Symmetry doi: 10.3390/sym10030073

Authors: Dan Popescu Loretta Ichim

The automatic detection, segmentation, localization, and evaluation of the optic disc, macula, exudates, and hemorrhages are very important for diagnosing retinal diseases. One of the difficulties in detecting such regions of interest (RoIs) with computer vision is their symmetries, e.g., between the optic disc and exudates and also between exudates and hemorrhages. This paper proposes an original, intelligent, and high-performing image processing system for the simultaneous detection and segmentation of retinal RoIs. The basic principles of the method are image decomposition in small boxes and local texture analysis. The processing flow contains three phases: preprocessing, learning, and operating. As a first novelty, we propose proper feature selection based on statistical analysis in confusion matrices for different feature types (extracted from a co-occurrence matrix, fractal type, and local binary patterns). Mainly, the selected features are chosen to differentiate between similar RoIs. The second novelty consists of local classifier fusion. To this end, the local classifiers associated with features are grouped in global classifiers corresponding to the RoIs. The local classifiers are based on minimum distances to the representatives of classes and the global classifiers are based on confidence intervals, weights, and a voting scheme. A deep convolutional neural network, based on supervised learning, for blood vessel segmentation is proposed in order to improve the RoI detection performance. Finally, the experimental results on real images from different databases demonstrate the rightness of our methodologies and algorithms.

]]>Symmetry doi: 10.3390/sym10030072

Authors: Philip Broadbridge Dimetre Triadis Dilruk Gallage Pierluigi Cesana

Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

]]>Symmetry doi: 10.3390/sym10030071

Authors: Muammar Sadrawi Wei-Zen Sun Matthew Ma Yu-Ting Yeh Maysam Abbod Jiann-Shing Shieh

Equally partitioned data are essential for prediction. However, in some important cases, the data distribution is severely unbalanced. In this study, several algorithms are utilized to maximize the learning accuracy when dealing with a highly unbalanced dataset. A linguistic algorithm is applied to evaluate the input and output relationship, namely Fuzzy c-Means (FCM), which is applied as a clustering algorithm for the majority class to balance the minority class data from about 3 million cases. Each cluster is used to train several artificial neural network (ANN) models. Different techniques are applied to generate an ensemble genetic fuzzy neuro model (EGFNM) in order to select the models. The first ensemble technique, the intra-cluster EGFNM, works by evaluating the best combination from all the models generated by each cluster. Another ensemble technique is the inter-cluster model EGFNM, which is based on selecting the best model from each cluster. The accuracy of these techniques is evaluated using the receiver operating characteristic (ROC) via its area under the curve (AUC). Results show that the AUC of the unbalanced data is 0.67974. The random cluster and best ANN single model have AUCs of 0.7177 and 0.72806, respectively. For the ensemble evaluations, the intra-cluster and the inter-cluster EGFNMs produce 0.7293 and 0.73038, respectively. In conclusion, this study achieved improved results by performing the EGFNM method compared with the unbalanced training. This study concludes that selecting several best models will produce a better result compared with all models combined.

]]>Symmetry doi: 10.3390/sym10030070

Authors: Theodosios Christodoulakis Alexandros Karagiorgos Adamantia Zampeli

The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. When a valid reduced action principle exists, the symmetries of the configuration mini-supermetric space can also be used, in conjunction with the constraints, to provide local or non-local constants of motion. At the classical level, depending on their number, these integrals can even secure the acquisition of the entire solution space without any further solving of the dynamical equations. At the quantum level, their operator analogues can be used, along with the Wheeler–DeWitt equation, to define unique wave functions that exhibit singularity-free behavior at a semi-classical level.

]]>Symmetry doi: 10.3390/sym10030069

Authors: Mayra Machuca Winyu Chinthammit Weidong Huang Rainer Wasinger Henry Duh

Collaboration has been common in workplaces in various engineering settings and in our daily activities. However, how to effectively engage collaborators with collaborative tasks has long been an issue due to various situational and technical constraints. The research in this paper addresses the issue in a specific scenario, which is how to enable users to interact with public information from their own perspective. We describe a 3D mobile interaction technique that allows users to collaborate with other people by creating a symmetric and collaborative ambience. This in turn can increase their engagement with public displays. In order to better understand the benefits and limitations of this technique, we conducted a usability study with a total of 40 participants. The results indicate that the 3D mobile interaction technique promotes collaboration between users and also improves their engagement with the public displays.

]]>Symmetry doi: 10.3390/sym10030068

Authors: Kimball Milton Iver Brevik

It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with ε μ = 1 , a so-called isorefractive or diaphanous ball. Here we re-examine that example and attempt to extend it to an electromagnetic δ -function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented.

]]>Symmetry doi: 10.3390/sym10030067

Authors: Nikolai Erokhovets

A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. These polytopes are exactly simple 3-polytopes with cyclically 5-edge connected graphs. A Pogorelov polytope has no 3- and 4-gons and may have any prescribed numbers of k-gons, k ≥ 7 . Any simple polytope with only 5-, 6- and at most one 7-gon is Pogorelov. For any other prescribed numbers of k-gons, k ≥ 7 , we give an explicit construction of a Pogorelov and a non-Pogorelov polytope. Any Pogorelov polytope different from k-barrels (also known as Löbel polytopes, whose graphs are biladders on 2 k vertices) can be constructed from the 5- or the 6-barrel by cutting off pairs of adjacent edges and connected sums with the 5-barrel along a 5-gon with the intermediate polytopes being Pogorelov. For fullerenes, there is a stronger result. Any fullerene different from the 5-barrel and the ( 5 , 0 ) -nanotubes can be constructed by only cutting off adjacent edges from the 6-barrel with all the intermediate polytopes having 5-, 6- and at most one additional 7-gon adjacent to a 5-gon. This result cannot be literally extended to the latter class of polytopes. We prove that it becomes valid if we additionally allow connected sums with the 5-barrel and 3 new operations, which are compositions of cutting off adjacent edges. We generalize this result to the case when the 7-gon may be isolated from 5-gons.

]]>Symmetry doi: 10.3390/sym10030066

Authors: Kairong Duan Simon Fong Yan Zhuang Wei Song

The information of human occupancy plays a crucial role in building management. For instance, fewer people, less demand for heat and electricity supply, and vice versa. Moreover, when there is a fire in a building, it is convenient to know how many persons in a single room there are in order to plan a more efficient rescue strategy. However, currently most buildings have not installed adequate devices that can be used to count the number of people, and the most popular embedded fire alarm system triggers a warning only when a fire breaks out with plenty of smoke. In view of this constraint, in this paper we propose a carbon oxides gases based warning system to detect potential fire breakouts and to estimate the number of people in the proximity. In order to validate the efficiency of the devised system, we simulate its application in the Fog Computing environment. Furthermore, we also improve the iFogSim by giving data analytics capacity to it. Based on this framework, energy consumption, latency, and network usage of the designed system obtained from iFogSim are compared with those obtained from Cloud environment.

]]>Symmetry doi: 10.3390/sym10030065

Authors: David Orden Jose Gimenez-Guzman Ivan Marsa-Maestre Enrique de la Hoz

We introduce and explore a family of vertex-coloring problems, which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of interferences between each pair of colors, the Threshold Spectrum Coloring problem fixes the number of colors available and aims to minimize the interference threshold, i.e., the maximum of the interferences at the vertices. Conversely, the Chromatic Spectrum Coloring problem fixes a threshold and aims to minimize the number of colors for which respecting that threshold is possible. As the main theoretical results, we prove tight upper bounds for the solutions to each problem. Since both problems turn out to be NP-hard, we complete the scene with experimental results. We propose a DSATUR-based heuristic and study its performance to minimize the maximum vertex interference in Wi-Fi channel assignment, both for randomly-generated graphs and for a real-world scenario. Further, for all these graphs, we experimentally check the goodness of the theoretical bounds.

]]>Symmetry doi: 10.3390/sym10030064

Authors: Lin Zhang Xiyuan Li Junhao Huang Ying Shen Dongqing Wang

Recent years have witnessed a growing interest in developing automatic parking systems in the field of intelligent vehicles. However, how to effectively and efficiently locating parking-slots using a vision-based system is still an unresolved issue. Even more seriously, there is no publicly available labeled benchmark dataset for tuning and testing parking-slot detection algorithms. In this paper, we attempt to fill the above-mentioned research gaps to some extent and our contributions are twofold. Firstly, to facilitate the study of vision-based parking-slot detection, a large-scale parking-slot image database is established. This database comprises 8600 surround-view images collected from typical indoor and outdoor parking sites. For each image in this database, the marking-points and parking-slots are carefully labeled. Such a database can serve as a benchmark to design and validate parking-slot detection algorithms. Secondly, a learning-based parking-slot detection approach, namely P S D L , is proposed. Using P S D L , given a surround-view image, the marking-points will be detected first and then the valid parking-slots can be inferred. The efficacy and efficiency of P S D L have been corroborated on our database. It is expected that P S D L can serve as a baseline when the other researchers develop more sophisticated methods.

]]>Symmetry doi: 10.3390/sym10030063

Authors: Chenggui Zhao Behrooz Parhami

Virtual network embedding (VNE) is a key technology in network virtualization. Advantages of network symmetry are well known in the design of load-balanced routing algorithms and in network performance analysis. Our work in this paper shows that benefits of graph symmetry also extend to the domain of network embedding. Specifically, we propose an efficient VNE method based on modular and structured agency guidance, a regular graph function. The proposed method, which is based on symmetric intermediate graphs, offers two main advantages. Firstly, characteristics of the intermediate structures enhance the computational efficiency of the VNE process. Secondly, the static agency network modeled with such intermediate structures improves the quality of the resulting embedding. These two advantages of our method are elaborated upon and verified by examples and simulations, respectively. In addition, we present a theoretical analysis explaining the reasons behind the benefits offered by such middleware.

