Symmetry doi: 10.3390/sym11020124

Authors: Emre Ünver Qian Xiao Onur Güntürkün

Meta-control describes an interhemispheric response conflict that results from the perception of stimuli that elicit a different reaction in each hemisphere. The dominant hemisphere for the perceived stimulus class often wins this competition. There is evidence from pigeons that meta-control results from interhemispheric response conflicts that prolong reaction time when the animal is confronted with conflicting information. However, recent evidence in pigeons also makes it likely that the dominant hemisphere can slow down the subdominant hemisphere, such that meta-control could instead result from the interhemispheric speed differences. Since both explanations make different predictions for the effect of commissurotomy, we tested pigeons in a meta-control task both before and after transection of the commissura anterior. This fiber pathway is the largest pallial commissura of the avian brain. The results revealed a transient phase in which meta-control possibly resulted from interhemispheric response conflicts. In subsequent sessions and after commissurotomy, however, the results suggest interhemispheric speed differences as a basis for meta-control. Furthermore, they reveal that meta-control is modified by interhemispheric transmission via the commissura anterior, although it does not seem to depend on it.

]]>Symmetry doi: 10.3390/sym11020123

Authors: Michal Staš

The main aim of the paper is to give the crossing number of the join product G + D n for the disconnected graph G of order five consisting of one isolated vertex and of one vertex incident with some vertex of the three-cycle, and D n consists of n isolated vertices. In the proofs, the idea of the new representation of the minimum numbers of crossings between two different subgraphs that do not cross the edges of the graph G by the graph of configurations G D in the considered drawing D of G + D n will be used. Finally, by adding some edges to the graph G, we are able to obtain the crossing numbers of the join product with the discrete graph D n and with the path P n on n vertices for three other graphs.

]]>Symmetry doi: 10.3390/sym11010122

Authors: Xinan Hao Luyao Zhang

We study the existence, multiplicity, and uniqueness results of positive solutions for a fractional thermostat model. Our approach depends on the fixed point index theory, iterative method, and nonsymmetry property of the Green function. The properties of positive solutions depending on a parameter are also discussed.

]]>Symmetry doi: 10.3390/sym11010121

Authors: Tuz

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson&rsquo;s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel&rsquo;skii.

]]>Symmetry doi: 10.3390/sym11010120

Authors: S. James Gates Kevin Iga Lucas Kang Vadim Korotkikh Kory Stiffler

Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of B C 3 , the signed permutation group of three elements, and B C 4 , the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via B C 4 boson &times; B C 3 color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the gadget, which is used to distinguish adinkras. We show how 96 equivalence classes of adinkras that are based on the gadget emerge in terms of B C 3 and B C 4 . We also comment on the importance of the gadget as it relates to separating out dynamics in terms of K&auml;hler-like potentials. Thus, on the basis of the complete analysis of the supersymmetrical representations achieved in the preparatory first four sections, the final comprehensive achievement of this work is the construction of the universal B C 4 non-linear &sigma; -model.

]]>Symmetry doi: 10.3390/sym11010119

Authors: Michio Hori Masanori Kohda Satoshi Awata Satoshi Takahashi

Scale-eating cichlid fishes, Perissodus spp., in Lake Tanganyika have laterally asymmetrical bodies, and each population is composed of righty and lefty morphs. Righty morphs attack the right side of prey and lefty morphs do the opposite. This anti-symmetric dimorphism has a genetic basis. Temporal changes in the frequencies of morphs in two cohabiting scale-eating species (Perissodus microlepis and P. straeleni) were investigated over a 31-year period on a rocky shore at the southern end of the lake. Dimorphism was maintained dynamically during the period in both species, and the frequencies oscillated with a period of about four years in a semi-synchronized manner. Recent studies have indicated that this type of anti-symmetric dimorphism is shared widely among fishes, and is maintained by frequency-dependent selection between predator and prey species. The combinations of laterality in each scale-eater and its victim were surveyed. The results showed that &ldquo;cross-predation&rdquo;, in which righty predators catch lefty prey and lefty predators catch righty prey, occurred more frequently than the reverse combination (&ldquo;parallel-predation&rdquo;). The cause of the predominance of cross-predation is discussed from the viewpoint of the physical and sensory abilities of fishes.

]]>Symmetry doi: 10.3390/sym11010118

Authors: Jared Lynskey Kyi Thar Thant Zin Oo Choong Seon Hong

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks.

]]>Symmetry doi: 10.3390/sym11010117

Authors: Symmetry Editorial Office

Rigorous peer-review is the corner-stone of high-quality academic publishing [...]

]]>Symmetry doi: 10.3390/sym11010116

Authors: Andrew James Bruce

We extend the notion of super-Minkowski space-time to include Z 2 n -graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical framework we employ is the recently developed category of Z 2 n -manifolds understood as locally ringed spaces. The formalism we present resembles N -extended superspace (in the presence of central charges), but with some subtle differences due to the exotic nature of the grading employed.

]]>Symmetry doi: 10.3390/sym11010115

Authors: Yaocheng Zhang Wei Ren Tianqing Zhu Ehoche Faith

The development of mobile internet has led to a massive amount of data being generated from mobile devices daily, which has become a source for analyzing human behavior and trends in public sentiment. In this paper, we build a system called MoSa (Mobile Sentiment analysis) to analyze this data. In this system, sentiment analysis is used to analyze news comments on the THAAD (Terminal High Altitude Area Defense) event from Toutiao by employing algorithms to calculate the sentiment value of the comment. This paper is based on HowNet; after the comparison of different sentiment dictionaries, we discover that the method proposed in this paper, which use a mixed sentiment dictionary, has a higher accuracy rate in its analysis of comment sentiment tendency. We then statistically analyze the relevant attributes of the comments and their sentiment values and discover that the standard deviation of the comments&rsquo; sentiment value can quickly reflect sentiment changes among the public. Besides that, we also derive some special models from the data that can reflect some specific characteristics. We find that the intrinsic characteristics of situational awareness have implicit symmetry. By using our system, people can obtain some practical results to guide interaction design in applications including mobile Internet, social networks, and blockchain based crowdsourcing.

]]>Symmetry doi: 10.3390/sym11010114

Authors: Muhammad Aslam

The acceptance sampling plan plays an important role in maintaining the high quality of a product. The variable control chart, using classical statistics, helps in making acceptance or rejection decisions about the submitted lot of the product. Furthermore, the sampling plan, using classical statistics, assumes the complete or determinate information available about a lot of product. However, in some situations, data may be ambiguous, vague, imprecise, and incomplete or indeterminate. In this case, the use of neutrosophic statistics can be applied to guide the experimenters. In this paper, we originally proposed a new variable sampling plan using the neutrosophic interval statistical method. The neutrosophic operating characteristic (NOC) is derived using the neutrosophic normal distribution. The optimization solution is also presented for the proposed plan under the neutrosophic interval method. The effectiveness of the proposed plan is compared with the plan under classical statistics. The tables are presented for practical use and a real example is given to explain the neutrosophic fuzzy variable sampling plan in the industry.

]]>Symmetry doi: 10.3390/sym11010113

Authors: Tetsuya Hiraiwa Fu-Lai Wen Tatsuo Shibata Erina Kuranaga

Recent studies have revealed that intrinsic, individual cell behavior can provide the driving force for deforming a two-dimensional cell sheet to a three-dimensional tissue without the need for external regulatory elements. However, whether intrinsic, individual cell behavior could actually generate the force to induce tissue deformation was unclear, because there was no experimental method with which to verify it in vivo. In such cases, mathematical modeling can be effective for verifying whether a locally generated force can propagate through an entire tissue and induce deformation. Moreover, the mathematical model sometimes provides potential mechanistic insight beyond the information obtained from biological experimental results. Here, we present two examples of modeling tissue morphogenesis driven by cell deformation or cell interaction. In the first example, a mathematical study on tissue-autonomous folding based on a two-dimensional vertex model revealed that active modulations of cell mechanics along the basal&ndash;lateral surface, in addition to the apical side, can induce tissue-fold formation. In the second example, by applying a two-dimensional vertex model in an apical plane, a novel mechanism of tissue flow caused by asymmetric cell interactions was discovered, which explained the mechanics behind the collective cellular movement observed during epithelial morphogenesis.

]]>Symmetry doi: 10.3390/sym11010112

Authors: Xiangzhi Zhang Yufeng Zhang

In the paper, we discuss some similarity solutions of the time-fractional Burgers system (TFBS). Firstly, with the help of the Lie-point symmetry and the corresponding invariant variables, we transform the TFBS to a fractional ordinary differential system (FODS) under the case where the time-fractional derivative is the Riemann&ndash;Liouville type. The FODS can be approximated by some integer-order ordinary differential equations; here, we present three such integer-order ordinary differential equations (called IODE-1, IODE-2, and IODE-3, respectively). For IODE-1, we obtain its similarity solutions and numerical solutions, which approximate the similarity solutions and the numerical solutions of the TFBS. Secondly, we apply the numerical analysis method to obtain the numerical solutions of IODE-2 and IODE-3.

]]>Symmetry doi: 10.3390/sym11010111

Authors: M. Teresa de Bustos Antonio Fernández Miguel A. López Raquel Martínez Juan A. Vera

In this work, the periodic orbits&rsquo; phase portrait of the zonal J 2 + J 3 problem is studied. In particular, we center our attention on the periodic orbits of the third kind in the Poincar&eacute; sense using the averaging theory of dynamical systems. We find three families of polar periodic orbits and four families of inclined periodic orbits for which we are able to state their explicit expressions.

]]>Symmetry doi: 10.3390/sym11010110

Authors: Chiranjibe Jana Madhumangal Pal

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object of this paper is to lay a foundation for providing a new approach of single-valued neutrosophic soft tool which is considering many problems that contain uncertainties. In present study, a new aggregation operators of single-valued neutrosophic soft numbers have so far not yet been applied for ranking of the alternatives in decision-making problems. To this propose work, single-valued neutrosophic soft weighted arithmetic averaging (SVNSWA) operator, single-valued neutrosophic soft weighted geometric averaging (SVNSWGA) operator have been used to compare two single-valued neutrosophic soft numbers (SVNSNs) for aggregating different single-valued neutrosophic soft input arguments in neutrosophic soft environment. Then, its related properties have been investigated. Finally, a practical example for Medical diagnosis problems provided to test the feasibility and applicability of the proposed work.

]]>Symmetry doi: 10.3390/sym11010109

Authors: Tzu Chuen Lu

This book contains the successful invited submissions [...]

]]>Symmetry doi: 10.3390/sym11010108

Authors: Qiming Zhao Donghe Pei Yongqiao Wang

Developable surfaces, which are important objects of study, have attracted a lot of attention from many mathematicians. In this paper, we study the geometric properties of one-parameter developable surfaces associated with regular curves. According to singularity theory, the generic singularities of these developable surfaces are classified&mdash;they are swallowtails and cuspidal edges. In addition, we give some examples of developable surfaces which have symmetric singularity models.

