Symmetry doi: 10.3390/sym13030375

Authors: Fiscaletti Licata Tamburini

The problem of baryon asymmetry unifies cosmology and particle physics at the hearth of theoretical physics. In this work, we consider the point of view of archaic cosmology based on the de Sitter hypersphere as topology of quantum vacuum. We show CPT symmetry derives from the nucleation of particles that divides the hypersphere in two mirror universes and defines big bang as a bifurcation point, as the creation of a de Sitter universe or a pair of entangled universes from “nothing”. Then, we direct our attention to the behavior of neutrinos in a CPT universe and discuss the differences between Majorana and Dirac neutrinos in the observational imprints of the entangled universes.

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Authors: Coelho Fidalgo Crisóstomo Salas-González Coimbra Mendes

Measuring biometric tree characteristics to estimate the volume of wood in a forest area is a time consuming task. It is usually performed by a team of two or more people, who measure the diameter and height of several trees in sampling plots. The results are then extrapolated for the forest stand. The present paper describes a method which facilitates estimating tree biometric parameters using computational techniques. A camera takes two pictures of each sample tree, with an especially designed target placed close to the tree, to facilitate image processing and camera calibration steps. Taking advantage of the trees’ natural shape and assuming a symmetric stem, the diameter and height of the tree stems are estimated from the images and the volumes of the tree stems are calculated. Experimental trials show promising results, exhibiting errors similar to the traditional methods used currently, in the range of 10%, showing that the method is suitable for forest inventory.

]]>Symmetry doi: 10.3390/sym13030373

Authors: Shahanaz Parvin Siti Suzilliana Putri Mohamed Isa Norihan Md Arifin Fadzilah Md Ali

The development of the mathematical modeling of Casson fluid flow and heat and mass transfer is presented in this paper. The model is subjected to the following physical parameters: shrinking parameter, mixed convection, concentration buoyancy ratio parameter, Soret number, and Dufour number. This model is also subjected to the inclined magnetic field and shrinking sheet at a certain angle projected from the y- and x-axes, respectively. The MATLAB bvp4c program is the main mathematical program that was used to obtain the final numerical solutions for the reduced ordinary differential equations (ODEs). These ODEs originate from the governing partial differential equations (PDEs), where the transformation can be achieved by applying similarity transformations. The MATLAB bvp4c program was also implemented to develop stability analysis, where this calculation was executed to recognize the most stable numerical solution. Numerical graphics were made for the skin friction coefficient, local Nusselt number, local Sherwood number, velocity profile, temperature profile, and concentration profile for certain values of the physical parameters. It is found that all the governed parameters affected the variations of the Casson fluid flow, heat transfer, mass transfer, and the profiles of velocity, temperature, and concentration. In addition, a stable solution can be applied to predict the impact of physical parameters on the actual fluid model by using a mathematical fluid model.

]]>Symmetry doi: 10.3390/sym13030372

Authors: Nir Hacker Boris A. Malomed

We consider a two-component linearly coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO’s ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carries over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas–Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

]]>Symmetry doi: 10.3390/sym13030371

Authors: Petko D. Proinov

In this work, two broad classes of iteration functions in n-dimensional vector spaces are introduced. They are called iteration functions of the first and second kind at a fixed point of the corresponding iteration function. Two general local convergence theorems are presented for Picard-type iterative methods with high Q-order of convergence. In particular, it is shown that if an iterative method is generated by an iteration function of first or second kind, then it is Q-convergent under each initial approximation that is sufficiently close to the fixed point. As an application, a detailed local convergence analysis of two fourth-order iterative methods is provided for finding all zeros of a polynomial simultaneously. The new results improve the previous ones for these methods in several directions.

]]>Symmetry doi: 10.3390/sym13030370

Authors: Chia-Nan Wang Van Thanh Nguyen Jui-Chung Kao Chih-Cheng Chen Viet Tinh Nguyen

The European Union (EU) is the largest shrimp consumer market in the world in terms of requirements for shrimp product imports. Therefore, other enterprises that export frozen shrimp to the EU must consider many criteria when choosing suppliers of raw shrimp. The difficulty of choosing suppliers of raw shrimp makes selecting raw material suppliers in the fisheries sector a multi-criteria decision-making problem. In such problems, the decision makers must review and evaluate many criteria—including qualitative and quantitative factors—to achieve an optimal result. While there have been multiple multi-criteria decision making models developed to support supplier selection processes in different industries, none of these have been developed to solve the particular problems facing the shrimp industry, especially as it concerns a fuzzy decision-making environment. In this research, the authors propose a Multi-Criteria Decision Making model (MCDM) including the Fuzzy Analytical Network Process (FANP) and Weighted Aggregated Sum Product Assessment (WASPAS) for the evaluation and selection process of shrimp suppliers in the fisheries industry. The model is applied to a real-world case study and the results show that Supplier 3 (SA3) is the most optimal supplier of raw shrimp. The contribution of this work is the employment of FANP and WASPAS to propose an MCDM for ranking potential suppliers in the fisheries industry in a fuzzy environment. The proposed approach can also be modified to support complex decision-making processes in fuzzy environments in different industries.

]]>Symmetry doi: 10.3390/sym13030369

Authors: Lichao Huang Ülo Niinemets Jianzhong Ma Julian Schrader Rong Wang Peijian Shi

Leaf area is among the most important leaf functional traits, and it determines leaf temperature and alters light harvesting. The calculation of individual leaf area is the basis of calculating the leaf area index (i.e., the total leaf area per unit ground area) that is directly associated with the ability of plants to intercept light for photosynthesis. It is valuable to provide a fast and reliable approach to measuring leaf area. Here, we examined the validity and calculation accuracy of the Montgomery equation (ME), which describes the area of a leaf as a product of leaf length, width and a specific coefficient referred to as the Montgomery parameter, MP. Using ME, we calculated leaf areas of different age groups of bamboo culms. For most broad-leaved plants, leaf area is proportional to the product of leaf length and width, and MP falls within a range of 1/2 to π/4, depending on leaf shape. However, it is unknown whether there is an intra-specific variation in MP resulting from age structure and whether such a variation can significantly reduce the predictability of ME in calculating leaf area. This is relevant as a population of perennial plants usually composes of different age groups. We used Moso bamboos as model as this species is of ecological and economic importance in southern China, and pure stands can cover six to seven plant age groups. We used five age groups of moso bamboo and sampled 260–380 leaves for each group to test whether ME holds true for each group and all groups combined, whether there are significant differences in MP among different age groups, and whether the differences in MP can lead to large prediction errors for leaf area. We observed that for each age group and all groups combined, there were significant proportional relationships between leaf area and the product of leaf length and width. There were small but significant differences in MP among the five age groups (MP values ranged from 0.6738 to 0.7116 for individual plant ages; MP = 0.6936 for all age groups combined), which can be accounted for by the minor intergroup variation of leaf shape (reflected by the leaf width/length ratio). For all age classes, MP estimated for the pooled data resulted in &lt;4% mean absolute percentage error, indicating that the effect of variation in MP among different age groups was small. We conclude that ME can serve as a useful tool for accurate calculations of leaf area in moso bamboo independent of culm age, which is valuable for estimation of leaf area index as well as evaluating the productivity and carbon sequestration capacity of bamboo forests.

]]>Symmetry doi: 10.3390/sym13030368

Authors: Moein Khalighi Leila Eftekhari Soleiman Hosseinpour Leo Lahti

In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.

]]>Symmetry doi: 10.3390/sym13030367

Authors: Shyam Sundar Santra Debasish Majumder Rupak Bhattacharjee Omar Bazighifan Khaled Mohamed Khedher Marin Marin

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form p(ι)w′(ι)α′+r(ι)uβ(ν(ι))=0,ι≥ι0 where w(ι)=u(ι)+q(ι)u(ζ(ι)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

]]>Symmetry doi: 10.3390/sym13030366

Authors: Alexander Kritov

This paper presents a novel approach to the cosmological constant problem by the use of the Clifford algebras of space Cl3,0 and anti-space Cl0,3 with a particular focus on the paravector representation, emphasizing the fact that both algebras have a center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3H0c. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl3,0 corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl0,3 leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.

]]>Symmetry doi: 10.3390/sym13030365

Authors: Yun Jiang Wenhuan Liu Chao Wu Huixiao Yao

The accurate segmentation of retinal images is a basic step in screening for retinopathy and glaucoma. Most existing retinal image segmentation methods have insufficient feature information extraction. They are susceptible to the impact of the lesion area and poor image quality, resulting in the poor recovery of contextual information. This also causes the segmentation results of the model to be noisy and low in accuracy. Therefore, this paper proposes a multi-scale and multi-branch convolutional neural network model (multi-scale and multi-branch network (MSMB-Net)) for retinal image segmentation. The model uses atrous convolution with different expansion rates and skip connections to reduce the loss of feature information. Receiving domains of different sizes captures global context information. The model fully integrates shallow and deep semantic information and retains rich spatial information. The network embeds an improved attention mechanism to obtain more detailed information, which can improve the accuracy of segmentation. Finally, the method of this paper was validated on the fundus vascular datasets, DRIVE, STARE and CHASE datasets, with accuracies/F1 of 0.9708/0.8320, 0.9753/0.8469 and 0.9767/0.8190, respectively. The effectiveness of the method in this paper was further validated on the optic disc visual cup DRISHTI-GS1 dataset with an accuracy/F1 of 0.9985/0.9770. Experimental results show that, compared with existing retinal image segmentation methods, our proposed method has good segmentation performance in all four benchmark tests.

]]>Symmetry doi: 10.3390/sym13030364

Authors: Shu-Shun Liu Agung Budiwirawan Muhammad Faizal Ardhiansyah Arifin Wei Tong Chen Ying-Hua Huang

When heavy rain strikes Taiwan, it always results in cracks in road pavement, and damages arising from potholes. Tremendously compromising road safety, road users may have fatal accidents caused by untimely repair actions. The road maintenance department needs to take the responsibilities for road sections in the form of inspections and faces the decision about how to properly allocate available resources to repair pavement damages immediately. When performing pavement repair works, we need to consider the resource consumption behavior and explore the mechanism of replenishing resources and calculating the return time. Therefore, in order to help maintenance units to deal with consumable resource issues, this study proposes a novel approach to offer the mechanism of consumable resource calculation, which is difficult to solve through the traditional vehicle routing problem (VRP) approach. This proposed model treats the pothole repair problem as a resource-constrained project scheduling problem (RCPSP), which is capable of resolving such consumable resource considerations. The proposed model was developed by adopting constraint programming (CP) techniques. Research results showed that the proposed model is capable of providing the optimal decisions of pavement pothole repair tasks and also meets practical requirements to make appropriate adjustment, and helps the maintenance unit to shorten total repair duration and optimize resource assignment decisions of pavement maintenance objectives.

