Symmetry

21 pages, 4037 KiB

Open AccessArticle

Canonical Correlations and Nonlinear Dependencies

by Nicola Maria Rinaldo Loperfido

Symmetry 2021, 13(7), 1308; https://doi.org/10.3390/sym13071308 - 20 Jul 2021

Cited by 1 | Viewed by 1842

Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric [...] Read more.

Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric model where CCA provides an insight into their nonlinear dependence structure. The paper also investigates some of its probabilistic and inferential properties, including marginal and conditional distributions, nonlinear transformations, maximum likelihood estimation and independence testing. Perturbed independence distributions are closely related to skew-symmetric ones. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Multivariate Statistics and Data Science)

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21 pages, 1316 KiB

Open AccessReview

Non-Coding RNAs and Reactive Oxygen Species–Symmetric Players of the Pathogenesis Associated with Bacterial and Viral Infections

by Zaki Milhem, Paul Chiroi, Andreea Nutu, Maximilian Ilea, Mihaela Lupse, Oana Zanoaga and Ioana Berindan-Neagoe

Symmetry 2021, 13(7), 1307; https://doi.org/10.3390/sym13071307 - 20 Jul 2021

Cited by 1 | Viewed by 5305

Abstract

Infections can be triggered by a wide range of pathogens. However, there are few strains of bacteria that cause illness, but some are quite life-threatening. Likewise, viral infections are responsible for many human diseases, usually characterized by high contagiousness. Hence, as bacterial and [...] Read more.

Infections can be triggered by a wide range of pathogens. However, there are few strains of bacteria that cause illness, but some are quite life-threatening. Likewise, viral infections are responsible for many human diseases, usually characterized by high contagiousness. Hence, as bacterial and viral infections can both cause similar symptoms, it can be difficult to determine the exact cause of a specific infection, and this limitation is critical. However, recent scientific advances have geared us up with the proper tools required for better diagnoses. Recent discoveries have confirmed the involvement of non-coding RNAs (ncRNAs) in regulating the pathogenesis of certain bacterial or viral infections. Moreover, the presence of reactive oxygen species (ROS) is also known as a common infection trait that can be used to achieve a more complete description of such pathogen-driven conditions. Thus, this opens further research opportunities, allowing scientists to explore infection-associated genetic patterns and develop better diagnosis and treatment methods. Therefore, the aim of this review is to summarize the current knowledge of the implication of ncRNAs and ROS in bacterial and viral infections, with great emphasis on their symmetry but, also, on their main differences. Full article

(This article belongs to the Special Issue Biochemistry, Gene Symmetry and Molecular Biology)

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12 pages, 299 KiB

Open AccessArticle

Temporal Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

by Wensheng Wang and Changkai Zhou

Symmetry 2021, 13(7), 1306; https://doi.org/10.3390/sym13071306 - 20 Jul 2021

Cited by 2 | Viewed by 1230

Abstract

Let

U = U (t, x)

for

(t, x) \in R_{+} \times R^{d}

and

\partial_{x} U = \partial_{x} U (t, x)

for [...] Read more.

Let

U = U (t, x)

for

(t, x) \in R_{+} \times R^{d}

and

\partial_{x} U = \partial_{x} U (t, x)

for

(t, x) \in R_{+} \times R

be the solution and gradient solution of the fourth order linearized Kuramoto–Sivashinsky (L-KS) SPDE driven by the space-time white noise in one-to-three dimensional spaces, respectively. We use the underlying explicit kernels and symmetry analysis, yielding exact, dimension-dependent, and temporal moduli of non-differentiability for

U (\cdot, x)

and

\partial_{x} U (\cdot, x)

. It has been confirmed that almost all sample paths of

U (\cdot, x)

and

\partial_{x} U (\cdot, x)

, in time, are nowhere differentiable. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines)

27 pages, 2613 KiB

Open AccessArticle

Research on Collaborative Order Decision-Making Method for Symmetric Participants in Complex Shipbuilding Projects

by Xuezhang Mao, Jinghua Li, Boxin Yang and Hui Guo

Symmetry 2021, 13(7), 1305; https://doi.org/10.3390/sym13071305 - 20 Jul 2021

Cited by 1 | Viewed by 1782

Abstract

More extensive enterprise cooperation is an effective means to increase the competitiveness of shipbuilding companies in the current distributed manufacturing environment. Most cross-enterprise collaborative processes for shipbuilding projects have been widely concerned. However, the symmetry and cooperativity among the order decision-making process is [...] Read more.