]]>Symmetry doi: 10.3390/sym11010107

Authors: Mujtaba Husnain Malik Muhammad Saad Missen Shahzad Mumtaz Muhammad Muzzamil Luqman Mickaël Coustaty Jean-Marc Ogier

We applied t-distributed stochastic neighbor embedding (t-SNE) to visualize Urdu handwritten numerals (or digits). The data set used consists of 28 &times; 28 images of handwritten Urdu numerals. The data set was created by inviting authors from different categories of native Urdu speakers. One of the challenging and critical issues for the correct visualization of Urdu numerals is shape similarity between some of the digits. This issue was resolved using t-SNE, by exploiting local and global structures of the large data set at different scales. The global structure consists of geometrical features and local structure is the pixel-based information for each class of Urdu digits. We introduce a novel approach that allows the fusion of these two independent spaces using Euclidean pairwise distances in a highly organized and principled way. The fusion matrix embedded with t-SNE helps to locate each data point in a two (or three-) dimensional map in a very different way. Furthermore, our proposed approach focuses on preserving the local structure of the high-dimensional data while mapping to a low-dimensional plane. The visualizations produced by t-SNE outperformed other classical techniques like principal component analysis (PCA) and auto-encoders (AE) on our handwritten Urdu numeral dataset.

]]>Symmetry doi: 10.3390/sym11010106

Authors: Qiang Guo Jichen Yan Wei Xu

Flying ad hoc network (FANET) is a communication network for data transmission among Unmanned Aerial Vehicles (UAVs). In ad hoc network, the UAVs movement is usually applied to improve network fault-tolerance, but it easily causes the disconnection of communication links, and the success rate is low. In this paper, we propose a local fault-tolerant control algorithm based on node movement freedom degree (LFTMF). Under the constraint of node movement freedom degree, the algorithm transforms the single-connected network into bi-connected network through the autonomous movement of UAVs to improve the fault-tolerant ability of the FANET network. Firstly, the consistency between k-hop cut-points and global cut-points in FANET network is analyzed. Then, based on the k-hop local topology of FANET network, the UAV node movement freedom degree model is established. Finally, according to the location distribution of k-hop cut-points in the FANET network, the bi-connected fault-tolerant network is realized by UAVs cascade movement. Compared with the existing algorithms, simulation results show that the proposed algorithm achieves better performance in success rate, deviation distance, cascade movement ratio and adjustment period.

]]>Symmetry doi: 10.3390/sym11010105

Authors: Yonghui Qin Xiaoji Liu Julio Benítez

Based on the conditions a b 2 = 0 and b &pi; ( a b ) &isin; A d , we derive that ( a b ) n , ( b a ) n , and a b + b a are all generalized Drazin invertible in a Banach algebra A , where n &isin; N and a and b are elements of A . By using these results, some results on the symmetry representations for the generalized Drazin inverse of a b + b a are given. We also consider that additive properties for the generalized Drazin inverse of the sum a + b .

]]>Symmetry doi: 10.3390/sym11010104

Authors: Dmitry Kazakov Leonid Bork Arthur Borlakov Denis Tolkachev Dmitry Vlasenko

Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions, they are free from UV divergences but are IR divergent on shell; in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows, we consider the four-point on-shell scattering amplitudes in D = 6 , 8 , 10 supersymmetric Yang&ndash;Mills theory in the planar limit within the spinor-helicity and on-shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the R -operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure, which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behavior and find that, while each term of PT increases as a power of energy, the total sum behaves differently: in D = 6 two partial amplitudes decrease with energy and the third one increases exponentially, while in D = 8 and 10 the amplitudes possess an infinite number of periodic poles at finite energy.

]]>Symmetry doi: 10.3390/sym11010103

Authors: Ramandeep Behl Ioannis K. Argyros J.A. Tenreiro Machado Ali Saleh Alshomrani

This article considers the fourth-order family of weighted-Newton methods. It provides the range of initial guesses that ensure the convergence. The analysis is given for Banach space-valued mappings, and the hypotheses involve the derivative of order one. The convergence radius, error estimations, and results on uniqueness also depend on this derivative. The scope of application of the method is extended, since no derivatives of higher order are required as in previous works. Finally, we demonstrate the applicability of the proposed method in real-life problems and discuss a case where previous studies cannot be adopted.

]]>Symmetry doi: 10.3390/sym11010102

Authors: Atsushi Tamada

Left–right brain asymmetry is a fundamental property observed across phyla from invertebrates to humans, but the mechanisms underlying its formation are still largely unknown. Rapid progress in our knowledge of the formation of body asymmetry suggests that brain asymmetry might be controlled by the same mechanisms. However, most of the functional brain laterality, including language processing and handedness, does not share common mechanisms with visceral asymmetry. Accumulating evidence indicates that asymmetry is manifested as chirality at the single cellular level. In neurons, the growth cone filopodia at the tips of neurites exhibit a myosin V-dependent, left-helical, and right-screw rotation, which drives the clockwise circular growth of neurites on adhesive substrates. Here, I propose an alternative model for the formation of brain asymmetry that is based on chiral neuronal motility. According to this chiral neuron model, the molecular chirality of actin filaments and myosin motors is converted into chiral neuronal motility, which is in turn transformed into the left–right asymmetry of neural circuits and lateralized brain functions. I also introduce automated, numerical, and quantitative methods to analyze the chirality and the left–right asymmetry that would enable the efficient testing of the model and to accelerate future investigations in this field.

]]>Symmetry doi: 10.3390/sym11010101

Authors: Adithya B. Pavan Kumar B. N. Young Ho Chai Ashok Kumar Patil

Human eyeballs move relative to the head, resulting in optimal changes in the viewpoint. We tested similar vestibular ocular reflex (VOR)-based movement on Zenmuse-X3 gimbal camera relative to pre-defined YAW movements of the DJI Matrice-100 unmanned aerial vehicle (UAV). Changes in viewpoint have various consequences for visual and graphical rendering. Therefore, this study investigated how to minimize these changes. OpenGL visualization was performed to simulate and measure viewpoint changes using the proposed VOR-based eyeball movement algorithm and compared with results of VOR based gimbal movement. The gimbal camera was setup to render images (scenes) on flat monitors. Positions of pre-fixed targets in the images were used to measure the viewpoint changes. The proposed approach could successfully control and significantly reduce the viewpoint changes and stabilize the image to improve visual tracking of targets on flat monitors. The proposed method can also be used to render real-time camera feed to a head-mounted display (HMD) in an ergonomically pleasing way.

]]>Symmetry doi: 10.3390/sym11010100

Authors: Dariush Heidari Irina Cristea

In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of R&eacute;dei&rsquo;s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups.

]]>Symmetry doi: 10.3390/sym11010099

Authors: Ahmed M. Ali Saif M. Ramadhan Fadhil R. Tahir

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x = y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array ( 1 &times; 3 ) cells. The paper concerns on the design and implementation of 2 &times; 2 and 3 &times; 3 2 D -grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

]]>Symmetry doi: 10.3390/sym11010098

Authors: Maria Antonietta Salamone

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos&mdash;Fire and Earth&mdash;through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a&ndash;b, Plato uses Pingala&rsquo;s Mātrāmeru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the pint of identifying the two supreme principles of the Cosmos&mdash;the One (1) and the Indefinite Dyad (&Phi; and1/&Phi;)&mdash;with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = &Phi;) and the Mātrāmeru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible.

]]>Symmetry doi: 10.3390/sym11010097

Authors: Jianyong Zheng Hongbo Fan Zhining Li Qi Zhang

In order to identify the orientation or recognize the attitude of small symmetric magnetic anomaly objects at shallow depth, we propose a method of extracting local binary pattern (LBP) features from denoised magnetic anomaly signals and classifying symmetric magnetic objects that have different orientations based on support vector machine (SVM). First, nine component signals, such as magnetic gradient tensor matrix, total magnetic intensity (TMI), and so forth, are calculated from the original signal detected by the flux gate sensors. The nine component signals are processed by discrete wavelet transform (DWT), which aims to reduce noise and make the signal&rsquo;s features clear. Then we extract LBP texture features from the denoised nine component signals. From the simulation analysis, we can conclude that the LBP texture features of the nine component signals have good interclass discrimination and intraclass aggregation, which can be used for pattern recognition. Finally, the LBP texture features are constructed into feature vectors. The orientations of symmetric ferromagnetic objects underground are identified by SVM based on the feature vectors. Through experiments, we can conclude that the orientation recognition accuracy rate reaches 90%. This suggests that we can obtain the details of magnetic anomalies through our method.

]]>Symmetry doi: 10.3390/sym11010096

Authors: Ya Su Zhe Liu Xiaojuan Ban

Image registration is an important process in image processing which is used to improve the performance of computer vision related tasks. In this paper, a novel self-registration method, namely symmetric face normalization (SFN) algorithm, is proposed. There are three contributions in this paper. Firstly, a self-normalization algorithm for face images is proposed, which normalizes a face image to be reflection symmetric horizontally. It has the advantage that no face model needs to be built, which is always severely time-consuming. Moreover, it can be considered as a pre-processing procedure which greatly decreases the parameters needed to be adjusted. Secondly, an iterative algorithm is designed to solve the self-normalization algorithm. Finally, SFN is applied to the between-image alignment problem, which results in the symmetric face alignment (SFA) algorithm. Experiments performed on face databases show that the accuracy of SFN is higher than 0.95 when the translation on the x-axis is lower than 15 pixels, or the rotation angle is lower than 18&deg;. Moreover, the proposed SFA outperforms the state-of-the-art between-image alignment algorithm in efficiency (about four times) without loss of accuracy.

]]>Symmetry doi: 10.3390/sym11010095

Authors: Mariusz Oszust

Image processing methods often introduce distortions, which affect the way an image is subjectively perceived by a human observer. To avoid inconvenient subjective tests in cases in which reference images are not available, it is desirable to develop an automatic no-reference image quality assessment (NR-IQA) technique. In this paper, a novel NR-IQA technique is proposed in which the distributions of local gradient orientations in image regions of different sizes are used to characterize an image. To evaluate the objective quality of an image, its luminance and chrominance channels are processed, as well as their high-order derivatives. Finally, statistics of used perceptual features are mapped to subjective scores by the support vector regression (SVR) technique. The extensive experimental evaluation on six popular IQA benchmark datasets reveals that the proposed technique is highly correlated with subjective scores and outperforms related state-of-the-art hand-crafted and deep learning approaches.

]]>Symmetry doi: 10.3390/sym11010094

Authors: Israr Ullah Muhammad Fayaz DoHyeun Kim

Prediction algorithms enable computers to learn from historical data in order to make accurate decisions about an uncertain future to maximize expected benefit or avoid potential loss. Conventional prediction algorithms are usually based on a trained model, which is learned from historical data. However, the problem with such prediction algorithms is their inability to adapt to dynamic scenarios and changing conditions. This paper presents a novel learning to prediction model to improve the performance of prediction algorithms under dynamic conditions. In the proposed model, a learning module is attached to the prediction algorithm, which acts as a supervisor to monitor and improve the performance of the prediction algorithm continuously by analyzing its output and considering external factors that may have an influence on its performance. To evaluate the effectiveness of the proposed learning to prediction model, we have developed the artificial neural network (ANN)-based learning module to improve the prediction accuracy of the Kalman filter algorithm as a case study. For experimental analysis, we consider a scenario where the Kalman filter algorithm is used to predict actual temperature from noisy sensor readings. the Kalman filter algorithm uses fixed process error covariance R, which is not suitable for dynamic situations where the error in sensor readings varies due to some external factors. In this study, we assume variable error in temperature sensor readings due to the changing humidity level. We have developed a learning module based on ANN to estimate the amount of error in current readings and to update R in the Kalman filter accordingly. Through experiments, we observed that the Kalman filter with the learning module performed better (4.41%&ndash;11.19%) than the conventional Kalman filter algorithm in terms of the root mean squared error metric.

