Symmetry

Vibrating technological equipment for the introduction of piles and columns into the ground of construction foundations (named vibratory piling machines) is crucial in the process of building stable and resilient foundations for civil engineering, hydrotechnical construction, special construction (e.g., military constructions), bridges, roads and industrial platforms. During the works carried out by the construction companies in various geographical areas of Romania, particularities of the dynamic technological regimes influenced by the nature of the land were identified at the deep introduction of the construction elements in the form of piles or circular (tubular) columns. The results of applied research, rheological modeling and optimization of vibrating equipment, highlight the need for an analytical approach that takes into account the parametric variations of the elastic and damping characteristics of some categories of soils on the depth of piles or foundation columns. In this context, the paper presents the calculation model with the dynamic response for the vibrating equipment of insertion with disturbing forces of 200–1250 kN for piles or columns with lengths of 10–30 m. The novelty of the research study consists in the linear rheological model, which was adopted in the form of a Maxwell–Voigt–Kelvin schematic of the type (E-V)–(E|V), with a discrete variation in four values for stiffness and damping of the soil, as the piles or columns vibrate and advance in the ground foundation. Practical experience of the authors in the field of using vibrogenerators for the introduction of piles in various types of ground foundations led to the adoption of the rheological model with variable damping coefficients depending on the depth of penetration into the soil. The curves of the dissipated power confirm the experimental data obtained in situ, in accordance with the rheological indoor tests of the different types of soil foundations. Full article

Periodic boundary conditions are natural in many scientific problems, and often lead to particular symmetries. Working with datasets that express periodicity properties requires special approaches when analyzing these phenomena. Periodic boundary conditions often help to solve or describe the problem in a much simpler way. The angular rotational symmetry is an example of periodic boundary conditions. This symmetry implies angular momentum conservation. On the other hand, clustering is one of the first and most basic methods used in data analysis. It is often a starting point when new data are acquired and understood. K-means clustering is one of the most commonly used clustering methods. It can be applied to many different situations with reasonably good results. Unfortunately, the original k-means approach does not cope well with the periodic properties of the data. For example, the original k-means algorithm treats a zero angle as very far from an angle that is 359 degrees. Periodic boundary conditions often change the classical distance measure and introduce an error in k-means clustering. In the paper, we discuss the problem of periodicity in the dataset and present a periodic k-means algorithm that modifies the original approach. Considering that many data scientists prefer on-the-shelf solutions, such as libraries available in Python, we present how easily they can incorporate periodicity into existing k-means implementation in the PyClustering library. It allows anyone to integrate periodic conditions without significant additional costs. The paper evaluates the described method using three different datasets: the artificial dataset, wind direction measurement, and the New York taxi service dataset. The proposed periodic k-means provides better results when the dataset manifests some periodic properties. Full article

In statistical process control (SPC), the ratio of two normal random variables (RZ) is a valuable statistical indicator to be taken as the charting statistic. In this work, we propose a triple exponentially weighted moving average (TEWMA) chart for monitoring the RZ. Additionally, the variable sampling interval (VSI) strategy has been adopted to different control charts by researchers. With the application of this strategy, the VSI-TEWMA-RZ chart is then developed to further improve the performance of the proposed TEWMA-RZ chart. The run length (RL) properties of the proposed TEWMA-RZ and VSI-TEWMA-RZ charts are obtained by the widely used Monte-Carlo (MC) simulations. Through the comparisons with the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts, the VSI-TEWMA-RZ chart is statistically more sensitive than the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts in detecting small and moderate shifts. Moreover, it turned out that the VSI-TEWMA-RZ chart has better performance than the TEWMA-RZ chart on the whole. Furthermore, this paper illustrates the implementation of the proposed charts with an example from the food industry. Full article

An antimagic labeling of a graph $G=(V,E)$ is a bijection from the set of edges of G to $\left\{1,2,\cdots ,\left|E\left(G\right)\right|\right\}$ and such that any two vertices of G have distinct vertex sums where the vertex sum of a vertex v in $V\left(G\right)$ is nothing but the sum of all the incident edge labeling of G. In this paper, we discussed the antimagicness of rooted product and corona product of graphs. We proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the rooted product of graph G and H admits antimagic labeling if $t\ge k$. Moreover, we proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the corona product of graph G and H admits antimagic labeling for all $t,k\ge 2$. Full article