More extensive enterprise cooperation is an effective means to increase the competitiveness of shipbuilding companies in the current distributed manufacturing environment. Most cross-enterprise collaborative processes for shipbuilding projects have been widely concerned. However, the symmetry and cooperativity among the order decision-making process is rarely involved. A key issue for decision makers is to balance the interests of each symmetric participant and realize the consistent decision-making for the order. Existing order decision-making methods in the shipbuilding industry are low efficiency. The aim of this paper is to provide an assistant decision-making method to support effective order decision-making and multi-party cooperation for the multi-wining negotiation objectives. To solve this problem, a collaborative order decision-making framework based on decision support system (DSS) and multi-agent system (MAS) theory is presented, simulating the collaborative order decision-making process, and bridging the order decision-making with production scheduling. Then, a multi-stage negotiation method is provided to solve the distributed and symmetric order decision-making problem, and an illustrative example is conducted to demonstrate the effectiveness and rationality of the methods. Finally, an application case using a prototype system will be reported as a result. Full article

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8 pages, 280 KiB

Open AccessArticle

Resummed Quantum Gravity: A Review with Applications

by B. F. L. Ward

Symmetry 2021, 13(7), 1304; https://doi.org/10.3390/sym13071304 - 20 Jul 2021

Viewed by 1512

Abstract

We summarize the status of the theory of resummed quantum gravity. In the context of the Planck scale cosmology formulation of Bonanno and Reuter, we review the use of our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the [...] Read more.

We summarize the status of the theory of resummed quantum gravity. In the context of the Planck scale cosmology formulation of Bonanno and Reuter, we review the use of our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as

ρ_{Λ}

= (0.0024 eV)

^{4}

. Constraints on susy GUT models that follow from the closeness of the estimate to experiment are noted. Various consistency checks on the calculation are discussed. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of

ρ_{Λ}

. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

29 pages, 14046 KiB

Open AccessArticle

by Alexander B. Kukushkin and Pavel V. Minashin

Symmetry 2021, 13(7), 1303; https://doi.org/10.3390/sym13071303 - 20 Jul 2021

Cited by 2 | Viewed by 1939

Abstract

Radiative Transfer (RT) in a continuous spectrum in plasmas is caused by the emission and absorption of electromagnetic waves (EM) by free electrons. For a wide class of problems, the deviation of the velocity distribution function (VDF) of free electrons from the thermodynamic [...] Read more.

Radiative Transfer (RT) in a continuous spectrum in plasmas is caused by the emission and absorption of electromagnetic waves (EM) by free electrons. For a wide class of problems, the deviation of the velocity distribution function (VDF) of free electrons from the thermodynamic equilibrium, the Maxwellian VDF, can be neglected. In this case, RT in the geometric optics approximation is reduced to a single transport equation for the intensity of EM waves with source and sink functions dependent on the macroscopic parameters of the plasma (temperature and density of electrons). Integration of this equation for RT of radio-frequency EM waves in laboratory plasmas with highly reflecting metallic walls is substantially complicated by the multiple reflections which make the waves with the long free path the dominant contributors to the power balance profile. This in turn makes the RT substantially nonlocal with the spatial–spectral profile of the power balance determined by the spatial integrals of the plasma parameters. The geometric symmetry of the bounding walls, especially when enhanced by the diffuse reflectivity, provides a semi-analytic description of the RT problem. Analysis of the accuracy of such an approach reveals an approximate self-similarity of the power balance profile and the radiation intensity spectrum in both approximate and ab initio modeling. This phenomenon is shown here for a wide range of plasma parameters and wall reflectivity, including data from various numeric codes. The relationship between the revealed self-similarity and the accuracy of numeric codes is discussed. Full article

(This article belongs to the Special Issue New Trends in Plasma Physics)

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9 pages, 298 KiB

Open AccessArticle

Invariant Scalar Product and Associated Structures for Tachyonic Klein–Gordon Equation and Helmholtz Equation

by Francisco F. López-Ruiz, Julio Guerrero and Victor Aldaya

Symmetry 2021, 13(7), 1302; https://doi.org/10.3390/sym13071302 - 20 Jul 2021

Cited by 1 | Viewed by 1452

Abstract

Although describing very different physical systems, both the Klein–Gordon equation for tachyons (

m^{2} < 0

) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a suitable subspace of solutions is [...] Read more.

Although describing very different physical systems, both the Klein–Gordon equation for tachyons (

m^{2} < 0

) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a suitable subspace of solutions is only achieved if a non-local scalar product is defined. Then, a subset of oscillatory solutions of the Helmholtz equation supports a unirrep of the Euclidean group, and a subset of oscillatory solutions of the Klein–Gordon equation with

m^{2} < 0

supports the scalar tachyonic representation of the Poincaré group. As a consequence, these systems also share similar structures, such as certain singularized solutions and projectors on the representation spaces, but they must be treated carefully in each case. We analyze differences and analogies, compare both equations with the conventional

m^{2} > 0

Klein–Gordon equation, and provide a unified framework for the scalar products of the three equations. Full article

(This article belongs to the Special Issue Black Holes, Cosmology, Quantum Gravity, and Their Symmetries)

54 pages, 1793 KiB

Open AccessArticle

Circuit Complexity from Cosmological Islands

by Sayantan Choudhury, Satyaki Chowdhury, Nitin Gupta, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino, Chiranjeeb Singha and Abinash Swain

Symmetry 2021, 13(7), 1301; https://doi.org/10.3390/sym13071301 - 20 Jul 2021

Cited by 51 | Viewed by 3907

Abstract

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this [...] Read more.