]]>Symmetry doi: 10.3390/sym11010093

Authors: Zhenhua Ma Azhar Hussain Muhammad Adeel Nawab Hussain Ekrem Savas

In this paper, we introduce the notion of C &acute; iri c &acute; type &alpha; - &psi; - &Theta; -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + &sum; i = 1 m A i &lowast; &gamma; ( X ) A i and give a numerical example.

]]>Symmetry doi: 10.3390/sym11010092

Authors: Muhammad Sharif Saadia Saba

In this paper, we study the reconstruction paradigm for Tsallis holographic dark energy model using generalized Tsallis entropy conjecture with Hubble horizon in the framework of f ( G , T ) gravity (G and T represent the Gauss-Bonnet invariant and trace of the energy-momentum tensor). We take the flat Friedmann-Robertson-Walker universe model with dust fluid configuration. The cosmological evolution of reconstructed models is examined through cosmic diagnostic parameters and phase planes. The equation of the state parameter indicates phantom phase while the deceleration parameter demonstrates accelerated cosmic epoch for both conserved as well as non-conserved energy-momentum tensor. The squared speed of the sound parameter shows instability of the conserved model while stable non-conserved model for the entire cosmic evolutionary paradigm. The trajectories of the &omega; G T &minus; &omega; G T &prime; plane correspond to freezing as well as thawing regimes for the conserved and non-conserved scenario, respectively. The r &minus; s plane gives phantom and quintessence dark energy epochs for conserved while Chaplygin gas model regime for the non-conserved case. We conclude that, upon the appropriate choice of the free parameters involved, the derived models demonstrate a self-consistent phantom universe behavior.

]]>Symmetry doi: 10.3390/sym11010091

Authors: Yan Sun Xia Liang Xinya Li Chen Zhang

Demand uncertainty is an important issue that influences the strategic, tactical, and operational-level decision making in the transportation/logistics/supply chain planning. In this study, we explore the effect of demand uncertainty on the operational-level freight routing problem in the capacitated multimodal transportation network that consists of schedule-based rail transportation and time-flexible road transportation. Considering the imprecise characteristic of the demand, we adopt fuzzy set theory to model its uncertainty and use trapezoidal fuzzy numbers to represent the fuzzy demands. We set multiple transportation orders as the optimization object and employ soft time windows to reflect the customer requirement on on-time transportation. Under the above situation, we establish a fuzzy mixed integer nonlinear programming (FMINLP) model to formulate the capacitated road&ndash;rail multimodal routing problem with demand uncertainty and time windows. We first use the fuzzy expected value model and credibility measure based fuzzy chance-constrained programming to realize the defuzziness of the model and then adopt linearization technique to reformulate the crisp model to finally generate an equivalent mixed integer linear programming (MILP) model that can be solved by standard mathematical programming software. Finally, a numerical case is presented to demonstrate the feasibility of the proposed method. Sensitivity analysis and fuzzy simulation are combined to quantify the effect of demand uncertainty on the routing problem and also reveal some helpful insights and managerial implications.

]]>Symmetry doi: 10.3390/sym11010090

Authors: Irina Dymnikova Anna Dobosz

We present the regular cosmological models of the Lema&icirc;tre class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame of one self-consistent theoretical scheme based on the algebraic classification of stress-energy tensors and spacetime symmetry directly related to their structure. Cosmological evolution starts with the nonsingular non-simultaneous de Sitter bang, followed by the Kasner-type anisotropic expansion, and goes towards the present de Sitter state. Spacetime symmetry provides a mechanism of reducing cosmological constant to a certain non-zero value involving the holographic principle which singles out the special class of the Lema&icirc;tre dark energy models with the global structure of the de Sitter spacetime. For this class cosmological evolution is guided by quantum evaporation of the cosmological horizon whose dynamics entirely determines the final value of the cosmological constant. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale for the inflationary value of cosmological constant, its final value agrees with that given by observations. Anisotropy grows quickly at the postinflationary stage, then remains constant and decreases to A &lt; 10 &minus; 6 when the vacuum density starts to dominate.

]]>Symmetry doi: 10.3390/sym11010089

Authors: Tuong Le Sung Wook Baik

Recently, a standard dataset namely SCADI (Self-Care Activities Dataset) based on the International Classification of Functioning, Disability, and Health for Children and Youth framework for self-care problems identification of children with physical and motor disabilities was introduced. This is a very interesting, important and challenging topic due to its usefulness in medical diagnosis. This study proposes a robust framework using a sampling technique and extreme gradient boosting (FSX) to improve the prediction performance for the SCADI dataset. The proposed framework first converts the original dataset to a new dataset with a smaller number of dimensions. Then, our proposed framework balances the new dataset in the previous step using oversampling techniques with different ratios. Next, extreme gradient boosting was used to diagnose the problems. The experiments in terms of prediction performance and feature importance were conducted to show the effectiveness of FSX as well as to analyse the results. The experimental results show that FSX that uses the Synthetic Minority Over-sampling Technique (SMOTE) for the oversampling module outperforms the ANN (Artificial Neural Network) -based approach, Support vector machine (SVM) and Random Forest for the SCADI dataset. The overall accuracy of the proposed framework reaches 85.4%, a pretty high performance, which can be used for self-care problem classification in medical diagnosis.

]]>Symmetry doi: 10.3390/sym11010088

Authors: Zhe Xia Yining Liu Ching-Fang Hsu Chin-Chen Chang

E-lottery schemes have attracted much interest from both industry and academia recently, because they are not only useful to raise funds for charity institutions, but also can be used as the major building blocks to design micro-payment systems. In the literature, a number of e-lottery schemes have been introduced over the last two decades. However, most of these schemes rely on some computational assumptions. In this paper, we introduce a novel e-lottery scheme that achieves information theoretical security. Our proposed scheme is designed using symmetric bivariate polynomials, and it satisfies the required security properties, such as correctness, unpredictability, verifiability, and robustness. Moreover, the winning number is generated in a distributed fashion, so that no trusted third party needs to be involved and the danger of a single point of failure is minimized.

]]>Symmetry doi: 10.3390/sym11010087

Authors: Herbert W. Hamber

In quantum gravity perturbation theory, Newton&rsquo;s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that pathologies encountered in the case of gravity are more likely the result of inadequate analytical treatment, and not necessarily a reflection of some intrinsic insurmountable problem. The nonperturbative treatment of quantum gravity via the Regge&ndash;Wheeler lattice path integral formulation reveals the existence of a new phase involving a nontrivial gravitational vacuum condensate, and a new set of scaling exponents characterizing both the running of G and the long-distance behavior of invariant correlation functions. The appearance of such a gravitational condensate is viewed as analogous to the (equally nonperturbative) gluon and chiral condensates known to describe the physical vacuum of QCD. The resulting quantum theory of gravity is highly constrained, and its physical predictions are found to depend only on one adjustable parameter, a genuinely nonperturbative scale &xi; in many ways analogous to the scaling violation parameter &Lambda; M &macr; S of QCD. Recent results point to significant deviations from classical gravity on distance scales approaching the effective infrared cutoff set by the observed cosmological constant. Such subtle quantum effects are expected to be initially small on current cosmological scales, but could become detectable in future high precision satellite experiments.

]]>Symmetry doi: 10.3390/sym11010086

Authors: Eskandar Ameer Hassen Aydi Muhammad Arshad Habes Alsamir Mohd Selmi Noorani

In this paper, we initiate the notion of generalized multivalued ( &alpha; K * , &Upsilon; , &Lambda; ) -contractions and provide some new common fixed point results in the class of &alpha; K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

]]>Symmetry doi: 10.3390/sym11010085

Authors: Zhan Su Zeshui Xu Hua Zhao Shousheng Liu

Modern cognitive psychologists believe that the decision act of cognitive bias on decision results is universal. To reduce their negative effect on dual hesitant fuzzy decision-making, we propose three weighting methods based on distribution characteristics of data. The main ideas are to assign higher weights to the mid arguments considered to be fair and lower weights to the ones on the edges regarded as the biased ones. The means and the variances of the dual hesitant fuzzy elements (DHFEs) are put forward to describe the importance degrees of the arguments. After that, these results are expanded to deal with the hesitant fuzzy information and some examples are given to show their feasibilities and validities.

]]>Symmetry doi: 10.3390/sym11010084

Authors: Zhixian Yang Kun Qu Xiang Liu

A new method for generating frequency-octupling millimeter-wave (mm-wave) vector signals in optical fields via a Sagnac loop is proposed. In this scheme, two orthogonally polarized fourth order sidebands can be obtained through an integrated dual-polarization quadrature phase shift keying (DP-QPSK) modulator. The two optical sidebands are sent into an I/Q modulator-based Sagnac loop. The I/Q modulator is modulated by a 16QAM baseband signal. In the Sagnac loop, one of the sidebands is modulated by the baseband vector signal along one direction, and the other sideband is unmodulated along the opposite direction because the I/Q modulator has the traveling-wave nature. Thanks to this modulation property and the symmetrical structure of the Sagnac loop, a frequency-octupling mm-wave vector signal that is free from interband beating and fiber chromatic dispersion interference can be generated by the photodetector (PD). After simulating a 20 km single-mode fiber (SMF) transmission, the generated frequency-octupling vector signal was good in function.

]]>Symmetry doi: 10.3390/sym11010083

Authors: Nam Thanh Pham Jong-Weon Lee Goo-Rak Kwon Chun-Su Park

Recently, the task of validating the authenticity of images and the localization of tampered regions has been actively studied. In this paper, we go one step further by providing solid evidence for image manipulation. If a certain image is proved to be the spliced image, we try to retrieve the original authentic images that were used to generate the spliced image. Especially for the image retrieval of spliced images, we propose a hybrid image-retrieval method exploiting Zernike moment and Scale Invariant Feature Transform (SIFT) features. Due to the symmetry and antisymmetry properties of the Zernike moment, the scaling invariant property of SIFT and their common rotation invariant property, the proposed hybrid image-retrieval method is efficient in matching regions with different manipulation operations. Our simulation shows that the proposed method significantly increases the retrieval accuracy of the spliced images.