In situ nanoindentation is extensively employed for online observing deformation and mechanical behaviors of bio-materials. However, the existing designs of the positioning stages have limited performances for testing soft or hard biomaterials. Consequently, this paper proposes a new structural design of a compliant one degree of freedom (01-DOF) stage with faster response. In addition to a new design, this article applies an analytical method to estimate the kinematic and dynamic behaviors of the stage. Firstly, the 01-DOF stage is designed with two modules, including a displacement amplifier with six levers and a symmetric parallelogram mechanism. Secondly, a kinetostatic diagram of the stage is built by pseudo-rigid-body method. Then, the dynamic equation of the proposed stage is formulated using the Lagrange method. In order to speed up the response of the indentation system, the structural optimization of the stage is conducted via the Firefly algorithm. The results showed that the theoretical first-order resonant frequency is found at about 226.8458 Hz. The theoretical consequences are nearby to the verified simulation. Besides, this achieved frequency of the presented stage is greater than that of previous stages. In an upcoming study, the prototype will be fabricated by additive manufacturing method or a computerized wire cutting method in order to verify the analytical results with experimental results. Full article

Mesh denoising is a classical task in mesh processing. Many state-of-the-art methods are still unable to quickly and robustly denoise multifarious noisy 3D meshes, especially in the case of high noise. Recently, neural network-based models have played a leading role in natural language, audio, image, video, and 3D model processing. Inspired by these works, we propose a data-driven mesh denoising method based on recurrent neural networks, which learns the relationship between the feature descriptors and the ground-truth normals. The recurrent neural network has a feedback loop before entering the output layer. By means of the self-feedback of neurons, the output of a recurrent neural network is related not only to the current input but also to the output of the previous moments. To deal with meshes with various geometric features, we use k-means to cluster the faces of the mesh according to geometric similarity and train neural networks for each category individually in the offline learning stage. Each network model, acting similar to a normal regression function, will map the geometric feature descriptor of each facet extracted from the mesh to the denoised facet normal. Then, the denoised normals are used to calculate the new feature descriptors, which become the input of the next similar regression model. In this system, three normal regression modules are cascaded to generate the last facet normals. Lastly, the model’s vertex positions are updated according to the denoised normals. A large number of visual and numerical results have demonstrated that the proposed model outperforms the state-of-the-art methods in most cases. Full article

In this work, a controller is developed for a continuous bioreactor with an unknown reaction rate term, subject to input saturation. The substrate concentration and the dilution rate are chosen as output and input, respectively. The controller formulation and the stability analysis are performed by the theory of dead zone Lyapunov functions, Lyapunov stability, and model reference adaptive control. As the main results, the dynamics of the Lyapunov function is determined separately for saturation and non-saturation events, and then a unified expression is deduced. In addition, the asymptotic convergence of the tracking error and boundedness of updated parameters are determined for the whole closed loop regime encompassing saturation and non-saturation events, and also for input saturation events, as a function of the terms and parameters of the reference and system models. The main contributions over closely related control designs, are (i) the effect of input constraint limits and desired output on the convergence of the tracking error during input saturation events are determined, considering settling behavior of the desired output with a steep section; (ii) the upper limit of the input constraint that guarantees output convergence during input saturation events is determined as function of the model terms, but independently of the time derivative of the desired output and its limit; (iii) a new dead zone Lyapunov function is proposed which allows proving asymptotic convergence of the tracking error during input saturation events in the presence of a fast variation in the desired output. Finally, the effectiveness and advantages of the developed controller are illustrated by simulation. Full article

This paper tackles the problem of forecasting real-life crime. However, the recollected data only produced thirty-five short-sized crime time series for three urban areas. We present a comparative analysis of four simple and four machine-learning-based ensemble forecasting methods. Additionally, we propose five forecasting techniques that manage the seasonal component of the time series. Furthermore, we used the symmetric mean average percentage error and a Friedman test to compare the performance of the forecasting methods and proposed techniques. The results showed that simple moving average with seasonal removal techniques produce the best performance for these series. It is important to highlight that a high percentage of the time series has no auto-correlation and a high level of symmetry, which is deemed as white noise and, therefore, difficult to forecast. Full article

A vehicular ad hoc network (VANET) is essential in building an intelligent transportation system that optimizes traffic conditions and makes traffic information conveniently accessible. However, malicious vehicles may disrupt the traffic order via propagating forged traffic/road information. Therefore, using digital certificates based on cryptography, some existing authentication schemes were proposed to manage vehicles’ identities. At first glance, these schemes can effectively identify malicious vehicles. However, these schemes require more computation and storage resources to maintain certificates. This is because the data storage of the database increases in a near-linear trend as the number of certificates grows. In this paper, we propose an efficient blockchain-based authentication scheme for secure communication in VANET (EBAS) to address the aforementioned issues. In EBAS, the regional trusted authority (RTA) receives traffic messages uploaded by the vehicle, together with transactions constructed via the unspent transaction output (UTXO) model. The verifier checks the legitimacy of the single input contained in the uploaded transaction to verify the legitimacy of the message sender’s identity. In terms of privacy preservation, a asymmetric key encryption technique, elliptic curve cryptography (ECC), is applied for constructing the transaction pseudonym, and users participate in the authentication process anonymously. In addition, our scheme guarantees the scalability of EBAS by proposing a transaction update mechanism, which can keep data storage at a stable level rather than near-linear growth. Under the simulation, the retrieving overhead remains at approximately 0.32 ms while the storage cost is stable at around 32.7 M for the blockchain state database. In terms of authentication efficiency, the average overhead of the proposed scheme is around 0.942 ms, which outperforms the existing schemes. Full article