]]>Symmetry doi: 10.3390/sym13020363

Authors: Marina Dolfin Leone Leonida Eleonora Muzzupappa

This paper adopts the Kinetic Theory for Active Particles (KTAP) approach to model the dynamics of liquidity profiles on a complex adaptive network system that mimic a stylized financial market. Individual incentives of investors to form or delete a link is driven, in our modelling framework, by stochastic game-type interactions modelling the phenomenology related to policy rules implemented under Basel III, and it is exogeneously and dynamically influenced by a measure of overnight interest rate. The strategic network formation dynamics that emerges from the introduced transition probabilities modelling individual incentives of investors to form or delete links, provides a wide range of measures using which networks might be considered “best” from the point of view of the overall welfare of the system. We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures.

]]>Symmetry doi: 10.3390/sym13020362

Authors: Arshad Jamal Tahir Mahmood Muhamad Riaz Hassan M. Al-Ahmadi

Statistical modeling of historical crash data can provide essential insights to safety managers for proactive highway safety management. While numerous studies have contributed to the advancement from the statistical methodological front, minimal research efforts have been dedicated to real-time monitoring of highway safety situations. This study advocates the use of statistical monitoring methods for real-time highway safety surveillance using three years of crash data for rural highways in Saudi Arabia. First, three well-known count data models (Poisson, negative binomial, and Conway–Maxwell–Poisson) are applied to identify the best fit model for the number of crashes. Conway–Maxwell–Poisson was identified as the best fit model, which was used to find the significant explanatory variables for the number of crashes. The results revealed that the road type and road surface conditions significantly contribute to the number of crashes. From the perspective of real-time highway safety monitoring, generalized linear model (GLM)-based exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are proposed using the randomized quantile residuals and deviance residuals of Conway–Maxwell (COM)–Poisson regression. A detailed simulation-based study is designed for predictive performance evaluation of the proposed control charts with existing counterparts (i.e., Shewhart charts) in terms of the run-length properties. The study results showed that the EWMA type control charts have better detection ability compared with the CUSUM type and Shewhart control charts under small and/or moderate shift sizes. Finally, the proposed monitoring methods are successfully implemented on actual traffic crash data to highlight the efficacy of the proposed methods. The outcome of this study could provide the analysts with insights to plan sound policy recommendations for achieving desired safety goals.

]]>Symmetry doi: 10.3390/sym13020361

Authors: Michiya Kamio Weina Jiang Hiroki Osada Masayuki Fukuoka Hajime Uchida Ryuichi Watanabe Toshiyuki Suzuki Hiroshi Nagai

A novel symmetrical macrocyclic phthalate hexaester (1) and a known macrocyclic phthalate tetraester (2) were isolated during a natural product-exploring program on the cyanobacterium Moorea producens. Their structures were elucidated based on spectroscopic data, including nuclear magnetic resonance and high-resolution mass spectra. In the antibacterial activity test, compounds 1 and 2 showed no bioactivity at the concentrations tested.

]]>Symmetry doi: 10.3390/sym13020360

Authors: Muhammad Riaz Zameer Abbas Hafiz Zafar Nazir Muhammad Abid

To detect sustainable changes in the manufacturing processes, memory-type charting schemes are frequently functioning. The recently designed, homogenously weighted moving average (HWMA) technique is effective for identifying substantial changes in the processes. To make the HWMA chart more effective for persistent shifts in the industrial processes, a double HWMA (DHWMA) chart has been proposed recently. This study intends to develop a triple HWMA (THWMA) chart for efficient monitoring of the process mean under zero- and steady-state scenarios. The non-normal effects of monitoring characteristics under in-control situations for heavy-tailed highly skewed and contaminated normal environments are computed under both states. The relative efficiency of the proposed structure is compared with HWMA, DHWMA, exponentially weighted moving average (EWMA), double EWMA, and the more effective triple EWMA control charting schemes. The relative analysis reveals that the proposed THWMA design performs more efficiently than the existing counterparts. An illustrative application related to substrate manufacturing is also incorporated to demonstrate the proposal.

]]>Symmetry doi: 10.3390/sym13020359

Authors: Jing Huang Huafeng Liu Fuxia Xu

In this paper, we study two-dimensional divisor problems of the Fourier coefficients of some automorphic product L-functions attached to the primitive holomorphic cusp form f(z) with weight k for the full modular group SL2(Z). Additionally, we establish the upper bound and the asymptotic formula for these divisor problems on average, respectively.

]]>Symmetry doi: 10.3390/sym13020358

Authors: Roberto Casadio Andrea Giusti

Bootstrapped Newtonian gravity was developed with the purpose of estimating the impact of quantum physics in the nonlinear regime of the gravitational interaction, akin to corpuscular models of black holes and inflation. In this work, we set the ground for extending the bootstrapped Newtonian picture to cosmological spaces. We further discuss how such models of quantum cosmology can lead to a natural solution to the cosmological constant problem.

]]>Symmetry doi: 10.3390/sym13020357

Authors: Imran Naeem Iqbal Shabir Ahmad Do Hyeun Kim

The ageing population’s problems directly impact countries’ socio-economic structure, as more resources are required to monitor the aged population’s health. The growth in human life expectancy is increasing due to medical technologies and nutritional science innovations. The Internet of Things (IoT) is the connectivity of physical objects called things to the Internet. IoT has a wide range of health monitoring applications based on biomedical sensing devices to monitor health conditions. This paper proposes elderly patients’ health monitoring architecture based on an intelligent task mapping approach for a closed-loop IoT healthcare environment. As a case study, a health monitoring system was developed based on the proposed architecture for elderly patients’ health monitoring in the home, ambulance, and hospital environment. The system detects and notifies deteriorating conditions to the authorities based on biomedical sensors for faster interventions. Wearable biomedical sensors are used for monitoring body temperature, heart rate, blood glucose level, and patient body position. Threshold and machine learning-based approaches were used to detect anomalies in the health sensing data. The proposed architecture’s performance analysis is evaluated in terms of round trip time, reliability, task drop rate, and latency performance metrics. Performance results show that the proposed architecture of the elderly patient health monitoring can provide reliable solutions for critical tasks in IoT environments.

]]>Symmetry doi: 10.3390/sym13020356

Authors: Shubham Mahajan Akshay Raina Xiao-Zhi Gao Amit Kant Pandit

Plant species recognition from visual data has always been a challenging task for Artificial Intelligence (AI) researchers, due to a number of complications in the task, such as the enormous data to be processed due to vast number of floral species. There are many sources from a plant that can be used as feature aspects for an AI-based model, but features related to parts like leaves are considered as more significant for the task, primarily due to easy accessibility, than other parts like flowers, stems, etc. With this notion, we propose a plant species recognition model based on morphological features extracted from corresponding leaves’ images using the support vector machine (SVM) with adaptive boosting technique. This proposed framework includes the pre-processing, extraction of features and classification into one of the species. Various morphological features like centroid, major axis length, minor axis length, solidity, perimeter, and orientation are extracted from the digital images of various categories of leaves. In addition to this, transfer learning, as suggested by some previous studies, has also been used in the feature extraction process. Various classifiers like the kNN, decision trees, and multilayer perceptron (with and without AdaBoost) are employed on the opensource dataset, FLAVIA, to certify our study in its robustness, in contrast to other classifier frameworks. With this, our study also signifies the additional advantage of 10-fold cross validation over other dataset partitioning strategies, thereby achieving a precision rate of 95.85%.

]]>Symmetry doi: 10.3390/sym13020355

Authors: Haixia Lin Jianhong Cui Xiangwei Bai

The ocean occupies more than two-thirds of the earth’s area, providing a lot of oxygen and materials for human survival and development. However, with human activities, a large number of sewage, plastic bags, and other wastes are discharged into the ocean, and the problem of marine water pollution has become a hot topic in the world. In order to extract the characteristics of marine water pollution, this study proposed K-means clustering technology based on cosine distance and discrimination to study the polluted water. In this study, the polygonal area method combined with six parameters of water quality is used to analyze the marine water body anomalies, so as to realize the rapid and real-time monitoring of marine water body anomalies. At the same time, the cosine distance method and discrimination are used to classify marine water pollutants, so as to improve the classification accuracy. The results show that the detection rate of water quality anomalies is more than 88.2%, and the overall classification accuracy of water pollution is 96.3%, which proves the effectiveness of the method. It is hoped that this study can provide timely and effective data support for the detection of marine water bodies.

]]>Symmetry doi: 10.3390/sym13020354

Authors: Alexander Apelblat Francesco Mainardi

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0&lt;ν&lt;1 are presented.

]]>Symmetry doi: 10.3390/sym13020353

Authors: Ligia Munteanu Dan Dumitriu Cornel Brisan Mircea Bara Veturia Chiroiu Nicoleta Nedelcu Cristian Rugina

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

]]>Symmetry doi: 10.3390/sym13020352

Authors: Abdel-Baset A. Mohamed Eied. M. Khalil Mahmoud M. Selim Hichem Eleuch

The dynamics of two charged qubits containing Josephson Junctions inside a cavity are investigated under the intrinsic decoherence effect. New types of quantum correlations via local quantum Fisher information and Bures distance norm are explored. We show that we can control the quantum correlations robustness by the intrinsic decoherence rate, the qubit-qubit coupling as well as by the initial coherent states superposition. The phenomenon of sudden changes and the freezing behavior for the local quantum Fisher information are sensitive to the initial coherent state superposition and the intrinsic decoherence.

]]>Symmetry doi: 10.3390/sym13020351

Authors: Michael Th. Rassias Bicheng Yang Andrei Raigorodskii

In this work we establish a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of the arc tangent function. We prove that the constant factor, which is associated with the cosine function, is optimal. Some special cases as well as some operator expressions are also presented.