]]>Symmetry doi: 10.3390/sym10030062

Authors: Sven Heinemeyer Myriam Mondragón Gregory Patellis Nicholas Tracas George Zoupanos

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. The latter consists of searching for renormalization group invariant relations among parameters of a renormalizable theory holding to all orders in perturbation theory. FUTs have proven very successful so far. In particular, they predicted the top quark mass one and half years before its experimental discovery, while around five years before the Higgs boson discovery, a particular FUT was predicting the light Higgs boson in the mass range ∼121–126 GeV, in striking agreement with the discovery at LHC. Here, we review the basic properties of the supersymmetric theories and in particular finite theories resulting from the application of the method of reduction of couplings in their dimensionless and dimensionful sectors. Then, we analyze the phenomenologically-favored FUT, based on SU(5). This particular FUT leads to a finiteness constrained version of the Minimal SUSY Standard Model (MSSM), which naturally predicts a relatively heavy spectrum with colored supersymmetric particles above 2.7 TeV, consistent with the non-observation of those particles at the LHC. The electroweak supersymmetric spectrum starts below 1 TeV, and large parts of the allowed spectrum of the lighter might be accessible at CLIC. The FCC-hhwill be able to fully test the predicted spectrum.

]]>Symmetry doi: 10.3390/sym10030061

Authors: Gang Deng Ling Pei Ni Hu Yang Liu Jin-Rong Zhu

Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that the Casimir force, especially in the direction of the force, can be significantly affected by the anisotropy of the intervening material. We also discuss the combined influence of dispersion and anisotropy, and analyze the impact of the external electric filed on the Casimir force by affecting the anisotropy of the intervening material by Kerr electro-optical effect.

]]>Symmetry doi: 10.3390/sym10030060

Authors: Karolina Nurzynska

The automatic analysis of the state of the corneal endothelium is of much interest in ophthalmology. Up till now, several manual and semi-automatic methods have been introduced, but the need of fully-automatic segmentation of cells in the endothelium is still in search. This work addresses the problem of automatic delineation of cells in the corneal endothelium images and suggests to use the convolutional neural network (CNN) to classify between cell center, cell body, and cell border in order to achieve precise segmentation. Additionally, a method to automatically select and split merged cells is given. In order to skeletonize the result, the best-fit method is used. The achieved outcomes are compared to manual annotations in order to define the mutual overlapping. The Dice index, Jaccard coefficient, modified Hausdorff distance, and several other metrics for mosaic overlapping are used. As a final check-up, the visual inspection is shown. The performed experiments revealed the best architecture for CNN. The correctness and precision of the segmentation were evaluated on Endothelial Cell “Alizarine” dataset. According to the Dice index and Jaccard coefficient, the automatically achieved cell delineation overlaps the original one with 93% precision. While modified Hausdorff distance shows 0.14 pixel distance, proving very high accuracy. These findings are confirmed by other metrics and also supported by presented visual inspection of achieved segmentations. To conclude, the methodology to achieve fully-automatic delineation of cell boundaries in the corneal endothelium images was presented. The segmentation obtained as a result of pixel classification with CNN proved very high precision.

]]>Symmetry doi: 10.3390/sym10030059

Authors: Dariusz Bochenek Przemysław Niemiec Joanna Korzekwa Bartłomiej Durtka Zbigniew Stokłosa

The paper presents the technology of ferroelectric-ferromagnetic ceramic composites obtained from PLZT powder (the chemical formula Pb0.98La0.02(Zr0.90Ti0.10)0.995O3) and ferrite powder (Ni0.64Zn0.36Fe2O4), as well as the results of X-ray powder-diffraction data (XRD) measurement, microstructure, dielectric, ferroelectric, and magnetic properties of the composite samples. The ferroelectric-ferromagnetic composite (P-F) was obtained by mixing and the synthesis of 90% of PLZT and 10% of ferrite powders. The XRD test of the P-F composite shows a two-phase structure derived from the PLZT component (strong peaks) and the ferrite component (weak peaks). The symmetry of PLZT was identified as a rhombohedral ferroelectric phase, while the ferrite was identified as a spinel structure. Scanning electron microscope (SEM) microstructure analysis of the P-F ceramic composites showed that fine grains of the PLZT component surrounded large ferrite grains. At room temperature P-F composites exhibit both ferroelectric and ferromagnetic properties. The P-F composite samples have lower values of the maximum dielectric permittivity at the Curie temperature and a higher dielectric loss compared to the PLZT ceramics, however, the exhibit overall good multiferroic properties.

]]>Symmetry doi: 10.3390/sym10030058

Authors: Andrés Iglesias Akemi Gálvez Patricia Suárez Mikio Shinya Norimasa Yoshida César Otero Cristina Manchado Valentin Gomez-Jauregui

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.

]]>Symmetry doi: 10.3390/sym10030057

Authors: Byung-Kil Han Seung-Chan Kim Dong-Soo Kwon

This paper proposes a novel tangible interface system to enhance the immersive experience in virtual reality environments. The proposed system allows representing physical properties of the tool, such as the deflection of the elastic rods, which users handle in a virtual and physical environment. This system is composed of two parts; one is an articulated interface to visually represent the physical behavior and the other is a computational algorithm that can compute a set of 6-DOF positions of the links. The proposed computational algorithm extends an active contour model, which is used primarily in computer vision and image processing, incorporating a spring and damping constraint energy functional. An elastic rod is modeled as a series of rigid line segments with a symmetric relationship between neighboring segments, and its shape is modeled to be influenced by energies that are induced by a user, and the external deformation of the spline. The symmetric and sparse properties of the proposed model enable an efficient energy minimization process, and the modification of a number of the line segments. Based on this configuration, we construct an energy generation method based on the positional displacement of the base element to generate the deflection behavior of the contour according to the user’s motion in the space. Therefore, the physical device can simulate a variety of deformable objects by modulating energy parameters during the energy minimization process. Experimental results demonstrate the feasibility of emulating various behaviors of deformable splines, and applying to virtual reality system without interfering with the motion-to-photon latency. We also discuss the method’s limitations and explore its potential.

]]>Symmetry doi: 10.3390/sym10030056

Authors: Milan Melnik Peter Mikus Clive Holloway

This manuscript summarizes and analyzes X-ray data of monomeric cis-PtP2CCl derivatives. These complexes crystallize in the following crystal systems: tetragonal, P42/n (3), triclinic, Pī (10), orthorhombic, P212121 (prevails)(16), and monoclinic, P21/c (prevails) (36) examples. There are three sub-groups of the respective complexes: Pt(η1-PL)2(η1-CL)(η1-Cl); Pt(η2-P2L)(η1-CL)(η1-Cl) and Pt(η1-PL)(η2-P,CL)(η1-Cl). The chelating P,P-donor ligands form: four-(POP, PCP), five-(PC2P), six-(PC3P, PCNCP), seven-(PC4P) and even ten-(PCNCNCNCP) membered rings. The chelating P.C-donor ligands create three-(PC), four-(PCC) and five-(PC2C) membered rings. The mean Pt-L bond distance elongates in the sequence: 2.10 Å (C, trans to P) &lt; 2.222 Å (P, trans to Cl) &lt; 2.312 Å (P, trans to C) &lt; 2.360 Å (Cl, trans to P). There are examples which exist in two isomeric forms, of the distortion isomer type.

]]>Symmetry doi: 10.3390/sym10030055

Authors: Mao-Ting Chien Hiroshi Nakazato

Let A be an n × n complex matrix. Assume the determinantal curve V A = { [ ( x , y , z ) ] ∈ CP 2 : F A ( x , y , z ) = det ( x ℜ ( A ) + y ℑ ( A ) + z I n ) = 0 } is a rational curve. The Fiedler formula provides a complex symmetric matrix S satisfying F S ( x , y , z ) = F A ( x , y , z ) . It is also known that every Toeplitz matrix is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity of the symmetric matrix S and the matrix A in the Fiedler theorem for a specific parametrized family of 4 × 4 nilpotent Toeplitz matrices A. We show that there are either one or at least three unitarily inequivalent symmetric matrices which admit the determinantal representation of the ternary from F A ( x , y , z ) associated to the specific 4 × 4 nilpotent Toeplitz matrices.

]]>Symmetry doi: 10.3390/sym10030054

Authors: Stephen Fulling Thomas Settlemyre Kimball Milton

The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential.

]]>Symmetry doi: 10.3390/sym10030053

Authors: A. Shapovalov V. Obukhov

This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed.

]]>Symmetry doi: 10.3390/sym10030052

Authors: Tiberiu Tudor

In the frame of a generic language extended from the polarization theory—comprising the notions of Poincaré vectors, Poincaré sphere, and P-spheres—a geometric approach to Lorentz transformations alternative to the Minkowskian one is given. Unlike the four-dimensional Minkowskian approach, this new approach operates in the three-dimensional space of Poincaré vectors.

]]>Symmetry doi: 10.3390/sym10020051

Authors: Nilanjan Dey Venkatesan Rajinikanth Amira Ashour João Manuel Tavares

The segmentation of medical images by computational methods has been claimed by the medical community, which has promoted the development of several algorithms regarding different tissues, organs and imaging modalities. Nowadays, skin melanoma is one of the most common serious malignancies in the human community. Consequently, automated and robust approaches have become an emerging need for accurate and fast clinical detection and diagnosis of skin cancer. Digital dermatoscopy is a clinically accepted device to register and to investigate suspicious regions in the skin. During the skin melanoma examination, mining the suspicious regions from dermoscopy images is generally demanded in order to make a clear diagnosis about skin diseases, mainly based on features of the region under analysis like border symmetry and regularity. Predominantly, the successful estimation of the skin cancer depends on the used computational techniques of image segmentation and analysis. In the current work, a social group optimization (SGO) supported automated tool was developed to examine skin melanoma in dermoscopy images. The proposed tool has two main steps, mainly the image pre-processing step using the Otsu/Kapur based thresholding technique and the image post-processing step using the level set/active contour based segmentation technique. The experimental work was conducted using three well-known dermoscopy image datasets. Similarity metrics were used to evaluate the clinical significance of the proposed tool such as Jaccard’s coefficient, Dice’s coefficient, false positive/negative rate, accuracy, sensitivity and specificity. The experimental findings suggest that the proposed tool achieved superior performance relatively to the ground truth images provided by a skin cancer physician. Generally, the proposed SGO based Kapur’s thresholding technique combined with the level set based segmentation technique is very effective for identifying melanoma dermoscopy digital images with high sensitivity, specificity and accuracy.