Heart rate asymmetry (HRA) refers to how asymmetrically the acceleration and deceleration patterns in heartbeat fluctuations are distributed. There is limited evidence regarding HRA changes in athletes and their association with autonomic regulation. This study aimed to compare the short-term HRA of high-performance athletes and non-athletes during an autonomic function test by calculating relevant HRA measures. This exploratory study obtained beat-to-beat RR interval time series from 15 high-performance athletes and 12 non-athletes during a standardized autonomic function test. This test includes rest, postural change, controlled respiration, prolonged orthostatism, exercise, and recovery phases. The following HRA parameters were computed from the RR time series for both groups: asymmetric spread index (ASI), slope index (SI), Porta’s index (PI), Guzik’s index (GI), and Ehlers’ index (EI). We found significant differences (p < 0.01) in the mean value of several HRA parameters between athletes and non-athletes and across the autonomic function test phases, mainly in postural change and recovery phases. Our results indicate that high-performance athletes manifest a higher number and magnitude of cardiac decelerations than non-athletes after an orthostatic challenge, as indicated by GI and EI. In addition, lower HRA was found in athletes in the recovery phase than in non-athletes, as indicated by ASI. Full article

This work presents a detailed, comprehensive study of a new structural design of protective devices with a circular cross-section (CS) (protective cables) for protecting equipment against ultra-wideband (UWB) pulses. Multiconductor structures with 2–5 conductors with and without a protective shield are considered. The disadvantages of using symmetric configurations of protective cables are shown. Their simulation, multivariate analysis, and optimization through heuristic search, as well as evolutionary strategies, were carried out. Optimization was carried out according to the amplitude (to minimize the maximum voltage level at the output of the structures) and time (to maximize the duration of the exciting signal) criteria. The optimization results allowed for increasing the duration and overall attenuation of the exciting UWB pulse. The article shows the possibility of improving the characteristics of such structures through their cascade connection, both among themselves and with strip protective structures. The results of parametric optimization of such structures are presented in the range of real (used in practice) geometric and electrophysical parameters in terms of amplitude and time criteria, as well as the matching criterion. The article also presents the developed prototypes of protective structures with a circular CS of three types: circular 3-conductor cable, flat 3-conductor cable, and circular 4-conductor cable. The experimental results describe how these prototypes were developed and created and confirm the feasibility of these protective structures to decompose the exciting pulse signal, which was previously shown only in simulation. Finally, it is shown that the use of asymmetry in the proposed cable structures can improve their protective characteristics. Full article

Big Data is impacting and changing the way we live, and its core lies in the use of machine learning to extract valuable information from huge amounts of data. Optimization problems are a common problem in many steps of machine learning. In the face of complex optimization problems, evolutionary computation has shown advantages over traditional methods. Therefore, many researchers are working on improving the performance of algorithms for solving various optimization problems in machine learning. The equilibrium optimizer (EO) is a member of evolutionary computation and is inspired by the mass balance model in environmental engineering. Using particles and their concentrations as search agents, it simulates the process of finding equilibrium states for optimization. In this paper, we propose an improved equilibrium optimizer (IEO) based on a decreasing equilibrium pool. IEO provides more sources of information for particle updates and maintains a higher population diversity. It can discard some exploration in later stages to enhance exploitation, thus achieving a better search balance. The performance of IEO is verified using 29 benchmark functions from IEEE CEC2017, a dynamic economic dispatch problem, a spacecraft trajectory optimization problem, and an artificial neural network model training problem. In addition, the changes in population diversity and computational complexity brought by the proposed method are analyzed. Full article

We provide a systematic procedure for generating the coefficients of the continued fraction expansion of the test function associated with the characteristic polynomial of a stable system of difference equations. We illustrate the feasibility of the procedure, and we provide an application on the stability of two-dimensional digital filters. Full article