]]>Symmetry doi: 10.3390/sym13020350

Authors: Manuel Gadella José Hernández-Muñoz Luis Miguel Nieto Carlos San Millán

We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator −d2/dx2 on L2[−a,a], a&gt;0, that is, the one dimensional infinite square well. First of all, we classify these self-adjoint extensions in terms of several choices of the parameters determining each of the extensions. There are essentially two big groups of extensions. In one, the ground state has strictly positive energy. On the other, either the ground state has zero or negative energy. In the present paper, we show that each of the extensions belonging to the first group (energy of ground state strictly positive) has an infinite sequence of supersymmetric partners, such that the ℓ-th order partner differs in one energy level from both the (ℓ−1)-th and the (ℓ+1)-th order partners. In general, the eigenvalues for each of the self-adjoint extensions of −d2/dx2 come from a transcendental equation and are all infinite. For the case under our study, we determine the eigenvalues, which are also infinite, all the extensions have a purely discrete spectrum, and their respective eigenfunctions for all of its ℓ-th supersymmetric partners of each extension.

]]>Symmetry doi: 10.3390/sym13020349

Authors: Łukasz Pawik Paweł Wietecki Artur Leśkow Andżelika Pajchert Kozłowska Sławomir Żarek Radosław Górski Malwina Pawik Felicja Fink-Lwow Wiktor Urbański Piotr Morasiewicz

The aim of this study was to comprehensively assess the gait parameters in patients who had undergone treatment of pilon fractures by the Ilizarov method. We analyzed gait parameters in patients who had undergone treatment for pilon fractures by the Ilizarov method; 20 patients aged 47.0 years (25.2–78.6) were included in the study. The control group consisted of 32 healthy volunteers. Gait examination was performed using the pedobarographic platform. Statistically significant differences in the following gait parameters: maximum forefoot force (%), step length (cm), and step time (s) were found between the study group and the control group, between the nonoperated leg, and both the operated leg and the dominant limb. Statistically significant differences in the study group between the treated lower limb and the healthy lower limb were only observed in the case of the maximum forefoot force parameter (%). Healthy subjects from the control group obtained significantly higher values during locomotion for stride time, cadence step, and velocity than the patients, with stride time being statistically significantly shorter and the velocity and the cadence step higher. We observed symmetry in the gait parameters after treating pilon fractures by the Ilizarov method. This method of stabilization allows the restoration of gait parameters, with results similar to those obtained after the treatment of other motor organ pathologies described in the literature, although different from those observed in healthy subjects. In particular, the biomechanics of the lower limbs remain disturbed.

]]>Symmetry doi: 10.3390/sym13020347

Authors: Gaoyang Jiang Genfeng Liu Hansong Yu

The adaptive trajectory and attitude control is essential for the four-dimensional (4D) trajectory operation of civil aircraft in symmetric thrust flight. In this work, an integrated trajectory and attitude control scheme is proposed based on the =multi-input multi-output (MIMO) model free adaptive control (MFAC) method. First, the full-form dynamic linearization technique is adopted to build the equivalent data model of aircraft. Also, the MIMO MFAC scheme with saturation constraint is designed to achieve an accurate tracking control for a given 4D trajectory and attitude. Besides, the performance limitations of aircraft are taken into consideration, and the MIMO MFAC scheme with hard constraints is designed. In addition, to improve the simulation efficiency, a control scheme with mixed constraints, i.e., saturation and hard constraints, is further proposed. It can be seen from the simulation results that the proposed method can perform an integrated control of the aircraft 4D trajectory and attitude without precise modeling, and the control performance is better than that of the model-based control method in terms of flight altitude and yaw angle control. The integrated data-driven control scheme proposed in this paper provides a theoretical solution for the precise operation of aircraft under 4D trajectory.

]]>Symmetry doi: 10.3390/sym13020348

Authors: Merced Montesinos Diego Gonzalez Rodrigo Romero Mariano Celada

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

]]>Symmetry doi: 10.3390/sym13020346

Authors: Sergey B. Makarov Mingxin Liu Anna S. Ovsyannikova Sergey V. Zavjalov ILya Lavrenyuk Wei Xue Yidong Xu

The increase in the throughput of digital television and radio broadcasting (DVB) channels can be achieved due to application of signals with a compact spectrum and a relatively small peak-to-average power ratio (PAPR). The reason is the usage of traveling wave tubes (TWT) for amplifying and transmitting signals from a satellite repeater in DVB-S2X systems. At the same time, given that the bandwidth allocated for transmission should be used as efficiently as possible, a high reduction rate of out-of-band emissions level is required. The most effective solution in this direction is the transition to spectrum-economic signals, such as optimal Faster-Than-Nyquist (FTN) signals, which can provide a certain reduction rate of the out-of-band emissions level and minimum acceptable PAPR. This article proposes a method for obtaining optimal FTN pulses, which have symmetry in time domain, with specified PAPR and reduction rate of out-of-band emissions for the quadrature phase shift keying (QPSK) and offset quadrature phase shift keying (OQPSK). The possibility of synthesizing signals with OQPSK modulation is presented theoretically for the first time. Optimal FTN signals can provide PAPR reduction by at most 3 dB and outperform known root raised cosine (RRC) pulses. The simulation model adopts an architecture for quadrature generation of optimal FTN signals with OQPSK modulation with blocks for adjustable pre-amplification, clipping, and power amplification. The proposed signals can be used to increase the spectral and energy efficiencies of satellite broadcasting systems, such as DVB-S2/S2X, as well as low-rate return channels of interactive broadcasting systems with a frequency resource shortage.

]]>Symmetry doi: 10.3390/sym13020345

Authors: Zhenfei Wang Yan Wang Liying Zhang Chuchu Zhang Xingjin Zhang

Data modeling and dimensionality reduction are important research points in the field of big data. At present, there is no effective model to realize the consistent representation and fusion of different types of data of students in unstructured campus big data. In addition, in the process of big data processing, the amount of data is too large and the intermediate results are too complex, which seriously affects the efficiency of big data dimension reduction. To solve the above problems, this paper proposes an incremental high order singular value decomposition dimensionality (icHOSVD) reduction algorithm for unstructured campus big data. In this algorithm, the characteristics of audio, video, image and text data in unstructured campus student data are tensioned to form a sub-tensor model, and the semi-tensor product is used to fuse the sub-tensor model into a unified model as the individual student tensor model. On the basis of individual model fusion, the campus big data fusion model was segmented, and each segmented small tensor model was dimensioned by icHOSVD reduction to obtain an approximate tensor as the symmetric tensor that could replace the original tensor, so as to solve the problem of large volume of tensor fusion model and repeated calculation of intermediate results in data processing. The experimental results show that the proposed algorithm can effectively reduce the computational complexity and improve the performance compared with traditional data dimension reduction algorithms. The research results can be applied to campus big data analysis and decision-making.

]]>Symmetry doi: 10.3390/sym13020344

Authors: Alejandro Humberto García Ruiz Salvador Ibarra Martínez José Antonio Castán Rocha Jesús David Terán Villanueva Julio Laria Menchaca Mayra Guadalupe Treviño Berrones Mirna Patricia Ponce Flores Aurelio Alejandro Santiago Pineda

Electricity is one of the most important resources for the growth and sustainability of the population. This paper assesses the energy consumption and user satisfaction of a simulated air conditioning system controlled with two different optimization algorithms. The algorithms are a genetic algorithm (GA), implemented from the state of the art, and a non-dominated sorting genetic algorithm II (NSGA II) proposed in this paper; these algorithms control an air conditioning system considering user preferences. It is worth noting that we made several modifications to the objective function’s definition to make it more robust. The energy-saving optimization is essential to reduce CO2 emissions and economic costs; on the other hand, it is desirable for the user to feel comfortable, yet it will entail a higher energy consumption. Thus, we integrate user preferences with energy-saving on a single weighted function and a Pareto bi-objective problem to increase user satisfaction and decrease electrical energy consumption. To assess the experimentation, we constructed a simulator by training a backpropagation neural network with real data from a laboratory’s air conditioning system. According to the results, we conclude that NSGA II provides better results than the state of the art (GA) regarding user preferences and energy-saving.

]]>Symmetry doi: 10.3390/sym13020343

Authors: Anatoliy V. Kharkhurin Morteza Charkhabi

The study is a part of a research project, which explores the role of creative perception in creative behavior. We operationalized creative behavior as an ability to overcome structured imagination, as measured by the Invented Alien Creature test, and operationalized creative perception as a preference for complexity and asymmetry, which we assessed using a standard Barron–Welsh Art Scale. Our group of participants was composed of ninety-three undergraduate students from the United Arab Emirates. The degree to which one preferred complexity and asymmetry measurably contributed to their ability to overcome structured imagination. This finding adds another brick to the rising seventh pillar of the creativity construct, namely, creative perception. The article provides a first sketch of the creative perception paradigm.

]]>Symmetry doi: 10.3390/sym13020342

Authors: Wolf-Dieter Richter

Three-complex numbers are introduced for using a geometric vector product in the three-dimensional Euclidean vector space R3 and proving its equivalence with a spherical coordinate product. Based upon the definitions of the geometric power and geometric exponential functions, some Euler-type trigonometric representations of three-complex numbers are derived. Further, a general l23−complex algebraic structure together with its matrix, polynomial and variable basis vector representations are considered. Then, the classes of lp3-complex numbers are introduced. As an application, Euler-type formulas are used to construct directional probability laws on the Euclidean unit sphere in R3.

]]>Symmetry doi: 10.3390/sym13020341

Authors: Shaobo He Hayder Natiq Santo Banerjee Kehui Sun

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

]]>Symmetry doi: 10.3390/sym13020338

Authors: Jaime Nebot Juan A. Peña Carmelo López Gómez

At present, traditional 3D modeling programs consist of a set of tools that reflect conventional means of mechanical manufacturing and have limitations in relation with the current manufacturing capacities. On the other hand, organic and morphing 3D modeling programs are designed to transform a model from one known shape to another also known shape. Generative design helps the designers to detach themselves during the design process and can provide them with completely unexpected geometrical solutions. In this paper, starting from 3D morphing techniques and genetic algorithms, a new methodology of product shape definition is developed, capable of imitating processes that occur in nature and aimed at creating new and different product designs. This methodology enables to overcome the limitations imposed by design fixation and allows better exploitation of the great possibilities granted by the new manufacturing techniques, most notably additive manufacturing. The initial process of research and information gathering gives this work a solid basis to develop the new methodology. The results of this initial process are briefly resumed in this paper in order to explain the main motivation for developing this work. The workflow of this methodology is presented as a theoretical process, since its implementation has not been, at least for the moment, put into practice. Before presenting the conclusion for this proposal, several examples have been formulated in order to help the reader to catch the point of the entire process.