]]>Symmetry doi: 10.3390/sym10020050

Authors: Xin Li Xiaohong Zhang

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions. First, taking advantage of the Choquet integral and that it can reflect more correlations of attributes in MADM, two aggregation operators are defined based on the Choquet integral, specifically, the single-valued neutrosophic hesitant fuzzy Choquet ordered averaging (SVNHFCOA) operator and single-valued neutrosophic hesitant fuzzy Choquet ordered geometric (SVNHFCOG) operator, and their properties are also discussed in detail. Then, novel MADM approaches based on the SVNHFCOA and SVNHFCOG operators are established to process single-valued neutrosophic hesitant fuzzy information. Finally, this work provides a numerical example of investment alternatives to validate the application and effectiveness of the proposed approaches.

]]>Symmetry doi: 10.3390/sym10020049

Authors: Xiaokai Niu Dingli Zhang Jie Su Hong Guo

To exploit the influence of the tunnel face and the distance between the diameter and the orifice of a blast pipe on the ventilation effect in symmetric tunnel construction, this paper uses Fluent to establish a three-dimensional model and numerical simulation. Firstly, the accuracy of the numerical simulation is tested and then the distance between the orifice and tunnel face and the influence of the air duct diameter on the ventilation effect are studied, respectively. The results show that the ventilation effect is best when the wind pipe is arranged on one side of the tunnel wall (an asymmetrical layout), although the space in the tunnel is axisymmetric, and that the error of the numerical simulation is less than 5% of the measured value. When the distance between the orifice and tunnel face is 5 m, the uniformity of the air flow field near the tunnel face is poor; when the distance is 10 m and 12 m, an obvious vertex area appears in the tunnel. Furthermore, the uniformity of the wind velocity flow field is optimal when the distance is 8 m. When the air duct diameter is less than 1.4 m, there is a uniformity of the flow field near the tunnel face of the upper and lower benches; when the air duct diameter is more than 1.4 m, the tunnel face of the upper bench near the ground shows more obvious backflow. Therefore, it was determined that taking the air duct diameter as 1.4 m and the distance between the orifice and tunnel face as 8 m was the best combination for the design of ventilation in this project. It was also found that a better ventilation effect can be achieved when the distance between the nozzle of the ventilator and the tunnel face is 6 m–9 m and the wind speed of the nozzle is 6 m/s–8 m/s. In practical engineering, the wind speed and the required air volume should be taken into consideration to determine the diameter of the ventilator.

]]>Symmetry doi: 10.3390/sym10020048

Authors: Laszlo Iantovics Matthias Dehmer Frank Emmert-Streib

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective measure of the machine intelligence quotient. The most important drawbacks of the designed metrics presented in the scientific literature consist in the limitation in universality, accuracy, and robustness. In this paper, we propose a novel universal metric called MetrIntSimil capable of making an accurate and robust symmetric comparison of the similarity in intelligence of any number of cooperative multiagent systems specialized in difficult problem solving. The universality is an important necessary property based on the large variety of designed intelligent systems. MetrIntSimil makes a comparison by taking into consideration the variability in intelligence in the problem solving of the compared cooperative multiagent systems. It allows a classification of the cooperative multiagent systems based on their similarity in intelligence. A cooperative multiagent system has variability in the problem solving intelligence, and it can manifest lower or higher intelligence in different problem solving tasks. More cooperative multiagent systems with similar intelligence can be included in the same class. For the evaluation of the proposed metric, we conducted a case study for more intelligent cooperative multiagent systems composed of simple computing agents applied for solving the Symmetric Travelling Salesman Problem (STSP) that is a class of NP-hard problems. STSP is the problem of finding the shortest Hamiltonian cycle/tour in a weighted undirected graph that does not have loops or multiple edges. The distance between two cities is the same in each opposite direction. Two classes of similar intelligence denoted IntClassA and IntClassB were identified. The experimental results show that the agent belonging to IntClassA intelligence class is less intelligent than the agents that belong to the IntClassB intelligence class.

]]>Symmetry doi: 10.3390/sym10020047

Authors: Xiao-Zhu Xie Chia-Chen Lin Chin-Chen Chang

Data hiding is a technology that embeds data into a cover carrier in an imperceptible way while still allowing the hidden data to be extracted accurately from the stego-carrier, which is one important branch of computer science and has drawn attention of scholars in the last decade. Turtle shell-based (TSB) schemes have become popular in recent years due to their higher embedding capacity (EC) and better visual quality of the stego-image than most of the none magic matrices based (MMB) schemes. This paper proposes a two-layer turtle shell matrix-based (TTSMB) scheme for data hiding, in which an extra attribute presented by a 4-ary digit is assigned to each element of the turtle shell matrix with symmetrical distribution. Therefore, compared with the original TSB scheme, two more bits are embedded into each pixel pair to obtain a higher EC up to 2.5 bits per pixel (bpp). The experimental results reveal that under the condition of the same visual quality, the EC of the proposed scheme outperforms state-of-the-art data hiding schemes.

]]>Symmetry doi: 10.3390/sym10020046

Authors: Kajal Chatterjee Edmundas Kazimieras Zavadskas Jolanta Tamošaitienė Krishnendu Adhikary Samarjit Kar

Multi-stakeholder based construction projects are subject to potential risk factors due to dynamic business environment and stakeholders’ lack of knowledge. When solving project management tasks, it is necessary to quantify the main risk indicators of the projects. Managing these requires suitable risk mitigation strategies to evaluate and analyse their severity. The existence of information asymmetry also causes difficulties with achieving Pareto efficiency. Hence, to ensure balanced satisfaction of all participants, risk evaluation of these projects can be considered as an important part of the multi-criteria decision-making (MCDM) process. In real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D numbers domain to handle three types of ambiguous information’s, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D numbers based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster–Shafer (D–S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D numbers extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D numbers is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches in D numbers domain. Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed to verify the robustness of the proposed method.

]]>Symmetry doi: 10.3390/sym10020045

Authors: Jalil Dahooie Edmundas Zavadskas Mahdi Abolhasani Amirsalar Vanaki Zenonas Turskis

The beginning of the 21st-century resulted in a more developed multi-attribute decision-making (MADM) tool and inspired new application areas that have resulted in discoveries in sustainable construction and building life cycle analysis. Construction and civil engineering stand for the central axis of a body consisting of a multidisciplinary (multi-dimensional) world with ties to disciplines constituting the surface, and with the disciplines, as a consequence, tied to each other. When dealing with multi-attribute decision-making problems generally multiple solutions exist, especially when there is a large number of attributes, and the concept of Pareto-optimality is inefficient. The symmetry and structural regularity are essential concepts in many natural and man-made objects and play a crucial role in the design, engineering, and development of the world. The complexity and risks inherent in projects along with different effective indicators for success and failure may contribute to the difficulties in performance evaluation. In such situations, increasing the importance of uncertainty is observed. This paper proposes a novel integrated tool to find a balance between sustainable development, environmental impact and human well-being, i. e. to find symmetry axe with respect to goals, risks, and constraints (attributes) to cope with the complicated problems. The concept of “optimal solution” as the maximum degree of implemented goals (attributes) is very important. The model is built using the most relevant variables cited in the reviewed project literature and integrates two methods: the Step-Wise Weight Assessment Ratio Analysis (SWARA) method and a novel interval-valued fuzzy extension of the Additive Ratio Assessment (ARAS) method. This model was used to solve real case study of oil and gas well drilling projects evaluation. Despite the importance of oil and gas well drilling projects, there is lack of literature that describes and evaluates performance in this field projects. On the other hand, no structured assessment methodology has been presented for these types of projects. Given the limited research on performance evaluation in oil &amp; gas well-drilling projects, the research identifies a set of performance criteria and proposes an evaluation model using fuzzy Delphi method. An illustrative example shows that the proposed method is a useful and alternative decision-making method.

]]>Symmetry doi: 10.3390/sym10020044

Authors: Ekkehard Krüger

As shown in former papers, the nonadiabatic Heisenberg model presents a mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled “superconducting bands” of special symmetry. The formation of Cooper pairs is not only the result of an attractive electron–electron interaction but is additionally the outcome of quantum mechanical constraining forces. There is theoretical and experimental evidence that only these constraining forces operating in superconducting bands may produce eigenstates in which the electrons form Cooper pairs. Here, we report evidence that also the experimentally found superconducting state in bismuth at ambient as well as at high pressure is stabilized by constraining forces.

]]>Symmetry doi: 10.3390/sym10020043

Authors: Eligijus Sakalauskas

A new enhanced matrix power function (MPF) is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ) problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left–right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1) the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2) the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ) problem which can be reckoned as hard; (3) the estimation of the effectiveness of direct MPF value computation; and (4) the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF), since the effective (polynomial-time) inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP) is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources.

]]>Symmetry doi: 10.3390/sym10020042

Authors: Syahirbanun Isa Zanariah Abdul Majid Fudziah Ismail Faranak Rabiei

In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala’s derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations.

]]>Symmetry doi: 10.3390/sym10020041

Authors: Vasyl’ Davydovych

Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs) and an example of the exact solution with a biological interpretation are found.

]]>Symmetry doi: 10.3390/sym10020040

Authors: Ming Li

This article addresses three classes of fractional oscillators named Class I, II and III. It is known that the solutions to fractional oscillators of Class I type are represented by the Mittag-Leffler functions. However, closed form solutions to fractional oscillators in Classes II and III are unknown. In this article, we present a theory of equivalent systems with respect to three classes of fractional oscillators. In methodology, we first transform fractional oscillators with constant coefficients to be linear 2-order oscillators with variable coefficients (variable mass and damping). Then, we derive the closed form solutions to three classes of fractional oscillators using elementary functions. The present theory of equivalent oscillators consists of the main highlights as follows. (1) Proposing three equivalent 2-order oscillation equations corresponding to three classes of fractional oscillators; (2) Presenting the closed form expressions of equivalent mass, equivalent damping, equivalent natural frequencies, equivalent damping ratio for each class of fractional oscillators; (3) Putting forward the closed form formulas of responses (free, impulse, unit step, frequency, sinusoidal) to each class of fractional oscillators; (4) Revealing the power laws of equivalent mass and equivalent damping for each class of fractional oscillators in terms of oscillation frequency; (5) Giving analytic expressions of the logarithmic decrements of three classes of fractional oscillators; (6) Representing the closed form representations of some of the generalized Mittag-Leffler functions with elementary functions. The present results suggest a novel theory of fractional oscillators. This may facilitate the application of the theory of fractional oscillators to practice.