]]>Symmetry doi: 10.3390/sym11010082

Authors: Li Liu Lifang Wang Yun-Qing Shi Chin-Chen Chang

As cloud computing becomes popular, the security of users&rsquo; data is faced with a great threat, i.e., how to protect users&rsquo; privacy has become a pressing research topic. The combination of data hiding and encryption can provide dual protection for private data during cloud computing. In this paper, we propose a new separable data-hiding scheme for encrypted images based on block compressive sensing. First, the original uncompressed image is compressed and encrypted by block compressive sensing (BCS) using a measurement matrix, which is known as an encryption key. Then, some additional data can be hidden into the four least significant bits of measurement using the data-hiding key during the process of encoding. With an encrypted image that contains hidden data, the receiver can extract the hidden data or decrypt/reconstruct the protected private image, according to the key he/she possesses. This scheme has important features of flexible compression and anti-data-loss. The image reconstruction and data extraction are separate processes. Experimental results have proven the expected merits of the proposed scheme. Compared with the previous work, our proposed scheme reduces the complexity of the scheme and also achieves better performance in compression, anti-data-loss, and hiding capacity.

]]>Symmetry doi: 10.3390/sym11010081

Authors: Farkhat Zaripov

This work is the extension of author&rsquo;s research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and &ldquo;restructuring&rdquo; (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological &ldquo;constants&rdquo;, which are defined by the &ldquo;mean square&rdquo; of the scalar fields. In obtained solutions the values of such parameters as &ldquo;Hubble parameter&rdquo;, gravitational and cosmological &ldquo;constants&rdquo; in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton&rsquo;s law of gravitational interaction, antigravity.

]]>Symmetry doi: 10.3390/sym11010080

Authors: Muhammad Aslam Nasrullah Khan Ali Hussein AL-Marshadi

The sampling plans have been widely used for the inspection of a lot of the product. In practice, the measurement data may be imprecise, uncertain, unclear or fuzzy. When there is uncertainty in the observations, the sampling plans designed using classical statistics cannot be applied for the inspection of a lot of the product. The neutrosophic statistic, which is the generalization of the classical statistics, can be used when data is not precise, uncertain, unclear or fuzzy. In this paper, we will design the variable sampling plan under the Pareto distribution using the neutrosophic statistics. We used the symmetry property of the normal distribution. We assume uncertainty in measurement data and sample size required for the inspection of a lot of the product. We will determine the neutrosophic plan parameters using the neutrosophic optimization problem. Some tables are given for practical use and are discussed with the help of an example.

]]>Symmetry doi: 10.3390/sym11010079

Authors: Lin Li Chia-Chen Lin Chin-Chen Chang

A subtopic of visual secret sharing (VSS) is information hiding-based VSS (IH-VSS), which embeds secret messages into images using an information hiding technique. In the IH-VSS scheme, stego-images are divided into shadows under the guidance and constraint of some predetermined approaches. In order to achieve the purpose of security and reliability, the hidden information cannot be recovered unless a certain amount or all of the credible shadows work together. In this paper, we propose a (2, 2) IH-VSS scheme with reversibility and friendliness. In the shadow generation phase, two meaningful shadow images are produced and then distributed. In the extraction and restoration phase, the hidden secret information and cover image, respectively, can be reconstructed credibly and correctly. No complex computation of shadow generation is involved, but high security is achieved. Moreover, a satisfying peak-signal-to-noise ratio (PSNR) is obtained with the high embedding capacity of 1.59 bpp in a very simple and effective way.

]]>Symmetry doi: 10.3390/sym11010078

Authors: Ruomeng Xu Jieren Cheng Fengkai Wang Xiangyan Tang Jinying Xu

Distributed Denial of Service (DDoS) has developed multiple variants, one of which is Distributed Reflective Denial of Service (DRDoS). With the increasing number of Internet of Things (IoT) devices, the threat of DRDoS attack is growing, and the damage of a DRDoS attack is more destructive than other types. The existing DDoS detection methods cannot be generalized in DRDoS early detection, which leads to heavy load or degradation of service when deployed at the final point. In this paper, we propose a DRDoS detection and defense method based on deep forest model (DDDF), and then we integrate differentiated service into defense model to filter out DRDoS attack flow. Firstly, from the statistics perspective on different stages of DRDoS attack flow in the big data environment, we extract a host-based DRDoS threat index (HDTI) from the network flows. Secondly, using the HDTI feature we build a DRDoS detection and defense model based on the deep forest, which consists of 1 extreme gradient boost (XGBoost) forest estimator, 2 random forest estimators, and 2 extra random forest estimators in each layer. Lastly, the differentiated service procedure applies the detection result from DDDF to drop the traffic identified in different stages and different detection points. Theoretical analysis and experiments show that the method we proposed can effectively identify DRDoS attack with higher detection rate and a lower false alarm rate, the defense model also shows distinguishing ability to effectively eliminate the DRDoS attack flows, and dramatically mitigate the damage of a DRDoS attack.

]]>Symmetry doi: 10.3390/sym11010077

Authors: Dandan Shi Yufeng Zhang Wenhao Liu Jiangen Liu

In this paper, we investigate the invariant properties of the coupled time-fractional Boussinesq-Burgers system. The coupled time-fractional Boussinesq-Burgers system is established to study the fluid flow in the power system and describe the propagation of shallow water waves. Firstly, the Lie symmetry analysis method is used to consider the Lie point symmetry, similarity transformation. Using the obtained symmetries, then the coupled time-fractional Boussinesq-Burgers system is reduced to nonlinear fractional ordinary differential equations (FODEs), with E r d e ´ l y i - K o b e r fractional differential operator. Secondly, we solve the reduced system of FODEs by using a power series expansion method. Meanwhile, the convergence of the power series solution is analyzed. Thirdly, by using the new conservation theorem, the conservation laws of the coupled time-fractional Boussinesq-Burgers system is constructed. In particular, the presentation of the numerical simulations of q-homotopy analysis method of coupled time fractional Boussinesq-Burgers system is dedicated.

]]>Symmetry doi: 10.3390/sym11010076

Authors: Yuan Yuan Rekha Srivastava Jin-Lin Liu

We consider the order of the strongly-starlikeness of the generalized &alpha; -convex functions. Some sufficient conditions for functions to be p-valently strongly-starlike are given.

]]>Symmetry doi: 10.3390/sym11010075

Authors: Chiranjibe Jana Madhumangal Pal

In the age of the knowledge-based economy and the rapid development of information technology, enterprise management is facing great challenges and has entered an era of prudent management. Traditional enterprise performance evaluation focuses on the interests of shareholders. Investors take financial data as their base and pay attention to the study of material attraction and the results; if they do not, they cannot adjust to a new economy period. Therefore, enterprise performance reflects the interests of shareholders and business strategists for the needs of stakeholders, which is important for the future of lively competition. With that in mind, aggregation of information is an important research tool that has recently drawn the attention of researchers for information analysis. In this paper, we have developed multiple-attribute decision-making methods for enterprise performance evaluation with picture fuzzy information. We have applied Hamacher aggregation operators such as the picture fuzzy Hamacher weighted averaging (PFHWA) operator and picture fuzzy Hamacher weighted geometric (PFHWG) operator in picture fuzzy environment for the assessment of the best enterprise selection. Finally, we justified the proposed approach with the existing methods for feasibility and effectiveness.

]]>Symmetry doi: 10.3390/sym11010074

Authors: Sarfaraz Hashemkhani Zolfani Prasenjit Chatterjee

For a few years, there has been an increasing consciousness to design structures that are concurrently economic and environmentally responsive. Eco-friendly inferences of building designs include lower energy consumption, reduction in CO2 emissions, assimilated energy in buildings and enhancement of indoor air quality. With the aim of fulfilling design objectives, designers normally encounter a situation in which the selection of the most appropriate material from a set of various material alternatives is essential. Sustainability has been developing as a new concept in all human activities to create a better balance between social, environmental and economic issues. Designing materials based on the sustainability concept is a key step to enable a better balance because there is no need to re-structure phases and procedures to make the system more efficient in comparison to previous models. Some of the most commonly used materials are household furnishing materials, which can be electrical devices, kitchen gears or general furnishing materials. The volume of production and consumption of these materials is considerable, therefore a newer sustainable plan for a better designed system is justifiable. In the literature, the application of multi-attribute decision-making (MADM) methods has been found to be very suitable for evaluating materials and developing general plans for them. This study contributes by applying two approaches based on MADM methods for weighting the criteria related to the sustainable design of household furnishing materials. Step-Wise Weight Assessment Ratio Analysis (SWARA) and Best Worst Method (BWM) are two specialized and new methods for weighting criteria with different approaches. This paper has not only investigated the weighting of important and related criteria for sustainable design but has also evaluated the similarities and differences between the considered weighting methods. A comparative study of SWARA and BWM methods has never been conducted to date. The results show that, except pairwise comparisons, SWARA and BWM are certainly similar and in some cases SWARA can be more accurate and effective.

]]>Symmetry doi: 10.3390/sym11010073

Authors: Djumaklich Amanov Gafurjan Ibragimov Adem Kılıçman

In the present paper, we study a generalization of the initial-boundary problem for the inhomogeneous vibrating string equation. The initial conditions include the higher order derivatives of the unknown function. The problem is studied under homogeneous boundary conditions of the first kind. The uniqueness and existence of a regular solution of the problem are proved. To prove the main result we use the spectral decomposition method.

]]>Symmetry doi: 10.3390/sym11010072

Authors: Tran Thai Hoc Ly Hoang-Sy Nguyen Thanh-Sang Nguyen Van Van Huynh Thanh-Long Nguyen Miroslav Voznak

In recent years, non-orthogonal multiple access (NOMA) has become a promising technology for the advancement of future wireless communications. In principle, the relay node with better channel conditions can support others to enhance the system performance by using successive interference cancellation (SIC) technique. In this paper, we take advantage of NOMA in the study of a relaying cooperative system operating in half-duplex (HD) fixed decode-and-forward (DF) relaying scheme. In the two time slots, two data symbols are received at the destination node resulting in a higher transmission rate. Besides that, we study energy harvesting (EH) with power splitting (PS) protocol. For performance analysis, approximate and exact closed-form expressions for outage probability (OP) are obtained. Following that, we examine the average bit error probability (ABEP) while expressions for the throughput in delay-limited mode are given. It can be seen that our simulation results match well with the Monte Carlo simulations.

]]>Symmetry doi: 10.3390/sym11010071

Authors: Naji Ma Ming Diao

The wireless channel is volatile in nature, due to various signal attenuation factors including path-loss, shadowing, and multipath fading. Existing media access control (MAC) protocols, such as the widely adopted 802.11 wireless fidelity (Wi-Fi) family, advocate masking harsh channel conditions with persistent retransmission and backoff, in order to provide a packet-level best-effort service. However, the asymmetry of the network environment of client nodes in space is not fully considered in the method, which leads to the decline of the transmission efficiency of the good ones. In this paper, we propose CoFi, a coding-assisted file distribution protocol for 802.11 based wireless local area networks (LANs). CoFi groups data into batches and transmits a random linear combination of packets within each batch, thereby reducing redundant packet and acknowledgement (ACK) retransmissions when the channel is lossy. In addition, CoFi adopts a MAC layer caching scheme that allows clients to store the overheard coded packets and use such cached packets to assist nearby peers. With this measure, it further improves the effective throughput and shortens the buffering delay when running applications such as bulk data transmission and video streaming. Our trace based simulation demonstrates that CoFi can maintain a similar level of packet delay to 802.11, but increases the throughput performance by a significant margin in a lossy wireless LAN. Furthermore, we perform a reverse-engineering on CoFi and 802.11 using a simple analytical framework, proving that they asymptotically approach different fairness measures, thus resulting in a disparate performance.

