Concept Of Symmetry Research Articles

Performance Improvement of Mechanically Beam-Steerable Transmitarray Antennas by Using Offset Unifocal Phase Symmetry

This communication presents the concept of offset unifocal phase symmetry to improve the performance (gain, gain roll-off, sidelobe level, etc.,) of mechanically beam-steerable transmitarray (TA) antennas. The phase shifts are initially determined from an offset feed source to make the corresponding TA antenna radiate a tilted beam with high gain. The phase shifts are asymmetric and can be broadly divided into dominant and ordinary phase shifts with respect to the offset feed source. By mirroring the dominant phase shifts to make the phase shifts symmetric, it can enable symmetric radiation beams for symmetric offset feed sources and improve phase error. When the offset feed source is moving inward to steer the main beam, the phase error of the phase-shifting surface with respect to the feed source starts to occur, while the electric-field spillover/illumination from the feed source is improved, which can maintain the gains of scanning beams. To verify the validity of the concept, the performance of a beam-steerable TA antenna enabled by the offset unifocal phase symmetry has been simulated and compared with the counterparts of unifocal and bifocal beam-steerable TA antennas. The measured results agree well with the simulated ones, revealing that the beam-steerable TA antenna enabled by the offset unifocal phase symmetry can maintain realized gains of scanning beams, suppress sidelobe levels, and reduce gain roll-off within the beam-scanning coverage. The offset unifocal phase symmetry, in principle, is a generalized approach and applicable to reflectarray antennas to improve the beam-steerable performance as well.

A szimmetria jelenléte Silviu Purcărete előadásaiban

The Greek word symmetry means correct proportion. The basis for this study is the interesting fact according to which symmetry has been known to be the father of boredom in the theatre at least since Meiningenism. To describe a work of art as symmetrical is to say that the bisector axis divides the whole into two exactly corresponding parts. This articulation expresses immobility and constancy, and evokes a sense of these in the viewer, or in the listener in the case of a poem, theatre or music performance. Therefore, the more or less regular use of symmetry today seems a kind of reminiscence of a hundred years ago. In contrast, Silviu Purcărete – whom Lehmann classifies as a post-dramatic director, and who, according to other opinions, can be considered a fully 21st-century director – is a keen user of symmetry in his performances. We will first briefly discuss the concept of symmetry. This will be followed by examples of symmetry from three theatre performances by Silviu Purcărete. Finally, some reflections are presented on the use of symmetry in Silviu Purcărete’s case.

A VVC Video Steganography Based on Coding Units in Chroma Components with a Deep Learning Network

Versatile Video Coding (VVC) is the latest video coding standard, but currently, most steganographic algorithms are based on High-Efficiency Video Coding (HEVC). The concept of symmetry is often adopted in deep neural networks. With the rapid rise of new multimedia, video steganography shows great research potential. This paper proposes a VVC steganographic algorithm based on Coding Units (CUs). Considering the novel techniques in VVC, the proposed steganography only uses chroma CUs to embed secret information. Based on modifying the partition modes of chroma CUs, we propose four different embedding levels to satisfy the different needs of visual quality, capacity and video bitrate. In order to reduce the bitrate of stego-videos and improve the distortion caused by modifying them, we propose a novel convolutional neural network (CNN) as an additional in-loop filter in the VVC codec to achieve better restoration. Furthermore, the proposed steganography algorithm based on chroma components has an advantage in resisting most of the video steganalysis algorithms, since few VVC steganalysis algorithms have been proposed thus far and most HEVC steganalysis algorithms are based on the luminance component. Experimental results show that the proposed VVC steganography algorithm achieves excellent performance on visual quality, bitrate cost and capacity.