]]>Symmetry doi: 10.3390/sym10020039

Authors: Lidong Wang Yanjun Wang Xiaodong Liu

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness.

]]>Symmetry doi: 10.3390/sym10020038

Authors: Davide Fermi Livio Pizzocchero

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type potentials concentrated at points of R 3 ; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on R 3 \ { 0 } , with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of R 3 \ { 0 } ; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours.

]]>Symmetry doi: 10.3390/sym10020037

Authors: Romain Guérout Gert-Ludwig Ingold Astrid Lambrecht Serge Reynaud

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account implicitly. We prove that this formula is also valid when the surrounding medium is dissipative.

]]>Symmetry doi: 10.3390/sym10020036

Authors: Wien Hong

In this paper, an efficient data hiding method that embeds data into absolute moment block truncation coding (AMBTC) codes is proposed. The AMBTC method represents image blocks by trios, and each trio consists of two quantization levels and an asymmetrically distributed bitmap. However, the asymmetric phenomena of bitmaps cause large degradation in image quality during data embedment. With the help of reference tables filled with symmetrical patterns, the proposed method exploits a symmetry adjustment model to modify the quantization levels in those smooth blocks to achieve the smallest distortion. If the block is complex, a lossless embedding method is performed to carry one additional bit. A sophisticated division switching mechanism is also proposed to modify a block from smooth to complex if the solution to the minimal distortion cannot be found. The payload can be adjusted by varying the threshold, or by embedding more bits into the quantization levels. The experiments indicate that the proposed work provides the best stego image quality under various payloads when comparing to the related prior works.

]]>Symmetry doi: 10.3390/sym10020035

Authors: Jean-Guillaume Eon

A description of the 11 well-known uninodal planar nets is given by Cayley color graphs or alternative Cayley color graphs of plane groups. By applying methods from topological graph theory, the nets are derived from the bouquet B n with rotations mostly as voltages. It thus appears that translation, as a symmetry operation in these nets, is no more fundamental than rotations.

]]>Symmetry doi: 10.3390/sym10020034

Authors: Vaibhav N. Khose Marina E. John Anita D. Pandey Victor Borovkov Anil V. Karnik

The majority of biomolecules found in living beings are chiral, therefore chiral molecular recognition in living systems is crucial to life. Following Cram’s seminal work on the crown-based chiral recognition, prominent research groups have reported innumerable chiral receptors with distinctly different geometrical features and asymmetry elements. Main applications of such chiral receptors are found in chiral chromatography, as for analytical purposes and for bulk separation of racemates.Incorporation of heterocyclic rings in these recognition systems added a new dimension to the existing group of receptors. Heterocycles have additional features such as availability of unshared electron pairs, pronounced conformational features, introduction of hydrogen bonding and presence of permanent dipoles as well as specific spectral properties in certain cases. These features are found to enhance binding properties of the receptors and the selectivity factors between opposite enantiomers, allowing them to be effectively separated. The review presents the synthetic approaches towards these heterocyclic receptors and their distinctly different behavior vis-à-vis carbocyclic receptors.

]]>Symmetry doi: 10.3390/sym10020033

Authors: Peter Schuller-Götzburg Thomas Forte Werner Pomwenger Alexander Petutschnigg Franz Watzinger Karl Entacher

Purpose: the aim of the computational 3D-finite element study is to evaluate the influence of an augmented sinus lift with additional inserted bone grafting. The bone graft block stabilizes the implant in conjunction with conventional bone augmentation. Two finite element models were applied: the real geometry based bone models and the simplified geometry models. The bone graft block was placed in three different positions. The implants were loaded first with an axial force and then with forces simulating laterotrusion and protrusion. This study examines whether the calculated stress behavior is symmetrical for both models. Having established a symmetry between the primary axis, the laterotrusion and protrusion behavior reduces calculation efforts, by simplifying the model. Material and Methods: a simplified U-shaped 3D finite element model of the molar region of the upper jaw and a more complex anatomical model of the left maxilla with less cortical bone were created. The bone graft block was placed in the maxillary sinus. Then the von Mises stress distribution was calculated and analyzed at three block positions: at contact with the sinus floor, in the middle of the implant helix and in the upper third of the implant. The two finite element models were then compared to simplify the modelling. Results: the position of the bone graft block significantly influences the magnitude of stress distribution. A bone graft block positioned in the upper third or middle of the implant reduces the quantity of stress compared to the reference model without a bone graft block. The low bone graft block position is clearly associated with lower stress distribution in compact bone. We registered no significant differences in stress in compact bone with regard to laterotrusion or protrusion. Conclusions: maximum values of von Mises stresses in compact bone can be reduced significantly by using a bone graft block. The reduction of stress is nearly the same for positions in the upper third and the middle of the implant. It is much more pronounced when the bone graft block is in the lower third of the implant near the sinus floor, which appeared to be the best position in the present study.

]]>Symmetry doi: 10.3390/sym10010032

Authors: Jose Rodriguez

This book contains the successful invited submissions [1–10] to a special issue of Symmetry on the subject area of ‘graph theory’ [...]

]]>Symmetry doi: 10.3390/sym10010031

Authors: Klaus Kirsten Yoonweon Lee

We provide a completely new perspective for the analysis of Casimir forces in very general piston configurations. To this end, in order to be self-contained, we prove a “gluing formula” well known in mathematics and relate it with Casimir forces in piston configurations. At the center of our description is the Dirichlet-to-Neumann operator, which encodes all the information about those forces. As an application, the results for previously considered piston configurations are reproduced in a streamlined fashion.

]]>Symmetry doi: 10.3390/sym10010030

Authors: JongBeom Lim Joon-Min Gil HeonChang Yu

Many artificial intelligence applications often require a huge amount of computing resources. As a result, cloud computing adoption rates are increasing in the artificial intelligence field. To support the demand for artificial intelligence applications and guarantee the service level agreement, cloud computing should provide not only computing resources but also fundamental mechanisms for efficient computing. In this regard, a snapshot protocol has been used to create a consistent snapshot of the global state in cloud computing environments. However, the existing snapshot protocols are not optimized in the context of artificial intelligence applications, where large-scale iterative computation is the norm. In this paper, we present a distributed snapshot protocol for efficient artificial intelligence computation in cloud computing environments. The proposed snapshot protocol is based on a distributed algorithm to run interconnected multiple nodes in a scalable fashion. Our snapshot protocol is able to deal with artificial intelligence applications, in which a large number of computing nodes are running. We reveal that our distributed snapshot protocol guarantees the correctness, safety, and liveness conditions.

]]>Symmetry doi: 10.3390/sym10010029

Authors: Fabian Ball Andreas Geyer-Schulz

The analysis of symmetry is a main principle in natural sciences, especially physics. For network sciences, for example, in social sciences, computer science and data science, only a few small-scale studies of the symmetry of complex real-world graphs exist. Graph symmetry is a topic rooted in mathematics and is not yet well-received and applied in practice. This article underlines the importance of analyzing symmetry by showing the existence of symmetry in real-world graphs. An analysis of over 1500 graph datasets from the meta-repository networkrepository.com is carried out and a normalized version of the “network redundancy” measure is presented. It quantifies graph symmetry in terms of the number of orbits of the symmetry group from zero (no symmetries) to one (completely symmetric), and improves the recognition of asymmetric graphs. Over 70% of the analyzed graphs contain symmetries (i.e., graph automorphisms), independent of size and modularity. Therefore, we conclude that real-world graphs are likely to contain symmetries. This contribution is the first larger-scale study of symmetry in graphs and it shows the necessity of handling symmetry in data analysis: The existence of symmetries in graphs is the cause of two problems in graph clustering we are aware of, namely, the existence of multiple equivalent solutions with the same value of the clustering criterion and, secondly, the inability of all standard partition-comparison measures of cluster analysis to identify automorphic partitions as equivalent.

]]>Symmetry doi: 10.3390/sym10010028

Authors: Symmetry Editorial Office

Peer review is an essential part in the publication process, ensuring that Symmetry maintains high quality standards for its published papers. In 2017, a total of 328 papers were published in the journal.[...]

]]>Symmetry doi: 10.3390/sym10010027

Authors: Thomas Jacobsen Stina Klein Andreas Löw

Symmetry is an important cue for the aesthetic judgment of beauty. Using a binary forced-choice format in a cued mixed design, Jacobsen and Höfel (2003) compared aesthetic judgments of beauty and symmetry judgments of novel graphic patterns. A late posterior sustained negativity elicited by symmetric patterns was observed in the symmetry judgment condition, but not in the beauty judgement condition. Therefore, this negativity appeared to be mainly driven by the task.In a series of studies, Bertamini, Makin, and colleagues observed a comparable sustained posterior negativity (SPN) to symmetric stimuli, mainly taken to reflect obligatory symmetry processing independent of task requirements. We reanalyzed the data by Jacobsen and Höfel (2003) using similar parameters for data analysis as Bertamini, Makin, and colleagues to examine these apparent differences. The reanalysis confirmed both a task-driven effect on the posterior sustained negativity/SPN to symmetric patterns in the symmetry judgment condition and a strong symmetry-driven SPN to symmetric patterns. Differences between the references used for analyses of the electroencephalogram (EEG) had an effect. Based on the reanalysis, the Jacobsen and Höfel (2003) data also fit well with Bertamini’s, Makin’s, and colleagues’ account of obligatory symmetry processing.

]]>Symmetry doi: 10.3390/sym10010026

Authors: María Alvarez

In this note, we consider degenerations between complex 2-step nilpotent Lie algebras of dimension 7 within the variety N 7 2 . This allows us to obtain the rigid algebras in N 7 2 , whose closures give the irreducible components of the variety.

]]>Symmetry doi: 10.3390/sym10010025

Authors: Dipali Singh Karen Berntsen Coos Baakman Gert Vriend Tapobrata Lahiri

It is much easier to determine a protein’s sequence than to determine its three dimensional structure and consequently homology modeling will be an essential aspect of most studies that require 3D protein structure data. Homology modeling templates tend to be PDB files. About 88% of all protein structures in the PDB have been determined with X-ray crystallography, and thus are based on crystals that by necessity hold non-natural packing contacts in accordance with the crystal symmetry. Active site residues, residues involved in intermolecular interactions, residues that get post-translationally modified, or other sites of interest, normally are located at the protein surface so that it is particularly important to correctly model surface-located residues. Unfortunately, surface residues are just those that suffer most from crystal packing artifacts. Our study of the influence of crystal packing artifacts on the quality of homology models reveals that this influence is much larger than generally assumed, and that the evaluation of the quality of homology models should properly account for these artifacts.