]]>Symmetry doi: 10.3390/sym13020337

Authors: Alexey V. Melkikh

If the isolated system of bosons and fermions was initially in a pure maximally entangled quantum state, then, as a result of decoherence caused by the creation and annihilation of particles, this system not only enters a mixed state but also achieves equilibrium. The time of such a transition does not depend on the size of the system but is determined only by the properties of the particles. This phenomenon allows the problem of the horizon (the homogeneity of the universe) to be solved, since the transition time of different parts of the universe (if they were originally entangled with each other) to equilibrium will not depend on their sizes, and the speed of the interaction may be greater than the speed of light. Based on the decay of entangled states, the problem of the predominance of matter over antimatter in the universe can also be solved.

]]>Symmetry doi: 10.3390/sym13020340

Authors: Junxia Wang Li Xiao Karthikeyan Rajagopal Akif Akgul Serdar Cicek Burak Aricioglu

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et.al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system.

]]>Symmetry doi: 10.3390/sym13020339

Authors: Ahmed El-Sayed Ahmed

Some weighted classes of hyperbolic function spaces are defined and studied in this paper. Finally, by using the chordal metric concept, some investigations for a class of general hyperbolic functions are also given.

]]>Symmetry doi: 10.3390/sym13020336

Authors: Askhat Diveev Elizaveta Shmalko

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

]]>Symmetry doi: 10.3390/sym13020335

Authors: Daniel Antón José-Lázaro Amaro-Mellado

Engineering graphics are present in the design stage, but also constitute a way to communicate, analyse, and synthesise. In the Architecture-Engineering-Construction sector, graphical data become essential in analysing buildings and constructions throughout their lifecycles, such as in the thermal behaviour assessment of building envelopes. Scientific research has addressed the thermal image mapping onto three-dimensional (3D) models for visualisation and analysis. However, the 3D point cloud data creation of buildings’ thermal behaviour directly from rectified infrared thermography (IRT) thermograms is yet to be investigated. Therefore, this paper develops an open-source software graphical method to produce 3D thermal data from IRT images for temperature visualisation and subsequent analysis. This low-cost approach uses both a geographic information system for the thermographic image rectification and the point clouds production, and 3D point cloud processing software. The methodology has been proven useful to obtain, without perspective distortions, 3D thermograms even from non-radiometric raster images. The results also revealed that non-rectangular thermograms enable over 95% of the 3D thermal data generated from IRT against rectangular shapes (over 85%). Finally, the 3D thermal data produced allow further thermal behaviour assessment, including calculating the object’s heat loss and thermal transmittance for diverse applications such as energy audits, restoration, monitoring, or product quality control.

]]>Symmetry doi: 10.3390/sym13020334

Authors: Chia-Nan Wang Thanh-Tuan Dang Hector Tibo Duy-Hung Duong

Climate change and air pollution are among the key drivers of energy transition worldwide. The adoption of renewable resources can act as a peacemaker and give stability regarding the damaging effects of fossil fuels challenging public health as well as the tension made between countries in global prices of oil and gas. Understanding the potential and capabilities to produce renewable energy resources is a crucial pre-requisite for countries to utilize them and to scale up clean and stable sources of electricity generation. This paper presents a hybrid methodology that combines the data envelopment analysis (DEA) Window model, and fuzzy technique for order of preference by similarity to ideal solution (FTOPSIS) in order to evaluate the capabilities of 42 countries in terms of renewable energy production potential. Based on three inputs (population, total energy consumption, and total renewable energy capacity) and two outputs (gross domestic product and total energy production), DEA window analysis chose the list of potential countries, including Norway, United Kingdom, Kuwait, Australia, Netherlands, United Arab Emirates, United States, Japan, Colombia, and Italy. Following that, the FTOPSIS model pointed out the top three countries (United States, Japan, and Australia) that have the greatest capabilities in producing renewable energies based on five main criteria, which are available resources, energy security, technological infrastructure, economic stability, and social acceptance. This paper aims to offer an evaluation method for countries to understand their potential of renewable energy production in designing stimulus packages for a cleaner energy future, thereby accelerating sustainable development.

]]>Symmetry doi: 10.3390/sym13020333

Authors: Amy H. I. Lee He-Yau Kang Chong-Lin Chen

Assembly lines are often indispensable in factories, and in order to attain a certain level of assembly line productivity, multiple goals must be considered at the same time. However, these multiple goals may conflict with each other, and this is a multi-objective assembly line balancing problem. This study considers four objectives, namely minimizing the cycle time, minimizing the number of workstations, minimizing the workload variance, and minimizing the workstation idle time. Since the objectives conflict with each other, for example, minimizing the cycle time may increase the number of workstations, the fuzzy multi-objective linear programming model is used to maximize the satisfaction level. When the problem becomes too complicated, it may not be solved by the fuzzy multi-objective linear programming model using a mathematical software package. Therefore, a genetic algorithm model is proposed to solve the problem efficiently. By studying practical cases of an automobile manufacturer, the results show that the proposed fuzzy multi-objective linear programming model and the genetic algorithm model can solve small-scale multi-objective assembly line balancing problems efficiently, and the genetic algorithm model can obtain good solutions for large-scale problems in a short computational time. Datasets from previous works are adopted to examine the applicability of the proposed models. The results show that both the fuzzy multi-objective linear programming model and the genetic algorithm model can solve the smaller problem cases and that the genetic algorithm model can solve larger problems. The proposed models can be applied by practitioners in managing a multi-objective assembly line balancing problem.

]]>Symmetry doi: 10.3390/sym13020331

Authors: Junjian Zhao Marko Kostić Wei-Shih Du

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.

]]>Symmetry doi: 10.3390/sym13020332

Authors: Jorge Martínez Carracedo Adriana Suárez Corona

In this paper, we analyze the security of a group key establishment scheme proposed by López-Ramos et al. This proposal aims at allowing a group of users to agree on a common key. We present several attacks against the security of the proposed protocol. In particular, an active attack is presented, and it is also proved that the protocol does not provide forward secrecy.

]]>Symmetry doi: 10.3390/sym13020330

Authors: Gennady G. Knyazev Vadim L. Ushakov Vyacheslav A. Orlov Denis G. Malakhov Sergey I. Kartashov Alexander N. Savostyanov Andrey V. Bocharov Boris M. Velichkovsky

Insight is described as the sudden solution of a problem and is contrasted with an analytical, step-by-step approach. Traditionally, insight is thought to be associated with activity of the right hemisphere, whereas analytical solutions are thought to be associated with activity of the left hemisphere. However, empirical evidence as to the localization of insight-related brain activity is mixed and inconclusive. Some studies seem to confirm the traditional view, whereas others do not. Moreover, results of EEG and fMRI studies frequently contradict each other. In this study, EEG and fMRI data were recorded while subjects performed the remote association test and for each solved problem were asked to report whether the solution was reached analytically or insightfully. The data were analyzed in a 16-second fragment preceding the subject’s response. Source localization techniques were used in the analysis of EEG data. Based on EEG data, insightful as compared to analytical problem solving was accompanied by high-frequency synchronization in semantic cortical areas of the left hemisphere 10–12 s before the subject’s response. Based on fMRI data, however, insightful solutions were accompanied by increased activity in frontal and temporal regions of the right hemisphere. The results are interpreted in terms of different cognitive processes involved in insightful problem solving, which could be differently reflected in EEG and fMRI data.

]]>Symmetry doi: 10.3390/sym13020329

Authors: Shen-Tsu Wang Meng-Hua Li Chun-Chi Lien

Blockchain technology has been applied to logistics tracking, but it is not cost-effective. The development of smart lockers has solved the problem of repeated distribution to improve logistics efficiency, thereby becoming a solution with convenience and privacy compared to the in-store purchase and pickup alternative. This study prioritized the key factors of smart lockers using a simulated annealing–genetic algorithm by fractional factorial design (FFD-SAGA) and grey relational analysis, and investigated the main users of smart lockers by grey multiple attribute decision analysis. The results show that the Web application programming interface (API) concatenation and money flow provider are the key success factors of smart lockers, and office workers are the main users of the lockers. Hence, how to better meet the needs of office workers will be an issue of concern for service providers.

]]>Symmetry doi: 10.3390/sym13020328

Authors: Mouna Derbel Wafik Hachicha Awad M. Aljuaid

Inventory-pooling (IP) is an effective tool to mitigate demand uncertainty and variability, to reduce operational costs, and consequently to increase the profit. The major assumptions of the previous works in literature on IP include the following: (1) Independents demand, which satisfy the typical normal independent and identically distributed (iid) random variables; (2) dependents (correlated) symmetric demands, which follows to a multivariate normal distribution. The effect of the dependent asymmetric demand is not yet studied. The aim of this paper is to consider this more realistic case. Indeed, the contribution of this paper is twofold. Firstly, it analyzes both the sensitivity of dependence structure and the levels of skewness of distributions on IP policies in terms of optimal total cost and demand satisfaction constraint. Secondly, both symmetric and asymmetric demand distributions are modeled using various beta distribution and the dependance between demands are modeled using various copulas. A newsvendor problem inspired by the literature, with two decentralized locations and two centralized locations, is considered the empirical study. For each dependance situation, three IP models are considered: inventory centralization, regular transshipments, and independent systems. The results suggest divergences in the decisions in about 9% of cases. Bad choice of marginal distributions given that the copula is appropriate can lead to divergences that vary between 2.2% and 4%, depending on whether the demand distributions are symmetric or asymmetric.

]]>Symmetry doi: 10.3390/sym13020327

Authors: Alina Alb Lupaş Georgia Irina Oros

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.

]]>Symmetry doi: 10.3390/sym13020326

Authors: Purhadi Purhadi M. Fathurahman

This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with 3p degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

]]>Symmetry doi: 10.3390/sym13020325

Authors: Tomasz Mądry Agnieszka Czapik Marcin Kwit

The electronic circular dichroism (CD)-silent 2,5-bis(biphen-2-yl)terephthalaldehyde has been used as a sensor (reporter) of chirality for primary amines. The through-space inductor–reporter interactions force a change in the chromophore conformation toward one of the diastereomeric forms. The structure of the reporter, with the terminal flipping biphenyl groups, led to generating Cotton effects in both lower- and higher-energy regions of the ECD spectrum. The induction of an optical activity in the chromophore was due to the cascade point-to-axial chirality transmission mechanism. The reporter system turned out to be sensitive to the subtle differences in the inductor structure. Despite the size of the chiral substituent, the molecular structure of the inductor–reporter systems in the solid-state showed many similarities. The most important one was the tendency of the core part of the molecules to adapt pseudocentrosymmetric conformation. Supported by a weak dispersion and Van der Waals interactions, the face-to-face and edge-to-face interactions between the π-electron systems present in the molecule were found to be responsible for the molecular arrangement in the crystal.