Cosmic strings from pure Yang–Mills theory

We discuss the formation of cosmic strings or macroscopic color flux tubes at the phase transition from the deconfinement to confinement phase in pure Yang--Mills (YM) theory, such as $\mathrm{SU}(N)$, $\mathrm{Sp}(N)$, $\mathrm{SO}(N)$, and $\text{Spin}(N)$, based on the current understanding of theoretical physics. According to the holographic dual descriptions, the cosmic strings are dual to fundamental strings or wrapped D-branes in the gravity side depending on the structure of the gauge group, and the reconnection probability is suppressed by $\mathcal{O}({N}^{\ensuremath{-}2})$ and ${e}^{\ensuremath{-}\mathcal{O}(N)}$, respectively. The pure YM theory thus provides a simple realization of cosmic F- and D-strings without the need for a brane-inflationary scenario or extra dimension. We also review the stability of cosmic strings based on the concept of 1-form symmetry, which further implies the existence of a baryon vertex in some YM theory. We calculate the gravitational wave spectrum that is emitted from the cosmic strings based on an extended velocity-dependent one-scale model and discuss its detectability based on ongoing and planned gravitational-wave experiments. In particular, the SKA and LISA can observe gravitational signals if the confinement scale is higher than $\mathcal{O}({10}^{12})\text{ }\text{ }\mathrm{GeV}$ and $\mathcal{O}({10}^{10})\text{ }\text{ }\mathrm{GeV}$ for $\mathrm{SU}(N)$ with $N=\mathcal{O}(1)$, respectively.

Lie symmetries of nonlinear systems with unknown inputs

It has been revealed that a dynamical system being unobservable or unidentifiable for a given set of observations is fundamentally related to the existence of Lie symmetries. Lie symmetries thus have the potentiality of providing useful tools to analyze and improve the observability and identifiability properties of dynamical systems from a fundamental perspective. This work proposes a computational framework for finding general Lie symmetries of nonlinear systems in the presence of unknown inputs. The occurring framework does not rely on mathematical Ansatz as the typical setting in the existing methods, and it is therefore capable of computing all the groups of Lie symmetries admitted by the system of interest. To alleviate the computation burden of the general framework, an alternative method is developed which is based on a priori assumptions on the functional forms of Lie symmetries to be calculated. The two proposed computation methods can be used as complementary tools to handle real engineering systems efficiently and robustly. Furthermore, utilization of the calculated Lie symmetries to detect and improve observability properties (with identifiability being the observability of unknown model parameters) is systematically discussed. Effective strategies of changing sensor placement, transforming system model and adding model assumptions are introduced to improve observability, and optimally render an unobservable system observable. The concept, computation and application of Lie symmetries are illustrated through several examples of linear, nonlinear and non-smooth dynamical systems.

Cooperative Multi-Objective Control of Heterogeneous Vehicle Platoons on Highway with Varying Slopes

Stability, vehicle safety, energy saving, and passenger comfort are the major objectives of vehicle platooning control. These objectives are coupled, interrelated, and even conflicting, so integrated optimization of multiple objectives is quite challenging. Particularly for heterogeneous platoons, the difficulties are intensified for the differences in vehicle dynamics. In this paper, the concept of symmetry is utilized in the platooning control, that is, the design method of each vehicle’s controller is the same. For each controller, it is to solve the optimal solution of multi-objective collaborative optimization. The concept of asymmetry is meanwhile embodied in the parameter setting of each controller, for the vehicle heterogeneity. The contents of this study are as follows. First, a mathematical model is established, in which the differences in vehicle dynamic characteristics of heterogeneous platoon, road slope, and aerodynamics are all taken into account. Then, based on distributed nonlinear model predictive control (DNMPC) method, multi-objective control strategies are proposed for the leader and followers, cooperatively. Furthermore, a weight coefficient optimization method is presented, to further improve the platoon’s multi-objective synthesis performance. Finally, comparative experiments are carried out. Results demonstrate that, compared with the classic cruise control method of vehicle platoons, the proposed approach can reduce energy consumption by more than 5% and improve tracking performance on the premise of passenger comfort. Real-road experiments verify that the proposed control system can function effectively and satisfy the computational requirements in real applications.

Nonlinear Radiative Nanofluidic Hydrothermal Unsteady Bidirectional Transport with Thermal/Mass Convection Aspects

The collective effect of thermal and mass convection along with the significance of thermal radiation, heat source/sink, and magneto-nanofluid are considered. A bi-directional stretching device is used to generate the symmetry of the flowing structure. Nonlinear behavior of thermal radiation is considered here. The magnetic field is considered non-uniform and vertically upward. Significances of pedesis motion and Ludwig–Soret are also revealed in an innovative way with heat source/sink effects. The concept of symmetry is used to transmute the transport equations from PDE type to nonlinear ODE type. We solved the transformed setup numerically by adopting Keller-box method criteria with the targeted accuracy rate. Graphical interpretations are explored with code verification. It is important to conclude that friction coefficients decline for incremental values of stretching parameter (0.1≤α≤0.9), magnetic field (0.3≤M≤0.9), and unsteady parameter (0.2≤Λ≤0.9) along with the bidirectional velocity components, and the rate of heat transmission rises with temperature ratio (1.3≤Γ≤1.7) and temperature Biot number (0.3≤BiT≤0.9) amplification. Moreso, the rate of mass transfer is enhanced with growing values of pedesis motion (0.2≤Nb≤0.6), unsteady parameter and concentration Biot number (0.3≤BiC≤0.9) with opposite effect when the Ludwig–Soret parameter (0.3≤Nt≤0.6) is boosted.