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of quantum extremal islands in negative (or positive) cosmological constant with radiation in the background of Friedmann-Lema

\hat{i}

tre-Robertson-Walker (FLRW) space-time, i.e., the presence and absence of islands in anti de Sitter and the de Sitter space-time having SO(2, 3) and SO(1, 4) isometries, respectively. Without using any explicit details of any gravity model, we study the behavior of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, out-of-time ordered correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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15 pages, 394 KiB

Open AccessArticle

Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results

by Evgenii S. Baranovskii, Vyacheslav V. Provotorov, Mikhail A. Artemov and Alexey P. Zhabko

Symmetry 2021, 13(7), 1300; https://doi.org/10.3390/sym13071300 - 19 Jul 2021

Cited by 9 | Viewed by 1653

Abstract

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance [...] Read more.

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains. Full article

(This article belongs to the Special Issue Mathematical Fluid Dynamics and Symmetry)

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16 pages, 1089 KiB

Open AccessArticle

Analysis of Flame Suppression Capabilities Using Low-Frequency Acoustic Waves and Frequency Sweeping Techniques

by Jacek Łukasz Wilk-Jakubowski

Symmetry 2021, 13(7), 1299; https://doi.org/10.3390/sym13071299 - 19 Jul 2021

Cited by 14 | Viewed by 3377

Abstract

Symmetry plays a key role in the processing and analysis of not only visual but also acoustic signals in various multidisciplinary areas. New innovative and environmentally friendly methods for extinguishing flames are still being sought worldwide. One of these techniques appears to be [...] Read more.

Symmetry plays a key role in the processing and analysis of not only visual but also acoustic signals in various multidisciplinary areas. New innovative and environmentally friendly methods for extinguishing flames are still being sought worldwide. One of these techniques appears to be the acoustic method. A laboratory stand was built for this purpose, which was coupled with the tested prototype of a high-power acoustic extinguisher, and then the original experiments and analyses of extinguishing effectiveness were carried out. For extinguishing, waveforms with specified parameters selected symmetrically around the frequency for which the extinguisher was designed were used. The aim of this article is to present and discuss selected measurement results concerning the possibility of flame extinguishing with the use of sinusoidal acoustic waves of low frequency (below 21 Hz), as well as with the use of frequency sweeping techniques with set parameters. Such an extinguisher can be equipped with an intelligent module so that the extinguisher may be activated automatically (without human intervention) when flames are detected. The benefits of this combination as well as the importance of image processing for flame detection are also presented in this paper. This solution, with its good fire detection and fast response, may be applicable for extinguishing firebreaks in particular. Full article

(This article belongs to the Special Issue Multidimensional Signal Processing and Its Applications)

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15 pages, 1290 KiB

Open AccessArticle

NMR Properties of the Cyanide Anion, a Quasisymmetric Two-Faced Hydrogen Bonding Acceptor

by Ilya G. Shenderovich and Gleb S. Denisov

Symmetry 2021, 13(7), 1298; https://doi.org/10.3390/sym13071298 - 19 Jul 2021

Cited by 2 | Viewed by 3158

Abstract

The isotopically enriched cyanide anion, (¹³C≡¹⁵N)⁻, has a great potential as the NMR probe of non-covalent interactions. However, hydrogen cyanide is highly toxic and can decompose explosively. It is therefore desirable to be able to theoretically estimate [...] Read more.

The isotopically enriched cyanide anion, (¹³C≡¹⁵N)⁻, has a great potential as the NMR probe of non-covalent interactions. However, hydrogen cyanide is highly toxic and can decompose explosively. It is therefore desirable to be able to theoretically estimate any valuable results of certain experiments in advance in order to carry out experimental studies only for the most suitable molecular systems. We report the effect of hydrogen bonding on NMR properties of ¹⁵N≡¹³CH···X and ¹³C≡¹⁵NH···X hydrogen bonding complexes in solution, where X = ¹⁹F, ¹⁵N, and O=³¹P, calculated at the ωB97XD/def2tzvp and the polarizable continuum model (PCM) approximations. In many cases, the isotropic ¹³C and ¹⁵N chemical shieldings of the cyanide anion are not the most informative NMR properties of such complexes. Instead, the anisotropy of these chemical shieldings and the values of scalar coupling constants, including those across hydrogen bonds, can be used to characterize the geometry of such complexes in solids and solutions. ¹J(¹⁵N¹³C) strongly correlates with the length of the N≡C bond. Full article

(This article belongs to the Special Issue Exploring Inter- and Intramolecular Interactions as Building Blocks of Larger Systems)

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16 pages, 993 KiB

Open AccessArticle

The Skewed-Elliptical Log-Linear Birnbaum–Saunders Alpha-Power Model

by Guillermo Martínez-Flórez, Heleno Bolfarine and Yolanda M. Gómez

Symmetry 2021, 13(7), 1297; https://doi.org/10.3390/sym13071297 - 19 Jul 2021

Cited by 3 | Viewed by 1465

Abstract

In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum–Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum–Saunders and skewed log-linear Birnbaum–Saunders distributions. As shown, it is able to [...] Read more.