]]>Symmetry doi: 10.3390/sym13020324

Authors: Vladimir A. Shurygin

The general coupling between particle transport and ionization-recombination processes in hot plasma is considered on the key concept of equilibrium charge state (CS) transport. A theoretical interpretation of particle and CS transport is gained in terms of a two-dimensional (2D) Markovian stochastic (random) processes, a discrete 2D Fokker-Plank-Kolmogorov equation (in charge and space variables) and generalized 2D coronal equilibrium between atomic processes and particle transport. The basic tool for analysis of CS equilibrium and transport is the equilibrium cell (EC) (two states on charge and two on space), which presents simultaneously a unit phase volume, the characteristic scales (in space and time) of local equilibrium, and a comprehensive solution for the simplest nonlinear relations between transport and atomic processes. The space-time relationships between the equilibrium constant, transport rates, density distributions, and impurity confinement time are found. The subsequent direct calculation of the total and partial density profiles and the transport coefficients of argon impurity showed a strong dependence of the 2D CS equilibrium and transport on the atomic structure of ions. A model for recovering the recombination rate profiles of carbon impurity was developed basing on the CS equilibrium conditions, the derived relationships, the data about density profiles, plasma parameters and ionization rates.

]]>Symmetry doi: 10.3390/sym13020323

Authors: Artur Przybysz Krystian Grzesiak Ireneusz Kubiak

Devices powered by electricity become sources of electromagnetic emissions in the course of their operation. In the case of devices oriented to process information, these emissions can have a character of revealing emissions, i.e., those whose reception and analysis allow for remote reconstruction of related data. The best known example of this phenomenon is the formation of revealing emissions during the operation of imaging devices: monitors, projectors or printers. Increasingly more often, these components are used for communication in the form of videoconferences with other network users. The article presents the result of tests and analyses of threats related to the use of such solutions (monitors, personal computers, VoIP terminals) for the confidentiality of conversations and the data presented during them. The focus is on video signals; however, the potential possibilities of revealing speech signals were also indicated. Such phenomenon causes a huge threat to data confidentiality because the combination of graphics and sound can undoubtedly contain much more information about the protected data than just graphics or sound separately. The presented results of analyses apply to graphic data, possibilities of non-invasive acquisition of such data, similarity of images and of patterns and reconstructed image and image recognition. The results indicate that there is still a risk of loss of data confidentiality due to a phenomenon of an electromagnetic leakage, and specialized instrumentation is not required for its interception under favorable circumstances. This may particularly apply to audio data that may be accidentally received by home radio receivers. In particular, the presented results of analyses apply to a Special Issue of Symmetry which is characterized by security and privacy in communication systems and networks, signal processing, video and image processing, multimedia communications and electromagnetic compatibility. All these scientific and technical areas have either symmetrical or asymmetrical approaches, and they have to be taken into consideration as a whole in order to choose the best combinations to protect processed information.

]]>Symmetry doi: 10.3390/sym13020322

Authors: Qinghua Wu Bin Wu Chengyu Hu Xuesong Yan

As one of the common methods to construct classifiers, naïve Bayes has become one of the most popular classification methods because of its solid theoretical basis, strong prior knowledge learning characteristics, unique knowledge expression forms, and high classification accuracy. This classification method has a symmetry phenomenon in the process of data classification. Although the naïve Bayes classifier has high classification performance in single-label classification problems, it is worth studying whether the multilabel classification problem is still valid. In this paper, with the naïve Bayes classifier as the basic research object, in view of the naïve Bayes classification algorithm’s shortage of conditional independence assumptions and label class selection strategies, the characteristics of weighted naïve Bayes is given a better label classifier algorithm framework; the introduction of cultural algorithms to search for and determine the optimal weights is proposed as the weighted naïve Bayes multilabel classification algorithm. Experimental results show that the algorithm proposed in this paper is superior to other algorithms in classification performance.

]]>Symmetry doi: 10.3390/sym13020321

Authors: Zehao Zhou Yichun Tai Jianlin Chen Zhijiang Zhang

Geometric feature extraction of 3D point clouds plays an important role in many 3D computer vision applications such as region labeling, 3D reconstruction, object segmentation, and recognition. However, hand-designed features on point clouds lack semantic information, so cannot meet these requirements. In this paper, we propose local feature extraction network (LFE-Net) which focus on extracting local feature for point clouds analysis. Such geometric features learning from a relation of local points can be used in a variety of shape analysis problems such as classification, part segmentation, and point matching. LFE-Net consists of local geometric relation (LGR) module which aims to learn a high-dimensional local feature to express the relation between points and their neighbors. Benefiting from the additional singular values of local points and hierarchical neural networks, the learned local features are robust to permutation and rigid transformation so that they can be transformed into 3D descriptors. Moreover, we embed prior spatial information of the local points into the sub-features for combining features from multiple levels. LFE-Net achieves state-of-the-art performances on standard benchmarks including ModelNet40, ShapeNetPart.

]]>Symmetry doi: 10.3390/sym13020320

Authors: Yue Zhao Xiaoqiang Ren Kun Hou Wentao Li

Automated brain tumor segmentation based on 3D magnetic resonance imaging (MRI) is critical to disease diagnosis. Moreover, robust and accurate achieving automatic extraction of brain tumor is a big challenge because of the inherent heterogeneity of the tumor structure. In this paper, we present an efficient semantic segmentation 3D recurrent multi-fiber network (RMFNet), which is based on encoder–decoder architecture to segment the brain tumor accurately. 3D RMFNet is applied in our paper to solve the problem of brain tumor segmentation, including a 3D recurrent unit and 3D multi-fiber unit. First of all, we propose that recurrent units segment brain tumors by connecting recurrent units and convolutional layers. This quality enhances the model’s ability to integrate contextual information and is of great significance to enhance the contextual information. Then, a 3D multi-fiber unit is added to the overall network to solve the high computational cost caused by the use of a 3D network architecture to capture local features. 3D RMFNet combines both advantages from a 3D recurrent unit and 3D multi-fiber unit. Extensive experiments on the Brain Tumor Segmentation (BraTS) 2018 challenge dataset show that our RMFNet remarkably outperforms state-of-the-art methods, and achieves average Dice scores of 89.62%, 83.65% and 78.72% for the whole tumor, tumor core and enhancing tumor, respectively. The experimental results prove our architecture to be an efficient tool for brain tumor segmentation accurately.

]]>Symmetry doi: 10.3390/sym13020319

Authors: Liang Han Feng Liu Li Zhang

Laser-induced breakdown spectroscopy (LIBS) is a powerful tool for qualitative and quantitative analysis. Component analysis is a significant issue for the LIBS instrument onboard the Mars Science Laboratory (MSL) rover Curiosity ChemCam and SuperCam on the Mars 2020 rover. The partial least squares (PLS) sub-model strategy is one of the outstanding multivariate analysis methods for calibration modeling, which is firstly developed by the ChemCam science team. We innovatively used a support vector machine (SVM) classifier to select the corresponding sub-model. Then conventional regression approaches partial least squares regression (PLSR) was utilized as a sub-model to prove that our selecting method was feasible, effective, and well-performed. For eight oxides, i.e., SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, and K2O, the modified SVM-PLSR blended sub-model method was 34.8% to 62.4% lower than the corresponding root mean square error of prediction (RMSEP) of the full model method. In order to avoid that SVM classifiers classifying the spectrum into an incorrect class, an optimized method was proposed which worked well in the modified PLSR blended sub-models.

]]>Symmetry doi: 10.3390/sym13020318

Authors: Osama Moaaz Amany Nabih Hammad Alotaibi Y. S. Hamed

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

]]>Symmetry doi: 10.3390/sym13020317

Authors: Chithambaramani Ramalingam Prakash Mohan

The increasing demand for cloud computing has shifted business toward a huge demand for cloud services, which offer platform, software, and infrastructure for the day-to-day use of cloud consumers. Numerous new cloud service providers have been introduced to the market with unique features that assist service developers collaborate and migrate services among multiple cloud service providers to address the varying requirements of cloud consumers. Many interfaces and proprietary application programming interfaces (API) are available for migration and collaboration services among cloud providers, but lack standardization efforts. The target of the research work was to summarize the issues involved in semantic cloud portability and interoperability in the multi-cloud environment and define the standardization effort imminently needed for migrating and collaborating services in the multi-cloud environment.

]]>Symmetry doi: 10.3390/sym13020316

Authors: Soheila Mahdavi Ali Reza Ashrafi Mohammad Ali Salahshour Abraham Albert Ungar

In this paper, a 2-gyrogroup G(n) of order 2n, n≥3, is constructed in which every proper subgyrogroup is either a cyclic or a dihedral group. It is proved that the subgyrogroup lattice and normal subgyrogroup lattice of G(n) are isomorphic to the subgroup lattice and normal subgroup lattice of the dihedral group of order 2n, which causes us to use the name dihedral gyrogroup for this class of gyrogroups of order 2n. Moreover, all proper subgyrogroups of G(n) are subgroups.

]]>Symmetry doi: 10.3390/sym13020315

Authors: Zeyun Shi Jinkeng Lin Jiong Chen Yao Jin Jin Huang

Many man-made or natural objects are composed of symmetric parts and possess symmetric physical behavior. Although its shape can exactly follow a symmetry in the designing or modeling stage, its discretized mesh in the analysis stage may be asymmetric because generating a mesh exactly following the symmetry is usually costly. As a consequence, the expected symmetric physical behavior may not be faithfully reproduced due to the asymmetry of the mesh. To solve this problem, we propose to optimize the material parameters of the mesh for static and kinematic symmetry behavior. Specifically, under the situation of static equilibrium, Young’s modulus is properly scaled so that a symmetric force field leads to symmetric displacement. For kinematics, the mass is optimized to reproduce symmetric acceleration under a symmetric force field. To efficiently measure the deviation from symmetry, we formulate a linear operator whose kernel contains all the symmetric vector fields, which helps to characterize the asymmetry error via a simple ℓ2 norm. To make the resulting material suitable for the general situation, the symmetric training force fields are derived from modal analysis in the above kernel space. Results show that our optimized material significantly reduces the asymmetric error on an asymmetric mesh in both static and dynamic simulations.