Formula omitted]-symmetries of distributions and integrability

An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. It is based on a generalization of the concept of symmetry of a distribution of vector fields, inspired in the extension of Lie point symmetries to C∞-symmetries for ODEs developed in the recent years. The new structures, named C∞-structures, play a fundamental role in the integrability of the distribution: the knowledge of a C∞-structure for a corank k involutive distribution allows to find its integral manifolds by solving k successive completely integrable Pfaffian equations. These results have important consequences for the integrability of differential equations. In particular, we derive a new procedure to integrate an mth-order ordinary differential equation by splitting the problem into m completely integrable Pfaffian equations. This step-by-step integration procedure is applied to fully integrate several equations that cannot be solved by standard procedures.

A Particle Swarm Optimization Method for AI Stream Scheduling in Edge Environments

With the development of IoT and 5G technologies, edge computing has become a key driver for providing compute, network and storage services. The dramatic increase in data size and the complexity of AI computation models have put higher demands on the performance of edge computing. Rational and optimal scheduling of AI data-intensive computation tasks can greatly improve the overall performance of edge computing. To this end, a particle swarm algorithm based on objective ranking is proposed to optimize task execution time and scheduling cost by designing a task scheduling model to achieve task scheduling in an edge computing environment. It is necessary to fully understand the concept of symmetry of resource utilization and task execution cost indicators. The method utilizes nonlinear inertia weights and shrinkage factor update mechanisms to improve the optimization-seeking ability and convergence speed of the particle-to-task scheduling solution space. The task execution time and scheduling cost are greatly reduced. Simulation experiments are conducted using the Cloudsim toolkit to experimentally compare the proposed algorithm TS-MOPSO with three other particle swarm improvement algorithms, and the experimental results show that the task execution time, maximum completion time and total task scheduling cost are reduced by 31.6%, 23.1% and 16.6%, respectively. The method is suitable for handling large and complex AI data-intensive task scheduling optimization efforts.

Koopman and Perron-Frobenius operators on reproducing kernel Banach spaces.

Koopman and Perron-Frobenius operators for dynamical systems are becoming popular in a number of fields in science recently. Properties of the Koopman operator essentially depend on the choice of function spaces where it acts. Particularly, the case of reproducing kernel Hilbert spaces (RKHSs) is drawing increasing attention in data science. In this paper, we give a general framework for Koopman and Perron-Frobenius operators on reproducing kernel Banach spaces (RKBSs). More precisely, we extend basic known properties of these operators from RKHSs to RKBSs and state new results, including symmetry and sparsity concepts, on these operators on RKBS for discrete and continuous time systems.

An In-depth Analysis of Symmetries and their Implications in Physics

The concept of symmetry is essential in understanding classical and quantum physics. Symmetry describes a system that remains unchanged in structure and behavior after undergoing a transformation. In this paper, I will describe the implications of symmetries (global and gauge) in Newton’s laws of mechanics, Maxwell’s electromagnetism equations, and quantum particle physics – in particular the Higgs mechanism – with the help of Noether’s Theorem. Purely based on symmetrical elements, this paper will then determine the isospin composition of pions given certain restraints. This solution will connect findings in preceding theories to current and future studies relevant to the subject of symmetry in physics.

Design of Chaotic Interleaver Based on Duffing Map for Turbo Code

This article presents the performance analysis and comparison of turbo codes for several interleavers with short blockchains. According to the symmetry concept, turbo codes consist of two symmetric convolutional codes preceded by an interleaver. Some interleavers can be described by symmetric 3 × 3 generator matrices, whereas others are represented through symmetric matrices in which the nonzero terms in the matrix are monomials. Interest in short blockchains has grown over the years because of their use in emerging applications that require the transmission of data units in the order of hundred bits. In this research, interleavers used are random interleaver, semi-random interleaver, quadratic polynomial permutation (QPP) interleaver, and chaotic Lozi map interleaver. For each interleaver, the turbo code is assessed with at least two short data distances; then, the interleavers are compared against each other. The performance of turbo codes is assessed based on bit error rate, particularly with lengths between 64 and 512 bits. Additionally, an interleaver based on Duffing chaotic maps is proposed, whose deterministic nature provides an advantage, and the performance results are presented, achieving excellent BER values for 64 bits. With these results, the effect of the interleaver on turbo codes and particularly on short block length interleavers, is studied.

