5270 KiB  
Article
DTSA: Dynamic Tree-Seed Algorithm with Velocity-Driven Seed Generation and Count-Based Adaptive Strategies
by Jianhua Jiang, Jiansheng Huang, Jiaqi Wu, Jinmeng Luo, Xi Yang and Weihua Li
Symmetry 2024, 16(7), 795; https://doi.org/10.3390/sym16070795 - 25 Jun 2024
Viewed by 232
Abstract
The Tree-Seed Algorithm (TSA) has been effective in addressing a multitude of optimization issues. However, it has faced challenges with early convergence and difficulties in managing high-dimensional, intricate optimization problems. To tackle these shortcomings, this paper introduces a TSA variant (DTSA). DTSA incorporates [...] Read more.
The Tree-Seed Algorithm (TSA) has been effective in addressing a multitude of optimization issues. However, it has faced challenges with early convergence and difficulties in managing high-dimensional, intricate optimization problems. To tackle these shortcomings, this paper introduces a TSA variant (DTSA). DTSA incorporates a suite of methodological enhancements that significantly bolster TSA’s capabilities. It introduces the PSO-inspired seed generation mechanism, which draws inspiration from Particle Swarm Optimization (PSO) to integrate velocity vectors, thereby enhancing the algorithm’s ability to explore and exploit solution spaces. Moreover, DTSA’s adaptive velocity adaptation mechanism based on count parameters employs a counter to dynamically adjust these velocity vectors, effectively curbing the risk of premature convergence and strategically reversing vectors to evade local optima. DTSA also integrates the trees population integrated evolutionary strategy, which leverages arithmetic crossover and natural selection to bolster population diversity, accelerate convergence, and improve solution accuracy. Through experimental validation on the IEEE CEC 2014 benchmark functions, DTSA has demonstrated its enhanced performance, outperforming recent TSA variants like STSA, EST-TSA, fb-TSA, and MTSA, as well as established benchmark algorithms such as GWO, PSO, BOA, GA, and RSA. In addition, the study analyzed the best value, mean, and standard deviation to demonstrate the algorithm’s efficiency and stability in handling complex optimization issues, and DTSA’s robustness and efficiency are proven through its successful application in five complex, constrained engineering scenarios, demonstrating its superiority over the traditional TSA by dynamically optimizing solutions and overcoming inherent limitations. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Their Applications)
21 pages, 2882 KiB  
Article
Human–Robot Collaboration on a Disassembly-Line Balancing Problem with an Advanced Multiobjective Discrete Bees Algorithm
by Yanda Shen, Weidong Lu, Haowen Sheng, Yangkun Liu, Guangdong Tian, Honghao Zhang and Zhiwu Li
Symmetry 2024, 16(7), 794; https://doi.org/10.3390/sym16070794 - 24 Jun 2024
Viewed by 338
Abstract
As resources become increasingly scarce and environmental demands grow, the recycling of products at the end of their lifecycle becomes crucial. Disassembly, as a key stage in the recycling process, plays a decisive role in the sustainability of the entire operation. Advances in [...] Read more.
As resources become increasingly scarce and environmental demands grow, the recycling of products at the end of their lifecycle becomes crucial. Disassembly, as a key stage in the recycling process, plays a decisive role in the sustainability of the entire operation. Advances in automation technology and the integration of Industry 5.0 principles make the balance of human–robot collaborative disassembly lines an important research topic. This study uses disassembly-precedence graphs to clarify disassembly-task information and converts it into a task-precedence matrix. This matrix includes both symmetry and asymmetry, reflecting the dependencies and independencies among disassembly tasks. Based on this, we develop a multiobjective optimisation model that integrates disassembly-task allocation, operation mode selection, and the use of collaborative robots. The objectives are to minimise the number of workstations, the idle rate of the disassembly line, and the energy consumption. Given the asymmetry in disassembly-task attributes, such as the time differences required for disassembling various components and the diverse operation modes, this study employs an evolutionary algorithm to address potential asymmetric optimisation problems. Specifically, we introduce an advanced multi-objective discrete bee algorithm and validate its effectiveness and superiority for solving the disassembly-line balancing problem through a comparative analysis with other algorithms. This research not only provides innovative optimisation strategies for the product-recycling field but also offers valuable experience and reference for the further development of industrial automation and human–robot collaboration. Full article
(This article belongs to the Section Engineering and Materials)
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9 pages, 262 KiB  
Article
Positive Radial Symmetric Solutions of Nonlinear Biharmonic Equations in an Annulus
by Yongxiang Li and Shengbin Yang
Symmetry 2024, 16(7), 793; https://doi.org/10.3390/sym16070793 - 24 Jun 2024
Viewed by 258
Abstract
This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵2u=f(u,▵u) on an annular domain Ω in RN with the Navier boundary conditions [...] Read more.
This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵2u=f(u,▵u) on an annular domain Ω in RN with the Navier boundary conditions u|∂Ω=0 and ▵u|∂Ω=0, where f:R+×R−→R+ is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f(ξ,η) to have superlinear or sublinear growth on ξ,η as |(ξ,η)|→0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
22 pages, 8574 KiB  
Article
Study on Mathematical Models for Precise Estimation of Tire–Road Friction Coefficient of Distributed Drive Electric Vehicles Based on Sensorless Control of the Permanent Magnet Synchronous Motor
by Binghao Yu, Yiming Hu and Dequan Zeng
Symmetry 2024, 16(7), 792; https://doi.org/10.3390/sym16070792 - 24 Jun 2024
Viewed by 327
Abstract
In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a [...] Read more.