]]>Symmetry doi: 10.3390/sym10010024

Authors: José Juan Carreño José Antonio Martínez María Luz Puertas

The location of resources in a network satisfying some optimization property is a classical combinatorial problem that can be modeled and solved by using graphs. Key tools in this problem are the domination-type properties, which have been defined and widely studied in different types of graph models, such as undirected and directed graphs, finite and infinite graphs, simple graphs and hypergraphs. When the required optimization property is that every node of the network must have access to exactly one node with the desired resource, the appropriate models are the efficient dominating sets. However, the existence of these vertex sets is not guaranteed in every graph, so relaxing some conditions is necessary to ensure the existence of some kind of dominating sets, as efficient as possible, in a larger number of graphs. In this paper, we study independent [ 1 , 2 ] -sets, a generalization of efficient dominating sets defined by Chellali et al., in the case of cylindrical networks. It is known that efficient dominating sets exist in very special cases of cylinders, but the particular symmetry of these graphs will allow us to provide regular patterns that guarantee the existence of independent [ 1 , 2 ] -sets in every cylinder, except in one single case, and to compute exact values of the optimal parameter, the independent [ 1 , 2 ] -number, in cylinders of selected sizes.

]]>Symmetry doi: 10.3390/sym10010022

Authors: Nazario Garcia Javier Puente Isabel Fernandez Paolo Priore

This paper designs a bidding and supplier evaluation model focused on strategic product procurement, and develops their respective evaluation knowledge bases. The model is built using the most relevant variables cited in the reviewed procurement literature and allows to compare two evaluation methods: a factor weighting method (WM) and a fuzzy inference system (FIS). By consulting an expert panel and using a two-tuples symbolic translation system, strong fuzzy partitions for all model variables are built. The method, based on central symmetry, permits to obtain the fuzzy label borders from their cores, which have been previously agreed among experts. The system also allows to agree the fuzzy rules to embed in the FIS. The results show the FIS method’s superiority as it allows to better manage the non-linear behavior and the uncertainty inherent to the supplier evaluation process.

]]>Symmetry doi: 10.3390/sym10010023

Authors: Wei-Liang Tai Ya-Fen Chang

We propose separable reversible data hiding in an encrypted signal with public key cryptography. In our separable framework, the image owner encrypts the original image by using a public key. On receipt of the encrypted signal, the data-hider embeds data in it by using a data-hiding key. The image decryption and data extraction are independent and separable at the receiver side. Even though the receiver, who has only the data-hiding key, does not learn about the decrypted content, he can extract data from the received marked encrypted signal. However, the receiver who has only the private key cannot extract the embedded data, but he can directly decrypt the received marked encrypted signal to obtain the original image without any error. Compared with other schemes using a cipher stream to encrypt the image, the proposed scheme is more appropriate for cloud services without degrading the security level.

]]>Symmetry doi: 10.3390/sym10010021

Authors: Qiang Guo Chen Li Guoqing Ruan

In modern electronic warfare, multiple input multiple output (MIMO) radar has become an important tool for electronic reconnaissance and intelligence transmission because of its anti-stealth, high resolution, low intercept and anti-destruction characteristics. As a common MIMO radar signal, discrete frequency coding waveform (DFCW) has a serious overlap of both time and frequency, so it cannot be directly used in the current radar signal separation problems. The existing fuzzy clustering algorithms have problems in initial value selection, low convergence rate and local extreme values which will lead to the low accuracy of the mixing matrix estimation. Consequently, a novel mixing matrix estimation algorithm based on data field and improved fuzzy C-means (FCM) clustering is proposed. First of all, the sparsity and linear clustering characteristics of the time–frequency domain MIMO radar signals are enhanced by using the single-source principal value of complex angular detection. Secondly, the data field uses the potential energy information to analyze the particle distribution, thus design a new clustering number selection scheme. Then the particle swarm optimization algorithm is introduced to improve the iterative clustering process of FCM, and finally get the estimated value of the mixing matrix. The simulation results show that the proposed algorithm improves both the estimation accuracy and the robustness of the mixing matrix.

]]>Symmetry doi: 10.3390/sym10010020

Authors: Keiji Hirose Masaya Ukimi Shota Ueda Chie Onoda Ryohei Kano Kyosuke Tsuda Yuko Hinohara Yoshito Tobe

Rotaxanes consisting of achiral axle and achiral ring components can possess supramolecular chirality due to their unique geometrical architectures. To synthesize such chiral rotaxanes, we adapted a prerotaxane method based on aminolysis of a metacyclophane type prerotaxane that had planar chirality, which is composed of an achiral stopper unit and a crown ether type ring component. The prerotaxanes were well resolved using chiral HPLC into a pair of enantiomerically pure prerotaxanes, which were transferred into corresponding chiral rotaxanes, respectively. Obtained chiral rotaxanes were revealed to have considerable enantioselectivity.

]]>Symmetry doi: 10.3390/sym10010018

Authors: Van Phi Ho Dong-Joo Park

For the past few years, flash memory has been widely used because of its prominent advantages such as fast access speed, nonvolatility, high reliability, and low power consumption. However, flash memory still has several drawbacks that need to be overcome, e.g., the erase-before-write characteristic and a limited life cycle. Among these drawbacks, the erase-before-write characteristic causes the B-tree implementation on flash memory to be inefficient because it generates many erase operations. This study introduces a novel B-tree index structure using a write pattern converter (WPCB-tree) for flash memory. A WPCB-tree can minimize the risk of data loss and can improve the performance of the B-tree on flash memory. This WPCB-tree uses some blocks of flash memory as a buffer that temporarily stores all updated nodes. When the buffer is full, a buffer block is selected by a greedy algorithm, then the node pages in the block are converted into a sequential write pattern, and finally they are written into flash memory. In addition, in the case that all key values of a leaf node are continuously inserted, the WPCB-tree does not split the leaf node. As a result, this mechanism helps the WPCB-tree reduce the number of write operations on the flash memory. The experimental results show that the proposed B-tree variant on flash memory yields a better performance than that of other existing variants of the B-tree.

]]>Symmetry doi: 10.3390/sym10010019

Authors: Yanjun Liu Chin-Chen Chang Peng-Cheng Huang Cheng-Yi Hsu

Data hiding is an efficient technique that conceals secret data into a digital medium. In 2006, Zhang and Wang proposed a data hiding scheme called exploiting modification direction (EMD) which has become a milestone in the field of data hiding. In recent years, many EMD-type data hiding schemes have been developed, but their embedding capacity remains restricted. In this paper, a novel data hiding scheme based on the combination of Chinese remainder theorem (CRT) and a new extraction function is proposed. By the proposed scheme, the cover image is divided into non-overlapping pixel groups for embedding to increase the embedding capacity. Experimental results show that the embedding capacity of the proposed scheme is significantly higher (greater than 2.5 bpp) than previously proposed schemes while ensuring very good visual quality of the stego image. In addition, security analysis is given to show that the proposed scheme can resist visual attack.

]]>Symmetry doi: 10.3390/sym10010017

Authors: Bin Weng Alexei Sourin

Simulation of cutting is essential for many applications such as virtual surgical training. Most existing methods use the same triangle mesh for both visualization and collision handling, although the requirements for them in the interactive simulation are different. We introduce visual-collision binding between high-resolution visual meshes and low-resolution collision meshes, and thus extend the spatially reduced framework to support cutting. There are two phases in our framework: pre-processing and simulation. In the pre-processing phase, the fvisual-collision binding is built based on the computation of geodesic paths. In the simulation phase, the cutting paths are detected on the collision triangles and then mapped to local 2D coordinates systems in which the intersections between visual mesh and the cutting paths are calculated. Both collision and visual meshes are then re-meshed locally. The visual-collision binding is updated after cutting, based on which the collision-simulation and visual-simulation embedding are updated locally. Experimental results show that our cutting method is an efficient and flexible tool for interactive cutting simulation.

]]>Symmetry doi: 10.3390/sym10010016

Authors: In-hwan Ryu Insu Won Jangwoo Kwon

This paper deals with a method for removing a ghost target that is not a real object from the output of a multiple object-tracking algorithm. This method uses an artificial neural network (multilayer perceptron) and introduces a structure, learning, verification, and evaluation method for the artificial neural network. The implemented system was tested at an intersection in a city center. Results from a 28-min measurement were 88% accurate when the multilayer perceptron for ghost target classification successfully detected the ghost targets, and 6.7% inaccurate when ghost targets were mistaken for actual targets. This method is expected to contribute to the advancement of intelligent transportation systems if the weaknesses revealed during the evaluation of the system are complemented and refined.

]]>Symmetry doi: 10.3390/sym10010015

Authors: Quan Liu Li Ma Shou-Zen Fan Maysam Abbod Jiann-Shing Shieh

Important information about the state dynamics of the brain during anesthesia is unraveled by Electroencephalogram (EEG) approaches. Patterns that are observed through EEG related to neural circuit mechanism under different molecular targets dependent anesthetics have recently attracted much attention. Propofol, a Gamma-amino butyric acid, is known with evidently increasing alpha oscillation. Desflurane shares the same receptor action and should be similar to propofol. To explore their dynamics, EEG under routine surgery level anesthetic depth is analyzed using multitaper spectral method from two groups: propofol (n = 28) and desflurane (n = 23). The time-varying spectrum comparison was undertaken to characterize their properties. Results show that both of the agents are dominated by slow and alpha waves. Especially, for increased alpha band feature, propofol unconsciousness shows maximum power at about 10 Hz (mean ± SD; frequency: 10.2 ± 1.4 Hz; peak power, −14.0 ± 1.6 dB), while it is approximate about 8 Hz (mean ± SD; frequency: 8.3 ± 1.3 Hz; peak power, −13.8 ± 1.6 dB) for desflurane with significantly lower frequency-resolved spectra for this band. In addition, the mean power of propofol is much higher from alpha to gamma band, including slow oscillation than that of desflurane. The patterns might give us an EEG biomarker for specific anesthetic. This study suggests that both of the anesthetics exhibit similar spectral dynamics, which could provide insight into some common neural circuit mechanism. However, differences between them also indicate their uniqueness where relevant.