Perturbed Mixed Variational-like Inequalities and Auxiliary Principle Pertaining to a Fuzzy Environment

Convex and non-convex fuzzy mappings are well known to be important in the research of fuzzy optimization. Symmetry and the idea of convexity are closely related. Therefore, the concept of symmetry and convexity is important in the discussion of inequalities because of how its definition behaves. This study aims to consider new class of generalized fuzzy variational-like inequality for fuzzy mapping which is known as perturbed fuzzy mixed variational-like inequality. We also introduce strongly fuzzy mixed variational inequality, as a particular case of perturbed fuzzy mixed variational-like inequality which is also a new one. Furthermore, by using the generalized auxiliary principle technique and some new analytic techniques, some existence results and efficient numerical techniques of perturbed fuzzy mixed variational-like inequality are established. As exceptional cases, some known and new results are obtained. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

Acceleration of structural topology optimization using symmetric element-by-element strategy for unstructured meshes on GPU

PurposeStructural topology optimization is computationally expensive due to the involvement of high-resolution mesh and repetitive use of finite element analysis (FEA) for computing the structural response. Since FEA consumes most of the computational time in each optimization iteration, a novel GPU-based parallel strategy for FEA is presented and applied to the large-scale structural topology optimization of 3D continuum structures.Design/methodology/approachA matrix-free solver based on preconditioned conjugate gradient (PCG) method is proposed to minimize the computational time associated with solution of linear system of equations in FEA. The proposed solver uses an innovative strategy to utilize only symmetric half of elemental stiffness matrices for implementation of the element-by-element matrix-free solver on GPU.FindingsUsing solid isotropic material with penalization (SIMP) method, the proposed matrix-free solver is tested over three 3D structural optimization problems that are discretized using all hexahedral structured and unstructured meshes. Results show that the proposed strategy demonstrates 3.1× –3.3× speedup for the FEA solver stage and overall speedup of 2.9× –3.3× over the standard element-by-element strategy on the GPU. Moreover, the proposed strategy requires almost 1.8× less GPU memory than the standard element-by-element strategy.Originality/valueThe proposed GPU-based matrix-free element-by-element solver takes a more general approach to the symmetry concept than previous works. It stores only symmetric half of the elemental matrices in memory and performs matrix-free sparse matrix-vector multiplication (SpMV) without any inter-thread communication. A customized data storage format is also proposed to store and access only symmetric half of elemental stiffness matrices for coalesced read and write operations on GPU over the unstructured mesh.

Ethnomatematics of geometry shape in the Gedongsongo Temple

The objective of the study is to explore and find out the ethnomathematics of Gedongsongo Temple, located in Central Java, Indoensia. The type of study is qualitative with an exploration way and ethnographic approach. The data obtained in the form of qualitative data, the source of research data obtained through observation, interviews, documentation, and study of literature related to Gedongsongo Temple. The data collection technique was done by questioning, observing, interviewing, and documenting. The results showed that the ethnomathematics of Gedongsongo Temple has the potential to be integrated into mathematics learning. Ethnomathematics that can be integrated includes the concept of flat area, volume of space, comparison/ratio, reflection, and symmetry. The flat-geometry concept is found in the several parts of Gedongsongo Temple including square, rectangle, triangle, and trapezoid. The spatial-geometry concept is also found in several parts of Gedongsongo Temple including cubes, blocks, tubes, and a triangle prism. Meanwhile, the comparison/ratio concept found is the Golden Ratio on the fore-temple of Perwara in the area of Candi Gedong III. The symmetry and reflection concept is found in Candi Gedong I. These concepts can be applied in mathematics learning as a contextual geometry problem as well as a way of introducing cultural elements to students.