]]>Symmetry doi: 10.3390/sym11010070

Authors: G. V. V. Jagannadha Rao S. K. Padhan Mihai Postolache

The notion of rational F-contractions using &alpha; -admissibility of type-S in b-metric-like spaces is introduced and the new fixed and periodic point theorems are proved for such mappings. Numerical examples are illustrated to check the efficiency and applicability of our fresh findings. It is also observed that some of the works reported in the literature are the particular cases of the present study.

]]>Symmetry doi: 10.3390/sym11010069

Authors: Zhen Wu Yi-Ning Liu Dong Wang Ching-Nung Yang

As a popular technology in information security, secret image sharing is a method to guarantee the secret image&rsquo;s security. Usually, the dealer would decompose the secret image into a series of shadows and then assign them to a number of participants, and only a quorum of participants could recover the secret image. Generally, it is assumed that every participant is equal. Actually, due to their position in many practical applications, some participants are given special privileges. Therefore, it is desirable to give an approach to generate shadows with different priorities shadows. In this paper, an efficient essential secret image sharing scheme using a derivative polynomial is proposed. Compared with existing related works, our proposed scheme can not only create the same-sized shadows with smaller size but also removes the concatenation operation in the sharing phase. Theoretical analysis and simulations confirm the security and effectiveness of the proposed scheme.

]]>Symmetry doi: 10.3390/sym11010068

Authors: Ioseph Buchbinder Evgeny Ivanov Boris Merzlikin Konstantin Stepanyantz

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang&ndash;Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

]]>Symmetry doi: 10.3390/sym11010067

Authors: Shan Bian Haoliang Li Tianji Gu Alex Chichung Kot

The analysis of video compression history is one of the important issues in video forensics. It can assist forensics analysts in many ways, e.g., to determine whether a video is original or potentially tampered with, or to evaluate the real quality of a re-encoded video, etc. In the existing literature, however, there are very few works targeting videos in HEVC format (the most recent standard), especially for the issue of the detection of transcoded videos. In this paper, we propose a novel method based on the statistics of Prediction Units (PUs) to detect transcoded HEVC videos from AVC format. According to the analysis of the footprints of HEVC videos, the frequencies of PUs (whether in symmetric patterns or not) are distinguishable between original HEVC videos and transcoded ones. The reason is that previous AVC encoding disturbs the PU partition scheme of HEVC. Based on this observation, a 5D and a 25D feature set are extracted from I frames and P frames, respectively, and are combined to form the proposed 30D feature set, which is finally fed to an SVM classifier. To validate the proposed method, extensive experiments are conducted on a dataset consisting of CIF ( 352 &times; 288 ) and HD 720p videos with a diversity of bitrates and different encoding parameters. Experimental results show that the proposed method is very effective at detecting transcoded HEVC videos and outperforms the most recent work.

]]>Symmetry doi: 10.3390/sym11010064

Authors: Ahmed Bachir Abdelkader Segres

T &isin; B ( H ) is said to be ( n , k ) -quasi-&lowast;-paranormal operator if, for non-negative integers k and n, ∥ T &lowast; ( T k x ) ∥ ( 1 + n ) &le; ∥ T ( 1 + n ) ( T k x ) ∥ ∥ T k x ∥ n ; for all x &isin; H . In this paper, the asymmetric Putnam-Fuglede theorem for the pair ( A , B ) of power-bounded operators is proved when (i) A and B &lowast; are n-&lowast;-paranormal operators (ii) A is a ( n , k ) -quasi-&lowast;-paranormal operator with reduced kernel and B &lowast; is n-&lowast;-paranormal operator. The class of ( n , k ) -quasi-&lowast;-paranormal operators properly contains the classes of n-&lowast;-paranormal operators, ( 1 , k ) -quasi-&lowast;-paranormal operators and k-quasi-&lowast;-class A operators. As a consequence, it is showed that if T is a completely non-normal ( n , k ) -quasi-&lowast;-paranormal operator for k = 0 , 1 such that the defect operator D T is Hilbert-Schmidt class, then T &isin; C 10 .

]]>Symmetry doi: 10.3390/sym11010066

Authors: Kai Liu Yuan Xu

This paper investigated the impact of asymmetric preference on travelers&rsquo; route choices. Firstly, a status quo-dependent route choice mode was developed to describe travelers&rsquo; route choices. Then, based on that model, a route choice experiment was conducted, and during the experiment, participants were requested to choose a route from two arbitrary non-dominated routes. Finally, according to the observation data, data analysis and model parameter estimation were conducted. The results show that participants used different measures to trade off travel cost and travel time. Additionally, there was a gap between most participants&rsquo; willingness to pay (WTP) and willingness to accept (WTA). Moreover, participants&rsquo; WTP greater than their own WTA was the key reason resulting in the inertial route choices. The empirical results in this paper can help the traffic manager to understand travelers&rsquo; inertial route choice behavior from a different perspective.

]]>Symmetry doi: 10.3390/sym11010065

Authors: Zhicong Wei Wei Yang Ruofu Xiao

Pressure fluctuation is the primary factor that affects the stability of turbomachines. The goal of the present work is to explore the propagation of pressure fluctuations in a two-stage double-suction centrifugal pump. The pressure fluctuation characteristics of each component of a two-stage double-suction centrifugal pump are simulated under four typical flow rates based on the SST k-&omega; turbulence model. It is shown that the pressure fluctuation frequency at blade passing frequency and its first harmonic is the same at the suction chamber, the leading edge, and the middle of the first-stage impeller, which is different from the rotor&ndash;stator interaction. Moreover, the uneven impeller inlet flow distribution will produce fluctuations with rotation frequency and its harmonics at the leading edge of the impellers in both stages. Finally, broadband frequency is found at the trailing edge of the impellers in both stages associated with the first harmonic of the rotation frequency, especially under the part load condition. The large size backflow vortex appears in the blade flow channel leading to the low-pressure zone between the impeller, the tongue, and the start of the partition. That is why the pressure drops significantly twice in one rotation period when the blades pass through the tongue and the start of the partition.

]]>Symmetry doi: 10.3390/sym11010063

Authors: Liming Zhao Yanqing Chen

Replacing traditional products with green products has become a key way to achieve decoupling between economic development and environmental pollution. As an incentive mechanism, subsidies can be provided by a government to facilitate the popularization and acceptance of green products. Subsidies play a significant role in encouraging the development of green products. We explored the proper optimal subsidy mechanism for green products from the angle of maximizing the net policy return, which cannot only encourage the development of green products but also do not aggravate financial burden for the government. In order to explore the optimal subsidy level for green products from the perspective of net policy benefit maximization, this paper established the optimal subsidy principal-agent models and a numerical example was presented to verify the effectiveness of the model we constructed. The results show that improving investors&rsquo; preference and eliminating asymmetric information contribute to reduce subsidy cost savings. Additionally, improving consumer environmental awareness, promoting the development and application of green technology, and reducing market risk reduce subsidy costs. This article provides policymakers with an effective subsidy scheme to accelerate the development of green products and achieve sustainable development goals.

]]>Symmetry doi: 10.3390/sym11010062

Authors: Wenpeng Zhang Li Chen

The main purpose of this paper is using the elementary and combinatorial methods to study the properties of the Catalan numbers, and give two new identities for them. In order to do this, we first introduce two new recursive sequences, then with the help of these sequences, we obtained the identities for the convolution involving the Catalan numbers.

]]>Symmetry doi: 10.3390/sym11010061

Authors: Humaira Muhammad Sarwar Poom Kumam

Owing to the notion of a complex-valued metric space, we prove fixed point results, which generalize some common fixed point results under contractive condition for rational expression in the context of complex-valued metric spaces. In application, we present a homotopy result to apply the results obtained herein.

]]>Symmetry doi: 10.3390/sym11010059

Authors: Thaiz Carrera-Arrabal José Luis Calvo-Guirado Fabricio Passador-Santos Carlos Eduardo Sorgi da Costa Frank Róger Teles Costa Antonio Carlos Aloise Marcelo Henrique Napimoga Juan Manuel Aragoneses André Antonio Pelegrine

The purpose of this study was to conduct a histomorphometric analysis of bone marrow-derived and adipose tissue-derived stem cells, associated with a xenograft block, in vertical bone constructions in rabbit calvaria. Ten rabbits received two xenograft blocks on the calvaria, after decortication of the parietal bone. The blocks were fixed with titanium screws. The blocks were combined with the bone marrow-derived mesenchymal stem cells in the bone marrow stem cell (BMSC) group (right side of the calvaria) or with the adipose tissue-derived mesenchymal stem cells in the adipose tissue stem cell (ATSC) group (left side of the calvaria). After 8 weeks, the animals were sacrificed and their parietal bones were fixed in 10% formalin for the histomorphometric analysis. The following parameters were evaluated&mdash;newly formed bone (NFB), xenogeneic residual particles (XRP), and non-mineralized tissue (NMT). The histomorphometric analysis revealed 11.9 &plusmn; 7.5% and 7.6 &plusmn; 5.6% for NFB, 22.14 &plusmn; 8.5% and 21.6 &plusmn; 8.5% for XRP, and 65.8 &plusmn; 10.4% and 70.8 &plusmn; 7.4% for NMT in groups BMSC and ATSC, respectively, with statistically significant differences in the NFB and the NMT between the groups, but no differences in the XRP. Therefore, it can be concluded that the bone marrow-derived stem cells seem to have more potential for the bone formation than do the adipose tissue-derived stem cells when used in combination with the xenogenous blocks in the vertical bone construction.

]]>Symmetry doi: 10.3390/sym11010060

Authors: Otilia-Sanda Prelipceanu Marius Prelipceanu Nicolae Paraschiv Alexandru Popa Oana Geman

In this paper the novel high-temperature resistant polymers with nonlinear optical properties have been synthesized, characterized and tested for use in electro-optical components with high bit rate optical signal processing systems and for dynamic holography. The characterization that has been reported include the measurement of second-order nonlinear susceptibility by second harmonic generation, UV-VIS spectroscopy, XRD measurement dielectric relaxation, glass transition temperature and molecular weight distribution before and after artificial ageing. Also, we have done AFM investigations and profilometry measurements for stamp patterning layers. The application of the new polyimides for electro-optic devices has been evaluated by creation of thin oriented polymer films on various substrates and preparation of planar and strip waveguides.