]]>Symmetry doi: 10.3390/sym13020314

Authors: Kateryna Czerniachowska Marcin Hernes

Shelf space on which products are exhibited is a scarce resource in the retail environment. Retailers regularly make decisions related to allocating products to their outlets’ limited shelf space. The aim of the paper was to develop a practical shelf space allocation model offering the possibility of horizontal and vertical product grouping, representing an item (product) with facings, capping, and nesting, with the objective of maximizing the retailer’s profit. Because real category-management problems address a lot of retailer’s rules, we expanded the basic shelf space allocation model, using shelf constraints, product constraints, multi-shelves constraints, and category constraints. To solve the problem, we proposed two adjustable methods that allowed us to achieve good results within a short time interval. The validity of algorithms was estimated, using the CPLEX solver and illustrated with example problems. Experiments were performed on data generated on the basis of real retail values. To estimate the performance of the proposed approach, 45 cases were tested. Among them, the proposed approach found solutions in 34 cases, while CPLEX found solutions only in 23 cases. The profit ratio of the proposed approach is, on average, 94.57%, with minimal and maximal values of 86.80% and 99.84%, accordingly.

]]>Symmetry doi: 10.3390/sym13020313

Authors: Polina Petriakova Arkady Popov Sergey Rubin

We study the universe evolution starting from the sub-Planckian scale to present times. The requirement for an exponential expansion of the space with the observed metric as a final stage leads to significant restrictions on the parameter values of a function f(R). An initial metric of the Universe is supposed to be maximally symmetric with the positive curvature.

]]>Symmetry doi: 10.3390/sym13020312

Authors: Viktor Zhelyabin Ualbai Umirbaev

Symmetries of algebraic systems are called automorphisms. An algebra admits an automorphism of finite order n if and only if it admits a Zn-grading. Let N=N0⊕N1⊕N2 be a Z3-graded Novikov algebra. The main goal of the paper is to prove that over a field of characteristic not equal to 3, the algebra N is solvable if N0 is solvable. We also show that a Z2-graded Novikov algebra N=N0⊕N1 over a field of characteristic not equal to 2 is solvable if N0 is solvable. This implies that for every n of the form n=2k3l, any Zn-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N0 is solvable.

]]>Symmetry doi: 10.3390/sym13020311

Authors: Renfei Kuang Xiaoping Chen Zhiming Zhang Zuchao Zhu Yu Li

This paper presents a large eddy simulation of a centrifugal pump impeller during a transient condition. The flow rate is sinusoidal and oscillates between 0.25Qd (Qd indicates design load) and 0.75Qd when the rotating speed is maintained. Research shows that in one period, the inlet flow rate will twice reach 0.5Qd, and among the impeller of one moment is a stall state, but the other is a non-stall state. In the process of flow development, the evolution of low-frequency pressure fluctuation shows an obviously sinusoidal form, whose frequency is insensitive to the monitoring position and equals to that of the flow rate. However, inside the impeller, the phase and amplitude in the stall passages lag behind more and are stronger than that in the non-stall passages. Meanwhile, the strongest region of the high-frequency pressure fluctuation appears in the stall passages at the transient rising stage. The second dominant frequency in stall passages is 2.5 times to that in non-stall passages. In addition, similar to the pressure fluctuation, the evolution of the low-frequency head shows a sinusoidal form, whose phase is lagging behind that by one-third of a period in the inlet flow rate.

]]>Symmetry doi: 10.3390/sym13020310

Authors: Husam N. Yasin Siti Hafizah Ab Hamid Raja Jamilah Raja Yusof

Android applications provide benefits to mobile phone users by offering operative functionalities and interactive user interfaces. However, application crashes give users an unsatisfactory experience, and negatively impact the application’s overall rating. Android application crashes can be avoided through intensive and extensive testing. In the related literature, the graphical user interface (GUI) test generation tools focus on generating tests and exploring application functions using different approaches. Such tools must choose not only which user interface element to interact with, but also which type of action to be performed, in order to increase the percentage of code coverage and to detect faults with a limited time budget. However, a common limitation in the tools is the low code coverage because of their inability to find the right combination of actions that can drive the application into new and important states. A Q-Learning-based test coverage approach developed in DroidbotX was proposed to generate GUI test cases for Android applications to maximize instruction coverage, method coverage, and activity coverage. The overall performance of the proposed solution was compared to five state-of-the-art test generation tools on 30 Android applications. The DroidbotX test coverage approach achieved 51.5% accuracy for instruction coverage, 57% for method coverage, and 86.5% for activity coverage. It triggered 18 crashes within the time limit and shortest event sequence length compared to the other tools. The results demonstrated that the adaptation of Q-Learning with upper confidence bound (UCB) exploration outperforms other existing state-of-the-art solutions.

]]>Symmetry doi: 10.3390/sym13020309

Authors: Sanaa Al-Marzouki Farrukh Jamal Christophe Chesneau Mohammed Elgarhy

The last years have revealed the importance of the inverse Lomax distribution in the understanding of lifetime heavy-tailed phenomena. However, the inverse Lomax modeling capabilities have certain limits that researchers aim to overcome. These limits include a certain stiffness in the modulation of the peak and tail properties of the related probability density function. In this paper, a solution is given by using the functionalities of the half logistic family. We introduce a new three-parameter extended inverse Lomax distribution called the half logistic inverse Lomax distribution. We highlight its superiority over the inverse Lomax distribution through various theoretical and practical approaches. The derived properties include the stochastic orders, quantiles, moments, incomplete moments, entropy (Rényi and q) and order statistics. Then, an emphasis is put on the corresponding parametric model. The parameters estimation is performed by six well-established methods. Numerical results are presented to compare the performance of the obtained estimates. Also, a simulation study on the estimation of the Rényi entropy is proposed. Finally, we consider three practical data sets, one containing environmental data, another dealing with engineering data and the last containing insurance data, to show how the practitioner can take advantage of the new half logistic inverse Lomax model.

]]>Symmetry doi: 10.3390/sym13020308

Authors: Yang Jie LilianAsimwe Leonidas Farhan Mumtaz Munsif Ali

Ship detection and tracking is an important task in video surveillance in inland waterways. However, ships in inland navigation are faced with accidents such as collisions. For collision avoidance, we should strengthen the monitoring of navigation and the robustness of the entire system. Hence, this paper presents ship detection and tracking of ships using the improved You Only Look Once version 3 (YOLOv3) detection algorithm and Deep Simple Online and Real-time Tracking (Deep SORT) tracking algorithm. Three improvements are made to the YOLOv3 target detection algorithm. Firstly, the Kmeans clustering algorithm is used to optimize the initial value of the anchor frame to make it more suitable for ship application scenarios. Secondly, the output classifier is modified to a single Softmax classifier to suit our ship dataset which has three ship categories and mutual exclusion. Finally, Soft Non-Maximum Suppression (Soft-NMS) is introduced to solve the deficiencies of the Non-Maximum Suppression (NMS) algorithm when screening candidate frames. Results showed the mean Average Precision (mAP) and Frame Per Second (FPS) of the improved algorithm are increased by about 5% and 2, respectively, compared with the existing YOLOv3 detecting Algorithm. Then the improved YOLOv3 is applied in Deep Sort and the performance result of Deep Sort showed that, it has greater performance in complex scenes, and is robust to interference such as occlusion and camera movement, compared to state of art algorithms such as KCF, MIL, MOSSE, TLD, and Median Flow. With this improvement, it will help in the safety of inland navigation and protection from collisions and accidents.

]]>Symmetry doi: 10.3390/sym13020307

Authors: Sami Alabiad Yousef Alkhamees

A finite ring with an identity whose lattice of ideals forms a unique chain is called a finite chain ring. Let R be a commutative chain ring with invariants p,n,r,k,m. It is known that R is an Eisenstein extension of degree k of a Galois ring S=GR(pn,r). If p−1 does not divide k, the structure of the unit group U(R) is known. The case (p−1)∣k was partially considered by M. Luis (1991) by providing counterexamples demonstrated that the results of Ayoub failed to capture the direct decomposition of U(R). In this article, we manage to determine the structure of U(R) when (p−1)∣k by fixing Ayoub’s approach. We also sharpen our results by introducing a system of generators for the unit group and enumerating the generators of the same order.

]]>Symmetry doi: 10.3390/sym13020306

Authors: Armando Martínez-Pérez Gabino Torres-Vega

We discuss quantum time states formed with a finite number of energy eigenstates with the purpose of obtaining a time coordinate. These time states are eigenstates of the recently introduced discrete time operator. The coordinate and momentum representations of these time eigenstates resemble classical time curves and become classical at high energies. To illustrate this behavior, we consider the simple example of the particle-in-a-box model. We can follow the quantum-classical transition of the system. Among the many existing solutions for the particle in a box, we use a set which leads to time eigenstates for use as a coordinate system.

]]>Symmetry doi: 10.3390/sym13020305

Authors: Nicuşor Minculete

The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.

]]>Symmetry doi: 10.3390/sym13020304

Authors: Omid Ekrami Peter Claes Ellen Van Assche Mark D. Shriver Seth M. Weinberg Mary L. Marazita Susan Walsh Stefan Van Dongen

(1) Background: Fluctuating asymmetry is often used as an indicator of developmental instability, and is proposed as a signal of genetic quality. The display of prominent masculine phenotypic features, which are a direct result of high androgen levels, is also believed to be a sign of genetic quality, as these hormones may act as immunosuppressants. Fluctuating asymmetry and masculinity are therefore expected to covary. However, there is lack of strong evidence in the literature regarding this hypothesis. (2) Materials and methods: In this study, we examined a large dataset of high-density 3D facial scans of 1260 adults (630 males and 630 females). We mapped a high-density 3D facial mask onto the facial scans in order to obtain a high number of quasi-landmarks on the faces. Multi-dimensional measures of fluctuating asymmetry were extracted from the landmarks using Principal Component Analysis, and masculinity/femininity scores were obtained for each face using Partial Least Squares. The possible correlation between these two qualities was then examined using Pearson’s coefficient and Canonical Correlation Analysis. (3) Results: We found no correlation between fluctuating asymmetry and masculinity in men. However, a weak but significant correlation was found between average fluctuating asymmetry and masculinity in women, in which feminine faces had higher levels of fluctuating asymmetry on average. This correlation could possibly point to genetic quality as an underlying mechanism for both asymmetry and masculinity; however, it might also be driven by other fitness or life history traits, such as fertility. (4) Conclusions: Our results question the idea that fluctuating asymmetry and masculinity should be (more strongly) correlated in men, which is in line with the recent literature. Future studies should possibly focus more on the evolutionary relevance of the observed correlation in women.