In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum–Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum–Saunders and skewed log-linear Birnbaum–Saunders distributions. As shown, it is able to surpass the ordinary sinh-normal models when fitting data sets with high (above the expected with the sinh-normal) degrees of asymmetry. Maximum likelihood estimation is developed with the inverse of the observed information matrix used for standard error estimation. Large sample properties of the maximum likelihood estimators such as consistency and asymptotic normality are established. An application is reported for the data set previously analyzed in the literature, where performance of the new distribution is shown when compared with other proposed alternative models. Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: Theoretical Developments and Applications Ⅲ)

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14 pages, 3296 KiB

Open AccessArticle

Dual Attention Network for Pitch Estimation of Monophonic Music

by Wenfang Ma, Ying Hu and Hao Huang

Symmetry 2021, 13(7), 1296; https://doi.org/10.3390/sym13071296 - 19 Jul 2021

Cited by 2 | Viewed by 1821

Abstract

The task of pitch estimation is an essential step in many audio signal processing applications. In this paper, we propose a data-driven pitch estimation network, the Dual Attention Network (DA-Net), which processes directly on the time-domain samples of monophonic music. DA-Net includes six [...] Read more.

The task of pitch estimation is an essential step in many audio signal processing applications. In this paper, we propose a data-driven pitch estimation network, the Dual Attention Network (DA-Net), which processes directly on the time-domain samples of monophonic music. DA-Net includes six Dual Attention Modules (DA-Modules), and each of them includes two kinds of attention: element-wise and channel-wise attention. DA-Net is to perform element attention and channel attention operations on convolution features, which reflects the idea of "symmetry". DA-Modules can model the semantic interdependencies between element-wise and channel-wise features. In the DA-Module, the element-wise attention mechanism is realized by a Convolutional Gated Linear Unit (ConvGLU), and the channel-wise attention mechanism is realized by a Squeeze-and-Excitation (SE) block. We explored three kinds of combination modes (serial mode, parallel mode, and tightly coupled mode) of the element-wise attention and channel-wise attention. Element-wise attention selectively emphasizes useful features by re-weighting the features at all positions. Channel-wise attention can learn to use global information to selectively emphasize the informative feature maps and suppress the less useful ones. Therefore, DA-Net adaptively integrates the local features with their global dependencies. The outputs of DA-Net are fed into a fully connected layer to generate a 360-dimensional vector corresponding to 360 pitches. We trained the proposed network on the iKala and MDB-stem-synth datasets, respectively. According to the experimental results, our proposed dual attention network with tightly coupled mode achieved the best performance. Full article

(This article belongs to the Section Computer)

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21 pages, 6770 KiB

Open AccessArticle

Identifying the Attack Sources of Botnets for a Renewable Energy Management System by Using a Revised Locust Swarm Optimisation Scheme

by Hsiao-Chung Lin, Ping Wang, Wen-Hui Lin, Kuo-Ming Chao and Zong-Yu Yang

Symmetry 2021, 13(7), 1295; https://doi.org/10.3390/sym13071295 - 19 Jul 2021

Cited by 2 | Viewed by 1736

Abstract

Distributed denial of service (DDoS) attacks often use botnets to generate a high volume of packets and adopt controlled zombies for flooding a victim’s network over the Internet. Analysing the multiple sources of DDoS attacks typically involves reconstructing attack paths between the victim [...] Read more.

Distributed denial of service (DDoS) attacks often use botnets to generate a high volume of packets and adopt controlled zombies for flooding a victim’s network over the Internet. Analysing the multiple sources of DDoS attacks typically involves reconstructing attack paths between the victim and attackers by using Internet protocol traceback (IPTBK) schemes. In general, traditional route-searching algorithms, such as particle swarm optimisation (PSO), have a high convergence speed for IPTBK, but easily fall into the local optima. This paper proposes an IPTBK analysis scheme for multimodal optimisation problems by applying a revised locust swarm optimisation (LSO) algorithm to the reconstructed attack path in order to identify the most probable attack paths. For evaluating the effectiveness of the DDoS control centres, networks with a topology size of 32 and 64 nodes were simulated using the ns-3 tool. The average accuracy of the LS-PSO algorithm reached 97.06 for the effects of dynamic traffic in two experimental networks (number of nodes = 32 and 64). Compared with traditional PSO algorithms, the revised LSO algorithm exhibited a superior searching performance in multimodal optimisation problems and increased the accuracy in traceability analysis for IPTBK problems. Full article

(This article belongs to the Topic Applied Metaheuristic Computing)

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10 pages, 274 KiB

Open AccessArticle

Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls

by Asif Ahmad, Qi Liu and Yongjin Li

Symmetry 2021, 13(7), 1294; https://doi.org/10.3390/sym13071294 - 19 Jul 2021

Cited by 2 | Viewed by 1794

Abstract

We introduce a new geometric constant

J i n (X)

based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties [...] Read more.