]]>Symmetry doi: 10.3390/sym11010058

Authors: Xuan-Qui Pham Tien-Dung Nguyen VanDung Nguyen Eui-Nam Huh

The resource limitation of multi-access edge computing (MEC) is one of the major issues in order to provide low-latency high-reliability computing services for Internet of Things (IoT) devices. Moreover, with the steep rise of task requests from IoT devices, the requirement of computation tasks needs dynamic scalability while using the potential of offloading tasks to mobile volunteer nodes (MVNs). We, therefore, propose a scalable vehicle-assisted MEC (SVMEC) paradigm, which cannot only relieve the resource limitation of MEC but also enhance the scalability of computing services for IoT devices and reduce the cost of using computing resources. In the SVMEC paradigm, a MEC provider can execute its users&rsquo; tasks by choosing one of three ways: (i) Do itself on local MEC, (ii) offload to the remote cloud, and (iii) offload to the MVNs. We formulate the problem of joint node selection and resource allocation as a Mixed Integer Nonlinear Programming (MINLP) problem, whose major objective is to minimize the total computation overhead in terms of the weighted-sum of task completion time and monetary cost for using computing resources. In order to solve it, we adopt alternative optimization techniques by decomposing the original problem into two sub-problems: Resource allocation sub-problem and node selection sub-problem. Simulation results demonstrate that our proposed scheme outperforms the existing schemes in terms of the total computation overhead.

]]>Symmetry doi: 10.3390/sym11010057

Authors: Muhammad Aslam Gadde Srinivasa Rao Nasrullah Khan Fahad A. Al-Abbasi

In this paper, we discuss the application of the exponentially weighted moving average (EWMA) control chart for the monitoring blood glucose in type-II diabetes patients. We present tables for the practical use in healthcare. From the simulation results and a real example, the efficiency of the proposed chart in detecting a shift in diabetic level is compared with the existing chart. It is found that the proposed chart provides a strict method to monitor the diabetic levels in diabetes patients. From the simulation results and a real example, it is concluded that the use of the proposed chart in health care issues may reduce the risk of heart disease by monitoring diabetic levels in an effective way.

]]>Symmetry doi: 10.3390/sym11010056

Authors: Jie Wang Hui Gao Guiwu Wei Yu Wei

In the practical world, there commonly exist different types of multiple-attribute group decision making (MAGDM) problems with uncertain information. Symmetry among some attributes&rsquo; information that is already known and unknown, and symmetry between the pure attribute sets and fuzzy attribute membership sets, can be an effective way to solve this type of MAGDM problem. In this paper, we investigate four forms of information aggregation operators, including the Hamy mean (HM) operator, weighted HM (WHM) operator, dual HM (DHM) operator, and the dual-weighted HM (WDHM) operator with the q-rung interval-valued orthopair fuzzy numbers (q-RIVOFNs). Then, some extended aggregation operators, such as the q-rung interval-valued orthopair fuzzy Hamy mean (q-RIVOFHM) operator; q-rung interval-valued orthopairfuzzy weighted Hamy mean (q-RIVOFWHM) operator; q-rung interval-valued orthopair fuzzy dual Hamy mean (q-RIVOFDHM) operator; and q-rung interval-valued orthopair fuzzy weighted dual Hamy mean (q-RIVOFWDHM) operator are presented, and some of their precious properties are studied in detail. Finally, a real example for green supplier selection in green supply chain management is provided, to demonstrate the proposed approach and to verify its rationality and scientific nature.

]]>Symmetry doi: 10.3390/sym11010055

Authors: Ilija Tanackov Darko Dragić Siniša Sremac Vuk Bogdanović Bojan Matić Milica Milojević

Designing the crossroads capacity is a prerequisite for achieving a high level of service with the same sustainability in stochastic traffic flow. Also, modeling of crossroad capacity can influence on balancing (symmetry) of traffic flow. Loss of priority in a left turn and optimal dimensioning of shared-short line is one of the permanent problems at intersections. A shared&ndash;short lane for taking a left turn from a priority direction at unsignalized intersections with a homogenous traffic flow and heterogeneous demands is a two-phase queueing system requiring a first in&ndash;first out (FIFO) service discipline and single-server service facility. The first phase (short lane) of the system is the queueing system M(p&lambda;)/M(&mu;)/1/&infin;, whereas the second phase (shared lane) is a system with a binomial distribution service. In this research, we explicitly derive the probability of the state of a queueing system with a short lane of a finite capacity for taking a left turn and shared lane of infinite capacity. The presented formulas are under the presumption that the system is Markovian, i.e., the vehicle arrivals in both the minor and major streams are distributed according to the Poisson law, and that the service of the vehicles is exponentially distributed. Complex recursive operations in the two-phase queueing system are explained and solved in manuscript.

]]>Symmetry doi: 10.3390/sym11010054

Authors: Viktor A. Rukavishnikov Alexey V. Rukavishnikov

In the paper, a new numerical approach for the rotation form of the Oseen system in a polygon &Omega; with an internal corner &omega; greater than 180 ∘ on its boundary is presented. The results of computational simulations have shown that the convergence rate of the approximate solution (velocity field) by weighted FEM to the exact solution does not depend on the value of the internal corner &omega; and equals O ( h ) in the norm of a space W 2 , &nu; 1 ( &Omega; ) .

]]>Symmetry doi: 10.3390/sym11010053

Authors: Muhammad Aslam Nasrullah Khan Mohammed Albassam

In this article, modified multiple dependent (or deferred) state sampling control charts for the attribute and the variable quality characteristics are presented. The proposed control charts are designed using the symmetry property of the normal distribution. The control chart coefficients are estimated through simulation at different levels of the parameters using the normal distribution. The proposed control chart scheme is evaluated by calculating the in-control average run lengths and out-of-control average run lengths. Tables are constructed for the selection of parameters for different control limit coefficients under several shift levels for the attribute data as well as the variable data. Examples are included for the practical application of the proposed control chart schemes. The proposed control chart scheme is also compared with the existing control charts. It has been observed that the proposed schemes are better in quick detection of the out-of-control processes.

]]>Symmetry doi: 10.3390/sym11010052

Authors: Xianzhang Pan Wenping Guo Xiaoying Guo Wenshu Li Junjie Xu Jinzhao Wu

The proposed method has 30 streams, i.e., 15 spatial streams and 15 temporal streams. Each spatial stream corresponds to each temporal stream. Therefore, this work correlates with the symmetry concept. It is a difficult task to classify video-based facial expression owing to the gap between the visual descriptors and the emotions. In order to bridge the gap, a new video descriptor for facial expression recognition is presented to aggregate spatial and temporal convolutional features across the entire extent of a video. The designed framework integrates a state-of-the-art 30 stream and has a trainable spatial&ndash;temporal feature aggregation layer. This framework is end-to-end trainable for video-based facial expression recognition. Thus, this framework can effectively avoid overfitting to the limited emotional video datasets, and the trainable strategy can learn to better represent an entire video. The different schemas for pooling spatial&ndash;temporal features are investigated, and the spatial and temporal streams are best aggregated by utilizing the proposed method. The extensive experiments on two public databases, BAUM-1s and eNTERFACE05, show that this framework has promising performance and outperforms the state-of-the-art strategies.

]]>Symmetry doi: 10.3390/sym11010051

Authors: Kaimeng Chen Chin-Chen Chang

In this paper, a novel, real-time, error-free, reversible data hiding method for encrypted images has been proposed. Based on the (7, 4) Hamming code, we designed an efficient encoding scheme to embed secret data into the least significant bits (LSBs) of the encrypted image. For reversibility, we designed a most significant bit (MSB) prediction scheme that can recover a portion of the modified MSBs after the image is decrypted. These MSBs can be modified to accommodate the additional information that is used to recover the LSBs. After embedding the data, the original image can be recovered with no error and the secret data can be extracted from both the encrypted image and the decrypted image. The experimental results proved that compared with existing methods, the proposed method can achieve higher embedding rate, better quality of the marked image and less execution time of data embedding. Therefore, the proposed method is suitable for real-time applications in the cloud.

]]>Symmetry doi: 10.3390/sym11010050

Authors: Omid Akbarzadeh Noor Asmawati Mohd Zabidi Nor Aliya Hamizi Yasmin Abdul Wahab Zulkifli Merican Aljunid Merican Wageeh A. Yehya Shamima Akhter Md. Shalauddin Elisa Rasouli Mohd Rafie Johan

Multiwalled carbon nanotubes (CNT) supported cobalt oxide was prepared as a catalyst by strong electrostatic adsorption (SEA) method. The CNT support was initially acid- and thermal-treated in order to functionalize the support to uptake more Co clusters. The Co/CNT were characterized by a range of analytical methods including transmission electron microscopy (TEM), temperature programmed reduction with hydrogen (H2-TPR), X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), Raman spectroscopy, atomic absorption spectroscopy (AAS), Zeta sizer particle size analysis and Brunauer&ndash;Emmett&ndash;Teller (BET) surface area analysis. TEM images showed cobalt particles were highly dispersed and impregnated at both exterior and interior walls of the CNT support with a narrow particle size distribution of 6&ndash;8 nm. In addition, the performance of the synthesized Co/CNT catalyst was tested using Fischer&ndash;Tropsch synthesis (FTS) reaction which was carried out in a fixed-bed micro-reactor. H2-TPR profiles indicated the lower reduction temperature of 420 &deg;C was required for the FTS reaction. The study revealed that cobalt is an effective metal for Co/CNT catalysts at pH 14 and at 900 &deg;C calcination temperature. Furthermore, FTS reaction results showed that CO conversion and C5+ selectivity were recorded at 58.7% and 83.2% respectively, which were higher than those obtained using a Co/CNT catalyst which pre-treated at a lower thermal treatment temperature and pH.

]]>Symmetry doi: 10.3390/sym11010049

Authors: Shaowei Weng Yi Chen Wien Hong Jeng-Shyang Pan Chin-Chen Chang Yijun Liu

After conducting deep research on all existing reversible data hiding (RDH) methods based on Alattar&rsquo;s integer transform, we discover that the frequently-used method in obtaining the difference value list of an image block may lead to high embedding distortion. To this end, we propose an improved Alattar&rsquo;s transform-based-RDH-method. Firstly, the irregular block partition method which makes full use of high correlation between two neighboring pixels is proposed to increase the embedding performance. Specifically, each image block is composed of a center pixel and several pixels surrounding this center pixel. Thus, the difference value list is created by using the center pixel to predict each pixel surrounding it. Since the center pixel is highly related to each pixel surrounding it, a sharp difference value histogram is generated. Secondly, the mean value of an image block in Alattar&rsquo;s integer transform has embedding invariance property, and therefore, it can be used for increasing the estimation performance of a block&rsquo;s local complexity. Finally, two-layer embedding is combined into our scheme in order to optimize the embedding performance. Experimental results show that our method is effective.

