Symmetry

Jones, Ethan R.;Chinthammit, Winyu;Huang, Weidong;Engelke, Ulrich;Lueg, Christopher

doi: 10.3390/sym10120680pmid: N/A

Control of robot arms is often required in engineering and can be performed by using different methods. This study examined and symmetrically compared the use of a controller, eye gaze tracker and a combination thereof in a multimodal setup for control of a robot arm. Tasks of different complexities were defined and twenty participants completed an experiment using these interaction modalities to solve the tasks. More specifically, there were three tasks: the first was to navigate a chess piece from a square to another pre-specified square; the second was the same as the first task, but required more moves to complete; and the third task was to move multiple pieces to reach a solution to a pre-defined arrangement of the pieces. Further, while gaze control has the potential to be more intuitive than a hand controller, it suffers from limitations with regard to spatial accuracy and target selection. The multimodal setup aimed to mitigate the weaknesses of the eye gaze tracker, creating a superior system without simply relying on the controller. The experiment shows that the multimodal setup improves performance over the eye gaze tracker alone ( p < 0.05 ) and was competitive with the controller only setup, although did not outperform it ( p > 0.05 ).

Yeom, Chan-Uk;Kwak, Keun-Chang

doi: 10.3390/sym10120700pmid: N/A

In this paper, we compare the predictive performance of the adaptive neuro-fuzzy inference system (ANFIS) models according to the input space segmentation method. The ANFIS model can be divided into four types according to the method of dividing the input space. In general, the ANFIS1 model using grid partitioning method, ANFIS2 model using subtractive clustering (SC) method, and the ANFIS3 model using fuzzy C-means (FCM) clustering method exist. In this paper, we propose the ANFIS4 model using a context-based fuzzy C-means (CFCM) clustering method. Context-based fuzzy C-means clustering is a clustering method that considers the characteristics of the output space as well as the input space. Here, the symmetric Gaussian membership functions are obtained by the clusters produced from each context in the design of the ANFIS4. In order to evaluate the performance of the ANFIS models according to the input space segmentation method, a prediction experiment was conducted using the combined cycle power plant (CCPP) data and the auto-MPG (miles per gallon) data. As a result of the prediction experiment, we confirmed that the ANFIS4 model using the proposed input space segmentation method shows better prediction performance than the ANFIS model (ANFIS1, ANFIS2, ANFIS3) using the existing input space segmentation method.

Asawasamrit, Suphawat;Ntouyas, Sotiris K.;Tariboon, Jessada;Nithiarayaphaks, Woraphak

doi: 10.3390/sym10120701pmid: N/A

This paper studies the existence and uniqueness of solutions for a new coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions, which include as special cases the well-known symmetric boundary conditions. Banach’s contraction principle, Leray–Schauder’s alternative, and Krasnoselskii’s fixed-point theorem were used to derive the desired results, which are well-illustrated with examples.

Wang, Jingqian;Zhang, Xiaohong

doi: 10.3390/sym10120710pmid: N/A

In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented. Firstly, the notion of SVN β -covering approximation space is proposed, and some concepts and properties in it are investigated. Secondly, based on SVN β -covering approximation spaces, two types of SVN covering rough set models are proposed. Then, some properties and the matrix representations of the newly defined SVN covering approximation operators are investigated. Finally, we propose a novel method to decision making (DM) problems based on one of the SVN covering rough set models. Moreover, the proposed DM method is compared with other methods in an example.

Kwun, Young Chel;Nizami, Abdul Rauf;Munir, Mobeen;Iqbal, Zaffar;Arshad, Dishya;Min Kang, Shin

doi: 10.3390/sym10120720pmid: N/A

Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article we give some Khovanov homology groups of 3-strand braid links Δ 2 k + 1 = x 1 2 k + 2 x 2 x 1 2 x 2 2 x 1 2 ⋯ x 2 2 x 1 2 x 1 2 , Δ 2 k + 1 x 2 , and Δ 2 k + 1 x 1 , where Δ is the Garside element x 1 x 2 x 1 , and which are three out of all six classes of the general braid x 1 x 2 x 1 x 2 ⋯ with n factors.