We introduce a new geometric constant

J i n (X)

based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties of this new coefficient. Next, it is shown that, for a Banach space,

J i n (X)

becomes 16 if and only if the norm is induced by an inner product. Moreover, its properties and some relations between other well-known geometric constants are studied. Finally, a sufficient condition which implies normal structure is presented. Full article

(This article belongs to the Special Issue Functional Equations and Inequalities 2021)

19 pages, 2164 KiB

Open AccessArticle

Research Risk Factors in Monitoring Well Drilling—A Case Study Using Machine Learning Methods

by Shamil Islamov, Alexey Grigoriev, Ilia Beloglazov, Sergey Savchenkov and Ove Tobias Gudmestad

Symmetry 2021, 13(7), 1293; https://doi.org/10.3390/sym13071293 - 18 Jul 2021

Cited by 31 | Viewed by 4550

Abstract

This article takes an approach to creating a machine learning model for the oil and gas industry. This task is dedicated to the most up-to-date issues of machine learning and artificial intelligence. One of the goals of this research was to build a [...] Read more.

This article takes an approach to creating a machine learning model for the oil and gas industry. This task is dedicated to the most up-to-date issues of machine learning and artificial intelligence. One of the goals of this research was to build a model to predict the possible risks arising in the process of drilling wells. Drilling of wells for oil and gas production is a highly complex and expensive part of reservoir development. Thus, together with injury prevention, there is a goal to save cost expenditures on downtime and repair of drilling equipment. Nowadays, companies have begun to look for ways to improve the efficiency of drilling and minimize non-production time with the help of new technologies. To support decisions in a narrow time frame, it is valuable to have an early warning system. Such a decision support system will help an engineer to intervene in the drilling process and prevent high expenses of unproductive time and equipment repair due to a problem. This work describes a comparison of machine learning algorithms for anomaly detection during well drilling. In particular, machine learning algorithms will make it possible to make decisions when determining the geometry of the grid of wells—the nature of the relative position of production and injection wells at the production facility. Development systems are most often subdivided into the following: placement of wells along a symmetric grid, and placement of wells along a non-symmetric grid (mainly in rows). The tested models classify drilling problems based on historical data from previously drilled wells. To validate anomaly detection algorithms, we used historical logs of drilling problems for 67 wells at a large brownfield in Siberia, Russia. Wells with problems were selected and analyzed. It should be noted that out of the 67 wells, 20 wells were drilled without expenses for unproductive time. The experiential results illustrate that a model based on gradient boosting can classify the complications in the drilling process better than other models. Full article

(This article belongs to the Special Issue Advanced Digital, Modeling and Control Applies into Various Processes)

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26 pages, 400 KiB

Open AccessArticle

Perturbative and Non-Pertrubative Trace Anomalies

by Loriano Bonora

Symmetry 2021, 13(7), 1292; https://doi.org/10.3390/sym13071292 - 18 Jul 2021

Cited by 3 | Viewed by 1446

Abstract

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition [...] Read more.

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case, we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

15 pages, 1791 KiB

Open AccessEditor’s ChoiceArticle

Feature Ranking and Differential Evolution for Feature Selection in Brushless DC Motor Fault Diagnosis

by Chun-Yao Lee and Chen-Hsu Hung

Symmetry 2021, 13(7), 1291; https://doi.org/10.3390/sym13071291 - 18 Jul 2021

Cited by 11 | Viewed by 2528

Abstract

A fault diagnosis system with the ability to recognize many different faults obviously has a certain complexity. Therefore, improving the performance of similar systems has attracted much research interest. This article proposes a system of feature ranking and differential evolution for feature selection [...] Read more.

A fault diagnosis system with the ability to recognize many different faults obviously has a certain complexity. Therefore, improving the performance of similar systems has attracted much research interest. This article proposes a system of feature ranking and differential evolution for feature selection in BLDC fault diagnosis. First, this study used the Hilbert–Huang transform (HHT) to extract the features of four different types of brushless DC motor Hall signal. When there is a fault, the symmetry of the Hall signal will be influenced. Second, we used feature selection based on a distance discriminant (FSDD) to calculate the feature factors which base on the category separability of features to select the features which have a positive correlation with the types. The features were entered sequentially into the two supervised classifiers: backpropagation neural network (BPNN) and linear discriminant analysis (LDA), and the identification results were then evaluated. The feature input for the classifier was derived from the FSDD, and then we optimized the feature rank using differential evolution (DE). Finally, the results were verified from the BLDC motor’s operating environment simulation with the same features by adding appropriate signal-to-noise ratio magnitudes. The identification system obtained an accuracy rate of 96% when there were 14 features. Additionally, the experimental results show that the proposed system has a robust anti-noise ability, and the accuracy rate is 92.04%, even when 20 dB of white Gaussian noise is added to the signal. Moreover, compared with the systems established from the discrete wavelet transform (DWT) and a variety of classifiers, our proposed system has a higher accuracy with fewer features. Full article

(This article belongs to the Special Issue Complex Systems and Its Applications)

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21 pages, 1615 KiB

Open AccessArticle

A New Feature Selection Method Based on a Self-Variant Genetic Algorithm Applied to Android Malware Detection

by Le Wang, Yuelin Gao, Shanshan Gao and Xin Yong

Symmetry 2021, 13(7), 1290; https://doi.org/10.3390/sym13071290 - 18 Jul 2021

Cited by 17 | Viewed by 2850

Abstract

In solving classification problems in the field of machine learning and pattern recognition, the pre-processing of data is particularly important. The processing of high-dimensional feature datasets increases the time and space complexity of computer processing and reduces the accuracy of classification models. Hence, [...] Read more.