]]>Symmetry doi: 10.3390/sym10010014

Authors: Kyungmin Park Samuel Woo Daesung Moon Hoon Choi

We propose a novel dynamic host mutation (DHM) architecture based on moving target defense (MTD) that can actively cope with cyberattacks. The goal of the DHM is to break the cyber kill chain, expand the attack surface to increase the attacker’s target analysis cost, and disrupt the attacker’s fingerprinting to disable the server trace. We define the participating entities that share the MTD policy within the enterprise network or the critical infrastructure, and define functional modules of each entity for DHM enforcement. The threat model of this study is an insider threat of a type not considered in previous studies. We define an attack model considering an insider threat and propose a decoy injection mechanism to confuse the attacker. In addition, we analyze the security of the proposed structure and mechanism based on the security requirements and propose a trade-off considering security and availability.

]]>Symmetry doi: 10.3390/sym10010013

Authors: Chin-Chen Chang Tzu-Chuen Lu Zhao-Hua Zhu Hui Tian

This paper proposes an image authentication scheme for mobile devices. The proposed scheme generates an image watermark by using discrete cosine transform (DCT) and hides the watermark in the spatial pixels for image authentication and tamper detection. The hiding operator used in this paper is very simple in a mobile environment allowing high-speed authentication using a low-power mobile device. The quality of the stego-image and the recovered image becomes excellent as a result of the proposed scheme.

]]>Symmetry doi: 10.3390/sym10010012

Authors: Juraj Gazda Peter Tóth Jana Zausinová Marcel Vološin Vladimír Gazda

Modern 5G networks offer a large space for innovation and a completely new approach to addressing network functioning. A fixed spectrum assignment policy is a significant limitation of today’s wireless communication network practice and is to be replaced by a completely new approach called dynamic spectrum access (DSA). However, there is no general agreement on the organization of the DSA. Some studies suggest that open access market can be inspired by the electricity or financial markets. It allows to treat operators with region coverage as investors entering the market and trading the spectra on an on-demand basis. Because investors operate in both the financial markets and the markets for spectra, new interference between both markets emerges. Our paper shows how the risk-free rate of return stemming from the financial markets influences the techno-economic properties of the network. We show that, for low risk-free returns, the spectrum market becomes oversupplied, which keeps service prices very low and spectrum trading volumes large. In contrast, if risk-free returns are high, then spectrum trading volumes decline and the market becomes price sensitive; in other words, economic rules begin to work better.

]]>Symmetry doi: 10.3390/sym10010010

Authors: Mohammed Hasan Victor Borovkov

Helicenes are unique helical chromophores possessing advanced and well-controlled spectral and chemical properties owing to their diverse functionalization and defined structures. Specific modification of these molecules by introducing aromatic rings of differing nature and different functional groups results in special chiroptical properties, making them effective chiral auxiliaries and supramolecular chirogenic hosts. This review aims to highlight these distinct structural features of helicenes; the different synthetic and supramolecular approaches responsible for their efficient chirality control; and their employment in the chirogenic systems, which are still not fully explored. It further covers the limitation, scope, and future prospects of helicene chromophores in chiral chemistry.

]]>Symmetry doi: 10.3390/sym10010011

Authors: Bin Liu Yun Zhang DongJian He Yuxiang Li

Mosaic, Rust, Brown spot, and Alternaria leaf spot are the four common types of apple leaf diseases. Early diagnosis and accurate identification of apple leaf diseases can control the spread of infection and ensure the healthy development of the apple industry. The existing research uses complex image preprocessing and cannot guarantee high recognition rates for apple leaf diseases. This paper proposes an accurate identifying approach for apple leaf diseases based on deep convolutional neural networks. It includes generating sufficient pathological images and designing a novel architecture of a deep convolutional neural network based on AlexNet to detect apple leaf diseases. Using a dataset of 13,689 images of diseased apple leaves, the proposed deep convolutional neural network model is trained to identify the four common apple leaf diseases. Under the hold-out test set, the experimental results show that the proposed disease identification approach based on the convolutional neural network achieves an overall accuracy of 97.62%, the model parameters are reduced by 51,206,928 compared with those in the standard AlexNet model, and the accuracy of the proposed model with generated pathological images obtains an improvement of 10.83%. This research indicates that the proposed deep learning model provides a better solution in disease control for apple leaf diseases with high accuracy and a faster convergence rate, and that the image generation technique proposed in this paper can enhance the robustness of the convolutional neural network model.

]]>Symmetry doi: 10.3390/sym10010008

Authors: Stevo Stević

The solvability of a k-dimensional system of difference equations of interest, which extends several recently studied ones, is investigated. A general sufficient condition for the solvability of the system is given, considerably extending some recent results in the literature.

]]>Symmetry doi: 10.3390/sym10010009

Authors: Ioseph Buchbinder Timofey Snegirev Yurii Zinoviev

We review the component Lagrangian construction of the supersymmetric higher spin models in three-dimensional (3D) Minkowski and anti de Sitter ( A d S ) spaces. The approach is based on the frame-like gauge-invariant formulation, where massive higher spin fields are realized through a system of massless ones. We develop a supersymmetric generalization of this formulation to the Lagrangian construction of the on-shell N = 1 , 3D higher spin supermultiplets. In 3D Minkowski space, we show that the massive supermultiplets can be constructed from one extended massless supermultiplet by adding the mass terms to the Lagrangian and the corresponding corrections to the supertransformations of the fermionic fields. In 3D A d S space, we construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge-invariant objects (curvatures) in the process of their consistent supersymmetric deformation.

]]>Symmetry doi: 10.3390/sym10010007

Authors: Darian Onchis Simone Zappalà

In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis operator in Banach spaces of distributions. The constructive nature of the proof for Theorem 2 enabled us to constructively realize the biorthogonal system of a given one. Then, inspired by the multiresolution analysis and the Lax equivalence for general discretization schemes, we approached the stability of a sequence of spline-type spaces as uniform boundedness of projection operators. Through Theorem 3, we characterize stable sequences of stable spline-type spaces.

]]>Symmetry doi: 10.3390/sym10010005

Authors: John Hu Yi-Chung Hu Amber Tsai

We employ the DEMATEL-based analytic network process (D-ANP) to evaluate the weight of various factors on S&amp;P 500 index futures. The general regression method is employed to prove the result. We then employed grey relational analysis (GRA) to examine predictive power of determinants suggested by 13 experts for fluctuations in S&amp;P 500 index futures. This study yields a number of empirical results. (1) The explanatory power of macroeconomic factors for S&amp;P 500 index futures outperforms that of technical indicators, as found in most of previous research papers; (2) The D-ANP revealed that five core factors (US dollar index, ISM manufacturing purchasing managers’ index (PMI), interest rate, volatility index, and unemployment rate) affect fluctuations in S&amp;P 500 index futures, of which the US dollar index is the most important; (3) A casual diagram shows that the US dollar index and interest rate have mutual effects, and the US dollar index unilaterally affects ISM manufacturing PMI, unemployment rate, and the volatility index; (4) Granger causality test results confirmed some similar results obtained via the D-ANP that the US dollar index, interest rate, and the PMI have major impacts on the S&amp;P 500 index futures; (5) The general regression results confirmed that four of five factors selected via the D-ANP (US dollar index, interest rate, volatility index, and unemployment rate) have strong explanatory power in forecasting the rate of return on S&amp;P 500 index futures; (6) The GRA revealed that the explanatory power of various factors selected via the D-ANP was better for S&amp;P 500 than for Dow Jones Industrial Average (DJIA) and Nasdaq 100 index futures; (7) The explanatory power is better for S&amp;P 500 Industrial than for S&amp;P 500 transportation, utility, and financial index futures.

]]>Symmetry doi: 10.3390/sym10010006

Authors: José Carlos R. Alcantud

This book contains the successful invited submissions [1–21] to a Special Issue of Symmetry on the subject area of “Fuzzy Techniques for Decision Making”.[...]

]]>Symmetry doi: 10.3390/sym10010004

Authors: Jaeyoung Yoon Daeho Lee

We propose a novel real-time video stitching method using camera path estimation and homography refinement. The method can stably stitch multiple frames acquired from moving cameras in real time. In the proposed method, one initial between-camera (BC) homography and each camera path (CP) homography are used to estimate the BC homography at every frame. The BC homography is refined by using block matching to adjust the errors of estimated CPs (homography refinement). For fast processing, we extract features using the difference of intensities and use the optical flow to estimate camera motion (CM) homographies, which are multiplied with the previous CMs to calculate CPs (camera path estimations). In experiments, we demonstrated the performance of the CP estimation and homography refinement approach by comparing it with other methods. The experimental results show that the proposed method can stably stitch two image sequences at a rate exceeding 13 fps (frames per second).

]]>Symmetry doi: 10.3390/sym10010003

Authors: Ye Yao Yunqing Shi Shaowei Weng Bo Guan

Passive video forensics has drawn much attention in recent years. However, research on detection of object-based forgery, especially for forged video encoded with advanced codec frameworks, is still a great challenge. In this paper, we propose a deep learning-based approach to detect object-based forgery in the advanced video. The presented deep learning approach utilizes a convolutional neural network (CNN) to automatically extract high-dimension features from the input image patches. Different from the traditional CNN models used in computer vision domain, we let video frames go through three preprocessing layers before being fed into our CNN model. They include a frame absolute difference layer to cut down temporal redundancy between video frames, a max pooling layer to reduce computational complexity of image convolution, and a high-pass filter layer to enhance the residual signal left by video forgery. In addition, an asymmetric data augmentation strategy has been established to get a similar number of positive and negative image patches before the training. The experiments have demonstrated that the proposed CNN-based model with the preprocessing layers has achieved excellent results.

]]>Symmetry doi: 10.3390/sym10010002

Authors: Ivan Morales Bruno Neves Zui Oporto Olivier Piguet

We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the latter being conserved when the external field is stationary. We also write the conservation laws for the linear and angular momenta. Finally, we find that the particle’s velocity may differ from c as a result of the spin—electromagnetic field interaction, without jeopardizing Lorentz invariance.