]]>Symmetry doi: 10.3390/sym13020303

Authors: Dorota Bród Andrzej Włoch

In this paper we introduce and study (2,k)-distance Fibonacci polynomials which are natural extensions of (2,k)-Fibonacci numbers. We give some properties of these polynomials—among others, a graph interpretation and matrix generators. Moreover, we present some connections of (2,k)-distance Fibonacci polynomials with Pascal’s triangle.

]]>Symmetry doi: 10.3390/sym13020302

Authors: Adel A. Attiya Abdel Moneim Lashin Ekram E. Ali Praveen Agarwal

In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By the virtue of the Faber polynomial expansions, the estimation of n−th(n≥3) Taylor–Maclaurin coefficients an is obtained. Furthermore, the bounds value of the first two coefficients of such functions is established.

]]>Symmetry doi: 10.3390/sym13020301

Authors: Alexander Musaev Ekaterina Borovinskaya

The problem of dynamic adaptation of prediction algorithms in chaotic environments based on identification of the situations-analogs in the database of retrospective observations is considered. Under conditions of symmetrical and unsymmetrical chaotic dynamics, traditional computational schemes of precedent prediction turn out to be ineffective. In this regard, a dynamic adaptation of precedent analysis algorithms based on the method of evolutionary modeling is proposed. Implementation of the computational precedent prediction scheme for chaotic processes as well as the evolutionary modeling method are described.

]]>Symmetry doi: 10.3390/sym13020300

Authors: Run Cheng Qian-Yi Wang Yong-Long Wang Hong-Shi Zong

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.

]]>Symmetry doi: 10.3390/sym13020299

Authors: Birgitta Dresp-Langley John M. Wandeto

Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. To this end, we exploit a neural network metric in the output of a biologically inspired Self-Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data.

]]>Symmetry doi: 10.3390/sym13020298

Authors: Chuu-Lian Terng Zhiwei Wu

A smooth map γ in the symplectic space R2n is Lagrangian if γ,γx,…, γx(2n−1) are linearly independent and the span of γ,γx,…,γx(n−1) is a Lagrangian subspace of R2n. In this paper, we (i) construct a complete set of differential invariants for Lagrangian curves in R2n with respect to the symplectic group Sp(2n), (ii) construct two hierarchies of commuting Hamiltonian Lagrangian curve flows of C-type and A-type, (iii) show that the differential invariants of solutions of Lagrangian curve flows of C-type and A-type are solutions of the Drinfeld-Sokolov’s C^n(1)-KdV flows and A^2n−1(2)-KdV flows respectively, (iv) construct Darboux transforms, Permutability formulas, and scaling transforms, and give an algorithm to construct explicit soliton solutions, (v) give bi-Hamiltonian structures and commuting conservation laws for these curve flows.

]]>Symmetry doi: 10.3390/sym13020297

Authors: Motoshi Goto Nilam Ramaiya

We have developed an atomic model for calculating the polarization state of the Lyman-α line in plasma caused by anisotropic electron collision excitations. The model assumes a nonequilibrium state of the electron temperature between the directions parallel (T‖) and perpendicular (T⊥) to the magnetic field. A simplified assumption on the formation of an excited state population in the model is justified by detailed analysis of population flows regarding the upper state of the Lyman-α transition with the help of collisional-radiative model calculations. Calculation results give the polarization degree of several percent under typical conditions in the edge region of a magnetically confined fusion plasma. It is also found that the relaxation of polarization due to collisional averaging among the magnetic sublevels is effective in the electron density region considered. An analysis of the experimental data measured in the Large Helical Device gives T⊥/T‖=7.6 at the expected Lyman-α emission location outside the confined region. The result is derived with the absolute polarization degree of 0.033, and T⊥=32 eV and ne=9.6×1018m−3 measured by the Thomson scattering diagnostic system.

]]>Symmetry doi: 10.3390/sym13020296

Authors: Sayyad Alizadeh Hossein B. Jond Vasif V. Nabiyev Cemal Kose

A shoeprint is a valuable clue found at a crime scene and plays a significant role in forensic investigations. In this paper, in order to maintain the local features of a shoeprint image and place a pattern in a block, a novel automatic method was proposed, referred to as Modified Multi-Block Local Binary Pattern (MMB-LBP). In this method, shoeprint images are divided into blocks according to two different models. The histograms of all blocks of the first and second models are separately measured and stored in the first and second feature matrices, respectively. The performance evaluations of the proposed method were carried out by comparing with state-of-the-art methods. The evaluation criteria are the successful retrieval rates obtained using the best match score at rank one and cumulative match score for the first five matches. The comparison results indicated that the proposed method performs better than other methods, in terms of retrieval of complete and incomplete shoeprints. That is, the proposed method was able to retrieve 97.63% of complete shoeprints, 96.5% of incomplete toe shoeprints, and 91.18% of incomplete heel shoeprints. Moreover, the experiments showed that the proposed method is significantly resistant to the rotation, salt and pepper noise, and Gaussian white noise distortions in comparison with the other methods.

]]>Symmetry doi: 10.3390/sym13020295

Authors: Hanif Yaghoobi Keivan Maghooli Masoud Asadi-Khiavi Nader Jafarnia Dabanloo

Gene regulatory networks (GRN) are one of the etiologies associated with cancer. Their dysregulation can be associated with cancer formation and asymmetric cellular functions in cancer stem cells, leading to disease persistence and resistance to treatment. Systems that model the complex dynamics of these networks along with adapting to partially known real omics data are closer to reality and may be useful to understand the mechanisms underlying neoplastic phenomena. In this paper, for the first time, modelling of GRNs is performed using delayed nonlinear variable order fractional (VOF) systems in the state space by a new tool called GENAVOS. Although the tool uses gene expression time series data to identify and optimize system parameters, it also models possible epigenetic signals, and the results show that the nonlinear VOF systems have very good flexibility in adapting to real data. We found that GRNs in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create weak chaotic, periodic, and quasi-periodic oscillations by changing the parameters. Chaos can be associated with the onset of cancer. Our findings indicate a profound effect of time-varying orders on these networks, which may be related to a type of cellular epigenetic memory. By changing the delay parameter and the variable order functions (possible epigenetics signals) for a normal cell system, its behaviour becomes quite similar to the behaviour of a cancer cell. This work confirms the effective role of the miR-17-92 cluster as an epigenetic factor in the cancer cell cycle.

]]>Symmetry doi: 10.3390/sym13020292

Authors: Ricardo Abreu-Blaya Sergio Bermudo José M. Rodríguez Eva Tourís

We obtain inequalities involving many topological indices in classical graph products by using the f-polynomial. In particular, we work with lexicographic product, Cartesian sum and Cartesian product, and with first Zagreb, forgotten, inverse degree and sum lordeg indices.

]]>Symmetry doi: 10.3390/sym13020294

Authors: Thomas Noblet Laurent Dreesen Abderrahmane Tadjeddine Christophe Humbert

Given the tunability of their optical properties over the UV–Visible–Near IR spectral range, ligand-capped quantum dots (QDs) are employed for the design of optical biosensors with low detection threshold. Thanks to non-linear optical spectroscopies, the absorption properties of QDs are indeed used to selectively enhance the local vibrational response of molecules located in their vicinity. Previous studies led to assume the existence of a vibroelectronic QD–molecule coupling based on dipolar interaction. However, no systematic study on the strength of this coupling has been performed to date. In order to address this issue, we use non-linear optical Two-Color Sum-Frequency Generation (2C-SFG) spectroscopy to probe thick QD layers deposited on calcium fluoride (CaF2) prisms previously functionalized by a self-assembled monolayer of phenyltriethoxysilane (PhTES) molecules. Here, 2C-SFG is performed in Attenuated Total Reflection (ATR) configuration. By comparing the molecular vibrational enhancement measured for QD–ligand coupling and QD–PhTES coupling, we show that the spatial dependence of the QD–molecule interactions (∼1/r3, with r the QD–molecule distance) is in agreement with the hypothesis of a dipole–dipole interaction.

]]>Symmetry doi: 10.3390/sym13020293

Authors: Petar Ćurković

Natural systems achieve favorable mechanical properties through coupling significantly different elastic moduli within a single tissue. However, when it comes to man-made materials and structures, there are a lack of methods which enable production of artifacts inspired by these phenomena. In this study, a method for design automation based on alternate deposition of soft and stiff struts within a multi-material 3D lattice structure with desired deformation behavior is proposed. These structures, once external forces are applied, conform to the geometry given in advance. For that purpose, a population-based algorithm was proposed and integrated with a multi-material physics simulator. To reduce the amount of data processed during optimization, a generative encoding method based on discrete cosine transform (DCT) was proposed. This enabled a compressed topological description and promoted symmetry in material distribution. The simulation results showed different three-dimensional lattice structures designed with proposed algorithm to meet a set of desired deformation behaviors. The relation between residual deformation error, targeted deformation geometry, and material distribution is discussed.

]]>Symmetry doi: 10.3390/sym13020291

Authors: Ya-Chen Chang Teh-Li Chan Cheng-Chung Lee Yi-Jun Jen Wei-Chieh Ma

A stratiform hyperbolic metamaterial comprises multiple units of symmetrical metal-dielectric film, stacked to have a precisely equivalent refractive index, admittance, and iso-frequency curve. A metamaterial that is composed of stacks of symmetrical films as a waveguide to couple a diffracted wave into a horizontally propagating plasmonic wave is designed herein. By tuning the parameters of the constituent thin films within a hyperbolic metamaterial, both the loss of the plasmonic wave and admittance matching are minimized and optimized, respectively.

]]>Symmetry doi: 10.3390/sym13020290

Authors: Qunsheng Ruan Yiru Zhang Yuhui Zheng Yingdong Wang Qingfeng Wu Tianqi Ma Xiling Liu

The traditional heterogeneous embedding method based on a random walk strategy does not focus on the random walk fundamentally because of higher-order Markov chains. One of the important properties of Markov chains is stationary distributions (SDs). However, in large-scale network computation, SDs are not feasible and consume a lot of memory. So, we use a non-Markovian space strategy, i.e., a heterogeneous personalized spacey random walk strategy, to efficiently get SDs between nodes and skip some unimportant intermediate nodes, which allows for more accurate vector representation and memory savings. This heterogeneous personalized spacey random walk strategy was extended to heterogeneous space embedding methods in combination with vector learning, which is better than the traditional heterogeneous embedding methods for node classification tasks. As an excellent embedding method can obtain more accurate vector representations, it is important for the improvement of the recommendation model. In this article, recommendation algorithm research was carried out based on the heterogeneous personalized spacey embedding method. For the problem that the standard random walk strategy used to compute the stationary distribution consumes a large amount of memory, which may lead to inefficient node vector representation, we propose a meta-path-based heterogenous personalized spacey random walk for recommendation (MPHSRec). The meta-path-based heterogeneous personalized spacey random walk strategy is used to generate a meaningful sequence of nodes for network representation learning, and the learned embedded vectors of different meta-paths are transformed by a nonlinear fusion function and integrated into a matrix decomposition model for rating prediction. The experimental results demonstrate that MPHSRec not only improves the accuracy, but also reduces the memory cost compared with other excellent algorithms.