In solving classification problems in the field of machine learning and pattern recognition, the pre-processing of data is particularly important. The processing of high-dimensional feature datasets increases the time and space complexity of computer processing and reduces the accuracy of classification models. Hence, the proposal of a good feature selection method is essential. This paper presents a new algorithm for solving feature selection, retaining the selection and mutation operators from traditional genetic algorithms. On the one hand, the global search capability of the algorithm is ensured by changing the population size, on the other hand, finding the optimal mutation probability for solving the feature selection problem based on different population sizes. During the iteration of the algorithm, the population size does not change, no matter how many transformations are made, and is the same as the initialized population size; this spatial invariance is physically defined as symmetry. The proposed method is compared with other algorithms and validated on different datasets. The experimental results show good performance of the algorithm, in addition to which we apply the algorithm to a practical Android software classification problem and the results also show the superiority of the algorithm. Full article

(This article belongs to the Special Issue Computational Intelligence and Soft Computing: Recent Applications)

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22 pages, 3144 KiB

Open AccessArticle

Semiclassical Spectral Series Localized on a Curve for the Gross–Pitaevskii Equation with a Nonlocal Interaction

by Anton E. Kulagin, Alexander V. Shapovalov and Andrey Y. Trifonov

Symmetry 2021, 13(7), 1289; https://doi.org/10.3390/sym13071289 - 17 Jul 2021

Cited by 2 | Viewed by 1694

Abstract

We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross–Pitaevskii equation with a nonlocal interaction term. The eigenvalues and eigenfunctions semiclassically concentrated on a curve are obtained. The curve is described by the dynamic system of moments of [...] Read more.

We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross–Pitaevskii equation with a nonlocal interaction term. The eigenvalues and eigenfunctions semiclassically concentrated on a curve are obtained. The curve is described by the dynamic system of moments of solutions to the nonlocal Gross–Pitaevskii equation. We solve the eigenvalue problem for the nonlocal stationary Gross–Pitaevskii equation basing on the semiclassical asymptotics found for the Cauchy problem of the parametric family of linear equations associated with the time-dependent Gross–Pitaevskii equation in the space of extended dimension. The approach proposed uses symmetries of equations in the space of extended dimension. Full article

(This article belongs to the Section Physics)

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19 pages, 288 KiB

Open AccessArticle

General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

by Silvestru Sever Dragomir

Symmetry 2021, 13(7), 1288; https://doi.org/10.3390/sym13071288 - 17 Jul 2021

Viewed by 1171

Abstract

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces. Full article

(This article belongs to the Special Issue New Directions in Theory of Approximation and Related Problems)

14 pages, 803 KiB

Open AccessArticle

On the Qualitative Behavior of Third-Order Differential Equations with a Neutral Term

by Omar Bazighifan, Fatemah Mofarreh and Kamsing Nonlaopon

Symmetry 2021, 13(7), 1287; https://doi.org/10.3390/sym13071287 - 17 Jul 2021

Cited by 4 | Viewed by 1325

Abstract

In this paper, we analyze the asymptotic behavior of solutions to a class of third-order neutral differential equations. Using different methods, we obtain some new results concerning the oscillation of this type of equation. Our new results complement related contributions to the subject. [...] Read more.

In this paper, we analyze the asymptotic behavior of solutions to a class of third-order neutral differential equations. Using different methods, we obtain some new results concerning the oscillation of this type of equation. Our new results complement related contributions to the subject. The symmetry plays a important and fundamental role in the study of oscillation of solutions to these equations. An example is presented in order to clarify the main results. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications)

13 pages, 1209 KiB

Open AccessArticle

Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm

by Yenni Angraini, Khairil Anwar Notodiputro, Henk Folmer, Asep Saefuddin and Toni Toharudin

Symmetry 2021, 13(7), 1286; https://doi.org/10.3390/sym13071286 - 17 Jul 2021

Cited by 1 | Viewed by 1489

Abstract

This paper deals with symmetrical data that can be modelled based on Gaussian distribution, such as linear mixed models for longitudinal data. The latent factor linear mixed model (LFLMM) is a method generally used for analysing changes in high-dimensional longitudinal data. It is [...] Read more.