: Singular systems play an important role in many fields, and some new fractional operators, which are general, have been proposed recently. Therefore, singular systems on the basis of the mixed derivatives including the integer order derivative and the generalized fractional operators are studied. Firstly, Lagrange equations within mixed derivatives are established, and the primary constraints are presented for the singular systems. Then the constrained Hamilton equations are constructed by introducing the Lagrange multipliers. Thirdly, Noether symmetry, Lie symmetry and the corresponding conserved quantities for the constrained Hamiltonian systems are investigated. And finally, an example is given to illustrate the methods and results. Full article

Conventional model predictive power control (MPPC) features a simple concept and quick dynamic response. However, it relies heavily on the systemmodel and its parameter accuracy. Furthermore, the steady ripples are still high due to the use of one voltage vector during one control period. Recently, model-free predictive current control (MFPCC) has been proposed in the current control of PWMrectifiers. Despite the strong parameter robustness, the principle of MFPCC cannot be directly applied to power control, because the relationship between power and converter voltage ismore complex. This paper first proposes a basicmodel-free predictive power control (MFPPC), which successfully extends the principle ofMFPCC to power control. Subsequently, an improvedMFPPC is proposed, which uses an extended finite control set of voltage vectors to improve the steady-state performance. Furthermore, by using the online updated ultralocalmodel of PWMrectifiers, the problemof stagnant power updating in basic MFPPC is solved. The ideal three-phase grid voltages are symmetrical and sinusoidal, but the actual grids are usually unsymmetrical. In this paper, the proposedmethod is extended to asymmetrical power grids by adding an appropriate compensated power to the original power references. The proposed basic MFPPC and improvedMFPPC are compared to conventionalMPPC. The presented experimental results confirmthe effectiveness of the proposedmethods. Full article

This article reflects on the Klein–Gordon model, which frequently arises in the fields of solid-state physics and quantum field theories. We analytically delve into solitons and composite rogue-type wave propagation solutions of the model via the generalized Kudryashov and the extended Sinh Gordon expansion approaches. We obtain a class of analytically exact solutions in the forms of exponential and hyperbolic functions involving some arbitrary parameters with the help of Maple, which included comparing symmetric and non-symmetric solutions with other methods. After analyzing the dynamical behaviors, we caught distinct conditions on the accessible parameters of the solutions for the model. By applying conditions to the existing parameters, we obtained various types of rogue waves, bright and dark bells, combing bright–dark, combined dark–bright bells, kink and anti-kink solitons, and multi-soliton solutions. The nature of the solitons is geometrically explained for particular choices of the arbitrary parameters. It is indicated that the nonlinear rogue-type wave packets are restricted in two dimensions that characterized the rogue-type wave envelopes. Full article

new class of statistical distributions called the Type II half-Logistic odd Fréchet-G class is proposed. The new class is a continuation of the unusual Fréchet class. This class is analytically feasible and could be used to evaluate real-world data effectively. The new suggested class of distributions has many new symmetrical and asymmetrical sub-models. We propose new four sub-models from the new class of distributions which are called Type II half-Logistic odd Fréchet exponential distribution, Type II half-Logistic odd Fréchet Rayleigh distribution, Type II half-Logistic odd FréchetWeibull distribution, and Type II half-Logistic odd Fréchet Lindley distribution. Some statistical features of Type II half-Logistic odd Fréchet-G class such as ordinary moments (ORMs), incomplete moments (INMs), moment generating function (MGEF), residual life (REL), and reversed residual life (RREL) functions, and Rényi entropy (RéE) are derived. Six methods of estimation such as maximum likelihood, least-square, a maximum product of spacing, weighted least square, Cram´ er-von Mises, and Anderson–Darling are produced to estimate the parameters. To test the six estimation methods’ performance, a simulation study is conducted. Four real-world data sets are utilized to highlight the importance and applicability of the proposed method. Full article

Each traceable graph must be a block-chain; however, a block-chain is not necessarily traceable in general. Whether a given graph is a block-chain or not can be easily verified by a polynomial algorithm. It occurs to us that forbidden subgraph conditions for a block-chain are traceable. In this article, we characterize all pairs of disconnected forbidden subgraphs for the traceability of block-chains, so as to completely solve pairs of forbidden subgraphs for the traceability of block-chains (including disconnected and connected). Full article

The main purpose of this article is to derive several convolutions for generalized Bernoulli and Euler–Genocchi polynomials of order $(r,m)$, $B_n^{(r,m)}\left(x\right)$ and $A_n^{(r,m)}\left(x\right)$, respectively. These polynomials have been introduced recently and contain the generalized Bernoulli, Euler and Genocchi polynomials as special members. Some of our results extend the results of M. Merca and others concerning Bernoulli numbers and polynomials. Probabilistic interpretations of the presented results are also given. Full article