In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a permanent magnet synchronous motor (PMSM). The algorithm replaces the wheel angular velocity signal with the rotor speed signal obtained from the sensorless control of the PMSM. Firstly, a seven-degree-of-freedom vehicle dynamics model and a mathematical model of the PMSM are established, and the maximum correntropy singular value decomposition generalized high-degree cubature Kalman filter algorithm (MCSVDGHCKF) is derived. Secondly, a sensorless control system of a PMSM based on the MCSVDGHCKF algorithm is established to estimate the rotor speed and position of the PMSM, and its effectiveness is verified. Finally, the feasibility of the algorithm for TRFC estimation in non-Gaussian noise is demonstrated through simulation experiments, the Root Mean Square Error (RMSE) of TRFC estimates for the right front wheel and the left rear wheel were reduced by at least 41.36% and 40.63%, respectively. The results show that the MCSVDGHCKF has a higher accuracy and stronger robustness compared to the maximum correntropy high-degree cubature Kalman filter (MCHCKF), singular value decomposition generalized high-degree cubature Kalman filter (SVDGHCKF), and high-degree cubature Kalman filter (HCKF). Full article
(This article belongs to the Section Engineering and Materials)
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17 pages, 5686 KiB  
Article
Fast Prediction of Airfoil Aerodynamic Characteristics Based on a Combined Autoencoder
by Xu Wang, Weiqi Qian, Tun Zhao, Lei He, Hai Chen, Haisheng Sun, Yuan Tian and Jinlei Cui
Symmetry 2024, 16(7), 791; https://doi.org/10.3390/sym16070791 - 24 Jun 2024
Viewed by 263
Abstract
Aircraft airfoils are classified into two main categories: symmetrical and asymmetrical. Both types of airfoils have a significant impact on the flight performance and safety of the aircraft. The fast prediction of the aerodynamic coefficients and pressure distributions of airfoils is crucial for [...] Read more.
Aircraft airfoils are classified into two main categories: symmetrical and asymmetrical. Both types of airfoils have a significant impact on the flight performance and safety of the aircraft. The fast prediction of the aerodynamic coefficients and pressure distributions of airfoils is crucial for the design of aircraft. The traditional wind tunnel test and CFD methods have the disadvantages of high test cost and high time consumption. To solve these problems, a combined autoencoder (CAE) network is proposed in this paper, which can achieve the fast prediction of airfoil aerodynamic coefficients and pressure distributions. The network consists of an airfoil shape autoencoder (AE) network and a multilayer perceptron (MLP) network. Firstly, an autoencoder network reflecting the characteristics of the airfoil shape is established, and the effects of different latent variables on the performance of the autoencoder network are investigated. Then, the latent variables obtained from the autoencoder are concatenated with the inflow conditions such as the Reynolds number and the angle of attack to be used as inputs to the MLP network, and the aerodynamic coefficients of different airfoils in different inflow conditions are predicted. The effects of various latent variable inputs, as well as the direct input of the airfoil shape into the MLP network, on the prediction performance of aerodynamic coefficients are compared and analyzed. The optimal aerodynamic coefficient prediction network is then obtained. Finally, the CAE network is also applied to predict the pressure distributions of different airfoils in different inflow conditions and the effects of different latent variables and input conditions on the prediction performance of the pressure distributions are analyzed and compared with the advantages and disadvantages of the CAE network and the conditional variational autoencoder (CVAE) network. The results demonstrate that the proposed method is capable of accurately predicting aerodynamic characteristics in a shorter time, offering a valuable reference for the fast and efficient design of aircraft airfoils. Full article
(This article belongs to the Section Engineering and Materials)
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17 pages, 382 KiB  
Article
Novel Algorithm for Comparing Phylogenetic Trees with Different but Overlapping Taxa
by Aleksandr Koshkarov and Nadia Tahiri
Symmetry 2024, 16(7), 790; https://doi.org/10.3390/sym16070790 - 24 Jun 2024
Viewed by 394
Abstract
Comparing phylogenetic trees is a prominent problem widely used in applications such as clustering and building the Tree of Life. While there are many well-developed distance measures for phylogenetic trees defined on the same set of taxa, the situation is contrasting for trees [...] Read more.
Comparing phylogenetic trees is a prominent problem widely used in applications such as clustering and building the Tree of Life. While there are many well-developed distance measures for phylogenetic trees defined on the same set of taxa, the situation is contrasting for trees defined on different but mutually overlapping sets of taxa. This paper presents a new polynomial-time algorithm for completing phylogenetic trees and computing the distance between trees defined on different but overlapping sets of taxa. This novel approach considers both the branch lengths and the topology of the phylogenetic trees being compared. We demonstrate that the distance measure applied to completed trees is a metric and provide several properties of the new method, including its symmetrical nature in tree completion. Full article
(This article belongs to the Special Issue Applications of Symmetry in Computational Biology)
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