This paper deals with symmetrical data that can be modelled based on Gaussian distribution, such as linear mixed models for longitudinal data. The latent factor linear mixed model (LFLMM) is a method generally used for analysing changes in high-dimensional longitudinal data. It is usual that the model estimates are based on the expectation-maximization (EM) algorithm, but unfortunately, the algorithm does not produce the standard errors of the regression coefficients, which then hampers testing procedures. To fill in the gap, the Supplemented EM (SEM) algorithm for the case of fixed variables is proposed in this paper. The computational aspects of the SEM algorithm have been investigated by means of simulation. We also calculate the variance matrix of beta using the second moment as a benchmark to compare with the asymptotic variance matrix of beta of SEM. Both the second moment and SEM produce symmetrical results, the variance estimates of beta are getting smaller when number of subjects in the simulation increases. In addition, the practical usefulness of this work was illustrated using real data on political attitudes and behaviour in Flanders-Belgium. Full article

(This article belongs to the Special Issue Symmetry in Statistics and Data Science)

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13 pages, 311 KiB

Open AccessArticle

Some Properties Concerning the J_L(X) and Y_J(X) Which Related to Some Special Inscribed Triangles of Unit Ball

by Asif Ahmad, Yuankang Fu and Yongjin Li

Symmetry 2021, 13(7), 1285; https://doi.org/10.3390/sym13071285 - 16 Jul 2021

Cited by 2 | Viewed by 1314

Abstract

In this paper, we will make some further discussions on the

J_{L} (X)

and

Y_{J} (X)

which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce [...] Read more.

In this paper, we will make some further discussions on the

J_{L} (X)

and

Y_{J} (X)

which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants

L_{1} (X, ▵)

,

L_{2} (X, ▵)

which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among

J_{L} (X)

,

Y_{J} (X)

and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for

J_{L} (X)

,

Y_{J} (X)

and some significant geometric constants, including the James constant

J (X)

and the von Neumann-Jordan constant

C_{NJ} (X)

. Finally, we introduce the two new geometric constants

L_{1} (X, ▵)

,

L_{2} (X, ▵)

, and calculate the bounds of

L_{1} (X, ▵)

and

L_{2} (X, ▵)

as well as the values of

L_{1} (X, ▵)

and

L_{2} (X, ▵)

for two Banach spaces. Full article

(This article belongs to the Special Issue Functional Equations and Inequalities 2021)

12 pages, 2237 KiB

Open AccessArticle

Fault Diagnosis of Main Pump in Converter Station Based on Deep Neural Network

by Qingsheng Zhao, Gong Cheng, Xiaoqing Han, Dingkang Liang and Xuping Wang

Symmetry 2021, 13(7), 1284; https://doi.org/10.3390/sym13071284 - 16 Jul 2021

Cited by 7 | Viewed by 1758

Abstract

As the core component of the valve cooling system in a converter station, the main pump plays a major role in ensuring the stable operation of the valve. Thus, accurate and efficient fault diagnosis of the main pump according to vibration signals is [...] Read more.

As the core component of the valve cooling system in a converter station, the main pump plays a major role in ensuring the stable operation of the valve. Thus, accurate and efficient fault diagnosis of the main pump according to vibration signals is of positive significance for the detection of failure equipment and reducing the maintenance cost. This paper proposed a new neural network based on the vibration signals of the main pump to classify four faults and one normal state of the main pump, which consisted of a convolutional neural network (CNN) and long short-term memory (LSTM). Multi-scale features were extracted by two CNNs with different kernel sizes, and temporal features were extracted by LSTM. Moreover, random sampling was used in data processing for imbalanced data, which is meaningful for data symmetry. Experimental results indicated that the accuracy of the network was 0.987 obtained from the test set, and the average values of F1-score, recall, and precision were 0.987, 0.987, and 0.988, respectively. It was found that the proposed network performed well in a multi-label fault diagnosis of the main pump and was superior to other methods. Full article

(This article belongs to the Section Computer)

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8 pages, 247 KiB

Open AccessArticle

Symmetry of Dressed Photon

by Hiroyuki Ochiai

Symmetry 2021, 13(7), 1283; https://doi.org/10.3390/sym13071283 - 16 Jul 2021

Cited by 1 | Viewed by 1260

Abstract

Motivated by describing the symmetry of a theoretical model of dressed photons, we introduce several spaces with Lie group actions and the morphisms between them depending on three integer parameters

n \geq r \geq s

on dimensions. We discuss the symmetry on these [...] Read more.

Motivated by describing the symmetry of a theoretical model of dressed photons, we introduce several spaces with Lie group actions and the morphisms between them depending on three integer parameters

n \geq r \geq s

on dimensions. We discuss the symmetry on these spaces using classical invariant theory, orbit decomposition of prehomogeneous vector spaces, and compact reductive homogeneous space such as Grassmann manifold and flag variety. Finally, we go back to the original dressed photon with

n = 4, r = 2, s = 1

. Full article

(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)

10 pages, 270 KiB

Open AccessArticle

From Total Roman Domination in Lexicographic Product Graphs to Strongly Total Roman Domination in Graphs

by Ana Almerich-Chulia, Abel Cabrera Martínez, Frank Angel Hernández Mira and Pedro Martin-Concepcion

Symmetry 2021, 13(7), 1282; https://doi.org/10.3390/sym13071282 - 16 Jul 2021

Cited by 1 | Viewed by 1397

Abstract

Let G be a graph with no isolated vertex and let

N (v)

be the open neighbourhood of

v \in V (G)

. Let

f : V (G) \to {0, 1, 2}

be [...] Read more.