]]>Symmetry doi: 10.3390/sym10010001

Authors: Kazuo Takemura Yoshinori Kametaka Atsushi Nagai

This paper clarifies the hierarchical structure of the sharp constants for the discrete Sobolev inequality on a weighted complete graph. To this end, we introduce a generalized-graph Laplacian A = I − B on the graph, and investigate two types of discrete Sobolev inequalities. The sharp constants C 0 ( N ; a ) and C 0 ( N ) were calculated through the Green matrix G ( a ) = ( A + a I ) − 1 ( 0 &lt; a &lt; ∞ ) and the pseudo-Green matrix G ∗ = A † . The sharp constants are expressed in terms of the expansion coefficients of the characteristic polynomial of A. Based on this new discovery, we provide the first proof that each set of the sharp constants { C 0 ( n ; a ) } n = 2 N and { C 0 ( n ) } n = 2 N satisfies a certain hierarchical structure.

]]>Symmetry doi: 10.3390/sym9120324

Authors: Yeong-Hyeon Byeon Keun-Chang Kwak

In this paper, we develop a genetically oriented rule-based Incremental Granular Model (IGM). The IGM is designed using a combination of a simple Linear Regression (LR) model and a local Linguistic Model (LM) to predict the modeling error obtained by the LR. The IGM has been successfully applied to various examples. However, the disadvantage of IGM is that the number of clusters in each context is determined, with the same number, by trial and error. Moreover, a weighting exponent is set to the typical value. In order to solve these problems, the goal of this paper is to design an optimized rule-based IGM with the use of a Genetic Algorithm (GA) to simultaneously optimize the number of cluster centers in each context, the number of contexts, and the weighting exponent. The experimental results regarding a coagulant dosing process in a water purification plant, an automobile mpg (miles per gallon) prediction, and a Boston housing data set revealed that the proposed GA-based IGM showed good performance, when compared with the Radial Basis Function Neural Network (RBFNN), LM, Takagi–Sugeno–Kang (TSK)-Linguistic Fuzzy Model (LFM), GA-based LM, and IGM itself.

]]>Symmetry doi: 10.3390/sym9120323

Authors: Stevo Stević Bratislav Iričanin Zdeněk Šmarda

It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C = { ( n , k ) : 0 ≤ k ≤ n , k ∈ N 0 , n ∈ N } , the so called combinatorial domain. The recurrent relations include some of the most important combinatorial ones, which, among other things, serve as a motivation for the investigation. The methods for solving the boundary value problems are presented and explained in detail.

]]>Symmetry doi: 10.3390/sym9120322

Authors: Krzysztof Małecki

A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to analyse applications of graph structures together with cellular automata. It proposes a graph cellular automaton with a variable configuration of cells and relation-based neighbourhoods (r–GCA). The developed mechanism enables modelling of phenomena found in complex systems (e.g., transport networks, urban logistics, social networks) taking into account the interaction between the existing objects. As an implementation example, modelling of moving vehicles has been made and r–GCA was compared to the other cellular automata models simulating the road traffic and used in the computer simulation process.

]]>Symmetry doi: 10.3390/sym9120320

Authors: Agbodah Kobina Decui Liang Xin He

As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances.

]]>Symmetry doi: 10.3390/sym9120321

Authors: Atcharin Klomsae Sansanee Auephanwiriyakul Nipon Theera-Umpon

Sign language is a basic method for solving communication problems between deaf and hearing people. In order to communicate, deaf and hearing people normally use hand gestures, which include a combination of hand positioning, hand shapes, and hand movements. Thai Sign Language is the communication method for Thai hearing-impaired people. Our objective is to improve the dynamic Thai Sign Language translation method with a video captioning technique that does not require prior hand region detection and segmentation through using the Scale Invariant Feature Transform (SIFT) method and the String Grammar Unsupervised Possibilistic C-Medians (sgUPCMed) algorithm. This work is the first to propose the sgUPCMed algorithm to cope with the unsupervised generation of multiple prototypes in the possibilistic sense for string data. In our experiments, the Thai Sign Language data set (10 isolated sign language words) was collected from 25 subjects. The best average result within the constrained environment of the blind test data sets of signer-dependent cases was 89–91%, and the successful rate of signer semi-independent cases was 81–85%, on average. For the blind test data sets of signer-independent cases, the best average classification rate was 77–80%. The average result of the system without a constrained environment was around 62–80% for the signer-independent experiments. To show that the proposed algorithm can be implemented in other sign languages, the American sign language (RWTH-BOSTON-50) data set, which consists of 31 isolated American Sign Language words, is also used in the experiment. The system provides 88.56% and 91.35% results on the validation set alone, and for both the training and validation sets, respectively.

]]>Symmetry doi: 10.3390/sym9120319

Authors: Musavarah Sarwar Muhammad Akram

Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when multiple linguistic properties are dealt with, emphasizing the need for a multi-index, multi-object, multi-agent, multi-attribute and multi-polar mathematical approach. An m-polar fuzzy set is introduced to overcome the limitations entailed in single-valued and two-valued uncertainty. Our aim in this research study is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of matroids. We introduce the notion of m-polar fuzzy matroids and investigate certain properties of various types of m-polar fuzzy matroids. Moreover, we apply the notion of the m-polar fuzzy matroid to graph theory and linear algebra. We present m-polar fuzzy circuits, closures of m-polar fuzzy matroids and put special emphasis on m-polar fuzzy rank functions. Finally, we also describe certain applications of m-polar fuzzy matroids in decision support systems, ordering of machines and network analysis.

]]>Symmetry doi: 10.3390/sym9120318

Authors: Alfred Grundland Alexander Hariton

In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version.

]]>Symmetry doi: 10.3390/sym9120317

Authors: Karolina Taczanowska Mikołaj Bielański Luis-Millán González Xavier Garcia-Massó José Toca-Herrera

Mountain protected areas (PAs) aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an approach to evaluate the structure and use of designated skiing zones in PAs combining Global Positioning System (GPS) tracking and analytical methods based on graph theory. The study is based on empirical data (n = 609 GPS tracks of backcountry skiers) collected in Tatra National Park (TNP), Poland. The physical structure of the entire skiing zones system has been simplified into a graph structure (structural network; undirected graph). In a second step, the actual use of the area by skiers (functional network; directed graph) was analyzed using a graph-theoretic approach. Network coherence (connectivity indices: β, γ, α), movement directions at path segments, and relative importance of network nodes (node centrality measures: degree, betweenness, closeness, and proximity prestige) were calculated. The system of designated backcountry skiing zones was not evenly used by the visitors. Therefore, the calculated parameters differ significantly between the structural and the functional network. In particular, measures related to the actually used trails are of high importance from the management point of view. Information about the most important node locations can be used for planning sign-posts, on-site maps, interpretative boards, or other tourist infrastructure.

]]>Symmetry doi: 10.3390/sym9120316

Authors: Jongyong Kim Cheongun Lee Seung-Hyun Yoon Sanghun Park

We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture image is projected onto the shape display. To minimize projection distortions, we present a sophisticated technique for projection mapping. Gesture-based user interfaces facilitate intuitive manipulations of visualization results. We demonstrate the effectiveness of our system by displaying and manipulating various terrain data using gesture-based interfaces.

]]>Symmetry doi: 10.3390/sym9120315

Authors: Neslihan Gügümcü Sofia Lambropoulou

This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to the study of proteins.

]]>Symmetry doi: 10.3390/sym9120313

Authors: Heng Yao Saihua Song Chuan Qin Zhenjun Tang Xiaokai Liu

Today’s H.264/AVC coded videos have a high quality, high data-compression ratio. They also have a strong fault tolerance, better network adaptability, and have been widely applied on the Internet. With the popularity of powerful and easy-to-use video editing software, digital videos can be tampered with in various ways. Therefore, the double compression in the H.264/AVC video can be used as a first step in the study of video-tampering forensics. This paper proposes a simple, but effective, double-compression detection method that analyzes the periodic features of the string of data bits (SODBs) and the skip macroblocks (S-MBs) for all I-frames and P-frames in a double-compressed H.264/AVC video. For a given suspicious video, the SODBs and S-MBs are extracted for each frame. Both features are then incorporated to generate one enhanced feature to represent the periodic artifact of the double-compressed video. Finally, a time-domain analysis is conducted to detect the periodicity of the features. The primary Group of Pictures (GOP) size is estimated based on an exhaustive strategy. The experimental results demonstrate the efficacy of the proposed method.

]]>Symmetry doi: 10.3390/sym9120312

Authors: Zia Bashir Jarosław Wątróbski Tabasam Rashid Sohail Zafar Wojciech Sałabun

Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led to rapid developments in cryptography, due to the imminent need for system security. Low-dimensional chaotic systems have low complexity and key space, yet they achieve high encryption speed. An image encryption scheme is proposed that, without compromising the security, uses reasonable resources. We introduced a chaotic dynamic state variables selection procedure (CDSVSP) to use all state variables of a hyper-chaotic four-dimensional dynamical system. As a result, less iterations of the dynamical system are required, and resources are saved, thus making the algorithm fast and suitable for practical use. The simulation results of security and other miscellaneous tests demonstrate that the suggested algorithm excels at robustness, security and high speed encryption.

]]>Symmetry doi: 10.3390/sym9120314

Authors: I. J. Zucker

New q-series in the spirit of Jacobi have been found in a publication first published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely new q-series, fresh lattice sums have been discovered and are presented here.

]]>Symmetry doi: 10.3390/sym9120311

Authors: Yan Li Byeong-Seok Shin

With the development of sensor technology and the popularization of the data-driven service paradigm, spatial crowdsourcing systems have become an important way of collecting map-based location data. However, large-scale task management and location privacy are important factors for participants in spatial crowdsourcing. In this paper, we propose the use of an R-tree spatial cloaking-based task-assignment method for large-scale spatial crowdsourcing. We use an estimated R-tree based on the requested crowdsourcing tasks to reduce the crowdsourcing server-side inserting cost and enable the scalability. By using Minimum Bounding Rectangle (MBR)-based spatial anonymous data without exact position data, this method preserves the location privacy of participants in a simple way. In our experiment, we showed that our proposed method is faster than the current method, and is very efficient when the scale is increased.

]]>Symmetry doi: 10.3390/sym9120310

Authors: Ye Lee Insoo Sohn

Despite recent progress in the study of complex systems, reconstruction of damaged networks due to random and targeted attack has not been addressed before. In this paper, we formulate the network reconstruction problem as an identification of network structure based on much reduced link information. Furthermore, a novel method based on multilayer perceptron neural network is proposed as a solution to the problem of network reconstruction. Based on simulation results, it was demonstrated that the proposed scheme achieves very high reconstruction accuracy in small-world network model and a robust performance in scale-free network model.