Ge, Mingtao;Wang, Jie;Xu, Yicun;Zhang, Fangfang;Bai, Ke;Ren, Xiangyang

doi: 10.3390/sym10120730pmid: N/A

Because of the cyclic symmetric structure of rolling bearings, its vibration signals are regular when the rolling bearing is working in a normal state. But when the rolling bearing fails, whether the outer race fault or the inner race fault, the symmetry of the rolling bearing is broken and the fault destroys the rolling bearing’s stable working state. Whenever the bearing passes through the fault point, it will send out vibration signals representing the fault characteristics. These signals are often non-linear, non-stationary, and full of Gaussian noise which are quite different from normal signals. According to this, the sub-modal obtained by empirical wavelet transform (EWT), secondary decomposition is tested by the Gaussian distribution hypothesis test. It is regarded that sub-modal following Gaussian distribution is Gaussian noise which is filtered during signal reconstruction. Then by taking advantage of the ambiguity function superiority in non-stationary signal processing and combining correlation coefficient, an ambiguity correlation classifier is constructed. After training, the classifier can recognize vibration signals of rolling bearings under different working conditions, so that the purpose of identifying rolling bearing faults can be achieved. Finally, the method effect was verified by experiments.

Ansari, Khursheed J.;Ahmad, Ishfaq;Mursaleen, M.;Hussain, Iqtadar

doi: 10.3390/sym10120731pmid: N/A

In this article, we propose a different generalization of ( p , q ) -BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where ( p , q ) -integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators.

Frasnelli, Elisa;Vallortigara, Giorgio

doi: 10.3390/sym10120739pmid: N/A

Lateralization, i.e., the different functional roles played by the left and right sides of the brain, is expressed in two main ways: (1) in single individuals, regardless of a common direction (bias) in the population (aka individual-level lateralization); or (2) in single individuals and in the same direction in most of them, so that the population is biased (aka population-level lateralization). Indeed, lateralization often occurs at the population-level, with 60–90% of individuals showing the same direction (right or left) of bias, depending on species and tasks. It is usually maintained that lateralization can increase the brain’s efficiency. However, this may explain individual-level lateralization, but not population-level lateralization, for individual brain efficiency is unrelated to the direction of the asymmetry in other individuals. From a theoretical point of view, a possible explanation for population-level lateralization is that it may reflect an evolutionarily stable strategy (ESS) that can develop when individually asymmetrical organisms are under specific selective pressures to coordinate their behavior with that of other asymmetrical organisms. This prediction has been sometimes misunderstood as it is equated with the idea that population-level lateralization should only be present in social species. However, population-level asymmetries have been observed in aggressive and mating displays in so-called “solitary” insects, suggesting that engagement in specific inter-individual interactions rather than “sociality” per se may promote population-level lateralization. Here, we clarify that the nature of inter-individuals interaction can generate evolutionarily stable strategies of lateralization at the individual- or population-level, depending on ecological contexts, showing that individual-level and population-level lateralization should be considered as two aspects of the same continuum.

Preda, Stefan;Oprea, Simona-Vasilica;Bâra, Adela;Belciu (Velicanu), Anda

doi: 10.3390/sym10120748pmid: N/A

Renewable energy systems (RES) are reliable by nature; the sun and wind are theoretically endless resources. From the beginnings of the power systems, the concern was to know “how much” energy will be generated. Initially, there were voltmeters and power meters; nowadays, there are much more advanced solar controllers, with small displays and built-in modules that handle big data. Usually, large photovoltaic (PV)-battery systems have sophisticated energy management strategies in order to operate unattended. By adding the information collected by sensors managed with powerful technologies such as big data and analytics, the system is able to efficiently react to environmental factors and respond to consumers’ requirements in real time. According to the weather parameters, the output of PV could be symmetric, supplying an asymmetric electricity demand. Thus, a smart adaptive switching module that includes a forecasting component is proposed to improve the symmetry between the PV output and daily load curve. A scaling approach for smaller off-grid systems that provides an accurate forecast of the PV output based on data collected from sensors is developed. The proposed methodology is based on sensor implementation in RES operation and big data technologies are considered for data processing and analytics. In this respect, we analyze data captured from loggers and forecast the PV output with Support Vector Machine (SVM) and linear regression, finding that Root Mean Square Error (RMSE) for prediction is considerably improved when using more parameters in the machine learning process.

Zhang, Xiujun;Wu, Xinling;Akhter, Shehnaz;Jamil, Muhammad Kamran;Liu, Jia-Bao;Farahani, Mohammad Reza

doi: 10.3390/sym10120751pmid: N/A

Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we propose a definition of generalized bridge molecular graphs that can model more kinds of long chain polymerization products than the bridge molecular graphs, and provide some results of the edge versions of atom-bond connectivity ( A B C e ) and geometric arithmetic ( G A e ) indices for some generalized bridge molecular graphs, which have regular, periodic and symmetrical structures. The results of this paper offer promising prospects in the applications for chemical and material engineering, especially in chemical industry research.