]]>Symmetry doi: 10.3390/sym11010048

Authors: Martine Hausberger Hugo Cousillas Anaïke Meter Genta Karino Isabelle George Alban Lemasson Catherine Blois-Heulin

Studies on auditory laterality have revealed asymmetries for processing, particularly species-specific signals, in vertebrates and that each hemisphere may process different features according to their functional &ldquo;value&rdquo;. Processing of novel, intense emotion-inducing or finer individual features may require attention and we hypothesised that the &ldquo;functional pertinence&rdquo; of the stimuli may be modulating attentional processes and hence lateralisation of sound processing. Behavioural measures in &ldquo;(food) distracted&rdquo; captive Campbell&rsquo;s monkeys and electrophysiological recordings in anesthetised (versus awake) European starlings were performed during the broadcast of auditory stimuli with different functional &ldquo;saliences&rdquo; (e.g., familiar/novel). In Campbell&rsquo;s monkeys, only novel sounds elicited lateralised responses, with a right hemisphere preference. Unfamiliar sounds elicited more head movements, reflecting enhanced attention, whereas familiar (usual in the home environment) sounds elicited few responses, and thus might not be arousing enough to stimulate attention. In starlings, in field L, when awake, individual identity was processed more in the right hemisphere, whereas, when anaesthetised, the left hemisphere was more involved in processing potentially socially meaningless sounds. These results suggest that the attention-getting property of stimuli may be an adapted concept for explaining hemispheric auditory specialisation. An attention-based model may reconcile the different existing hypotheses of a Right Hemisphere-arousal/intensity or individual based lateralisation.

]]>Symmetry doi: 10.3390/sym11010047

Authors: Amalia Luque Alejandro Carrasco Alejandro Martín Juan Ramón Lama

Selecting the proper performance metric constitutes a key issue for most classification problems in the field of machine learning. Although the specialized literature has addressed several topics regarding these metrics, their symmetries have yet to be systematically studied. This research focuses on ten metrics based on a binary confusion matrix and their symmetric behaviour is formally defined under all types of transformations. Through simulated experiments, which cover the full range of datasets and classification results, the symmetric behaviour of these metrics is explored by exposing them to hundreds of simple or combined symmetric transformations. Cross-symmetries among the metrics and statistical symmetries are also explored. The results obtained show that, in all cases, three and only three types of symmetries arise: labelling inversion (between positive and negative classes); scoring inversion (concerning good and bad classifiers); and the combination of these two inversions. Additionally, certain metrics have been shown to be independent of the imbalance in the dataset and two cross-symmetries have been identified. The results regarding their symmetries reveal a deeper insight into the behaviour of various performance metrics and offer an indicator to properly interpret their values and a guide for their selection for certain specific applications.

]]>Symmetry doi: 10.3390/sym11010046

Authors: Di Zhu Ran Tao Ruofu Xiao

Mixed-flow pumps compromise large flow rate and high head in fluid transferring. Long-axis mixed-flow pumps with radial&ndash;axial &ldquo;spacing&rdquo; guide vanes are usually installed deeply under water and suffer strong cavitation due to strong environmental pressure drops. In this case, a strategy combining the Diffusion-Angle Integral Design method, the Genetic Algorithm, and the Computational Fluid Dynamics method was used for optimizing the mixed-flow pump impeller. The Diffusion-Angle Integral Design method was used to parameterize the leading-edge geometry. The Genetic Algorithm was used to search for the optimal sample. The Computational Fluid Dynamics method was used for predicting the cavitation performance and head&ndash;efficiency performance of all the samples. The optimization designs quickly converged and got an optimal sample. This had an increased value for the minimum pressure coefficient, especially under off-design conditions. The sudden pressure drop around the leading-edge was weakened. The cavitation performance within the 0.5&ndash;1.2 Qd flow rate range, especially within the 0.62&ndash;0.78 Qd and 1.08&ndash;1.20 Qd ranges, was improved. The head and hydraulic efficiency was numerically checked without obvious change. This provided a good reference for optimizing the cavitation or other performances of bladed pumps.

]]>Symmetry doi: 10.3390/sym11010045

Authors: Saddaf Noreen Mohsan Raza Jin-Lin Liu Muhammad Arif

The aim of this paper is to investigate certain properties such as convexity of order &mu; , close-to-convexity of order 1 + &mu; /2 and starlikeness of normalized Mittag&ndash;Leffler function. We use some inequalities to prove our results. We also discuss the close-to-convexity of Mittag&ndash;Leffler functions with respect to certain starlike functions. Furthermore, we find the conditions for the above-mentioned function to belong to the Hardy space H p . Some of our results improve the results in the literature.

]]>Symmetry doi: 10.3390/sym11010044

Authors: Anas Al-Masarwah Abd Ghafur Ahmad

Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as B C K / B C I -algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar ( &alpha; , &beta; ) -fuzzy ideals in B C K / B C I -algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, ( &alpha; , &beta; ) -fuzzy ideals, and bipolar ( &alpha; , &beta; ) -fuzzy ideals in B C K / B C I -algebras. We describe the characterization of m-polar ( &isin; , &isin; &or; q ) -fuzzy ideals in B C K / B C I -algebras by level cut subsets. Moreover, we define m-polar ( &isin; , &isin; &or; q ) -fuzzy commutative ideals and explore some pertinent properties.

]]>Symmetry doi: 10.3390/sym11010043

Authors: Julia Calatayud Gregori Benito M. Chen-Charpentier Juan Carlos Cortés López Marc Jornet Sanz

In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions of the solution stochastic process, and second, to show the capability of our theoretical findings to deal with some important epidemiological models. The approximations are constructed in terms of a polynomial evaluated at the random input parameter, by means of generalized polynomial chaos expansions and the stochastic Galerkin projection technique. The probability density function of the aforementioned univariate polynomial is computed via the random variable transformation method, by taking into account the domains where the polynomial is strictly monotone. The algebraic/exponential convergence of the Galerkin projections gives rapid convergence of these density functions. The examples are based on fundamental epidemiological models formulated via linear and nonlinear differential and difference equations, where one of the input parameters is assumed to be a random variable.

]]>Symmetry doi: 10.3390/sym11010042

Authors: Chih-Fu Wu Wei-Jen Cho Kai-Chieh Lin Fang-Yi Lee

Light-emitting diode (LED) destination indicators mounted on the front of buses enable pedestrians to quickly identify bus numbers. In this study, the factors affecting their legibility were investigated. We aimed to deduce the process of enhancing the legibility of LED destination indicators. Combinations of different text colors, text fonts and information display locations were investigated in this study. Significant differences were observed at the longest visual range when these combinations were used. The optimal information display was obtained using the New Johnston Medium typeface with yellow font color on a black background. For the glare distance, significant differences were observed when different information display locations were used. Superior results were obtained when information was centered. This study is of practical importance to people who depend on public transport, especially those in an emergency. In the future, these results can be used as a guide for designing LED destination indicators that are mounted on the front of public buses.

]]>Symmetry doi: 10.3390/sym11010041

Authors: Xuxin Chen Ping He Zhe Qin Jianye Li Yanping Gong

This paper presents a new statistical damage constitutive model using symmetric normal distribution. The broken rock microbody obeyed symmetric normal distribution and the equivalent strain principle in damage mechanics. The uniaxial compression tests of samples subjected to dry-wet cycles were performed. The damage model was established using the equivalent strain principle and symmetric normal distribution. The damage variable was defined by the elastic modulus under various dry-wet cycles. Parameters of the damage constitutive model were identified using MATLAB software, and the proposed model is verified to be in good agreement with uniaxial compression test results. Fracturing of the rock microbody is well described by symmetric normal distribution, and the proposed statistical damage constitutive model has good adaptability to the uniaxial compression stress-strain curve.

]]>Symmetry doi: 10.3390/sym11010040

Authors: Tahair Rasham Abdullah Shoaib Nawab Hussain Badriah A. S. Alamri Muhammad Arshad

The purpose of this paper is to find out fixed point results for a pair of semi &alpha; * -dominated multivalued mappings fulfilling a generalized locally F-dominated multivalued contractive condition on a closed ball in complete dislocated b-metric space. Some new fixed point results with graphic contractions on closed ball for a pair of multi graph dominated mappings on dislocated b-metric space have been established. An application to the existence of unique common solution of a system of integral equations is presented. 2010 Mathematics Subject Classification: 46Txx, 47H04, 47H10; 54H25.

]]>Symmetry doi: 10.3390/sym11010039

Authors: Kobina Agbodah Adjei Peter Darko

One of the major problems of varied knowledge-based systems has to do with aggregation and fusion. Pang&rsquo;s probabilistic linguistic term sets denotes aggregation of fuzzy information and it has attracted tremendous interest from researchers recently. The purpose of this article is to deal investigating methods of information aggregation under the probabilistic linguistic environment. In this situation we defined certain Einstein operational laws on probabilistic linguistic term elements (PLTESs) based on Einstein product and Einstein sum. Consequently, we develop some probabilistic linguistic aggregation operators, notably the probabilistic linguistic Einstein average (PLEA) operators, probabilistic linguistic Einstein geometric (PLEG) operators, weighted probabilistic linguistic Einstein average (WPLEA) operators, weighted probabilistic linguistic Einstein geometric (WPLEG) operators. These operators extend the weighted averaging operator and the weighted geometric operator for the purpose of aggregating probabilistic linguistic terms values respectively. Einstein t-norm and Einstein t-conorm constitute effective aggregation tools and they allow input arguments to reinforce each other downwardly and upwardly respectively. We then generate various properties of these operators. With the aid of the WPLEA and WPLEG, we originate the approaches for the application of multiple attribute group decision making (MAGDM) with the probabilistic linguistic term sets (PLTSs). Lastly, we apply an illustrative example to elucidate our proposed methods and also validate their potentials.

]]>Symmetry doi: 10.3390/sym11010038

Authors: Salama Nagy Daoud

Edge Even Graceful Labelingwas first defined byElsonbaty and Daoud in 2017. An edge even graceful labeling of a simple graph G with p vertices and q edges is a bijection f from the edges of the graph to the set { 2 , 4 , &hellip; , 2 q } such that, when each vertex is assigned the sum of all edges incident to it mod 2 r where r = max { p , q } , the resulting vertex labels are distinct. In this paper we proved necessary and sufficient conditions for the polar grid graph to be edge even graceful graph.

]]>Symmetry doi: 10.3390/sym11010037

Authors: Sang H. Kang

In large-area wireless sensor networks with hierarchical cluster-based routing protocols, the average number of clusters, k, and the transmission range for the control messages, R, significantly affect the network lifespan. We analyze energy consumption in depth as a function of ( k , R ) , taking into account the energy dissipation of cluster head nodes and the member nodes, separately. To achieve joint optimization of ( k o p t , R o p t ) , we adopt derivative-free Nelder&ndash;Mead Simplex method. Computer simulations have shown that our approach effectively reduces energy consumption of sensor nodes in the process of clustering and data transmission in large-area sensor fields. Our optimization can be applied to existing cluster-based routing schemes to maximize their energy efficiency.

]]>Symmetry doi: 10.3390/sym11010036

Authors: Valerio Faraoni

Fields of spin s &ge; 1 / 2 satisfying wave equations in a curved space obey the Huygens principle under certain conditions clarified by a known theorem. Here, this theorem is generalized to spin zero and applied to an inflaton field in de Sitter-like space, showing that tails of scalar radiation are an unavoidable physical feature. Requiring the absence of tails, on the contrary, necessarily implies an unnatural tuning between cosmological constant, scalar field mass, and coupling constant to the curvature.