Let G be a graph with no isolated vertex and let

N (v)

be the open neighbourhood of

v \in V (G)

. Let

f : V (G) \to {0, 1, 2}

be a function and

V_{i} = {v \in V (G) : f (v) = i}

for every

i \in {0, 1, 2}

. We say that f is a strongly total Roman dominating function on G if the subgraph induced by

V_{1} \cup V_{2}

has no isolated vertex and

N (v) \cap V_{2} \neq \emptyset

for every

v \in V (G) \ V_{2}

. The strongly total Roman domination number of G, denoted by

γ_{t R}^{s} (G)

, is defined as the minimum weight

ω (f) = \sum_{x \in V (G)} f (x)

among all strongly total Roman dominating functions f on G. This paper is devoted to the study of the strongly total Roman domination number of a graph and it is a contribution to the Special Issue “Theoretical Computer Science and Discrete Mathematics” of Symmetry. In particular, we show that the theory of strongly total Roman domination is an appropriate framework for investigating the total Roman domination number of lexicographic product graphs. We also obtain tight bounds on this parameter and provide closed formulas for some product graphs. Finally and as a consequence of the study, we prove that the problem of computing

γ_{t R}^{s} (G)

is NP-hard. Full article

(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics)

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31 pages, 36774 KiB

Open AccessArticle

Atoms in Highly Symmetric Environments: H in Rhodium and Cobalt Cages, H in an Octahedral Hole in MgO, and Metal Atoms Ca-Zn in C₂₀ Fullerenes

by Zikri Altun, Erdi Ata Bleda and Carl Trindle

Symmetry 2021, 13(7), 1281; https://doi.org/10.3390/sym13071281 - 16 Jul 2021

Viewed by 1708

Abstract

An atom trapped in a crystal vacancy, a metal cage, or a fullerene might have many immediate neighbors. Then, the familiar concept of valency or even coordination number seems inadequate to describe the environment of that atom. This difficulty in terminology is illustrated [...] Read more.

An atom trapped in a crystal vacancy, a metal cage, or a fullerene might have many immediate neighbors. Then, the familiar concept of valency or even coordination number seems inadequate to describe the environment of that atom. This difficulty in terminology is illustrated here by four systems: H atoms in tetragonal-pyramidal rhodium cages, H atom in an octahedral cobalt cage, H atom in a MgO octahedral hole, and metal atoms in C₂₀ fullerenes. Density functional theory defines structure and energetics for the systems. Interactions of the atom with its container are characterized by the quantum theory of atoms in molecules (QTAIM) and the theory of non-covalent interactions (NCI). We establish that H atoms in H₂Rh₁₃(CO)₂₄³⁻ trianion cannot be considered pentavalent, H atom in HCo₆(CO)₁₅¹⁻ anion cannot be considered hexavalent, and H atom in MgO cannot be considered hexavalent. Instead, one should consider the H atom to be set in an environmental field defined by its 5, 6, and 6 neighbors; with interactions described by QTAIM. This point is further illustrated by the electronic structures and QTAIM parameters of M@C₂₀, M=Ca to Zn. The analysis describes the systematic deformation and restoration of the symmetric fullerene in that series. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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13 pages, 253 KiB

Open AccessArticle

Generalized Lie Triple Derivations of Lie Color Algebras and Their Subalgebras

by Sania Asif and Zhixiang Wu

Symmetry 2021, 13(7), 1280; https://doi.org/10.3390/sym13071280 - 16 Jul 2021

Cited by 3 | Viewed by 1457

Abstract

Consider a Lie color algebra, denoted by

L

. Our aim in this paper is to study the Lie triple derivations

T D e r (L)

and generalized Lie triple derivations

G T D e r (L)

of Lie [...] Read more.

Consider a Lie color algebra, denoted by

L

. Our aim in this paper is to study the Lie triple derivations

T D e r (L)

and generalized Lie triple derivations

G T D e r (L)

of Lie color algebras. We discuss the centroids, quasi centroids and central triple derivations of Lie color algebras, where we show the relationship of triple centroids, triple quasi centroids and central triple derivation with Lie triple derivations and generalized Lie triple derivations of Lie color algebras

L

. A classification of Lie triple derivations algebra of all perfect Lie color algebras is given, where we prove that for a perfect and centerless Lie color algebra,

T D e r (L) = D e r (L)

and

T D e r (D e r (L)) = I n n (D e r (L))

. Full article

(This article belongs to the Section Mathematics)

15 pages, 313 KiB

Open AccessArticle

Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries

by Irfan Nazeer, Tabasam Rashid, Muhammad Tanveer Hussain and Juan Luis García Guirao

Symmetry 2021, 13(7), 1279; https://doi.org/10.3390/sym13071279 - 16 Jul 2021

Cited by 9 | Viewed by 1662

Abstract

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to [...] Read more.

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are

M [γ_{s} (C_{l} (σ, ϕ, η))] = ⌈ \frac{l}{3} ⌉

. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization. Full article

(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems II)

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