]]>Symmetry doi: 10.3390/sym9120309

Authors: Yasutaka Mizui Tetsuya Kojima Shigeyuki Miyagi Osamu Sakai

Various sizes of chemical reaction network exist, from small graphs of linear networks with several inorganic species to huge complex networks composed of protein reactions or metabolic systems. Huge complex networks of organic substrates have been well studied using statistical properties such as degree distributions. However, when the size is relatively small, statistical data suffers from significant errors coming from irregular effects by species, and a macroscopic analysis is frequently unsuccessful. In this study, we demonstrate a graphical classification method for chemical networks that contain tens of species. Betweenness and closeness centrality indices of a graph can create a two-dimensional diagram with information of node distribution for a complex chemical network. This diagram successfully reveals systematic sharing of roles among species as a semi-statistical property in chemical reactions, and distinguishes it from the ones in random networks, which has no functional node distributions. This analytical approach is applicable for rapid and approximate understanding of complex chemical network systems such as plasma-enhanced reactions as well as visualization and classification of other graphs.

]]>Symmetry doi: 10.3390/sym9120308

Authors: Wei-Liang Liu Hui-Shih Leng Chuan-Kuei Huang Dyi-Cheng Chen

Due to the increased digital media on the Internet, data security and privacy protection issue have attracted the attention of data communication. Data hiding has become a topic of considerable importance. Nowadays, a new challenge consists of reversible data hiding in the encrypted image because of the correlations of local pixels that are destroyed in an encrypted image; it is difficult to embed secret messages in encrypted images using the difference of neighboring pixels. In this paper, the proposed method uses a block-based division mask and a new encrypted method based on the logistic map and an additive homomorphism to embed data in an encrypted image by histogram shifting technique. Our experimental results show that the proposed method achieves a higher payload than other works and is more immune to attack upon the cryptosystem.

]]>Symmetry doi: 10.3390/sym9120307

Authors: Ya-Fen Chang Wei-Liang Tai Min-How Hsu

With the rapid growth of network technologies, users are used to accessing various services with their mobile devices. To ensure security and privacy in mobility networks, proper mechanisms to authenticate the mobile user are essential. In this paper, a mobility network authentication scheme based on elliptic curve cryptography is proposed. In the proposed scheme, a mobile user can be authenticated without revealing who he is for user anonymity, and a session key is also negotiated to protect the following communications. The proposed mobility network authentication scheme is analyzed to show that it can ensure security, user anonymity, and convenience. Moreover, Burrows-Abadi-Needham logic (BAN logic) is used to deduce the completeness of the proposed authentication scheme.

]]>Symmetry doi: 10.3390/sym9120306

Authors: Tom Chang

Complexity phenomena in cosmological evolution due to the scale-running of the propagator coupling constant can yield new insights related to virtual particles and antiscreening effects with dark matter consequences. This idea was developed in accordance with the differential-integral functional formulation of the Wilsonian renormalization group based on the one-particle irreducible scale-dependent effective action for gravitational evolution. In this tutorial communication, we briefly describe the essence of the result with minimal mathematical details and then consider a few simple examples to provide a basic understanding of such an interesting and intriguing complexity process in terms of fractional calculus.

]]>Symmetry doi: 10.3390/sym9120305

Authors: Shun-Yi Wang Shih-Hung Yang Yon-Ping Chen Jyun-We Huang

Face recognition systems have been widely adopted for user authentication in security systems due to their simplicity and effectiveness. However, spoofing attacks, including printed photos, displayed photos, and replayed video attacks, are critical challenges to authentication, and these spoofing attacks allow malicious invaders to gain access to the system. This paper proposes two novel features for face liveness detection systems to protect against printed photo attacks and replayed attacks for biometric authentication systems. The first feature obtains the texture difference between red and green channels of face images inspired by the observation that skin blood flow in the face has properties that enable distinction between live and spoofing face images. The second feature estimates the color distribution in the local regions of face images, instead of whole images, because image quality might be more discriminative in small areas of face images. These two features are concatenated together, along with a multi-scale local binary pattern feature, and a support vector machine classifier is trained to discriminate between live and spoofing face images. The experimental results show that the performance of the proposed method for face spoof detection is promising when compared with that of previously published methods. Furthermore, the proposed system can be implemented in real time, which is valuable for mobile applications.

]]>Symmetry doi: 10.3390/sym9120304

Authors: He Yu Guohui Yang Fanyi Meng Yingsong Li

This paper introduces the principle and key technology of single radio frequency (RF) link Multiple-Input Multiple-Output (MIMO) system based on a switched parasitic antenna (SPA). The software SystemVue is adopted for signal processing and system-level simulation with merit of strong operability and high efficiency, which provides tools for the single RF link MIMO system research. A single RF link of a 2 × 2 MIMO system based on the switch parasitic antenna is proposed in this paper. The binary codes are modulated to the baseband Binary Phase Shift Keying (BPSK) signals and transmitted with a 2.4 GHz carrier frequency. The receiver based on the super-heterodyne prototype adopts the channel equalization algorithm for restoring symbols, and it can effectively reduce the system error rate. The simulation results show that the MIMO system built on the platform can achieve equivalent performance with traditional MIMO system, which validates the effectiveness of the proposed scheme. The switched parasitic antenna and equalization algorithm provide new research ideas for single RF link MIMO system and have theoretical significance for further research.

]]>Symmetry doi: 10.3390/sym9120303

Authors: Yongju Bae In Lee

In this paper, we introduce formulae for the determinants of matrices with certain symmetry. As applications, we will study the Alexander polynomial and the determinant of a periodic link which is presented as the closure of an oriented 4-tangle.

]]>Symmetry doi: 10.3390/sym9120301

Authors: Juan Ruiz-Rosero Gustavo Ramirez-Gonzalez Jennifer Williams Huaping Liu Rahul Khanna Greeshma Pisharody

Internet of Things (IoT) is connecting billions of devices to the Internet. These IoT devices chain sensing, computation, and communication techniques, which facilitates remote data collection and analysis. wireless sensor networks (WSN) connect sensing devices together on a local network, thereby eliminating wires, which generate a large number of samples, creating a big data challenge. This IoT paradigm has gained traction in recent years, yielding extensive research from an increasing variety of perspectives, including scientific reviews. These reviews cover surveys related to IoT vision, enabling technologies, applications, key features, co-word and cluster analysis, and future directions. Nevertheless, we lack an IoT scientometrics review that uses scientific databases to perform a quantitative analysis. This paper develops a scientometric review about IoT over a data set of 19,035 documents published over a period of 15 years (2002–2016) in two main scientific databases (Clarivate Web of Science and Scopus). A Python script called ScientoPy was developed to perform quantitative analysis of this data set. This provides insight into research trends by investigating a lead author’s country affiliation, most published authors, top research applications, communication protocols, software processing, hardware, operating systems, and trending topics. Furthermore, we evaluate the top trending IoT topics and the popular hardware and software platforms that are used to research these trends.

]]>Symmetry doi: 10.3390/sym9120297

Authors: Lina Song Rong Tang

In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to Out ( h ) . Then for a general Hom-Lie algebra morphism from g to Out ( h ) , we construct a cohomology class as the obstruction of existence of a non-abelian extension that induces the given Hom-Lie algebra morphism.

]]>Symmetry doi: 10.3390/sym9120302

Authors: Laurent Bataille Francisco Cavas-Martínez Daniel G. Fernández-Pacheco Francisco J. F. Cañavate Jorge L. Alio

The aim of this study is to describe a new keratoconus detection method based on the analysis of certain parametric morphogeometric operators extracted from a custom patient-specific three-dimensional (3D) model of the human cornea. A corneal geometric reconstruction is firstly performed using zonal functions and retrospective Scheimpflug tomography data from 107 eyes of 107 patients. The posterior corneal surface is later analysed using an optimised computational geometry technique and the morphology of healthy and keratoconic corneas is characterized by means of geometric variables. The performance of these variables as predictors of a new geometric marker is assessed through a receiver operating characteristic (ROC) curve analysis and their correlations are analysed through Pearson or Spearman coefficients. The posterior apex deviation variable shows the best keratoconus diagnosis capability. However, the strongest correlations in both healthy and pathological corneas are provided by the metrics directly related to the thickness as the sagittal plane area at the apex and the sagittal plane area at the minimum thickness point. A comparison of the screening of keratoconus provided by the Sirius topographer and the detection of corneal ectasia using the posterior apex deviation parameter is also performed, demonstrating the accuracy of this characterization as an effective marker of the diagnosis and ectatic disease progression.

]]>Symmetry doi: 10.3390/sym9120300

Authors: Misun Ahn SeungGwan Lee Sungwon Lee

This paper proposes a virtualized network function orchestration system based on Network Function Virtualization (NFV), one of the main technologies in 5G mobile networks. This system should provide connectivity between network devices and be able to create flexible network function and distribution. This system focuses more on access networks. By experimenting with various scenarios of user service established and activated in a network, we examine whether rapid adoption of new service is possible and whether network resources can be managed efficiently. The proposed method is based on Bluetooth transfer technology and mesh networking to provide automatic connections between network machines and on a Docker flat form, which is a container virtualization technology for setting and managing key functions. Additionally, the system includes a clustering and recovery measure regarding network function based on the Docker platform. We will briefly introduce the QR code perceived service as a user service to examine the proposal and based on this given service, we evaluate the function of the proposal and present analysis. Through the proposed approach, container relocation has been implemented according to a network device’s CPU usage and we confirm successful service through function evaluation on a real test bed. We estimate QR code recognition speed as the amount of network equipment is gradually increased, improving user service and confirm that the speed of recognition is increased as the assigned number of network devices is increased by the user service.

]]>Symmetry doi: 10.3390/sym9120299

Authors: Hsien-Chung Wu

To fuzzify the crisp functions, the extension principle has been widely used for performing this fuzzification. The purpose of this paper is to investigate the continuity of fuzzified function using the more generalized extension principle. The Hausdorff metric will be invoked to study the continuity of fuzzified function. We also apply the principle of continuity of fuzzified function to the fuzzy topological vector space.

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