The Symmetry Effect: Symmetrical Shapes Increase Consumer’s Health Perception of Food

Focusing on the physical appearance of the food itself, and limiting the focus on shape to the concept of symmetry, this research investigated how food shape influences consumer perceptions of healthiness and naturalness and their subsequent food preferences. By conducting three empirical studies involving self-reported preference and trade-off choices, this research verified that it is a two-staged process of naturalness and healthiness that mediates the main effect of symmetry on foods preference. Furthermore, the incremental perceived unhealthiness of food would mitigate the positive effect of food symmetry. These findings are meaningful for food marketing managers and policymakers when making food-related decisions.

Dynamics of a Novel IVRD Pandemic Model of a Large Population over a Long Time with Efficient Numerical Methods

The model of any epidemic illness is evolved from the current susceptibility. We aim to construct a model, based on the literature, different to the conventional examinations in epidemiology, i.e., what will occur depends on the susceptible cases, which is not always the case; one must consider a model with aspects such as infections, recoveries, deaths, and vaccinated populations. Much of this information may not be available. So without artificially assuming the unknown aspects, we frame a new model known as IVRD. Apart from qualitative evaluation, numerical evaluation has been completed to aid the results. A novel approach of calculating the fundamental reproduction/transmission range is presented, with a view to estimating the largest number of aspects possible, with minimal restrictions on the spread of any disease. An additional novel aspect of this model is that we include vaccines with the actively infected cases, which is not common. A few infections such as rabies, ebola, etc., can apply this model. In general, the concept of symmetry or asymmetry will exist in every epidemic model. This model and method can be applied in scientific research in the fields of epidemic modeling, the medical sciences, virology, and other areas, particularly concerning rabies, ebola, and similar diseases, to show how immunity develops after being infected by these viruses.

Simulation Tool to Evaluate Fault Diagnosis Techniques for DC-DC Converters

This paper presents a tool that evaluates the applicability of a fault diagnostics technique (FDT) for Switch-Mode Non-Isolated DC-DC converters (SMNI DC-DC). The proposed tool simulates the operation of a Type II controller for a buck converter under different operating conditions and, simultaneously, implements the FDT. In this way, it is possible to evaluate the applicability of the FDT in real-time. The proposed tool is implemented in Python, and requires the partitioning of the code into different modules. The first module is responsible for modeling the different states of the converter. The second module contributes to the production of the PWM signal. The concepts of symmetry and asymmetry are implicit to the signal processing methods used in the design of the FDTs that compose the third module. Finally, all of the modules are properly included in the main function, which represents the fourth module. The validation of the proposed tool is carried out by comparing the results with the LTspice simulator and with an experimental prototype built for this purpose. Different operating conditions are considered. In addition to the proposed tool, an algorithm for the design of both the power section and the converter compensator is presented.

Introduction to the special issue on symmetry in the life sciences - symmetry and asymmetry across biological scales.

In this special issue of Emerging Topics in Life Sciences, we present a series of mini-reviews of some of the most exciting research involving the concept of symmetry. This research spans the biological sciences from proteins to ecosystems. The reviews examine protein and floral symmetry, primate brain and behavioral asymmetries, geometric morphometrics, and various fluctuating asymmetries.

Soft Sensing and Multi-objective Optimization of Pulp Washing Process Based on Data-Driven Technology

Due to the multi-variable, time-delay, and nonlinear characteristics of the pulp washing process, it is difficult to accurately measure and optimize the process. An asymmetrical nonlinear control system can be decomposed into a group of low-dimensional subsystems, which brings great convenience to the analysis and design of the system. In this paper, the concept of symmetry is used to simplify nonlinear optimal control problems, and data-driven theory is used to solve optimal policy problems. This paper proposes a data-driven operating model optimization method to model and optimizes the pulp washing process. The most important quality indicators of pulp washing performance are the alkali residue in washing pulp and the Baumé degree of the extracted black liquor. Considering the difficulty of modeling, online measurement of these indicators, two-step neural network, and multiple logistic regression were used to build a prediction model for soda water and Baumé degree. The mathematical model of the washing process can be identified, and the indicators meet the production requirements. With the goal of better product quality, low cost, and low energy consumption, based on the optimized operation mode database, the ant colony optimization (ACO) algorithm was used to solve the multi-objective problem. Theoretical analysis and practical application were carried out, and the optimal control system of the pulp washing process was designed. The actual results showed that the pulp output was increased by 20%, and the water consumption was reduced by nearly 30%. This method is effective during pulp washing.