]]>Symmetry doi: 10.3390/sym13020289

Authors: Danko Markovinović Nikola Kranjčić Bojan Đurin Olga Bjelotomić Oršulić

Seawater level changes are affected by natural and anthropogenic impacts. While climate changes are considered to be a cause for all significant recent variations in meteorological and hydrological parameters, there is still a need for the analysis at the smaller regional scale, especially of the seawater level changes. A regional analysis is essential for early warning of upcoming changes that could, firstly, affect islands and coastal areas and, subsequently, expand on larger areas. The determined regional changes could affect the salinity of drinking water sources, increase the presence of natural flooding, and impact land degradation. In this paper, an analysis of local seawater level fluctuations is provided for three available locations in Croatia distributed along the Adriatic Sea’s coast. The rescaled adjusted partial sums (RAPS) method was used and applied on time series of the average daily seawater levels for each location. Visual interpretation of the RAPS method indicated the appearance of common regularities of the observed quantities, in this case, averaged daily seawater level changes. Also, it was shown that the regional shape and indentation of the coast did not have a strong effect on the seawater level’s rise. Seasonal changes in the sea level are mostly periodic and, therefore, have symmetry visible in its behavior. Fluctuations in the dynamics of sea level studied in this paper were not regular and predictable with simple linear equations, but the symmetry was also found to be present in the irregularities identified with the RAPS method.

]]>Symmetry doi: 10.3390/sym13020288

Authors: Alexei Kushner Valentin Lychagin

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

]]>Symmetry doi: 10.3390/sym13020287

Authors: Pannapa Changpetch

A model-building framework is proposed that combines two data mining techniques, TreeNet and association rules analysis (ASA) with multinomial logit model building. TreeNet provides plots that play a key role in transforming quantitative variables into better forms for the model fit, whereas ASA is important in finding interactions (low- and high-order) among variables. With the implementation of TreeNet and ASA, new variables and interactions are generated, which serve as candidate predictors in building an optimal multinomial logit model. A real-life example in the context of health care is used to illustrate the major role of these newly generated variables and interactions in advancing multinomial logit modeling to a new level of performance. This method has an explanatory and predictive ability that cannot be achieved using existing methods.

]]>Symmetry doi: 10.3390/sym13020286

Authors: Guohua Wu Mingyao Wang Qiuhua Wang Ye Yao Lifeng Yuan Gongxun Miao

In secret image sharing, the image is divided into several stego images, which are managed by corresponding participants. The secret image can be recovered only when the number of authorized participants is no less than the threshold. Thus, it is widely used to protect essential images, such as engineering drawings and product design drawings. In the traditional secret image sharing scheme, the threshold is fixed and unique. However, in practice, the security policy and the adversarial structure may change; therefore, the threshold must be adjusted dynamically. In this paper, we propose a novel secret image sharing scheme with a changeable threshold capability. Our scheme eliminates the limit of the changeable threshold and reduces the computation required. Also, our scheme is the first threshold changeable secret image sharing scheme that can recover an undistorted cover image. The theoretical analysis shows that our scheme is safe even if the threshold is changed. The experiments demonstrated that the stego image generated by our algorithm has better quality than other changeable-threshold, secret image sharing algorithms.

]]>Symmetry doi: 10.3390/sym13020284

Authors: Yakov M. Shnir

We present an overview of multisoliton chains arising in various non-integrable field theories and discuss different mechanisms which may lead to the occurrence of such axially-symmetric classical solutions. We explain the pattern of interactions between different solitons, in particular Q-balls, Skyrmions, and monopoles, and show how chains of interacting non-BPS solitons may form in a dynamic equilibrium between repulsive and attractive forces.

]]>Symmetry doi: 10.3390/sym13020285

Authors: Saad Althobati Jehad Alzabut Omar Bazighifan

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

]]>Symmetry doi: 10.3390/sym13020283

Authors: Elena Belenkaya Igor Alexeev

In the planetary magnetospheres there are specific places connected with velocity breakdown, reconnection, and dynamo processes. Here we pay attention to sliding layers. Sliding layers are formed in the ionosphere, on separatrix surfaces, at the magnetopauses and boundaries of stellar astrospheres, and at the Alfvén radius in the equatorial magnetosphere of rapidly rotating strongly magnetized giant planets. Although sliding contacts usually occur in thin local layers, their influence on the global structure of the surrounding space is very great. Therefore, they are associated with non-local processes that play a key role on a large scale. There can be an exchange between different forms of energy, a generation of strong field-aligned currents and emissions, and an amplification of magnetic fields. Depending on the conditions in the magnetosphere of the planet/exoplanet and in the flow of magnetized plasma passing it, different numbers of sliding layers with different configurations appear. Some are associated with regions of auroras and possible radio emissions. The search for planetary radio emissions is a current task in the detection of exoplanets.

]]>Symmetry doi: 10.3390/sym13020282

Authors: Ginkyu Choi Soon-Mo Jung

We will prove the generalized Hyers–Ulam stability of isometries, with a focus on the stability for restricted domains. More precisely, we prove the generalized Hyers–Ulam stability of the orthogonality equation and we use this result to prove the stability of the equations ∥f(x)−f(y)∥=∥x−y∥ and ∥f(x)−f(y)∥2=∥x−y∥2 on the restricted domains. As we can easily see, these functional equations are symmetric in the sense that they become the same equations even if the roles of variables x and y are exchanged.

]]>Symmetry doi: 10.3390/sym13020281

Authors: Zhonghe Huang Jianping Tan Chuliang Liu Xiong Lu

Helicopter tail rotors adopt a segmented driveline connected by flexible couplings, and dry friction dampers to suppress resonance. Modeling for this system can provide a basic foundation for parameter analysis. In this work, the lateral-torsional vibration equation of the shaft with continuous internal damping is established. The static and dynamic effects caused by flexible diaphragm couplings subject to parallel and angular misalignment is derived. A novel dual rub-impact model between the shaft and dry friction damper with multiple stages is proposed. Finally, a model of a helicopter tail rotor driveline incorporating all the above elements is formulated. Numerical simulations are carried out by an improved Adams–Bashforth method following the design flowchart. The dynamics of multiple vibration suppression, and the static and dynamic misalignment are analyzed to illustrate the accuracy and characteristics of the model. The coeffect of the rub impact and the misalignment on shafts and dampers are presented through the results of simulation and experiment. It provides an accurate and comprehensive mathematical model for the helicopter driveline. Response characteristics of multiple damping stages, static and dynamic misalignment, and their interaction are revealed.

]]>Symmetry doi: 10.3390/sym13020280

Authors: Viswanathan Sangeetha Raghunathan Krishankumar Kattur Soundarapandian Ravichandran Fausto Cavallaro Samarjit Kar Dragan Pamucar Abbas Mardani

Path planning can be perceived as a combination of searching and executing the optimal path between the start and destination locations. Deliberative planning capabilities are essential for the motion of autonomous unmanned vehicles in real-world scenarios. There is a challenge in handling the uncertainty concerning the obstacles in a dynamic scenario, thus requiring an intelligent, robust algorithm, with the minimum computational overhead. In this work, a fuzzy gain-based dynamic ant colony optimization (FGDACO) for dynamic path planning is proposed to effectively plan collision-free and smooth paths, with feasible path length and the minimum time. The ant colony system’s pheromone update mechanism was enhanced with a sigmoid gain function for effective exploitation during path planning. Collision avoidance was achieved through the proposed fuzzy logic control. The results were validated using occupancy grids of variable size, and the results were compared against existing methods concerning performance metrics, namely, time and length. The consistency of the algorithm was also analyzed, and the results were statistically verified.

]]>Symmetry doi: 10.3390/sym13020279

Authors: Pablo G. Ortega David R. Entem

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the X(3872) was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance.

]]>Symmetry doi: 10.3390/sym13020278

Authors: Taher A. Nofal Omar Bazighifan Khaled Mohamed Khedher Mihai Postolache

In this work, we present several oscillation criteria for higher-order nonlinear delay differential equation with middle term. Our approach is based on the use of Riccati substitution, the integral averaging technique and the comparison technique. The symmetry contributes to deciding the right way to study oscillation of solutions of this equations. Our results unify and improve some known results for differential equations with middle term. Some illustrative examples are provided.

]]>Symmetry doi: 10.3390/sym13020277

Authors: Wenbin Zhao Jianbin Hu Kai Wang

In order to improve hydraulic efficiency, influence of inlet angle, outlet angle, wrap angle, inlet shape and outer edge camber lines of channel-diffuser blades on the energy performance of a three-stage centrifugal pump were studied and the pressure distributions on the blade of the first-stage channel-diffuser were particularly analyzed. The result shows that the efficiency of the pump is maximal when the blade inlet angle is 12°. The pressure variation in the model with the inlet angle of 12° was small and the amplitude of fluctuation was also not large. When the outlet angle was 90°, the pressure distribution in the outlet of the blades that are symmetrically distributed along the center of the diffuser shell was significantly better than that with other outlet angles. The effect of the blade wrap angle of the channel-diffuser on the energy performance of the pump was relatively small. The internal flow in the diffuser with the diffusion inlet shapes was steady for both the convex surface and concave surface. The diffusion inlet of the channel-diffuser blade corresponded to the outlet region of the impeller blade, which reflected a good matching. The fluctuation amplitude and the distribution range of the models with a uniform transition were smaller than those with non-uniform transition. In order to verify the effectiveness of the research results, an experimental test was carried out on the pump. The results show that when the flow rate is 850 m3/h, the head of the pump is 138.67 m and the efficiency of pump is 69.48%.

]]>Symmetry doi: 10.3390/sym13020274

Authors: Rudolf Podgornik

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact via long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson–Boltzmann and Maier–Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity to a charged planar wall. The nematic order parameter profile, the counterion density profile and the electrostatic potential profile are interpreted within the framework of a nematic–isotropic wetting phase with a Donnan potential difference.

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