]]>Symmetry doi: 10.3390/sym11010035

Authors: Emilio Elizalde

Based on historical facts, revisited from a present-day perspective, and on the documented opinions of the scientists involved in the discovery themselves, strong arguments are given in favor of a proposal to add prominent astronomer Vesto Slipher to the suggested addition of Georges Lema&icirc;tre&rsquo;s name to Hubble&rsquo;s law on the expansion of the universe and thus eventually call it the Hubble&ndash;Lema&icirc;tre&ndash;Slipher (HLS) law.

]]>Symmetry doi: 10.3390/sym11010034

Authors: Jisang Yoo Gyu-cheol Lee

Moving object detection task can be solved by the background subtraction algorithm if the camera is fixed. However, because the background moves, detecting moving objects in a moving car is a difficult problem. There were attempts to detect moving objects using LiDAR or stereo cameras, but when the car moved, the detection rate decreased. We propose a moving object detection algorithm using an object motion reflection model of motion vectors. The proposed method first obtains the disparity map by searching the corresponding region between stereo images. Then, we estimate road by applying v-disparity method to the disparity map. The optical flow is used to acquire the motion vectors of symmetric pixels between adjacent frames where the road has been removed. We designed a probability model of how much the local motion is reflected in the motion vector to determine if the object is moving. We have experimented with the proposed method on two datasets, and confirmed that the proposed method detects moving objects with higher accuracy than other methods.

]]>Symmetry doi: 10.3390/sym11010033

Authors: G. Ignisha Rajathi G. Wiselin Jiji

Chronic liver disease (CLD), which indicates the inflammatory condition of the liver, leads to cirrhosis or even partial or total liver dysfunction when left untreated. A non-invasive approach for evaluating CLD with computed tomography (CT) images is proposed using an ensemble of classifiers. To accurately classify CLD, the hybrid whale optimization algorithm with simulated annealing (WOA-SA) is used in selecting an optimal set of features. The proposed method employs seven sets of features with a total of 73&ndash;3D (three-dimensional) texture features. A hybrid ensemble classifier with support vector machine (SVM), k&mdash;Nearest Neighbor (k-NN), and random forest (RF) classifiers are used to classify liver diseases. Experimental analysis is performed on clinical CT images datasets, which include normal liver, fatty liver, metastasis, cirrhosis, and cancerous samples. The optimal features selected using the WOA-SA improve the accuracy of CLD classification for the five classes of diseases mentioned above. The accuracy of the liver classification using ensemble classifier yields approximately 98% with a 95% confidence interval (CI) of (0.7789, 1.0000) and an error rate of 1.9%. The performance of the proposed method is compared with two existing algorithms and the sensitivity and specificity yield an overall average of 96% and 93%, with 95% confidence interval of (0.7513, 1.0000) and (0.7126, 1.0000), respectively. Classification of CLD based on ensemble classifier illustrates the effectiveness of the proposed method and the comparison analysis demonstrates the superiority of the methodology.

]]>Symmetry doi: 10.3390/sym11010032

Authors: Cho-Young Jung Sang-Lok Yoo

Currently, globalization of the world economy has also resulted in a shipping volume increase. However, this growth in maritime traffic has led to increased risk of marine accidents. These accidents have a higher probability of occurring in regions where geographical features such as islands are present. Further, the positioning of rescue ships in a particular ocean region with a high level of maritime activity is critical for rescue operations. This paper proposes a method for determining an optimal set of locations for stationing rescue ships in an ocean region with numerous accident sites, such as in the Wando islands of South Korea. The computational challenge in this problem is identified as the positioning of numerous islands of varying sizes located in the region. Thus, the proposed method combines a clustering-based optimization method and an image processing approach that incorporates flood filling to calculate the shortest pixel value between two points in the ocean that detours around the islands. Experimental results indicate that the proposed method reduces the distance between rescue ships and each accident site by 5.0 km compared to the original rescue ship locations. Thus, rescue time is reduced.

]]>Symmetry doi: 10.3390/sym11010031

Authors: Min Feng Peide Liu Yushui Geng

Aiming at multiple attribute group decision making (MAGDM) problems, especially the attribute values of 2-tuple linguistic numbers and the interrelationships between each attribute needing to be considered, this paper proposes a new method of analysis. Firstly, we developed a few new aggregation operators, like the 2-tuple linguistic dependent weighted Maclaurin symmetric mean (2TLDWMSM) operator, the 2-tuple linguistic dependent weighted generalized Maclaurin symmetric mean (2TLDWGMSM) operator, and the 2-tuple linguistic dependent weighted geometric Maclaurin symmetric mean (2TLDWGeoMSM) operator. In the above operators, Maclaurin symmetric mean (MSM) operators can take the relationships between each attribute into account and dependent operators can mitigate the unfair parameters&rsquo; impact on the overall outcome, in which those &lsquo;&lsquo;incorrect&rsquo;&rsquo; and &lsquo;&lsquo;prejudiced&rsquo;&rsquo; parameters are distributed with low weights. Next, a method used by the 2TLDWMSM, 2TLDWGMSM, and 2TLDWGeoMSM operators for MAGDM is introduced. Finally, there is an explanative example to confirm the proposed approach and explain its availability and usefulness.

]]>Symmetry doi: 10.3390/sym11010030

Authors: Jie Hua Mao Lin Huang Weidong Huang Chenglin Zhao

Graphs are often used to model data with a relational structure and graphs are usually visualised into node-link diagrams for a better understanding of the underlying data. Node-link diagrams represent not only data entries in a graph, but also the relations among the data entries. Further, many graph drawing algorithms and graph centrality metrics have been successfully applied in visual analytics of various graph datasets, yet little attention has been paid to analytics of scientific standard data. This study attempts to adopt graph drawing methods (force-directed algorithms) to visualise scientific standard data and provide information with importance &lsquo;ranking&rsquo; based on graph centrality metrics such as Weighted Degree, PageRank, Eigenvector, Betweenness and Closeness factors. The outcomes show that our method can produce clear graph layouts of scientific standard for visual analytics, along with the importance &lsquo;ranking&rsquo; factors (represent via node colour, size etc.). Our method may assist users with tracking various relationships while understanding scientific standards with fewer relation issues (missing/wrong connection etc.) through focusing on higher priority standards.

]]>Symmetry doi: 10.3390/sym11010029

Authors: Qiang Guo Zhenwu Li Wenming Song Wenyu Fu

The conventional dynamic programming-based track-before-detect (DP-TBD) methods are usually intractable in multi-target scenarios. The adjacent targets may interfere with each other, and the computational complexity is increased with the number of targets. In this paper, a DP-TBD method using parallel computing (PC-DP-TBD) is proposed to solve the above problems. The search region of the proposed PC-DP-TBD is divided into several parts according to the possible target movement direction. The energy integration is carried out independently and parallel in each part. This contributes to reducing the computational complexity in each part, since the divided search region is smaller than the whole one. In addition, the target energy can only be integrated adequately in the part in which the search direction matches the target movement. This is beneficial to improve the ability to detect the targets with various movement directions in different parts with different search directions. The solution to the problem of the adjacent targets interfering with each other is discussed. The procedure of the parallel computing in the proposed PC-DP-TBD is presented in detail. Simulations are conducted to verify the superiority of the proposed PC-DP-TBD in terms of detection probability and computational complexity.

]]>Symmetry doi: 10.3390/sym11010028

Authors: Djalel Bounekhel Messaoud Bounkhel Mostafa Bachar

We prove an existence result, in the separable Banach spaces setting, for second order differential inclusions of type sweeping process. This type of differential inclusion is defined in terms of normal cones and it covers many dynamic quasi-variational inequalities. In the present paper, we prove in the nonconvex case an existence result of this type of differential inclusions when the separable Banach space is assumed to be q-uniformly convex and 2-uniformly smooth. In our proofs we use recent results on uniformly generalized prox-regular sets. Part of the novelty of the paper is the use of the usual Lipschitz continuity of the set-valued mapping which is very easy to verify contrarily to the ones used in the previous works. An example is stated at the end of the paper, showing the application of our existence result.

]]>Symmetry doi: 10.3390/sym11010027

Authors: Juling Zhang Guowu Yang William N. N. Hung Jinzhao Wu Yixin Zhu

In this paper, we address an NPN Boolean matching algorithm. The proposed structural difference signature (SDS) of a Boolean function significantly reduces the search space in the Boolean matching process. The paper analyses the size of the search space from three perspectives: the total number of possible transformations, the number of candidate transformations and the number of decompositions. We test the search space and run time on a large number of randomly generated circuits and Microelectronics Center of North Carolina (MCNC) benchmark circuits with 7&ndash;22 inputs. The experimental results show that the search space of Boolean matching is greatly reduced and the matching speed is obviously accelerated.

]]>Symmetry doi: 10.3390/sym11010026

Authors: José Domingo Villarroel María Merino Álvaro Antón

Young children love drawing; this is without question. Besides that, drawings are also of interest to scholars and educators, since they seem to provide food for thought regarding children&rsquo;s conceptual development during their early education. Different approaches are taken when it comes to analysing children&rsquo;s drawings but insufficient attention has been given to the issue of the spontaneous depictions of symmetrical motifs in young children&rsquo;s drawings. This pictorial phenomena might not go unnoticed by parents and teachers but the fact is that the scientific community has no reliable data regarding how children under 8 naturally draw symmetrical patterns to express themselves graphically. Accordingly, the present study analyses 116 drawings undertaken by children between 4 and 7 on a well-known natural issue in early childhood such as plant life. Pictorial motifs displaying both cyclic and dihedral symmetries were found in the pictorial sample under examination and the data gathered is put in perspective with the gender and educational level variables. The results of the study show that symmetry, particularly, dihedral symmetry, is a very common pictorial practice in the sample and, also, that the occurrence of symmetrical motifs displays a relationship with the independent variables considered in the study.

]]>Symmetry doi: 10.3390/sym11010025

Authors: Qiao Cheng Xiangke Wang Yifeng Niu Lincheng Shen

Transfer Learning (TL) has received a great deal of attention because of its ability to speed up Reinforcement Learning (RL) by reusing learned knowledge from other tasks. This paper proposes a new transfer learning framework, referred to as Transfer Learning via Artificial Neural Network Approximator (TL-ANNA). It builds an Artificial Neural Network (ANN) transfer approximator to transfer the related knowledge from the source task into the target task and reuses the transferred knowledge with a Probabilistic Policy Reuse (PPR) scheme. Specifically, the transfer approximator maps the state of the target task symmetrically to states of the source task with a certain mapping rule, and activates the related knowledge (components of the action-value function) of the source task as the input of the ANNs; it then predicts the quality of the actions in the target task with the ANNs. The target learner uses the PPR scheme to bias the RL with the suggested action from the transfer approximator. In this way, the transfer approximator builds a symmetric knowledge path between the target task and the source task. In addition, two mapping rules for the transfer approximator are designed, namely, Full Mapping Rule and Group Mapping Rule. Experiments performed on the RoboCup soccer Keepaway task verified that the proposed transfer learning methods outperform two other transfer learning methods in both jumpstart and time to threshold metrics and are more robust to the quality of source knowledge. In addition, the TL-ANNA with the group mapping rule exhibits slightly worse performance than the one with the full mapping rule, but with less computation and space cost when appropriate grouping method is used.

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